A method of measuring biaxial strains in coated fabric type materials
is presented whereby the strain is deduced from the distortion of a circular
impression made on the material. The impression is placed on the material
when loaded, enabling all measurements to be made with the material in its
relaxed, unloaded, state

Richards, D. M.

Webb, J.

English

Cranfield CERES

)111101,11NEllel CoA Memo. No. 201  September, 1969      THE COLLEGE OF AERONAUTICS DEPARTMENT OF AIRCRAFT DESIGN The measurement of biaxial strains in coated fabric materials using the disc-replica method - by - J. Webb and D.M. Richards Inflated Structures Report C.1206/1  - l - Summary A method of measuring biaxial strains in coated fabric type materials is presented whereby the strain is deduced from the distortion of a circular impression made on the material. The impression is placed on the material when loaded, enabling all measurements to be made with the material in its relaxed, unloaded, state. The method is simple to use, and requires a minimum of equipment. Notation x, y 	 reference or fabric axes x 	 Y`  , 	 apparent principal strain axes € / 6 I 	Fix ' fly 	 residual strains in the x'y' directions ' 	 Ty 	true strains. in the x' y'directions 1" true strains in the xy directions apparent angle between xy and x'y' axes true angle between xy and x'y' axes a 	 correction angle to 0 for residual effects See 	 d 	 basic impression diameter Fig. 	 alb]. 	 sizes of datum spot in the y,x directions 3 	 a2b2 	 sizes of reference spot in the x,y directions )12'2 	 initial sizes of grid in y,x directions final sizes of grid in y', x' directions f,c,r1 „r 	 see Fige. 4 A 	 Zit 2  -, 1 V2 1 €Tx 'Ty Q' - 2 - 1.1 Introduction Conventional methods of measuring strain become unsuitable when dealing with fabric, or similar materials, because not only are the strains involved generally very large, but also the presence of a bonded strain gauge may seriously influence the lOcal stiffness of the material. Although grids marked directly onto the fabric have been employed to measure strains in these materials, these have the disadvantage that the grid distortions must be measured with the structure in its loaded state, which may be difficult on curved surfaces. The 'Disc Replica' method, presented here, overcomes these difficulties. It will cope with large strains, does not influence the stiffness of the material, and all measurements are taken with the structure unloaded. Furthermore, the method is simple to use: and the only specialised measuring equipment required is a low-powered travelling microscope. 2.1 Disc Replica Method Two techniques are available: - i) 'Double Spot' technique ) 	 'Spot and Grid' technique. The most suitable technique to use in a given case will depend on the initial (no load) stiffness of the material, and the rapidity with which the strain changes from point to point in the loaded structure. 2.1.2. Double Spot Technique The method is shown diagrammatically in Fig. 1. The steps involved are: - (a) Small circular discs of, say, 0.25 ins.. diameter are cut from adhesive plastic tape, using a hollow punch. (b) In the region of the structure where strain is to be measured, an orthogonal grid is marked, (in the case of a single ply fabric material, it is convenient if the grid axes coincides with the fabric axes). (c) With the structure unloaded, and unpressurised in the case of an inflated structure, a disc is stuck into place, approximately over a grid intersection previously marked. French chalk is now brushed over the disc onto the surrounding material, and the disc removed, leaving a circular iraDression. (d) The structure is now pressurised and loaded, and allowed to stand for a few minutes to allow creep strains to settle. A further circular impression-is marked on the structure as above, adjacent to the original (reference) impression. 