introduction to strain gauging

7/27/2019 Introduction to Strain Gauging

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TECHNI MEASUREAlexandra Buildings, 59 Alcester Road, Studley, Warwickshire. 880 7NJ.Tel:01527854103 Fax:01527853267 e-mail:[email protected]

INTRODUCTIOI{ TO STRAIN GAt}cINc

Strain Gauee ApplicationsStrain gauges are used to deterniine or verifli component or structure stresses, or by rnanufacturers of load

cells" pressure and torque transducers, etc., where they wilise the physical parameter being measured to strain apart ofthe transducer in a linear way.Strain

Stress itself cannot be directly measured but strain can, and for rnany rnaterials within their elastic limit,tlrere is a linear relationship between stress and strain. For rmiaxial loading conditions, stress divided by strain isa constant lcrown as \bung's iVlodulus of Elasticity forthe material. Thus, if strain can be measured, stress canbe calculated.

Strain is defined as the linear deformation of a material. It can occur as the result of the application offorce or of temperature change. Unit Strain, e, is the ratio of change in length divided by original length This,,,r%rrl, o, ,noX,,r, (*/r) dimensionless ratio is generally a very small decimal fraction, and is therefore usuallymultiplied by 10", becoming "microstrain", Ft. Percentage strain is a term also used and the table below givessome conversions.

res $aiasqire Stran o'Y** Percent Strain Microstrain.nAnn< ,nn < 5n.0005 .l l\ {nn.nn I I 0fl0.nl 2 ?0 000ln I 00 000

Strain MeasurementStrain can be measured using many techniques, but the resistance strain gauge is generally the rnost direct

and convenient tool. Once bonded to the surface of the nraterial, any physical strain in the material is transmittedto the strain gauge's resistive element. This then experiences a proportional resistance change which in tum canbe measured using appropriate instrunrentation.Strain Gause Types and Construction

Both wire and foil strain gauges take the fonn of a grid pattem mounted within or onto an insulatingcarrier, capable of farthfully transrnitting the strain frorn the specimen. Weldable gauges have their resistiveelements mounted onto a metal carrier. Gauges can often be supplied with their elements heat treated.to providetemperature compensation for use on different materials.

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The foil gauge consists of a rnetallic alloy film laminated onto an insulating carrier. In a similar way toprinted circuit manufacturing techniques, this metallic deposit is rnasked and then etched to leave a resistance grid.A very wide variety of shapes and sizes is possible with this manufacturing technique and different alloys and basematerials ofFer a wide selection of gauges most suited to specific temperature or measurement applications.Special configurations are available which provide two or three separate grids precisely located with respect to oneanotirer. Active gauge lengths are available frorn 0'2mrn to 30mm, and resistances vary frorn 60CJ up to 2000f1.

The wire gauge consists of a grid of fine wire sandwiched between very thin insulating membranes. Thiscarrier serves as a support and protection for the grid and also as an electrical insulator between wire and testsurface. Gauges are available with nominal resistance generally of 120f2 rn gauge lengths up to 120mm. Specialconfigurations are also available which provide two or three separate wire grids on one carrier. Except for specialapplications, the wire gauge has been largely superseded by the foil gauge.

The weldable gauge is designed to be spot welded to a metal test specimen. Minimal surface preparationis required which enables fast application. Its construction makes it most useful for measurements in harshenvironments for long periods, or at very high temperatures. Gauges are normally available in effective gaugelengths from 6mm to l6mm but generally only as single elements. Resistance values are usually l20O or 350fJ.Choice of Gause

There may be an application - specific gauge designed for a particular measurement task such as residualstress detemrination, bolt force or intemal concrete strain evaluation. Otherwise, for general strain measurement,the choice rnust be made according to several criteria. These include anticipated strain level, operationaltemperature, installation and test environmental conditions, material being tested, temperature conrpensation,specimen and strain gauge carrier conrpatibility with chosen adhesive, and finally, gauge length A short gaugelength should only be chosen where the size of the specimor or expected stress concentration so dictates. Specimenmaterials formed of conrpacted or bound materials (cement, concrete, chipboard etc.) require gauge lengths to beat least three times that of the maximum particle size but, apaft frorn this consideration, there is no advantage inchoosing a long gauge. In general, ease of handling and installation, adhesive application, space availability andadequate perfom'unce will suggest a foil gauge of between 3 and l0rmn for use on metals.

