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Strain Gage Technology Technical Data
Vishay Micro-Measurements
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Table Contents
Vishay Micro-Measurements
Strain Gage Technology Technical Data
TN-501 Noise Control Strain Gage Measurements.3 TN-502 Optimizing Strain Gage Excitation Levels TN-503 Measurement Residual Stresses Hole-Drilling* Strain Gage Method TN-504 Strain Gage Thermal Output Gage Factor Variation with Temperature TN-505 Strain Gage Selection: Criteria, Procedures, Recommendations TN-506 Bondable Resistance Temperature Sensors Associated Circuitry TN-507 Errors Wheatstone Bridge Nonlinearity TN-508 Fatigue Characteristics Vishay Micro-Measurements Strain Gages TN-509 Errors Transverse Sensitivity Strain Gages TN-510 Design Considerations Diaphragm Pressure Transducers TN-511 Errors Misalignment Strain Gages. TN-512 Plane-Shear Measurement with Strain Gages TN-513 Measurement Thermal Expansion Coefficient Using Strain Gages TN-514 Shunt Calibration Strain Gage Instrumentation TN-515 Strain Gage Rosettes: Selection, Application Data Reduction TN-516 Errors Shared Leadwires Parallel Strain Gage Circuits TN-517 Introduction Digital Signal Processing TT-601 Techniques Bonding Leadwires Surfaces Experiencing High Centrifugal Forces TT-602 Silver Soldering Technique Attachment Leads Strain Gages TT-603 Proper Bondable Terminals Strain Gage Applications TT-604 Leadwire Attachment Techniques Obtaining Maximum Fatigue Life Strain Gages TT-605 High-Elongation Strain Measurements TT-606 Soldering Techniques Lead Attachment Strain Gages with Solder Dots TT-607 Strain Gage Installation Protection Field Environments. TT-608 Techniques Attaching Leadwires Unbonded Strain Gages .203 TT-609 Strain Gage Soldering Techniques TT-610 Strain Gage Clamping Techniques TT-611 Strain Gage Installations Concrete Structures TT-612 Three-Wire Quarter-Bridge Circuit
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Strain Gages Instruments
tech note tn-501-2
Noise Control Strain Gage Measurements
Introduction
Strain measurements must often made presence electric and/or magnetic fields which superimpose electrical noise measurement signals. controlled, noise lead inaccurate results incorrect interpretation strain signals; and, severe cases, obscure strain signals altogether. order control noise level, maximize signal-to-noise ratio, necessary first understand types characteristics electrical noise, well sources such noise. With this understanding, then possible apply most effective noise-reduction measures particular instrumentation problem. This technical note identifies some more common noise sources, describes routes which noise induced into strain gage circuits. should noted that treatment here limited noise from external electrical magnetic sources. This note does cover effects from nuclear thermal sources, does consider effects variable wiring contact resistance caused slip rings, connectors, switches, etc. Following discussion noise sources, specific methods given, varying with noise-coupling mechanism, noise avoidance. information this technical note equally applicable both analog digital systems employing amplifiers. also applies systems using carrier excitation carrier amplifiers. Electrical noise from these sources categorized into basic types: electrostatic magnetic. types noise fundamentally different, thus require different noise-reduction measures. Unfortunately, most common noise sources listed produce combinations noise types, which complicate noisereduction problem. Electrostatic fields generated presence voltage-with, without current low. Alternating electrical fields inject noise into strain gage systems through phenomenon capacitive coupling, which charges correspondingly alternating sign developed electrical conductors subjected field (Figure Fluorescent lighting more common sources electrostatic noise.
Noise Sources Pickup Media
Virtually every electrical device that generates, consumes, transmits power potential source causing noise strain gage circuits. And, general, higher voltage current level, closer strain gage circuit electrical device, greater will induced noise. Following list common electrical noise sources: power lines motors motor starters transformers relays generators rotating reciprocating machinery welders vibrators fluorescent lamps radio transmitters electrical storms soldering irons
Figure electrostatic noise coupling.
Magnetic fields ordinarily created either flow electric current presence permanent magnetism. Motors transformers examples former, earth's magnetic field instance latter. order noise voltage (emf) developed conductor, magnetic lines must "cut" conductor. Electric generators function this basic principle. presence alternating field, such that surrounding 50/60-Hz power line, voltage will induced into stationary conductor magnetic field expands collapses (Figure Similarly, conductor moving through earth's magnetic field noise voltage generated cuts lines flux.
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Tech Note TN-501-2
Vishay micro-measurements
Noise Control Strain Gage Measurements
Check line- ("mains-") radiated noise. feasible, reduce amplifier gain compensate increasing bridge voltage. Having eliminated satisfactorily minimized noise pickup instrument, turn next external circuitry. With excitation off, connect gage transducer circuit (including leadwires) instrument, observe noise. course, additional noise picked this step attributed leadwire and/or gage pickup. output changes when instrument chassis touched with finger, this indication poor ground and/or radiofrequency interference. Apply load part under test (with excitation still off). additional noise observed, noise something associated with loading system such motor creating magnetic field, motion gage wiring (generating emf). possible, remove load from test part apply excitation voltage bridge circuit. After balancing bridge, subsequent change output, gradual, zero-shift, noise. This gage selfheating effects (see Tech Note TN-502, Strain Gage Excitation Levels)-or other time-dependent resistance changes. following sections this Tech Note give recommended noise-reduction procedures electrostatic noise, magnetic noise.
Figure electromagnetic noise coupling.
Since most irons steels ferro-magnetic, moving machine members redirect existing lines flux, cause them adjacent sensitive conductors. result, signal conductors vicinity moving rotating machinery generally subject noise voltages from this source.
Detecting Troubleshooting
order effectively assess presence magnitude noise, strain gage instrument selected should incorporate simple, very significant feature- provision removing excitation from Wheatstone bridge. With such control, instrument output easily checked noise, independently strain signal. This represents very powerful tool evaluating effectiveness shields grounding, experimentally modifying these methods minimize effects noise. Vishay Micro-Measurements strain gage instruments data systems equipped with this important feature. following procedure used troubleshoot system noise: already known, determine tolerable levels noise output units (millivolts, inches deflection, etc.) observed readout such oscilloscope data system display. Consideration should given first noise sources affecting measurement system, isolated from external circuits. this purpose, disconnect strain gage leads, terminate S+/S- amplifier inputs with about same input impedance that amplifier normally senses (typically between 1000 ohms). excessive noise exists: Check ground loops (more than connection system ground).
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Electrostatic Noise Reduction
simplest most effective barrier against electrostatic noise pickup conductive shield, sometimes referred Faraday cage. functions capturing charges that would otherwise reach signal wiring. Once collected, these charges must drained satisfactory ground reference potential). provided with low-resistance drainage path, charges coupled into signal conductors through shield-to-cable capacitance (Figure
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Figure electrostatic shielding.
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Document number: 11051 revision 09-Apr-07
Tech Note TN-501-2
Vishay micro-measurements
Noise Control Strain Gage Measurements
most popular types cable shields braided wire conductive foil. braided-shield construction provides about percent coverage cable, characteristically resistance. Although commonly higher resistance, foil shields give percent cable coverage, also easier terminate. Following commercially available examples types shielded cable: braided: Vishay Micro-Measurements Type 430-FST (four conductors, twisted) foil: Vishay Micro-Measurements Type 422-DSV fully guarded amplifier system (for example, Vishay Micro-Measurements Model 2200 System), commonmode voltage bridge excitation supply signal input terminals "float" level guard shield. Connecting shield test structure source common-mode voltage gage installation site provide very effective noise reduction since voltage between signal conductors shield minimized. Another often-overlooked source noise leakage ground through strain gage and/or cabling. excessive, this leakage cause noise transfer from specimen gage circuit, since even supposedly well-grounded specimens carry some noise. uncommon have strain gages installed nominally grounded test objects that, fact, have noise levels expressible volts. And, course, strain gage installation conductive specimen forms classic capacitor which couple noise from specimen gage. light these considerations, always good practice make certain that specimen properly grounded that leakage between gage circuit specimen well within bounds. Prior connecting leadwires strain gage, insulation resistance from gage specimen should measured with megohm meter such Vishay Micro-Measurements Model 1300 Gage Installation Tester. reading megohms normally considered minimum satisfactory system operation. Readings below this level indicative possibly troublesome gage installation which deteriorate with time strain. should also kept mind, gage installations which will operate elevated temperatures, that leakage resistance tends decrease temperature increases. After cable placement connection gage-end cable, following resistance measurements should made, preferably from instrument-end cable: conductor-to-ground, shield-to-ground, conductor-toshield. Because distributed leakage, these resistances somewhat lower than gage-to-specimen resistance; cables with significantly lower resistances should investigated, excessive leakage eliminated avoid potential noise problems.
When long reaches multiple conductors adjacent each other, problems with crosstalk between conductors encountered. With runs feet more, significant levels noise induced into sensitive conductors through both magnetic electrostatic coupling. Even though bridge-excitation conductors carry only millivolt noise, there significant coupling signal conductors produce potentially troublesome microvolt-level noise those conductors. noise transfer minimized employing instrumentation cable composed individually shielded pairs-one pair excitation, pair signal. This type construction embodied Vishay MicroMeasurements Type 422-DSV cable. When using such cable (those having separate shields), both shields should grounded same, usually instrument, cable. Electromagnetic coupling between excitation signal pairs reduced somewhat using cable that conductor pairs twisted separate axes. Belden 8730 cable conductor pairs separately twisted, including pair shielded with foil. shield-to-conductor capacitance also become signif icant long runs, since capacitance proportional cable length. Therefore, significant portion residual noise coupled from even well-grounded shield sensitive conductors. minimize this effect, some strain gage instruments (for example, Vishay Micro-Measurements 2300 System) incorporate feature called driven guard. driven guard (also known driven shield) functions maintaining shield voltage equal average signal, common-mode voltage. Since, with this arrangement, voltage difference between conductors shield essentially zero, effective capacitance decreased, there minimal noise transfer. result very quiet shield. important note that, proper operation, driven shield connected only driven-guard instrument input connector. driven shield ordinarily surrounded second shield, which should grounded end.