3 (e) Finally, the structure is unloaded and depressurised. The impressions from steps (c) and (d) will now be elliptical in shape, and the major and minor axes of these ellipses are measured, using, say, a. travelling microscope. The angle between the marked axes. and the principal ellipse axes of the second (loaded state) impression is also measured. Note that s11 measurements are taken with the material laid flat, and unloaded. The initial (unloaded state) impression provides a measure of the residual strain in the structure. Creep recovery becomes unimportant, therefore, providing that any pair of impressions is measured within a reasonably short time interval. For low initial stiffness materials, it may be better to preload the structure slightly before making the first impression, since this removes uncertainties with regard to gauge length. In this case, the preloaded state becomes the datum state for strain measurement. 2.1.2 'Spot and Grid' Technique The method is shown diagrammatically in Fig. 2. The steps in the technique are:- (a) With the structure in its unloaded and unpressurised state, a grid is marked out on it locally in the region where the strain is to be measured. The grid size is then measured. (Note: for single ply fabrics it is convenient if the grid coincides with the fabric axes). (b) The structure is now pressurised and loaded, and allowed to stand for a few minutes to allow creep strains to settle. A disc is' now placed on the structure at a grid intersection, and using french chalk, an impression is made. The disc is now removed. (c) The structure is now unloaded and depressurised, and the major and minor axes of the ellipse resulting from the disc impression measured. The angle between the ellipse axes and grid is also measured, and finally the grid size itself is measured again as a check on residual strains. As in the previous method, all measurements are taken with the material laid flat. 3.0 Analysis of Results 3.1 Double Spot Technique Fig. 3 illustrates the appearance of the two spots after testing. Fig. 3(a) showing the final state of the first (datum) impression, and Fig. 3(b) the final state of the second (loaded) impression. Using the notation of Fig. 3, it can be shown that the residual strains in the xl and y' directions are respectively: Cf '(14-cos20/ )  eTy = 2a2b2  • (1-cos20/ )  2a2b2  ,-( 1a2-a2b1)cos201-a2b4 (bib2-alb2)cos20+alb2  1 	- I (4) / s-Rx sRy a Lal-b)  )cos2071-b, -d a 4 (1) The true strains in the x' and y' (al -a2)-(al,m1.21 )cos20  a2  Lalzki)cos204-(bi-bp)  b2 E / Tx  E / Ty are now:.- } 	 (2) Due to residual strains, 0 is not the true angle between the principal strain directions and the reference directions. From Fig. 11-1 if a is the correction to be applied to 6 then since f 	 c 	 sine -deo se  a _ ID]. _ cos9+deine (121 - 1)cote a = -al 	  12.1cot20+1 al  and true angle e' = e cC for small d true strains in the x and y directions (fabric directions for single materials) are now:- (1-cos20/ )  2a2b2 • (14-cos20/)  2a2b2  {( b lb 2 -alb2 )co s 20 + a lb 4 - 1 (ala2-a2bi)cos20+a24 shear strain in the x and y directions. / s 7 - in26 	 2e// a loos k la,-a2bli-alb2-bib2)÷a2b1-alb2  xy "2w2 When 0= 0, e' = 0, the principal strains are in the x and y direction and bi = 	 1, eiT 	 -9*-1 - 1, 7 	 = 0 wx a2 	 y b2 xy (5) The ply and 3.2 Spot and Grid' Technique Fig. 2 illustrates the information obtained from the spot and grid technique. The