Gauge area, in conjunction w'ith gauge resistance has also to be taken into account when totalinstrumentation stability is considered. The gauge's resistance and excitation voitage both dictate the power beinggenerated at the gauge, which along with the gauge's area will determine the power density. The amount of heatgenerated should be sufficiently srnall so that, over the period of measurement, there is acceptable temperaturestability. As a guide 0.005 wattslmm2 would be acceptable tbr static tests on metal specimens using fbilgauges where moderate accuracy was required. Foil gauges, by having a greater surface arealresistance ratio,can dissipate heat better than wire gauges of the same size. Metal specimens are better heat sinks than (e.g.)plastics, whilst short term or dynamic rneasurements require less fundarnental accuracy than those of staticconditions or long-term duration, so that the recommended power density figure can vary.


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Measurement Method and FormulaeThe mechanical strain experienced by the test specimen, aud thus aiso by the strain gauge, gives rise to

resistive strain of the gauge element. The special alloys used in strain gauges exhibit a near-linear ratio betweentheir resistive and mechanical strains. This ratio is krrown as the Gauge Factor and is approximateiy equal to 2.0for foil and wire strain gauges. The vaiue will be printed on each pack of precision strain gauges.

Resistir,e Strain Al{ R= --:i = 2.1)Lt .,/Li.e. Gauce Factor = A = Mechanical StninIt follows that, if the resistive strain can be measured, and with the gauge factor known, the mechanical strain canbe calculated and the stress subsequently deduced. Using a conventionai resistance-measuring meter, it would bedifficult even to detect, let alone accurately measure, the srnall change of 0'12 ohrn (: A'iW caused by 0'05%mechanical strain of a 120 ohm gauge. The Wheatstone Bridge circuit, shown in its basic form in fig. l, is anetwork of four resistances, one of which is an active straln gauge. When the ratio of resistance, R/n, is equal tothat of ''/i, fr" Bndge is said to be "balanced" and the voltage output is zero. When the resistance of the straingauge changes, the Bridge becomes unbalanced and a voltage output is created. Even though this may be small, itis a change from zero and can be amplified and measured using appropriate instrumentation.Fig. 1

Actrv*StrainDauqe

FxritationVollffge E

It can be sl-rown that for tlre circuit shown in Fig.l, the open-circuit output voitage A" is equal tothe input voltage E multiplied bythe factor ...otfr'.{'our, , and so, when Rr&= RrR+, A" = 0.(/ir +RzXrt: +rt+)For the convenient case where R = Rr = R.? = R: = R+,if Rr changes to R + AR due to straln, & becomes ^R%ro+ ) ^p\and if we ignore 2AR as being very small, A" becomes equal to oo%o

tK%nd since *y*= M.yL and Lt/, = Strain: t, A. becomesFor a two-active arm Wheatstone Bridge such as that shown in flg 8a, A. becomes S KI'/ and for afour-active arm bridge such as is shown in Fig 8b, A" becon,es tKE.


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Practical strain measurementBalance - in order to be able to commence strarn measurement with a zero output, it is necessary to baiance &eBridge which will invariably have some initial imbalance due to the small variations in resistance found betweenthe various gauges and fixed resistances of the Bridge. This can be acconrplished by using a low resistancepotentiometer P1 in series at a bridge apex (Fig. 2| or by having a high resistance potentiometer P2 circuit acrossopposite apexes (Fig. 3). Both balancing circuits are shom in their simplest forms and there are several morecomplex variations.

Fig.2 Fig.3

Altematively, the unbalanced Bridge output voltage can be "backed off'by an equal and opposite voltagegenerated withn tlte instmmentation.Calibration - The gauged specimen's strain output may be calibrated by loading or straining the specimen urlarown increments and recording the electrical output with known input voltage. The recording equiprnent shouidbe that with which the strain-gauged specimen will ultimately be used. The relationship of output against load orstrain is subsequently used for the evaluation ofactual test results.