Document number: 11051 revision 09-Apr-07
Electromagnetic Noise Reduction
most effective approach minimizing magnetically induced noise attempt magnetic shielding sensitive conductors; but, instead, ensure that noise voltages induced equally both sides amplifier input (Figure When analyzed, conventional strain gage bridge arrangements-quarter bridge (two- threewww.vishaymg.com
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Tech Note TN-501-2
Vishay micro-measurements
Noise Control Strain Gage Measurements
leadwire), half bridge, full bridge-reduce same basic circuit shown Figure This also true systems that employ "rotated" nonsymmetrical bridge circuit. Achievement noise cancellation method shown Figure requires that amplifier exhibit good common-mode rejection characteristics. Attention must also given, however, strain gage wiring, effects nearby power lines. example, evident from Figure that gradient magnetic field intensity exists with respect distance from current-carrying power line. series noise voltages induced signal wires will therefore depend greatly upon their distances from current-carrying conductors. Twisting signal conductors together tends make distances equal, average, thereby inducing equal noise voltages which will cancel each other. Correspondingly effective, magnetic field strengths radiated power lines reduced twisting power conductors. lengths input cable should eliminated; under circumstances should extra length disposed winding into coil illustrated Figure excess cable length cannot avoided, should folded half coiled indicated Figure that each clockwise current loop intimately accompanied counterclockwise loop. same cabling considerations apply both excitation leads signal leads, power cables. Unlike case electrostatic noise, simple, grounded
Figure Gage selection wiring technique. Figure noise cancellation amplifier common-mode rejection.
theory, least, more twists unit conductor length, better. Standard twisted-conductor cables, such Belden 8771, have sufficient twisting most applications. However, environments with high magnetic field gradients, such those found close motors, generators, transformers, tighter twisting required. particularly severe applications, conventional twisting inadequate, necessary special woven cable described later. When attaching leadwires strain gage operation magnetic field, connections should made directly solder tabs gage, rather than through auxiliary terminals. Vishay Micro-Measurements CEA-Series gages, with copper-coated solder tabs, particularly suited this type application. shown Figure gage selection wiring arrangements greatly affect sensitivity magnetic pickup. will noticed that preferred arrangement minimizes susceptible loop area between wires. same reason, flat ribbon cable very prone noise pickup, magnetic fields should avoided. When necessary this type cable, optimal conductor allocation, shown Figure help reduce pickup. addition, excess
Figure cable comparison.
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Figure Handling excess cable.
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Document number: 11051 revision 09-Apr-07
Tech Note TN-501-2
Vishay micro-measurements
Noise Control Strain Gage Measurements
conductive shield does function barrier magnetic noise. Magnetic shields operate different principle, serve bend shunt magnetic field around conductor rather than eliminate Magnetic shields made from high-permeability materials such iron other ferro-magnetic metals. relatively 50/60-Hz power line frequencies often encountered magnetic noise problems, shield thicknesses (using common iron example) order [2.5 needed before significant noise reduction achieved. Heavy-walled iron conduit also used provide some reduction magnetic noise pickup. However, there special highpermeability alloys (mu-metal®, instance) that have been developed specifically magnetic shielding purposes. These effective much thinner shields than with iron. When faced with apparent necessity magnetic shielding, attention should always given reducing noise source. example, transformers readily designed minimize leakage flux. grounding shield numerous points along length, optimum grounding scheme determined. Although leadwires ordinarily dominant medium noise induction strain gage circuit, noise pickup also occur gage itself. When needed, simple electrostatic shield fabricated forming aluminum-foil over gage unshielded leadwire terminations. gaged specimen small electrically conductive, aluminum tape with conductive adhesive should used connect cable shield, gage shield, specimen together. Conductive epoxy compounds also used this purpose. other hand, when gages installed machinery other large, conductive test objects, care must exercised prevent occurrence ground current loops shield. such cases, foil should electrically insulated from machine. machine should grounded with heavy-gauge copper wire least gauge heavier depending upon application) connected single-point ground near instrument. Care must also taken make certain that shield does form short circuit gage wiring. cable shields, then, ideally least, double-foil shield should used over strain gage. shields should connected together only instrument cable. word about ground connections order. important remember that conductors characterized resistance, inductance, shunt capacitance. result, attention should always given quality ground connections. effective, connection ground should made with heavy-gauge copper wire, should short practicable. nearest earth ground remote, 6-ft [2-m] copper driven into earth establish local ground.
Severe Noise Environments
preceding sections have treated standard methods noise reduction applicable majority instrumentation problems. This section describes techniques that become necessary when very high noise levels anticipated experienced.
Electrostatic Fields
Generally, when shielding against audio-frequency electrostatic noise (below kHz), good practice ground shield more than point. reason this that ground points different voltage levels, causing current flow through shield. Current flow such ground loops induce noise signalcarrying conductors through same phenomenon that occurs transformer. However, long cables severe noise environments, shield impedance from other become significant, particularly with high-frequency noise sources. When this occurs, noise charges captured shield longer find low-resistance drain ground, result noisy shield. Improved shield performance under such circumstances often obtained grounding shield both ends, and/or intermediate points-preferably points near localized sources electrostatic noise. Multiple-point ground connections also necessary when radio-frequency interference (RFI) problems encountered. these frequencies shield, segments shield between grounded points, display antenna behavior. experimentally
Electromagnetic Fields
with electrostatic noise pickup, leadwires commonly represent principal source magnetic noise induction strain gage circuits. intense electromagnetic fields with steep gradients (near motors, generators, similar equipment), ordinary wire-twisting techniques prove inadequate. view conventionally twisted pair reveal reason pickup. indicated Figure even induced noise were precisely equal both wires, amplifier noise output would zero only amplifier infinite common-mode rejection characteristics-an impossibility. order minimize common-mode noise voltages, special, woven, fourwire cable been designed that, seen from wire end, eliminates spiral inductive loops (Figure
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Allegheny Ludlum Steel
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Tech Note TN-501-2
Vishay micro-measurements
Noise Control Strain Gage Measurements
maximum cancellation electrostatic fields, pairs wires (composed wire from each plane) connected parallel. Referring figure, wires paralleled form conductor; wires form other. connected, this type cable largely insensitive magnetic field gradients, both parallel perpendicular cable length. cable known Inter-8 Weave, available from: Magnetic Shield Corp., Thomas Drive, Bensensville, Illinois 60106. flows opposite directions through grids, noise induced assembly tends self-cancelling. This arrangement particularly effective against magnetic field gradients their components parallel test surface. dual-element gage intended function Wheatstone bridge circuit; bridge usually completed with another gage same type, with fixed precision resistor. Standard practices followed when installing gages; Vishay Micro-Measurements M-Bond 600/610 adhesive system recommended bonding, since this will result thinnest glueline, placement grids close possible specimen surface. Available from Vishay Micro-Measurements types dual-element, noninductive stacked gages-linear H06A-AC1-125-700 three-gage rosette H06A-AD3-125-700. Precision Strain Gages Data Book details. addition strain gage size pattern, selection gage grid alloy should given careful consideration. grid alloy magnetic, will subject extraneous physical forces magnetic field; and, magnetoresistive, will undergo spurious resistance changes. Similarly, alloy magnetostrictive, grid will change length magnetic field. Isoelastic alloy, example, should used magnetic fields, since both strongly magnetoresistive magnetostrictive. Stemming from their comparative freedom from magnetic effects, constantan Karma-type alloys usually selected such applications. Constantan, however, cryogenic temperatures high magnetic fields (7-70 Tesla) becomes severely magnetoresistive. Karma-type alloy ordinarily preferred cryogenic service because generally superior performance magnetic fields very temperatures. When necessary, strain gages also shielded from electromagnetic fields some degree with magnetic shielding material such mu-metal. more layers shielding material required effect noticeable improvement. course, even this will ineffective source magnetic field beneath strain gage. When high-frequency fields encountered, sure that material suitable (high permeability) anticipated frequency.
Figure Woven cable reduce severe electromagnetic radiation pickup.
Even though strain gage much less frequently significant medium magnetic noise induction than leadwires, different gage patterns have differing sensitivities noise pickup. instance, gage both solder tabs end, noise pickup less than gage with each end. shown Figure difference noise sensitivity results from relative size inductive loop area each case. also worth noting that smaller gages, with more closely spaced grid lines, intrinsically quieter than large gages. severe magnetic fields, especially those with steep
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Suggested Additional Reading
gradients field intensity, additional measures required. this purpose, Vishay Micro-Measurements developed special gage configuration, H-Series, consisting identical grids, with stacked directly above, insulated from, other. connecting upper lower gage elements series that current Coffee, M.B., "Common-mode Rejection Techniques Low-Level Data Acquisition." Instrumentation Technology 45-49 (1977). Ficchi, R.F., Practical Design Electromagnetic Compatibility. York: Hayden Book Company, 1971.
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Document number: 11051 revision 09-Apr-07
Tech Note TN-501-2
Vishay micro-measurements
Noise Control Strain Gage Measurements
Freynik, H.S., al., "Nickel-Chromium Strain Gages Cryogenic Stress Analysis Super-Conducting Structures High Magnetic Fields." Proceedings Seventh Symposium Engineering Problems Fusion Research, October, 1977. Hayt, W.H., Jr., Engineering Electromagnetics. York: McGraw-Hill Book Company, 1967. Klipec, B.E., "How Avoid Noise Pickup Wire Cable." Instruments Control Systems 27-30 (1977). Krigman, Alan, "Sound Fury: Persistent Problem Electrical Noise." In-Tech 9-20 (1985). (Extensive bibliography). McDer mott, "EMI ielding Protective Components." 165-176 (1979). Morrison, Ralph, Grounding Shielding Techniques Instrumentation, York: John Wiley Sons, Inc., 1977. Severinsen, "Gaskets that Block EMI." Machine Design 74-77 (1975). Sitter, R.P., "RFI What Control Part Reduction Interference." Instrumentation Technology 59-65 (1978). *Stein, Peter "Spurious Signals Generated Strain Gages, Thermocouples Leads." Lf/MSE Publication April 1977. *Stein, Peter "The Response Transducers Their Environment, Problem Signal Noise." Lf/MSE Publication October 1969. "Strain Gages Operate 000-Gauss Magnetic Fields Fusion Research." Epsilonics (published Vishay Measurements Group, Inc.) (1982). D.R. Electromag netic Interfere Compatibility, Vol. Germantown, Maryland: White Consultants, 1973. *Available from: Stein Engineering Services, 5602 Monte Rosa, Phoenix, Arizona 85018.