process of analysing the results is similar to that used in the previous method. Using the notation of Fig. 2, it can be shown that the true strains in the x'y' directions are, after correcting for residual strains, En  IX - a2.t1t2 1 2 d V{Z - A cosi - 1 ery 	 VZ2 1 + A cosi - 1 JJ 	 (6) where A = -Fg2  V,  The correction to be applied to 0 for residual strains d - i)cote,/ 	 cot20+1) (7) where true angle 0' = e - d as before. The true strains in the x and y directions are 	 • 	 a2sin201(A cos204,2"1) 	 1 Er-Ex - a• 2b2,ft/2 	 4-b2c0s20/(qt2-Acos20) 	} - f• 	 .a2cos201(A cos?0,-PW1) 	- 1 €` Y;• -2173.62 	 cos24(8)  and the shear strain relative to the xy directions dsin20' 7xy alb 1'2 A cos20(a2-1-bp)-1-a2W1-bAt2  When 0 = 0' = 0, the principal strains coincide with the xy directions and = 	- 1 Lf2 a2 	 / ET 	- 1,FTt; 132 7 	 = 0 xy (9)  4.0 Application of Method to a Tensile Test Uniaxial tensile tests have been carried out on two specimens .062#  wide single ply neoprene coated nylon fabric (Dunlop PR7987). The strains on one specimen were measured by the 'Double Spot' technique and on the other using the 'Spot and Grid' technique. In both cases the strains were measured independently by simply measuring the change.in length of a known gauge length, using dividers. The weft direction of the fabric corresponded with the direction of loading in both cases, and since this material has zero initial stiffness in this direction, it was found to be beneficial to preload the material to 5 lb/ins for the 'Double Spot' test, and to use this as the datum strain level. This preloading tends to remove inaccuracies due to handling the material in its untrained state. The 'Spot and Grid' technique does not lend itself to such preloading, of course, since it is usually difficult to measure the grid size with the specimen loaded. The discs used for creating Chalk impressions were cut from 'Lassotape' adhesive backed P.V.C. tape, using a hollow punch. The disc impression size (diameter 'd' in Figs. 1 and 2) was taken as 6.47 m.m.)  this size being based on a statistical survey of 100 disc impressions (see Appendix 1). All measurements of grid and impression sizes were carried out using a travelling microscope. The test procedures followed that outlined in para. 2.2 and 2.3. The results of the test on specimen 1 ('Double Spot' method) are plotted in Graph 1, and those for the test on specimen 2 ('Spot and Grid' method) in Graph 2; in both cases the results obtained by measurement with dividers have been shown for comparison. 5.0 Conclusions A method of strain measurement for fabric type materials has been presented, and experimental strains obtained in this way compared with those measured with dividers over a known gauge length. The results show reasonable correlation. Of the two techniques employed, the 'Double Spot' method is the easier to use, and is also to be preferred where the material has a low initial stiffness. On the other hand, where greater accuracy is required, and where the material has a stress-strain relationship with a finite initial slope, the 'Spot and Grid' technique is the more satisfactory. -7 Appendix I Errors in Disc and Impression Sizes A survey of 100 disc diameters and their corresponding chalk impressions has been carried out in order to: (a) assess the variation of chalk impression diameter compared with disc diameter. (b) determine a mean diameter of the chalk impressions for use in subsequent calculations. The discs were cut from i liassotapel adhesive backed P.V.C. tape)  and were stuck onto a strip of neoprene coated nylon fabric in random orientations. The diameters of the discs were measured using a travelling microscope. The sane discs were used to create chalk impressions on the fibricl french chalk and a soft brush being used for this purpose. The diameters of the chalk impressions)  after removing the discs, were measured)  using the microscope as before. The results of this survey are shown in graphs 3 and 4, which show histograms of frequency v. measured size for the discs and impressions respectively. From these graphs for the discs:- mean dia. 	 = 6.438 m.m. standard deviation = 0.0416 , (0.647% of mean dia.) and for the impressions: mean dia. 	 = 6.471 m.m. standard deviation = 0.0827 m.m. (1.28% of mean dia.) Thus)  95% of the measured chalk impressions will lie within 12.56% of the mean size (6.438 m.m.). 'DOUBLE SPOT ' METHOD :7 REFERENCE AXES Mai2KED ON STE'acTuRE ALIONED vtiirbi FABRIC DirEcTioNS; WITH STtrucruez uNcoADED PRELOADED ifriPEESSioW MAEVED oN FASerc uSiNa FRENCH criALe ADHESIVE D1Sc - Disc E'EmOvED AFTEI? HALING 3. srevcrarg uivzoiaDED DEFLATED - IIRJ'oC Hirvoie AXES or , aLLiPsES 1  .el a Aft MEASOZED - aiVaLE MEAStleED. 3reverent& IS LoisIDED 	 ifriPeESSiaq '81 Is mAELPED ON FAgEIC - Disc is zEitrovED AFTER rAk n+Pd." Fi4 2 'SPOT 	 7 11)1 METHOD e Gail) 1414eeED oiJ 37-Eva-IRE A LI4Atel, b vI,TH FA5e,c DiZEcrioivg- SrizlicraleE UNLOADED c/FJPEESSURiSED STATE - 	 LENC774s ei 1e2 MEASciLEP 2. 'net/Cruel 	 3. LoADE'D Disc impekS3loAl mrifeED oAl -Disc ZEmovED AFTEZ riAzewa. SreciCTveE 15 1./LoADED DgFLArrt,  LEN41745 az b. Et AskiCa 9 AtE mgASVREP • F C 3 STRAIN DATA FROM 00(111LE SPOT' METHOD iNtriaL IMPEE5SION MATER/AL LoADEZ9 11V IT A L IMPRESSION (piATEZIAL oADED)  Fia 3a- DRTu, v? SPOT 	Pict 3b 15TZAIN SPOT WITH 5TeciCTueE 	win/ STRucTUZE FINALLY RELAXED 	denvALLY" RELAXED F C 4- coRREcnctAI TO 6 DUE TO RESIDUAL. STRAINS FINAL RELAKED SrarE OF ELEMENT ELEMENT' OF 1. mielTEPIAL IN RE41ON of DArati l sPor FABeic AxES 5r(irE OF ELEMENT PZIoR To Lon Dir.14 Zoo L OAD DOUBLE SPOT RESULTS D/ viDat? 0E5 I.,LTS 'GRAPH /  TENSILE TE ST ON 2.0 /Ns WIDE NYLON - piEoPPzigE SINGLE PLY FARRIC 5PEcit-i - WEFT DIRECT IoW St- OW1NC, GoRPELAT/Ohl SET .TEEN 1D/V1DEZ 1  IDougLE SPoT i RESULTS /00 ioibi PRELOAD 511•0/ REFERENCE STRAIN STATE O 	 0 STRAIN E ciRAP14 TENSILE TES:1* ON 2-0;ets WIDE NYLON- NEOPRENE SiN4LE PLY FABRIC 5PECtKEN - INEPT DIRECTION SHOWING corgELATtON BETWEEAI e 'CRID ts,  sPor‘ RESULTS STPArtsl 6 40 /0 6.3 crieR PH 3 HISTOGRAM OF MEASURED DISC SiZES POPULATIOIV 	 /00 MEAN SIZE: 	6.436 Pim STP^IDARD 	 p, c)414:- DEv/ArioN 	 t4  6-1 	 6-5 MEASURED SIZE MM. Jo GfRAPH  HISrociecon OF M,E13URE1) CHALK" IMPPESSION 5 ZES atcrE02 REF/10101%14 DISCS POPULATION/ 1oo MEAN SIZE : 6 ,471144 STA AID PD DE WATiON 0- 082-7m I 	  6-3 	 6-4 	 6,1.5 	 4;42 	 6.7 M>rA UZE P /ZE MM o 41  tu                                       40            Cie F9-1 3' 15-roGien Al OF MEASURED DISC ZES Po Pu icanOW 	 oo MEAN 5/ZE : 6.-939 Pim STANDARD 	 0.o416 DEviArtoN                                                              10                                                                                                                                                      6.3 	 10.5 	 (o6 mER.SuRE C) SIZE MM. 4R RPH 4 HISTOGRAM OF MEA25UZE17 CHALK' impeESSION 5 /2E5 AFTER RE MOYIIVG DISCS PoPULATION IQO MEA7iV SIZE 	 : 6.47/N .5-TPAIDAPA DEllinTION 0. otil 2.7mm 1 	  1 	 I ca-41 	 d:t-6 	 67 mEASueeEP SIZE MM 

The measurement of biaxial strains in coated fabric materials using the disc-replica method

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The measurement of biaxial strains in coated fabric materials using the disc-replica method

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