Ansther method is to cause Bridge imbalance by shunting a high resistance in parallel wiih one of thearms of the Wreatstone Bridge. This creates a precise arnount of resistive "strain" which therefore represents aknown rnechanical strain. The value of the resistance Rs necessar! to simulate the output due to a mechanicalstrain t at the active gauge is found from the approximate formula Rt = YXu where R is the resistance of thearm to be shunted and K is the gauge factor of the active strain gauge. Note that although shuntrng reduces theresistance of that particular arm of the Bridge, the Bridge ouQut is the same as that which would derive from anincreasecl resistance at an adjacent arm, thus, by shunting R+ (in fig.l) - which may weil be a fixed resistor withinthe instrumentation - the effect is the sarne as if a tensile strain were occurring at the active gauge, R1.


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Single Gauge Applications - For this use of strain gauges, only the one gauge is performing the measurement andit is general practice to have R: & R+ of the Wheatstone Bridge as fixed, high stability, resistors within theinstrumentation where they wili remain unaffected by any enyironmental changes.Fig.4

f't LllvtrSttainEauge

RzDurnnrlEtrain('ijuutr would interpret as mechanicalslrain) the gauge itself should be chosen, if possible, as one having temperature compensation for the materialbeing tested. & is made to be a "dummy" strair-r gauge of the same type as Rr, by mounting on the same type ofmaterial, but unstrained. The dunmry should be placed as close as possible to the active gauge, so that both it, andits associated wiring, will experience the same temperature changes as the active, such that identical effects on thetwo adjacent anns of the Bridge will cancel each other out.

When it is not practicable to employ a dummy gauge in this way, it would not be good practice to havedunrmy R, within the instrumentation and the active R1 connected to the Bridge using only two wires, becausetemperature effects on those wires would cause inaccuracies. In such cases it is good practice to employ a "3-wire" lead to the gauge. That shown in Fig.5 is one of several variants.Fig.5

In this arrangement, both the active gauge R1 andresistance R2 have an equal length of lead wire inseries, so that temperature effects on lead wireresistance are cancelled out. It should beremembered however &at the use of long leadwires will reduce the sensitivitv of the svstem.

Mutti-gauge and Transducer Applications - Single gauges can only be used, with the assurance of being able tocalculate stress from measured strain, when that stress is uniaxial and its direction known. In biaxial stress fields,it is necessary to know the strains along the two principal axes before the stresses can be calculated. If theorientation of these axes is known, then two gauges only (a 0", 90" pair) need to be used, but if orientation isuncertain, strain measurement in at least three directions has to be rnade in order to make the calculation. Three-gauge rosettes are available for this purpose, having resistance elements at 0o, 45o & 90".

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The active gauge R1 is remotefrom the instrumentation, andboth it and its associated u'iringare subject to resistance changesbrought about by auy variatiouin temperature. ln order tocompensate for such changes(which the instrumentation

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Measurement of Axial Strain Independent of Bending StrainFig.6

For certain components or structures, it may be necessary to know the value of solely the axial strain. lf abending moment is also present, a single gauge would be unabie to make the required measurement. If a pair ofactive gauges G1 and Gz can be mounted on the component and arranged in the Wheatstone Bridge as shown inFig. 6, the equal and opposite effects of bending on each gauge will cancel each other out, leaving a net resistancechange proportional only to the axial strain.

lVleasurement of Axial Strain, Independent of Bending Strain but with Full Temperature Compensation &Increased Output VoltageFig.7

In the arrangement shown in Fig 7, the equal effests of axial strain on gauges Gr and G: are additivewhilst the mutually opposite effects of bending cancel each other out. The transverse gauges Gz and C+ (whichindividually would measure the "Poisson" strain) each cor-rtribute that frastion (0'285 for steels) to the Bridgeoutput which would therefore be 2'57 times that of a single active gauge n (non-bending) axial strain. Thetransverse gauges also serve to provide full temperature compensation and the arrangement therefore becomessuitable for use in a simple ioad cell.