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Strain Gages Instruments
tech note tn-502
Optimizing Strain Gage Excitation Levels
Introduction
common request strain gage work obtain recommended value bridge excitation voltage particular size type gage. simple, definitive answer this question possible, unfortunately, because factors other than gage type involved. problem particularly difficult when maximum excitation level desired. This Tech Note intended outline most significant considerations that apply, suggest specif approaches optimizing excitation levels various strain gage applications. important realize that strain gages seldom damaged excitation voltages considerably excess proper values. usual result performance degradation, rather than gage failure; problem therefore becomes meeting total requirements each particular installation. Zero (no-load) stability strongly affected excessive excitation. This particularly true strain gages with high thermal output characteristics, when inherent half-bridge full-bridge compensation relied upon meet zero-shift temperature specification. zero-shift occurs because variation heat-sink conditions between gages bridge circuit. Another point should emphasized. tendency localized areas grid operate higher temperatures than rest grid will restrict allowable excitation levels. Creep instability particularly susceptible these "hot-spot" effects, which usually voids bubbles glueline discontinuities substrate. Imperfections gage itself cause spots develop, only gages highest quality should considered high-excitation applications. When other factors constant, power-dissipation capability strain gage varies approximately with area grid (active gage length active grid width). amount type waterproofing compound encapsulant relatively unimportant. Open-face gages mounted metal show only less power-handling capacity than fully encapsulated gages with same grid area. Note, however, that proper waterproofing materials must always applied open-face gages prevent loss performance through grid corrosion. sometimes stated that gage adhesives high thermal conductivity considerably improve power-handling capability strain gage installations. Generally, this correct. These adhesives incorporate high-conductivity fillers such aluminum oxide metal powders. This produces adhesive high viscosity, resulting excessively thick gluelines longer thermal path from gage substrate. gain thermal conductivity more than offset performance degradation thicker gluelines. much better, high gage excitation well normal gage applications, high-functionality adhesives that permit thin, void-free gluelines. smooth mounting surfaces, ideal glueline thicknesses range from 0.0001 0.0003 [0.0025 0.0075 mm].
Thermal Considerations
voltage applied strain gage bridge creates power loss each arm, which must dissipated form heat. Only negligible fraction power input available output circuit. This causes sensing grid every strain gage operate higher temperature than substrate which bonded. With exceptions, which discussed later, considered that heat generated within strain gage must transferred conduction mounting surface. heat flow through specimen causes temperature rise substrate, which function heat-sink capacity gage power level. Consequently, both sensing grid substrate operate temperatures higher than ambient. When temperature rise excessive, gage performance will affected follows: loss self-temperature-compensation (S-T-C) occurs when grid temperature considerably above specimen temperature. manufacturers' data S-T-C necessarily obtained excitation levels. Hysteresis creep effects magnified, since these dependent backing glueline temperatures. gage backing normally rated +250°F [+120°C] transducer service might have derated 50°F [10° 30°C] under high-excitation conditions.
revision 16-Jul-07
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Factors Affecting Optimum Excitation
factors mpor tanc determining optimum excitation level strain gage application:
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Tech Note TN-502
Vishay micro-measurements
Optimizing Strain Gage Excitation Levels
Strain gage grid area (active gage length active grid width). Gage resistance. High resistances permit higher voltages given power level. Heat-sink properties mounting surface. Heavy sections high-thermal-conductivity metals, such copper aluminum, excellent heat sinks. Thin sections low-thermal-conductivity metals, such stainless steel titanium, poor heat sinks. Also, shape gaged part create thermal stresses portions structure gage selfheating. Long warm-up times apparent gage instability result. situation often arises lowforce transducers, where thin sections intricate machining fairly common. Strain measurement plastic requires special consideration. Most plastics thermal insulators rather than heat sinks. Extremely values excitation required avoid serious self-heating effects. modulus elasticity common plastics drops rapidly temperature rises, increasing viscoelastic effects. This significantly affect material properties area under strain gage. Plastics that heavily loaded with inorganic fillers powder fibrous form present lesser problem, because such fillers reduce expansion coefficients, increase elastic modulus, improve thermal conductivity. Environmental operating temperature range gage installation. Creep gage backing adhesive will occur lower ambient temperatures when grid substrate temperatures raised self-heating effects. Thermal output temperature will also altered when grid substrate temperatures significantly different. Required operational specifications. Gages normal stress analysis excited higher level than under transducer conditions, where utmost stability, accuracy, repeatability needed. significant distinction exists between gages used dynamic strain measurement those used static measurement applications. various performance losses gage self-heating affect static characteristics gage much more seriously than dynamic response. Therefore, practical "drive" dynamic installations much harder, thus take advantage higher signal-to-noise ratio that results. Installation wiring technique. gage damaged during installation, solder tabs partially unbonded soldering heat, discontinuities formed glueline, high levels excitation will
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create serious problems. Proper technique essential obtaining consistent performance strain gage work, particularly under high-excitation conditions. addition preceding, secondary factors affect maximum permissible excitation levels. Poor grid design, such improper line-to-space ratio, will reduce heat transfer effectiveness. type gage matrix, terms resin filler, determines thermal conductivity backing. backing usually more important than adhesive selected because adhesive layer thinner than backing proper installations.
Stacked Rosette Gages
These represent special case, because thermal path length much greater from upper grid substrate, because temperature rise lower grids adds directly those above. three-element stacked rosette which three grids completely superimposed, grid will have times temperature rise similar single gage, grids receive same input power. keep temperature rise grid equal that similar single gage, three rosette sections should each receive power applied single gage. This corresponds reduction factor bridge excitation voltage, since power varies square applied voltage. two-element stacked rosettes, comparable derating factor power, bridge voltage. This discussion based rosettes square grid geometry, where each grid covers essentially grid(s) assembly. When substantial areas grids superimposed, derating factors mentioned above will somewhat conservative.
Cryogenic Gage Applications
Many strain gage measurements made under direct submersion liquefied gases such nitrogen, hydrogen, helium. Since these liquids electrically nonconductive, open-face gages have been used occasionally without protective waterproofing coating. interesting effect been reported under these conditions. excitation voltages kept sufficiently low, grid self-heating will cause bubbles form gridlines, thus partially insulate grid from cold liquid. Larger bubbles then created increased grid temperatures, bubbles periodically break loose rise toward surface. relative motion these insulating bubbles with respect gridlines produces local temperature changes, which appear output signal noise. Grid alloys that display very high values thermal output cryogenic temperatures (most constantan alloys, example) particularly susceptible this effect. remedy utilize very excitation levels, and/or
Document number: 11052 revision 16-Jul-07
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Tech Note TN-502
Vishay micro-measurements
Optimizing Strain Gage Excitation Levels
protective coatings over grid prevent direct liquid contact. Such coatings must necessarily retain sufficient flexibility cryogenic temperatures prevent cracking protective layer. necessary check errors excitation level. These networks greatly attenuate input bridge voltage, sensors therefore operated very power levels.
Experimental Determination Maximum Gage Excitation
certain that excitation level chosen given strain gage application excessive, necessary performance tests maximum environmental temperature. many cases, however, this rather complicated procedure greatly simplified gradually increasing bridge excitation under zero-load conditions until definite zero instability observed. excitation should then reduced until zero reading becomes stable again, without significant offset from low-excitation zero reading. most applications experimental stress analysis, this value bridge voltage highest that used safely without significant performance degradation. Conducting this test maximum operating temperature instead room temperature will increase likelihood that maximum safe bridge voltage been established. rigid operating requirements precision transducers make above procedure useful primarily first approximation; further verification usually required. performance tests most sensitive excessive excitation voltage are: zero-shift temperature stability under load maximum operating temperature.
Typical Strain Gage Excitation Values
data curves pages 15-17 represent general recommendations starting points determining optimum excitation levels. These curves plots bridge excitation voltage grid area (active gage length grid width) constant power-density levels watts/ kilowatts/m large number standard MicroMeasurements single-element gage patterns listed various grid areas they represent. Separate plots provided gage resistances 120, 350, 1000 ohms. other grid areas and/or other gage resistances, calculations made according following formulas recommended power-density levels: Power Dissipated Grid (watts)
Power Density Grid (watts/in2 kW/m
where: Gage resistance ohms Grid area (active gage length grid width) Bridge excitation volts Note that bridge voltage (EB) based equalarm bridge arrangement, where voltage across active one-half bridge voltage. When grid area (AG), gage resistance (RG), grid power density (P'G) known:
Excitation Levels Resistance Temperature Sensors
become increasingly common measure specimen temperatures strain gage work bondable nickel-grid temperature sensors such ETG-50 WTG-50. These sensors fabricated same manner strain gages, consequently experience environmental temperature changes same way. eliminating many measurement errors often encountered with thermocouples, temperature sensors ideal correcting strain gage data under rapidly changing temperature conditions. Like strain gages, temperature sensors adversely affected excessive excitation levels. Variation heat-sink conditions accuracy requirements make universally applicable excitation recommendations impossible, simple test procedure available. excitation level should increased until readout device indicates excessive grid temperature rise; should then reduced necessary. Since readout this case shows temperature measurement error directly, determination straightforward. Since temperature sensors most often used with linearization networks type, normally
Document number: 11052 revision 16-Jul-07
Grid Power-Density Curves
Selecting most appropriate power-density lines following charts depends, primarily, considerations: degree measurement accuracy required, substrate heat-sink capacity. series general recommendations follows, should verified procedures previously described critical applications.
Typical Power-Density Levels Watts/in2 [kW/m2]
interest that some commercial strain measurement/ instrumentation utilizes constant excitation voltage volts. power densities created gages various sizes resistances these bridge voltages taken directly from charts compared with Table very small gages, evident that commercial instruments
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Optimizing Strain Gage Excitation Levels
require voltage reduction proper results. simple circuit modification, which utilized when instrument voltage adjustable, involves insertion "dead" resistance form high-precision resistors Vishay type series with active dummy gages bridge circuit. Power density then reduced (multiplied factor RG)]2, where inactive series resistance ohms, active gage resistance ohms. Note that adjacent bridge must increased same maintain bridge balance under these conditions. sensitivity bridge will decreased this procedure, readings must multiplied ratio RG)/RG correct this desensitization. Alternately, shunt calibration resistor connected directly across dummy gage, instrument gage factor setting adjusted display proper calibration level. Case instrument with fixed 4.5V excitation used? not, what correction data points must made? determine power density 125AD gage given excitation level, refer Chart Enter left ordinate volts until intersecting abscissa value equivalent 125AD gage. power density W/in [4.2 kW/m which excess maximum power determined Case accuracy (i.e., data) acceptable, higher used. greater accuracy must maintained, several alternatives available: select higher resistance gage, select gage with larger voltage area,R reduce bridge(desired) with inactive series resistor, inactive resistor required reduce power density desired W/in (3.1 kW/m with given determined from following relationship: 19.5 ohms (desired) desired W/in2 (3.1 kW/m 19.5 ohms
Examples Chart
Case What excitation level safely applied EA-09-125AD-120 strain gage, mounted 1/16 [12.5 stainless-steel bar, static stress analysis test with moderate accuracy 5%)? From Table determine typical power-density level, W/in2 [1.6 kW/m corresponding fair heatsink condition stainless steel. Refer Chart Enter horizontal axis arrowhead 125AD gage 0.0156 [10.06 Mark intersection vertical line with W/in2 [1.6 kW/m sloped lines. Read horizontally left ordinate Bridge Excitation volts, respectively. strain indicator with maximum bridge excitation volts used.
nearest precision Select 19.5 resistor value greater than 1.16 19.5 ohmsRG actual strain values, accounting inserted inactive resistor, indicated strain readings must multiplied 19.5 1.16
Table Heat-Sink Conditions watts/in2 [kilowatts/m2]
Accuracy Requirements High STATIC Moderate High Moderate www.vishaymg.com EXCELLENT Heavy Aluminum Copper Specimen [3.1-7.8] 5-10 [7.8-16] 10-20 [16-31] 5-10 [7.8-16] 10-20 [16-31] 20-50 [31-78] GOOD Thick Steel [1.6-3.1] [3.1-7.8] 5-10 [7.8-16] 5-10 [7.8-16] 10-20 [16-31] 20-50 [31-78] FAIR Thin Stainless Steel Titanium 0.5-1 [0.78-1.6] [1.6-3.1] [3.1-7.8] [3.1-7.8] 5-10 [7.8-16] 10-20 [16-31] POOR Filled Plastic such Fiberglass/Epoxy 0.1-0.2 [0.16-0.31] 0.2-0.5 [0.31-0.78] 0.5-1 [0.78-1.6] 0.5-1 [0.78-1.6] [1.6-3.1] [3.1-7.8] VERY POOR Unfilled Plastic such Acrylic Polystyrene 0.01-0.02 [0.016-0.031] 0.02-0.05 [0.031-0.078] 0.05-0.1 [0.078-0.16] 0.01-0.05 [0.016-0.078] 0.05-0.2 [0.078-0.31] 0.2-0.5 [0.31-0.78] Document number: 11052 revision 16-Jul-07
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Optimizing Strain Gage Excitation Levels
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Strain Gages Instruments
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Measurement Residual Stresses Hole-Drilling* Strain Gage Method
Residual Stresses Their Measurement
Residual (locked-in) stresses structural material component those stresses that exist object without (and usually prior application service other external loads. Manufacturing processes most common causes residual stress. Virtually manufacturing fabricating processes casting, welding, machining, molding, heat treatment, etc. introduce residual stresses into manufactured object. Another common cause residual stress in-service repair modification. some instances, stress also induced later life structure installation assembly procedures, occasional overloads, ground settlement effects underground structures, dead loads which ultimately become integral part structure. effects residual stress either beneficial detrimental, depending upon magnitude, sign, distribution stress with respect loadinduced stresses. Very commonly, residual stresses detrimental, there many documented cases which these stresses were predominant factor contributing fatigue other structural failures when service stresses were superimposed already present residual stresses. particularly insidious aspect residual stress that presence generally goes unrecognized until after malfunction failure occurs. Measurement residual stress opaque objects cannot accomplished conventional procedures experimental stress analysis, since strain sensor (strain gage, photoelastic coating, etc.) totally insensitive history part, measures only changes strain after installation sensor. order measure residual stress with these standard sensors, locked-in stress must relieved some fashion (with sensor present) that sensor register change strain caused removal stress. This usually done destructively past cutting sectioning part, removal successive surface layers, trepanning coring. With strain sensors judiciously placed before dissecting part, sensors respond deformation produced relaxation stress with material removal. initial residual stress then inferred from measured strains elasticity considerations. Most these techniques limited laboratory applications
revision 15-Aug-07
flat cylindrical specimens, readily adaptable real test objects arbitrary size shape. X-ray diffraction strain measurement, which does require stress relaxation, offers nondestructive alternative foregoing methods, severe limitations. Aside from usual bulk complexity equipment, which preclude field application, technique limited strain measurements only very shallow surface layers. Although other nondestructive techniques (e.g., ultrasonic, electromagnetic) have been developed same purposes, these have achieve wide acceptance standardized methods residual stress analysis.
Hole-Drilling Method
most widely used modern technique measuring residual stress hole-drilling strain-gage method stress relaxation, illustrated Figure Briefly summarized, measurement procedure involves basic steps: special three- six-) element strain gage rosette installed test part point where residual stresses determined. gage grids wired connected multichannel static strain indicator, such Vishay Micro-Measurements Model (three-element gage), System 5000 (six-element gage).
Drilling implies methods introducing hole (i.e., drilling, milling, abrasion, etc).
Strain Gage rosette
Drilled Hole
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Figure Hole-Drilling Strain Gage method
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Measurement Residual Stresses Hole-Drilling Strain Gage Method
precision milling guide (Model RS-200, shown Figure attached test part accurately centered over drilling target rosette. After zero-balancing gage circuits, small, shallow hole drilled through geometric center rosette. Readings made relaxed strains, corresponding initial residual stress. Using special data-reduction relationships, principal residual stresses their angular orientation calculated from measured strains. location. This occurs because every perpendicular free surface (the hole surface, this case) necessarily principal axis which shear normal stresses zero. elimination these stresses hole surface changes stress immediately surrounding region, causing local strains surface test object change correspondingly. This principle foundation hole-drilling method residual stress measurement, first proposed Mathar.2 most practical applications method, drilled hole blind, with depth which about equal diameter, small compared thickness test object. Unfortunately, blind-hole geometry sufficiently complex that closed-form solution available from theory elasticity direct calculation residual stresses from measured strains except introduction empirical coefficients. solution obtained, however, simpler case hole drilled completely through thin plate which residual stress uniformly distributed through plate thickness. Because this, theoretical basis hole-drilling method will first developed through-hole geometry, subsequently extended application blind holes.
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foregoing procedure relatively simple, been standardized ASStandard Test Method 837.1 Using commercially available equipment supplies, adhering recommendations ASstandard, hole-drilling method applied routinely qualified stress analysis technician, since special expertise required making measurements. method also very versatile, performed either laboratory field, test objects ranging widely size shape. often referred "semidestructive" technique, since small hole will not, many cases, significantly impair structural integrity part being tested (the hole typically 1/32 3/16 [0.8 both diameter depth). With large test objects, sometimes feasible remove hole after testing completed, gently blending smoothing surface with small hand-held grinder. This must done very carefully, course, avoid introducing residual stresses process grinding. NOTE current state development, holedrilling method intended primarily applications which residual stresses uniform throughout drilling depth, essentially While procedures data acquisition reduction such cases wellestablished straightforward, seasoned engineering judgment generally required verify stress uniformity other criteria validity calculated stresses. This Tech Note contains basic information understanding method operates, cannot, course, encompass full background needed proper application cases. extensive list technical references provided Bibliography further users method. NOTE Manual calculation residual stresses from measured relaxed strains quite burdensome, there available specialized computer program, H-DRILL, that completely eliminates computational labor.
Through-Hole Analysis
Depicted Figure (following) local area within thin plate which subject uniform residual stress, initial stress state point expressed polar coordinates
(1a) (1b) (1c)
Figure represents same area plate after small hole been drilled through stresses vicinity hole quite different, since must zero everywhere hole surface. solution this case obtained Kirsch 1898, yields following expressions stresses point (2a)
Principle Theory Hole-Drilling Strain Gage Method
introduction hole (even very small diameter) into residually stressed body relaxes stresses that
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(2b) (2c)
hole radius
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Measurement Residual Stresses Hole-Drilling Strain Gage Method
(4a) (4b)
P(R, cos) cos)
preceding equations written simpler form, demonstrating that along circle radius relieved radial tangential strains vary sinusoidal manner:
(5a) (5b)
Compar ison Equations Equations demonstrates that coefficients have following definitions: (6a) (6b) (6c) Figure Stress states vary, complex way, with hole. Thus,2the relieved strains also This variation illustrated before after introduction distance from hole surface. Figure page where strains plotted along principal axes, 90°. shown where: figure, relieved strains generally decrease distance hole radius from hole increases. Because this, desirable arbitrary radius from hole center measure strains close edge hole order hole radius maximize strain gage output signal. other hole radius arbitrary radius from hole center effects also increase immediate hand, parasitic arbitrary radius from hole center vicinity hole. These considerations, along with practical aspects strain gage design application, Subtracting initial stresses from final (after drilling) necessitate compromise selecting optimum radius stresses gives change stress, stress relaxation gage location. Analytical experimental studies point drilling hole. That have established practical range 0.45 where (3a) radius longitudinal center gage. (3b) noticed from Figure that (along axis major principal stress) relieved radial strain, (3c) considerably greater than tangential strain, specified region measurement. result, commercial Substituting Equations into Equations yields strain gage rosettes residual stress analysis normally full expressions relaxed relieved) stresses. designed with radially oriented grids measure material plate homogeneous isotropic relieved radial strain, This being case, only Equation mechanical properties, linear-elastic stress/strain (5a) directly relevant further consideration this behavior, these equations then substituted into summary. also evident from figure that relieved biaxial Hooke's solve relieved normal radial strain along major principal axis opposite strains point resulting expressions sign initial residual stress. This occurs because follows:
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Measurement Residual Stresses Hole-Drilling Strain Gage Method
a=slightly different )form,( cos2
(9b)
Figure Variation relieved radial tangential strains with distance (along principal axes) from center drilled hole uniaxial residual stress.