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Nleasurement of Bending Strain Independent of Axial Strain Fig.8a

In ijiis two-active-arm arrangement, the equal effects of axial strain on Gr and G2 are cancelled out andtire bending efFects are additive, giving a bridge output double that which would derive from a single gauge in pureberrding. The arrangement also provides fu 11 temperature compensation.Fig.8b

hr this four-actrve-anl arrangement, axial strain effeets are again cancelled out and bending effbcts areadditive thus giving a four-fold sensitivity compared witl, a single gauge. Foil gauges can be supplied as parallelpairs of elements sn a single carrier thus eliminating the task of having to bond two gauges side-by-side in preciselocation and orientation relativeto one another.Measurement of Torsional Strain Independent of Axial or Bending Strains Fig.9

In this four-active-arrn arrallgement, the equal and opposite shearing strains of each gauge pair also give afour-fold output whilst any effects due to axial or bending strains and temperature are cancelled. Seveial pattemsof gauge suitable for this type of measurement are available, with element resistances up to 2000 ohms'

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INSTRT]CTIONS FOR BOI{DIJ\{G STANDARD TIVIL STRAIJ{ GAT]GES TO STEEI,An arca larger than the gauge to be bonded should be cleared of rust, scale, paint, etc. and polished withabrasive paper (approx. 200 grit) or a fure grinding tool. Final abrasion should be crosshatched at about4-5" to the ureasurement axis.Thoroughly degrease the area with a solvent such as acetone, rnethyi etl,yl ketone or isopropyl alcohol usingclean cofion buds. (Ensure good ventilation when using solvents.) Repeatedly apply the solvent and wipe offwith fresh cotton buds until the final wipe is stain free. Use continuous strokes working from the centre ofthe area to avoid picking up grease from tlre surrounding specimen. If the gauge backing has been handled,that should also be degreased with solvent. Use blunt, cleaned tweezers to handle the gauges.Ligltly mark location lines on the specimen using a ball point pen, and clean offas in (2). Avoid rnarkingwhere the gauge grid is to be placed.Place the gauge with grid and terminals upwards on a thoroughly cleaned surface together witir the solderterminals, if used, ensuring the lead wires are on top of the terminals. Place a strip of adhesive tape (aboutl00mm long, dependent on the gauge length) over tle strain gauge and terminal strip, then carefully lift thetape with gauge attached at a shallow angle, taking care not to bend tlre gauge excessively. (Fig I)

Fio ITratlsfer the gauge and tenninals to the specimen and position the alignment nrarks with the iocation lines onthe specimen. Carefully lift the tape (Fig.l) with the gauge and terminal, leaving one end of the tape stilladlieredtothe surface. Take care notto bedthe gauge excessively,Apply adhesive as follows Always refer to manufacturer's instructions.a) ClY cyanoacrylate adhesive recornrnended for post leld and GF piastics gauges and applications where afast bond is required. Apply a drop of adhesive to the gauge and to the terminal. Rapidly roll the gaugeonto the specimeu, pushing the adhesive along the gauge in one smooth action (Fig.2), ensuring no air istrapped under the gauge. Quickly cover with the polythene square supplied, and apply strong fingerpressure for at least one minute. When bonding Y series gauges, a pressure (approx. Skg/cni,) should beapplied for 3 minutes. Leave gauge for 3 minutes before carefully peeling offthe adhesive tape.b) P-2 polyester adhesive for long term requirements. Mix the adhesive and hardener as directed inmanufacturer's instructiotrs. Apply adhesive with clean spatula to the gauge, terminal and specimen.Position carefully alrd roll gauge onto specimen, pressirg out excess adhesive and air bubbles. Covergauge with polythene square supplied, and apply a pressure (approx. 2kglcm') using a metal backedrubber cushion to spread the load. Leave for at least 30 minutes. After setting, peel offthe adhesive tapec) NP-50 adhesive for high temperature. Proceed as for P-2 and post cure if required.If stuck, the lead wires should be carefully pulled out of tire adhesive before soldering.

This is a suggested method of gauge bonding, w-hich may not be convenient or appropriate in all circumstances.Sometirnes it is preferred to proceed without using tlre adhesive tape to locate the gauge, but tliis requires ratherrnore skill than the above method. Alternative cleaning chernicals rnay be used, but it is important to obtain aclean, grease-free, dry specimen before adhering tlre gauge. For further advice on any aspect of strain gaugeselection and use, gauge bonding - especially on other materials, environmental protection and amplifier systems,please contact Techni Measure. Tel. 01527 854103 Fax. 01527 853267 ernail. [email protected]

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introduction to strain gauging

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