coefficients Equation (5a) always negative, (for preceding treatment considered only simplest case, uniaxial residual stress. practice, however, residual stresses more often biaxial, with nonzero principal stresses. This condition readily incorporated analysis employing superposition principle, which applicable linear-elastic material behavior. Referring Figure again, apparent that uniaxial residual stress been along only axis instead axis, Equations would still apply, with replaced 90°), equivalent, -cos Thus, relieved radial strain point P(R, uniaxial residual stress only direction written
Equations represent basic relationship underlying hole-drilling method residual stress analysis. This relationship must inverted, course, solve principal stresses angle terms measured strains that accompany stress relaxation. Since there three unknown quantities, three independent measurements radial strain required complete solution. These three measurements substituted successively into Equation (9a) Equation (9b) yield three equations which then solved simultaneously magnitudes directions principal stresses. common procedure measuring relieved strains mount three resistance strain gages form rosette around site hole before drilling. Such rosette shown schematically Figure where three radially oriented strain gages located with their centers radius from center hole site. Although angles between gages arbitrary (but must known), 45-degree angular increment leads simplest analytical expressions, thus become standard commercial residual stress rosettes. indicated Figure acute angle from nearer principal axis gage while +45° 90°, with positive angles measured direction gage numbering. should noted that direction gage numbering rosette type sketched Figure clockwise, since gage although physically position effectively position gage numbering purposes. Equations used verify that both
cos2
And, employing corresponding notation, Equation (5a) becomes:
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cos2)
When both residual stresses present simultaneously, superposition principle permits algebraic addition Equations (8), that general expression relieved radial strain plane biaxial residual stress state (9a)
Figure Strain gage rosette arrangement determining residual stress.
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cos2
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Measurement Residual Stresses Hole-Drilling Strain Gage Method
locations gage produce same result providing residual stress uniform over area later occupied hole. general-purpose applications, location usually preferred, because minimizes possible errors caused eccentricity drilled hole. When space gage limited, measuring residual stresses near weld abutment, location permits positioning hole closest area interest. Equation (9b) written three times, once each gage rosette:
refers refers ±45° +45° -45°
Careful consideration must also given determining appropriate values coefficients defined algebraically Equations (6), they apply only when conditions imposed Kirsch solution met. This solution gives stress distribution points with coordinates around circular hole through thin, wide plate subjected uniform plane stress. However, comparison Figures illustrates that, since strain gage grids rosette have finite areas, they sense varying strain distributions such those plotted Figure Thus, output each gage tends represent average strain over area grid. Moreover, because grids usually composed parallel lines, those lines which directly centerline radially oriented grid radial. Therefore, gages slightly sensitive tangential strain, well radial strain. result, more accurate values coefficients obtained integrating Equations over areas respective gage grids. coefficients thus determined, which account finite strain gage area, designated here distinguish them from values point defined Equations (6). alternative method obtaining measure them experimental calibration. procedure doing described Section III, "Determining Coefficients When performed correctly, this procedure potentially most accurate means evaluating coefficients. When employing conventional strain gage rosettes experimental stress analysis, usually recommended that strain measurements corrected transverse sensitivity gages. Correction relationships this purpose given Tech Note TN-509. These relationships directly applicable, however, relieved strains measured with residual stress rosette hole-drilling method. residual stress case, individual gages rosette effectively different locations spatially varying strain field. result, relieved axial transverse strains applied each gage related same manner they uniform strain field. Rigorous correction would require evaluation coefficient [actually, integrated calibrated counterpart, Equations (6)], both through-hole blind-hole geometries. Because foregoing, fact that transverse sensitivities Vishay Micro-Measurements residual stress rosettes characteristically very (approximately 1%), considered necessary correct transverse sensitivity. Kabiri4, example, shown that error ignoring transverse sensitivity
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45°) 90°)
(10a) (10b) (10c)
When Equations (10) solved simultaneously principal stresses their direction, results expressed
(11a) (11b)
tan2
where angle from nearer principal axis gage direction gage numbering, positive; opposite, negative). Reversing sense more conveniently define angle from gage nearer axis, while retaining foregoing sign convention, tan2
(11c)
following important comments about Equations (11) should carefully noted. These equations very similar appearance data-reduction relationships conventional strain gage rosettes, differences significant. coefficients only incorporate elastic properties test material, also reflect severe attenuation relieved strains relative relaxed stress. observed, addition, that signs between terms Equations (11a) (11b) opposite those conventional rosette equations. This occurs because always negative; thus, since Equation (11a) algebraically greater than Equation (11b), former must represent maximum principal stress. Equation (11c) identical that conventional three-element rectangular rosette, must interpreted differently determine which principal stress referred gage following rules used this purpose:
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Measurement Residual Stresses Hole-Drilling Strain Gage Method
case uniaxial residual stress) negligible compared remaining uncertainties measurement datareduction procedures.
GAGE
Blind-Hole Analysis
theoretical background hole-drilling method developed preceding treatment basis small hole drilled completely through thin, wide, flat plate subjected uniform plane stress. Such configuration from typical practical test objects, however, since ordinary machine parts structural members requiring residual stress analysis size shape, rarely thin flat. Because this, shallow "blind" hole used most applications hole-drilling method. introduction blind hole into field plane stress produces very complex local stress state, which exact solution available from theory elasticity. Fortunately, however, been demonstrated Rendler Vigness5 that this case closely parallels through-hole condition general nature stress distribution. Thus, relieved strains drilling blind hole still vary sinusoidally along circle concentric with hole, manner described Equations (9). follows, then, that these equations, well data-reduction relationships Equations (11), equally applicable blind-hole implementation method when appropriate blind-hole coefficients employed. Since these coefficients cannot calculated directly from theoretical considerations, they must obtained empirical means; that experimental calibration numerical procedures such finite-element analysis. Several different investigators [e.g., (20)-(23)] have published finite-element studies blind-hole residual stress analysis. most recently developed coefficients Schajer incorporated ASstandard 837, shown graphically case uniform stress Figure this Tech Note. computer program H-DRILL uses these coefficients. Compared through-hole procedure, blind-hole analysis involves additional independent variable; namely, dimensionless hole depth, (see Figure Thus, generalized functional form, coefficients expressed Z/D) (12a) Z/D) (12b) given initial state residual stress, fixed hole diameter, relieved strains generally increase decreasing rate) hole depth increased. Therefore, order maximize strain signals, hole normally drilled depth corresponding least (ASE specifies maximum hole depth).
PERCENT STRAIN RELIEVED
Gage
Figure relieved strain versus ratio hole depth gage circle diameter (strains normalized 100% 0.4).
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general variation relieved strain with depth illustrated Figure where strains have been normalized, this case, 100% 0.4. data include experimental results from different investigators demonstrating manner which relieved-strain function affected ratio hole diameter gage circle diameter (Do/D). Both cases involve uniform uniaxial (plane) stress, specimens that thick compared maximum hole depth. curves plotted figure considered representative response expected when residual stress uniform throughout hole depth. important contribution Rendler Vigness work demonstration that, given material properties, coefficients simply geometric functions, thus constants geometrically similar cases. This means that once coefficients have been determined particular rosette configuration, rosette size scaled upward downward same coefficients will still apply when hole diameter depth similarly scaled (assuming, course, same material). Several different approaches have been taken attempting remove material dependency from leaving only geometric dependence. these, proposed Schajer,7 adopted this Tech Note. Schajer introduced coefficients, denoted here defined follows: (13a) (13b)
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Measurement Residual Stresses Hole-Drilling Strain Gage Method
comparison with Equations (6), seen that through hole, least material-independent, depends only weakly Poisson's ratio. Schajer determined from finite-element calculations that blind holes, vary less than range Poisson's ratio from 0.25 0.35. enough avoid risk local yielding stressconcentrating effect hole. Basically, calibration procedure involves measuring rosette strains under same applied load calibration stress, both before after drilling hole. Such procedure necessary order eliminate effect strain relief that occur relaxation initial residual stress calibration specimen. With this technique, observed strain difference (before after hole drilling) caused only applied calibration stress, uniquely related that stress. steps calibration procedure summarized briefly follows, noting that strains only grid grid need measured, since these grids known aligned with principal axes specimen. Zero-balance strain gage circuits. Apply load, specimen develop desired calibration stress, Measure strains (before drilling). Unload specimen, remove from testing machine. Drill hole, described Section "Experimental Techniques". Replace specimen testing machine, re-zero strain gage circuits, then reapply exactly same load, Measure strains (after drilling). calibration strains corresponding load, stress, then:
III. Determining Coefficients
Whether residual stress analysis application involves through-hole blind-hole drilling, coefficients must determined calculate stresses from relieved strains. case through hole, reasonably accurate values coefficients obtained particular case analytical means, desired. This done integrating, over area gage grid, component strain parallel primary strain-sensing axis gage. Given details grid geometry (line width spacing, number lines, etc.), Slightly greater accuracy obtained integrating along individual grid lines. This method cannot applied blind-hole analysis because closedform expressions relating relieved strains residual stress, terms hole depth, available.
Experimental Calibration
needed coefficients either through-hole blindhole analysis always determined experimental calibration. This procedure particularly attractive since automatically accounts mechanical properties test material, strain gage rosette geometry, hole depth diameter, strain-averaging effect strain gage grid. When performed correctly, with sufficient attention detail, potentially most accurate means determining coefficients. principal disadvantage that calibration must repeated each time different geometric parameters involved. Calibration accomplished installing residual stress strain gage rosette uniaxially stressed tensile specimen made from same material test part. rosette should oriented align grid parallel loading direction, placing grid along transverse axis specimen. Care must taken that tensile stress uniform over cross section test specimen; i.e., that bending stress negligible. minimize edge effects, specimen width should least times hole diameter, length between machine grips, least five times width. When determining blind-hole applications, specimen thickness five more times hole diameter recommended. through-hole calibration, thickness calibration specimen preferably same that test part. also important that maximum applied stress during calibration exceed one-half proportional limit stress test material. case, applied stress plus initial residual stress must
Document number: 11053 revision 15-Aug-07
Calibration reliability ordinarily improved loading specimen incrementally making strain measurements each load level, both before after drilling hole. This permits plotting graph versus that best-fit straight lines constructed through data points minimize effect random errors. will also help identify presence yielding, that should occur. resulting relationship between applied stress relieved strain usually more representative than that obtained single-point determination. Since calibration performed with only nonzero principal stress, Equation (5a) used develop expressions calibrated values Successively substituting (for grid (for grid into Equation (5a): (0°)] 90°)]
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Measurement Residual Stresses Hole-Drilling Strain Gage Method
Solving (14a) (14b) same hole form (through hole full-depth blind hole); uniform stress with depth; nominally uniform in-plane stress hole.
Coefficients Vishay Micro-Measurements Residual Stress Rosettes
Vishay Micro-Measurements supplies special strain gage rosettes residual stress analysis four basic configurations, illustrated described Figure Among other features, these rosette designs incorporate centering patterns positioning boring tool precisely center gage circle. designs have
EA-XX-062RE-120 this geometry conforms early rendler Vigness design5 been used most reported technical articles (see references). available range sizes accommodate applications requiring different hole diameters depths. CEA-XX-062UL-120 this rugged, encapsulated design incorporates practical advantages strain gage series (integral copper soldering tabs, conformability, etc.). Installation time expense greatly reduced, solder tabs side gage simplify leadwire routing from gage site. compatible with methods introducing hole, strain gage grid geometry identical 062re pattern. CEA-XX-062UM-120 Another ceA-Series strain gage, 062um grid widths have been reduced facilitate positioning three grids side measurement point shown. With this geometry, appropriate trimming, possible position hole closer welds other irregularities. user should reminded, however, that data reduction equations theoretically valid only when holes well removed from free boundaries, discontinuities, abrupt geometric changes, etc. design compatible with methods introducing hole. N2K-XX-030RR-350/DP K-alloy grids this open-faced sixelement rosette mounted thin, high-performance laminated polyimide film backing. Solder tabs duplex copper plated ease making solder joints lead attachment. Diametrically opposed circumferential radial grids wired half-bridge configurations. Figure residual stress strain gage rosettes (shown approximately 2X). Document number: 11053 revision 15-Aug-07
procedure described here applied throughhole specimen made from Type stainless steel, calibration data plotted Figure seen from figure that this geometry (Do/D 0.35) material, +39, respectively, when MPa]. Substituting into Equations (14), -0.25 psi-1 [-0.36 Pa-1] -0.65 psi-1 [-0.94 Pa-1] Although preceding numerical example referred through-hole coefficients, same procedure followed calibrating full-depth blind-hole coefficients. Once have been obtained this manner, corresponding material-independent coefficients, calculated from Equations (13) elastic modulus Poisson's ratio test material known. desired, procedure then repeated over practical range Do/D permit plotting curves cases interest. should noted that values basic coefficients obtained from particular calibration test strictly applicable only residual-stress measurement conditions that exactly match calibration conditions: material with same elastic properties; same rosette geometry (but rosette orientation arbitrary); same hole size;
STRESS [MPa]
GAGe STRESS (1000 psi)
GAGe
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-100
CALIBRATION MICROSTRAIN Figure Stress versus relieved strain calibration coefficients Stainless Steel (through-hole). www.vishaymg.com
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Measurement Residual Stresses Hole-Drilling Strain Gage Method
geometrically similar grid configurations, with gagecircle diameter equal 3.25 times active gage length. 062RE rosette, example, gage-circle diameter 0.202 [5.13 mm]. Because this similitude, same material-independent coefficients apply sizes rosette, rosette, geometrically similar holes (i.e., same Do/D ratios). 062UM rosette configuration same ratio gage circle grid length, grids narrower permit their close grouping side hole. result, sensitivity gage relieved strains slightly greater, coefficients specific 062UM required data reduction. 030RR rosette fundamentally different from other rosettes illustrated Figure begin with, this rosette includes both radially circumferentially oriented grids which connected half-bridge pairs. 030RR rosette incorporates number features that contribute greater output higher accuracy compared conventional three-element rosettes: individual gridlines radial elements purely radial, instead being simply parallel central gridline other rosettes; given maximum hole diameter, outermost radius grids considerably less than corresponding conventional rosettes, thus grids sense slightly greater average released strains; since radial circumferential grids connected half-bridge configuration, bridge output augmented correspondingly, circuit intrinsically selftemperature compensating. result these features, 030RR rosette yields about twice output three-element rosettes given state residual stress, while displaying better stability accuracy. Since sign residual stress primary importance determining effect structural integrity mechanical component, user six-element rosette (030RR) must exercise care connecting rosette grids into Wheatstone bridge circuits. obtain correct sign instrument output signal, radially oriented grids should always connected between positive excitation negative signal terminals, while tangentially oriented grids connected between negative signal negative excitation terminals. coefficients Vishay Micro-Measurements residual stress rosettes provided graphically Figure page where solid lines apply full-depth blind holes dashed lines through holes assuming, both cases, that initial residual stress uniform with depth. Both through-hole full-depth blind-hole coefficients plotted Figure were determined combination finite-element analysis experimental verification. These coefficients also supplied numerically tabular form 837-99, where RE/UL rosettes designated Type rosettes Type rosettes Type blind-hole coefficients
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ASstandard, "full depth" corresponds value 0.40 depth rosette-mean-diameter-ratio, Z/D.
Measuring Nonuniform Residual Stresses
coefficients given this Tech Note 837-99 strictly applicable only situations which residual stresses vary magnitude direction with depth from test-part surface. reality, however, residual stresses often vary significantly with depth, due, example, different manufacturing processes such casting, forging, heat treatment, shot peening, grinding, etc. Numerous finite-element studies have been made attempts treat this situation [see, instance, references (20) through (23)]. results finite element work Schajer have been incorporated computer program, H-DRILL, handling stress variation with depth. When measured strains from hole drilling reference curves Figure when there other basis suspecting significant nonuniformity, program H-DRILL some other finite-element-based program necessary accurately determine stresses from measured relaxed strains.
Experimental Techniques
experimental methods, proper materials, application procedures, instrumentation essential accurate results obtained. accuracy hole-drilling method dependent chiefly upon following technique-related factors: strain gage selection installation. hole alignment boring. strain-indicating instrumentation. understanding mechanical properties test material.
Strain Gage Selection Installation
Installing three individual strain gages, accurately spaced oriented small circle, neither easy advisable, since small errors gage location orientation produce large errors calculated residual stresses. rosette configurations shown Figure have been designed developed Vishay Micro-Measurements specifically residual stress measurement. rosette designs incorporate centering marks aligning boring tool precisely center gage circle, since this critical accuracy method.9,10,11 configurations available range temperature compensations common structural metals. However, only design offered different sizes (031RE, 062RE, 125RE), where three-digit prefix represents gage length mils (0.001 [0.0254 mm]). design available either open-faced with Option (solder dots encapsulation).
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ROSETTES
ROSETTE ROSETTE
COEFFICIENTS
COEFFICIENTS
COEFFICIENTS
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0.4D
Tech Note TN-503-6
0.4D
0.4D
Vishay micro-measurements
blind hole through hole
blind hole through hole
blind hole through hole
Measurement Residual Stresses Hole-Drilling Strain Gage Method
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SUGGESTED LIMITS 0.50 0.30 0.35 0.40 0.45 0.50 0.40 0.45
SUGGESTED LIMITS
0.30
0.35
0.40
0.45
SUGGESTED LIMITS
0.50
0.55
0.60
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Figure Full-depth data-reduction coefficients versus dimensionless hole diameter (typical) Vishay micro-measurements residual stress rosettes, accordance with AStm 837.
Tech Note TN-503-6
Vishay micro-measurements
Measurement Residual Stresses Hole-Drilling Strain Gage Method
configurations supplied 1/16 [1.6 gage leng both encapsulated. Both configurations have integral, coppercoated solder tabs, offer advantages popular C-Feature strain gage series. These residual stress rosettes constructed with self-temperature-compensated constantan foil, mounted flexible polyimide carrier. Gage resistance ohms ±0.4%. 030RR six-element rosette incorporates self-temperature-compensated K-alloy (modified Karma) foil laminated polyimide film backing. Solder tabs duplex copper plated ease making solder connections. Gage resistance ohms ±0.4%. Surface preparation installing rosettes basically standard, described Application Note B-129. Caution should observed, however, abrading surface test object, since abrasion alter initial state residual stress.12 general, important that surface-preparation gage-installation procedures highest quality, permit accurate measurement small strains typically registered with hole-drilling method. evidenced calibration data Figure relieved strains corresponding given residual stress magnitude considerably lower than those obtained conventional mechanical test same stress level. Because small measured strains, drift inaccuracy indicated gage output, whether improper gage installation, unstable instrumentation, otherwise, seriously affect calculated residual stresses. directly related operator's ability position milling cutter precisely center strain gage rosette." More recent studies have quantified error calculated stress eccentricity hole. example, with hole that 0.001 [0.025 off-center 062RE 062UL rosette, error calculated stress does exceed (for uniaxial stress state).9,10,11 practice, required alignment precision within 0.001 [0.025 accomplished using RS-200 Milling Guide shown Figure milling guide normally secured test object bonding three foot pads with quick-setting, frangible adhesive. microscope then installed unit visual alignment achieved with four adjustment screws exterior guide.
Boring
Numerous studies effects hole size shape machining procedures have been published. Rendler Vigness5 specified specially dressed mill which compatible with residual stress rosettes Figure mill ground remove side cutting edges, then relieved immediately behind cutting face avoid rubbing hole surface. imperative that milling cutter rigidly guided during drilling operation that cutter progresses straight line, without side pressure hole, friction noncutting edge. These mills generate desired lat-bottomed squarecornered hole shape initial surface contact, maintain appropriate shape until hole completed. doing they fulfill incremental drilling requirements stipulated 837. Specially dressed mills offer direct simple approach when measuring residual stresses readily machinable materials such mild steel some aluminum alloys. Figure shows RS-200 Milling Guide with microscope removed endmill assembly place. mill driven through universal joint assembly, either hand drill variable-speed electric drill. 1982, Flaman13 first reported excellent results residual stress measurement using high-speed rpm) turbine carbide cutters. This technique maintains advantages (good hole shape, adaptability incremental drilling, etc.) specially dressed mill while providing easier operation more consistent results. Further, turbine highly recommended with test materials that difficult machine, such Type stainless steel. Carbide cutters effective penetrating glass, most ceramics, very hard metals, etc.; diamond cutters have shown promise these kinds test materials. Figure shows turbine/carbide cutter assembly installed same basic RS-200 Milling Guide. Bush Kromer14 reported, 1972, that stress-free holes achieved using abrasive machining (AJM). Modifiwww.vishaymg.com
Strain-Measurement Instrumentation
residual stress rosettes described Figure impose special instrument requirements. When measurements made field, portable, battery-operated static strain indicator, supplemented precision switch-andbalance unit, ordinarily most effective convenient instrumentation. Model Strain Indicator Recorder ideally suited this type application. laboratory convenient computerized automatic data system such System 5000, which will rapidly acquire record data organized, readily accessible form. special line, Windows based computer program H-DRILL also available perform calculations determine residual stress magnitudes accordance with 837. database program includes values coefficients blind holes, covers full range recommended hole dimensions applicable Vishay Micro-Measurements residual stress rosettes.
tecH note
Alignment
Rendler Vigness observed that "the accuracy (hole-drilling) method field applications will
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Document number: 11053 revision 15-Aug-07
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Tech Note TN-503-6
Vishay micro-measurements
Measurement Residual Stresses Hole-Drilling Strain Gage Method
Alignment Setup microscope tube Locking collar Adjustments Vertical Height Adjustments Locking nuts eyepiece
Illuminator
Beaney,10 Bynum.15 Wnuk16 experienced good results mechanically adapting apparatus RS-200 Milling Guide. principal advantage reported ability generate stress-free holes virtually materials. chief limitations center about considerable changes hole shape function hole depth. initial shape saucer-like, final cylindrical with slightly rounded corners. During drilling there also uncertainty actual hole depth stage. These factors make less practical technique determining variation relieved strain with hole depth, recommended 837.
end-mill Drilling Setup milling with universal Joint Attached
Mechanical Properties
form experimental stress analysis, accuracy residual stress measurement limited accuracies which elastic modulus Poisson's ratio known. typical uncertainties mechanical properties common steel aluminum alloys neighborhood and, such, minor contributors potential errors residual stress analysis. Much larger errors introduced deviations from assumptions involved basic theory, described Section assumption, instance, linear-elastic material behavior. stress/strain relationship test material nonlinear case cast iron), yielding other causes, calculated residual stresses will error. When initial residual stress close yield strength test material, stress concentration caused presence hole induce localized yielding. therefore necessary establish threshold level residual stress below which yielding negligible. This problem been studied both experimentally analytically, there substantial agreement among different investigations.10,17,18 That errors negligible when residual stress less than proportional limit test material both blind holes through holes. other hand, when initial residual stress equal proportional limit, errors (and greater) have been observed. error magnitude obviously depends slope stress/strain diagram post-yield region; tends increase curve becomes flatter, approaching idealized perfectly plastic behavior.18
Locking collar micrometer Lock
micrometer Adjustment micrometer
mill
Hi-Speed Drilling Setup Supply turbine Assembly Grooved nylon collar Anti-rotation ring Adapter Basic rS-200 milling Guide carbide cutter Figure rS-200 milling Guide, used machining precisely located flat-bottomed hole.
Spring Assembly
mount
Data Reduction Interpretation Blind Hole
recommended 837, always preferable drill hole small increments depth, recording observed strains measured hole depth each increment. This done obtain data judging whether residual stress essentially uniform with depth, thus validating standard full-depth coefficients calculating stress magnitudes. incremental measurements taken, there means making
Document number: 11053 revision 15-Aug-07
tecH note
cations improvements were made Procter
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Tech Note TN-503-6
Vishay micro-measurements
Measurement Residual Stresses Hole-Drilling Strain Gage Method
inferences about stress uniformity, calculated residual stress considerably error. such cases, when stress varies with depth, should realized that calculated stress always lower than actual maximum. There currently absolute criterion verifying stress uniformity from surface test piece bottom full-depth hole. However, incremental data, consisting relieved strain versus hole depth, used different ways detecting nonuniform stress distribution. first these calculate, each depth increment, sums differences measured strain data, respectively.1 Express each data fractions their values when hole depth equals times mean diameter strain gage circle. Plot these percent strains versus normalized hole depth. These graphs should yield data points very close curves shown Figure Data points which removed from curves Figure indicate either substantial stress nonuniformity strain measurement errors. either case, measured data acceptable residual stress calculations using full-depth coefficients When principal residual stress direction closer axial direction gage Figure than either gage nos. strain will numerically larger than such case, percent strain data check should done using instead NOTE: This graphical test sensitive indicator stress field uniformity. Specimens with significantly nonuniform stress fields yield percentage relieved strain curves substantially similar those shown Figure main purpose test identify grossly nonuniform stress fields. Further, graphical comparison test using example, becomes ineffective when residual stress field approaches equal biaxial tension compression expected surface blasting heat treating procedures. Comparison plot ineffective when (pure shear); however, this condition relatively uncommon practical industrial setting.
ROSETTE PERCENT RELIEVED STRAIN
Gage
ROSETTE
PERCENT RELIEVED STRAIN
-0.1 ROSETTE
Gage
PERCENT RELIEVED STRAIN
Gage
Limitations Cautions
Finite-element studies hole-drilling method Schajer subsequent investigators 20,21,22,23 have shown that change strain produced drilling through depth increment (beyond first) caused only partly residual stress that increment. remainder incremental relieved strain generated residual stresses preceding increments, increasing compliance material, changing stress distribution, hole deepened. Moreover, relative contribution stress particular increment corresponding incremental change strain decreases rapidly with distance from surface. result,
Document number: 11053 revision 15-Aug-07
tecH note
-0.1
Figure Percent strain versus normalized hole depth uniform stress with depth different rosette types, after AStm 837.1 www.vishaymg.com
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Tech Note TN-503-6
Vishay micro-measurements
Measurement Residual Stresses Hole-Drilling Strain Gage Method
total relieved strain full-hole depth predominantly influenced stresses layers material closest surface say, upper third, perhaps half, hole depth. hole depths corresponding 0.2, stresses these increments have very little effect observed strains. This behavior confirmed (for uniform stress) shape normalized strain graph Figure where about total strain relief normally occurs first half hole depth. Because these characteristics, little, any, quantitative interpretation safely made incremental strain data increments beyond 0.2, irrespective analytical method employed data reduction. summarize, ideal application hole-drilling method which stress essentially uniform with depth. this case, data-reduction coefficients well-established, calculated stresses sufficiently accurate most engineering purposes assuming freedom from significant experimental errors. Incremental drilling data analysis should always performed, however, verify stress uniformity. graph percent-strain-relieved versus (see Figure suggests that stress nonuniform with hole depth, then procedure specified applicable, program such H-DRILL must used calculate stresses. Error uncertainty always present, varying degrees, measurements physical variables. And, rule, their magnitudes strongly dependent quality experimental technique well number parameters involved. Since residual stress determination hole-drilling method involves greater number variety techniques parameters than routine experimental stress analysis, potential error correspondingly greater. Because this, other considerations briefly outlined following, residual stresses cannot usually determined with same accuracy stresses externally applied static loads. Introduction small hole into test specimen most critical operations procedure. instruction manual RS-200 Milling Guide contains detailed directions making hole; these should followed rigorously obtain maximum accuracy. hole should concentric with drilling target special strain gage rosette. should also have prescribed shape terms cylindricity, flat bottom, sharp corner surface. particularly necessary that requirements hole configuration wellsatisfied when doing incremental drilling examine stress variation with depth. Under these same circumstances, important that hole depth each drilling increment measured accurately possible, since small absolute error depth produce large relative error calculated stress. Because practical limitations measuring shallow hole depths, first depth increment
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should ordinarily least 0.005 [0.13 mm]. Accurate measurement hole diameter also necessary. Finally, imperative that hole drilled (milled) without introducing significant additional residual stresses. degree that foregoing requirements fail met, accuracy will sacrificed accordingly. Strains relieved drilling hole measured conventionally, with static strain instrumentation. indicated strains characteristically much smaller, however, than they would same stress state externally loaded test part. result, need stable, accurate strain measurement greater than usual. With incremental drilling, strains measured first depth increments especially low, errors microstrain cause large percentage errors calculated stresses those depths. Beyond above, also necessary that underlying theoretical assumptions hole-drilling method reasonably satisfied. full-depth drilling 837, stress must essentially uniform with depth, both magnitude direction, obtain accurate results. With finite-element other procedures investigating stress variation subsurface layers, required only that directions principal stresses change appreciably with depth. conventional strain-gage rosette measurements, data-reduction relationships assume that stress uniformly distributed plane test surface. However, residual stress measurements effective "gage-length" hole diameter rather than relatively large dimensions overall rosette geometry. Consequently, uncertainties introduced in-plane surface strain gradients generally lower residual stress determination than conventional static load testing. generalization currently made about effects steeply varying, nonlinear stress distributions subsurface planes parallel rosette.
BIBLIOGRAPHY
"Determining Residual Stresses Hole-Drilling Strain-Gage Method." ASStandard 837. Mathar, "Determination Initial Stresses Measuring Deformation Around Drilled Holes." Trans., ASME 249-254 (1934). Timoshenko, J.M. Goodier, Theory Elasticity, York: McGraw-Hill (1951). Kabiri, "Measurement Residual Stresses Hole-Drilling Method: Influences Transverse Sensitiv Gage ieve Strai Coefficients," Experimental Mechanics (252-256) (Sept. 1984). Rendler, N.J. Vigness, "Hole-drilling Straingage Method Measuring Residual Stresses." Proc., SESA XXIII, 577-586 (1966).
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Document number: 11053 revision 15-Aug-07
Tech Note TN-503-6
Vishay micro-measurements
Measurement Residual Stresses Hole-Drilling Strain Gage Method
Kelsey, R.A., "Measuring Non-uniform Residual Stresses Hole-drilling Method." Proc., SESA XIV, 181-194 (1956). Schajer, G.S., "Appl ication Element Calculations Residual Stress Measurements." Journal Engineering Materials Technology 103: 157-163 (1981). Redner, C.C. Perry, "Factors Affecting Accuracy Residual Stress Measurements Using Blind-Hole Drilling Method." Proc., International Conference Experimental Stress Analysis. Haifa, Israel: Israel Institute Technology, 1982. Sandifer, J.P. G.E. Bowie, "Residual Stress Blindhole Method with Off-Center Hole." Experimental Mechanics 173-179 (May 1978). Procter, E.M. Beaney, "Recent Developments entre -hole ique sidu al-stre Measurement." Experimental Techniques 10-15 (December 1982). Wang, H.C., "The Alignment Error Hole-Drilling Method." Experimental Mechanics 23-27 (1979). Prevey, P.S., "Residual Stress Distributions Produced Strain Gage Surface Preparation." Proc., 1986 Conference Experimental Mechanics (1986). Flaman, M.T., "Brief Investigation Induced Drilling Stresses Center-hole Method Residual-stress Measurement." Experimental Mechanics 26-30 (January 1982). Bush, A.J. F.J. Kromer, "Simplification Holedrilling Method Residual Stress Measurements." Trans., 112, 249-260 (1973). Bynum, J.E., "Modifications Hole-drilling Technique Measuring Residual Stresses Improved cur-acy Reproducibility." Exper mental Mechanics 21-33 (January 1981). Wnuk, S.P. "Residual Stress Measurements Field Using Airbrasive Hole Drilling Method." Presented Technical Committee Strain Gages, Spring Meeting SESA, Dearborn, Michigan, June, 1981. Delameter, W.R. T.C. Mamaros, "Measurement Residual Stresses Hole-drilling Method." Sandia National Laboratories Report SAND-77-8006 (1977), (NTIS). Flaman, M.T. B.H. Manning, "Determination Residual Stress Variation with Depth HoleDrilling Method." Experimental Mechanics 205207 (1985). Niku-Lari, A.J. J.F. Flavenot, "Measurement Residual Stress Distribution Incremental HoleDrilling Method." Experimental Mechanics 175-185 (1985).
Document number: 11053 revision 15-Aug-07
Flaman, M.T., B.E. Mills, J.M. Boag, "Analysis Stress-Variation-With-Depth Measurement Procedures Centre Hole Method Residual Stress Measurements." Experimental Techniques 35-37 (June 1987). Schajer, G.S., "Measurement Non-Uniform Residual Stresses Using Hole Drilling Method," Journal Engineering Materials Technology, 110, Part 338-343; Part 344-349 (1988). Ajovalasit, "Measurement Residual Stresses Hole-Drilling Method: luence Hole Eccentricity." Journal Strain Analysis 171178 (1979). Beaney, E.M. Procter, Critical Evaluation Centre-hole Technique Measurement Residual Stresses." Strain, Journal BSSM 7-14 (1974). Nawwar, A.M., McLachlan, Shewchuk, Modified Hole-Drilling Technique Determining Residual Stresses Thin Plates." Experimental Mechanics 226-232 (June 1976). Witt, Lee, Rider, Comparison Residual Stress Measurements Using Blind-hole, Abrasive-jet Trepan-ring Methods." Experimental Techniques 41-45 (February 1983). Schajer, G.S., "Judgment Residual Stress Field Uniformity when Using Hole-Drilling Method," Proceedings International Conference Residual Stresses Nancy, France. November 23-25, 1988, 71-77. Flaman, M.T. J.A. Herring, "SEM/ASRoundRobin Residual-Stress-Measurement Study Phase Stainless-Steel Specimen," Experimental Techniques, 23-25. Yavelak, J.J. (compiler), "Bulk-Zero Stress Standard AISI 1018 Carbon-Steel Specimens, Round Robin Phase Experimental Techniques, 38-41 (1985). Schajer, G.S., "Strain Data Averaging HoleDrilling Method." Experimental Techniques. Vol. 25-28, 1991. Schajer, G.S. Altus, "Stress Calculation Error Analysis Incremental Hole-Drilling Residual Stress Measurements." Journal Engineering Materials Technology. Vol. 118, 120-126, 1996.
tecH note
Schajer, G.S., "Use Displacement Data Calculate Strain Gauge Response Non-Uniform Strain Fields." Strain. Vol. 9-13, 1993. Schajer, G.S. Tootoonian, Rosette Design More Reliable Hole-drilling Residual Stress Measurements." Experimental Mechanics. Vol. 299-306, 1997.
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Strain Gages Instruments
tech note tn-504-1
Strain Gage Thermal Output Gage Factor Variation with Temperature
Introduction
Ideally, strain gage bonded test part would respond only applied strain part, unaffected other variables environment. Unfortunately, resistance strain gage, common with other sensors, somewhat less than perfect. electrical resistance strain gage varies only with strain, with temperature well. addition, relationship between strain resistance change, gage factor, itself varies with temperature. These deviations from ideal behavior important under certain circumstances, cause significant errors properly accounted for. When underlying phenomena thoroughly understood, however, errors controlled virtually eliminated compensation correction. Section this Tech Note, thermal output (sometimes referred "temperature-induced apparent strain") defined, causes this effect described. Typical magnitudes thermal output then given, followed commonly used methods compensation correction. Section treats gage factor variation with temperature similar briefer manner since this error source generally much less significant. Methods simultaneous correction both thermal output gage factor errors given Section 4.0, accompanied numerical examples. compensation thermal output correct strain measurements presence. Thermal output caused concurrent algebraically additive effects strain gage installation. First, electrical resistivity grid conductor somewhat temperature dependent; and, result, gage resistance varies with temperature. second contribution thermal output differential thermal expansion between grid conductor test part substrate material which gage bonded. With temperature change, substrate expands contracts; and, since strain gage firmly bonded substrate, gage grid forced undergo same expansion contraction. extent that thermal expansion coefficient grid differs from that substrate, grid mechanically strained conforming free expansion contraction substrate. Because grid design, strain sensitive, gage exhibits resistance change proportional differential expansion. Each thermally induced resistance changes either positive negative sign with respect that temperature change, thermal output strain gage algebraic these. Thus, expressed terms unit resistance change, thermal output becomes: where, consistent units:
Thermal Output
Once installed strain gage connected strain indicator instrument balanced, subsequent change temperature gage installation will normally produce resistance change gage. This temperature-induced resistance change independent unrelated mechanical (stress-induced) strain test object which strain gage bonded. purely temperature change, thus called thermal output gage. Thermal output potentially most serious error source practice static strain measurement with strain gages. fact, when measuring strains temperatures remote from room temperature from initial balance temperature gage circuit), error thermal output, controlled, much greater than magnitude strain measured. temperature, temperature range, this error source requires careful consideration; usually necessary either provide
revision 15-Aug-07
unit change resistance from initial reference resistance, caused change temperature resulting thermal output. temperature coefficient resistance grid conductor. gage factor strain gage. transverse sensitivity strain gage. Poisson's ratio (0.285) standard test material used calibrating gage gage factor.
tecH note
this Tech Note, gage factor strain gage identified distinguish from gage factor setting measuring instrument, denoted here This distinction important, since gage factor setting instrument sometimes, matter convenience utility, different from that gage.
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Tech Note TN-504-1
Vishay micro-measurements
Strain Gage Thermal Output Gage Factor Variation with Temperature
difference thermal expansion coefficients substrate grid, respectively. temperature change from arbitrary initial reference temperature. correction factor transverse sensitivity 0Kt)] included Equation account fact that strain gage grid differential thermal expansion equal-biaxial, while gage factor, refers strain sensitivity calibrated uniaxial stress state, with principal strain ratio 1/(-0.285). should assumed from form Equation that thermal output linear with temperature change, because coefficients within brackets themselves functions temperature. equation clearly demonstrates, however, that thermal output depends only nature strain gage, also material which gage bonded. Because this, thermal output data meaningful only when referred particular type strain gage, bonded specified substrate material. convenience correcting measured strain data thermally induced resistance changes, thermal output gage usually expressed strain units. Thus, dividing Equation gage factor setting instrument,
structural materials vary thermal expansion characteristics from lot. best practice always evaluate more gages under thermal conditions nearly like those encountered testing program possible. Figure shows variation thermal output with temperature variety strain gage alloys bonded steel. These data illustrative only, making corrections. should noted, fact, that curves constantan Karma alloys. With self-temperature compensation (Section 2.1.2), employed Vishay Micro-Measurements strain gages, thermal output characteristics these alloys adjusted minimize error over normal range working temperatures.
TEMPERATURE +4000 +100 +150 +200 +250
+3000
ISOELASTI
NICHROME KARMA (FULL HARD)
THERMAL OUTPUT 2.0)
+2000
+1000
+24°C
+75°F
-1000
CONSTANTAN (FULL HARD)
-2000
-3000 ALLOYS BONDED STEEL SPECIMEN -4000 -100 +100 +200 +300 +400 +500 TEMPERATURE
where: thermal output strain units; that strain magnitude registered strain indicator (with gage factor setting when gage installation subjected temperature change, under conditions free thermal expansion substrate. When measuring stress-induced strains temperature different from initial balance temperature, thermal output from Equation superimposed gage output mechanical strain, causing measurement error that amount. Many factors affect thermal output strain gages. Some more important are: test specimen material shape, grid alloy lot, gage series pattern, transverse sensitivity gage, bonding encapsulating materials, installation procedures. never possible Vishay Micro-Measurements predict exactly what thermal output gage will when user bonded test structure. Even cases where applications involve same material that used Vishay MicroMeasurements tests, differences expected since
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Figure thermal output variation with temperature several strain gage alloys as-rolled metallurgical condition) bonded steel.
tecH note
indicated Figure errors thermal output become extremely large temperatures deviate from arbitrary reference temperature (ordinarily, room temperature) with respect which thermal output measured. illustration shows distinctly necessity compensation correction accurate static strain measurements made environment involving temperature changes. With respect latter statement, should remarked that feasible bring gaged test part test temperature test environment, maintaining test part completely free mechanically thermally induced stresses,
Document number: 11054 revision 15-Aug-07
technical support, contact micro-measurements@vishay.com
Tech Note TN-504-1
Vishay micro-measurements
Strain Gage Thermal Output Gage Factor Variation with Temperature
balance strain indicator zero strain under these conditions, thermal output error exists when subsequent strain measurements made this temperature. other words, when temperature change occurs between stress-free stressed conditions, strain measurements made without compensating correcting thermal output. practice, however, rare that foregoing requirements satisfied, stress analyst ordinarily finds necessary take full account thermal output effects. Also, case purely dynamic strain measurements, where there need maintain stable zero-strain reference, thermal output consequence. This because frequency dynamic strain signal usually very high with respect frequency temperature change, signals readily separable. however, there combined
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