Full report

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N O T I C E THIS DOCUMENT HAS BEEN REPRODUCED FROM MICROFICHE. ALTHOUGH IT IS RECOGNIZED THAT CERTAIN PORTIONS ARE ILLEGIBLE, IT IS BEING RELEASED IN THE INTEREST OF MAKING AVAILABLE AS MUCH INFORMATION AS POSSIBLE

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NASA TECHNICAL MEMORANDUM NASA TM 75719 DETERMINATION OF THE TECHNICAL CONSTANTS OF LAMINATES IN OBLIQUE DIREXTIONS F. Vidouse Translation of "Determination des constantes techniques des stratifies dap s les directions obliques - Theorie et resultats experimentaux", Centre de Recherches Scientifiques et Techniques de l'Industrie des Fabrications Metalliques: Brussels, Belgium, Report, CRIF PLr4, November 1973, pp 1-42 9 (NASA—TM-75719) OF THE N80-19207 DETERMINATION TECHNICAL CONSTANTS OF LAMINATES IN OBLIQUE DIRECTIONS (National Aeronautics and Space p HC A03/MF A01 CSCL 11D Unclas Administration) 43 G3/24 471154 Cam' h NATIONAL AERONAUTICS AND SPACE ADMINISTRATION WASHINGTON, D.C. 20546 OCTOBER 1979 I

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STAN,IA1 1 " , ;ITI r VI .r _ 1 1 Report No 2, Cnvrrnmrnt Atcr,aonn ti p 3, i cn+ninry itn NASA TM_ 7571 a, Tt1 ,, and subtitle errp,rnl'p DETERMINATION OF TF ;^ TECHNI- s. Report Dote t 1 CAL CONSTANTS OF LAMINATES IN OBLIQUE t..SlCT4.EE1^,1^979 DIRECTION S I b, Performing Organization Codn', 7. Authcr(,A FERNAND VIDOUSE, Centre ^de Re- ' 0. Performing organization Roport No. cherches Scientifiques et Techniques de .^ 1' Industrie des Fabrications Metallique 1o, Work Unit No, (Brussels, Belgium) Q . Performing Organization Nome and Address LEO KANNER ASSOCIATES 11. Contract or Grant No. ^ N SSW— ' 31.04 - 13, Type c! Report and Period Covered Redwood City, California 94063 12, Sponsoring Agenc) Name and Address TRANSLATION NATIONAL AERONAUTICS AND SPACE ADMIN- ISTRATION, Washington, ) a. Sponsoring Agency Coda DC 20546 15, Supplementary Notes Translation of "Determination des constantes techniques des stratifies dans les directions obliques - Theorie et resultats experimentaux", Centre de Recherches Scientifiques et Techniques de 1'Industrie des Fabrications Metal.liques, Brussels, Belgium, Report, CRIF PL-4, November 1973, pp 1-42 (N74-21166) 16. Abstract "An off-axis tensile test theory based on Hooke's Law and applied to glass fiber-reinforced laminates is presented. x.t___aa.m-s. at, taking - into..,ac osint.,-the..aniaotropywof..-..the....l.amin^_ ates. The theory introduces a corrective parameter dependent on the characteristics of the strain gauge used in order to account for the parasitic moments introduced when using common testing machines set up for isotropic materials. Theoretical results were compared for a variety of strain gauge with those obtained by a finite element method and with experimental results obtained on laminates reinforced with glass in various ways." 17. Key Words (Salected by Author(s)) 18. Distribution Statement UNCLASSIFIED - UNLIMITED 19. Security Clossif. (of this report) 20. Security Classif, (of this Pogo) 21. too. of Pages 22, Price UNCLASSIFIED UNCLASSIFIED 43 ii F, +,

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TABLE OF CONTENTS Summary Introduction 1. Purpose of Tests Page 1 1 2 2. Approximate Theory of Traction Tests in Oblique Directions 3 2.1 General 2.2 Traction Test Theory 3 4 Compatibility Equation 4 2.2.1 2.2.2 Limit Conditi)ns 6 Strain and Displacement Expressions 7 2.2.3 Magnitudes Yielded by the Test 8 2.2.4 2.2.5 Correction Coefficients for the Modulus of Elasticity 10 2.2.6 Correction Coefficient for the Poisson Coefficient 12 3. Comparison of the Approximate Theory and the Finite Element Theory 3.1 General 13 13 3.2 Comparison of Correction Coefficients Found by the Two Theories 14 4. Influence of Geometric Test Parameters on the Correction Coefficients 4.1 General 14 14 4.2 Influence of the Type of Extensometer and of T 1 15 4.3 Influence of the Length of the Test Piece 15 4.4 Influence of the Length of the Extensometer Measurement Base 16 4.5 Influence of the Length of the Strain Gauge Measuring e 16 5. Choice of a Type of Extensometer 16 6. Test Results Compared to the Puck Theory 17 6.1 Test Method 6.2 Materials Tested 6.3 Test Results 7. Conclusions 8. Acknowledgements References iii r h4 17 17 17 18 f 19 20

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I SYMBOLS 2b width of the test piece 2c extensometer measurement base 2d length of the transverse gauge (see Figure 5) e thickness of the test piece E modulus of elasticity G modulus of slippage A length of the test piece m surface glass content P load applied to the test piece . matrix of flexibility Sij T glass content by weight T i coefficient defined in Section 4.1 U, v displacement along the x and y axes x, y axial orientation of the test piece 1, 2 orientation of the principal axes of the test piece a term defined in equation (30) S term defined in equation (30) y angular deformation C normal deformation (1 correction coefficient for the Poisson coefficient (compare equations (37) and (38)) n xy , n yx coupling coefficients (l - n I ) correction coefficients for the modulus of elasticity (1 - nII) 6 angle formed by the fibers and the x-axis of the test pieces Poisson coefficient term defined in equation (30) s normal strain T tangential strain glass content by volume (1 -) correction coefficient for the Poisson coefficient (compare equations (37) and (38)) 0 section of the test piece iv

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INDICES m matrix f fibers * indicates an apparent magnitude yielded by the measurements v t

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DETERMINATION OF THE TECHNICAL CONSTANTS OF LAMINATES IN OBLIQUE DIRECTIONS P. Vidouse Metallic Manufacturing Industry Scientific and Technical Research Center Summary An off-axis tensile test theory is explained and coefficients are given to correct experimental results obtained working on usual testing machines. Theoretical results are compared with those obtained by R.X', Courtade with a finite element method and with experimental results obtained on laminates reinforced with glass in various ways. Introduction /1* This work constitutes the fourth part of the research undertaken by the Centre de Recherches Scientifiques et Techniques de 11Industrie des Fabrications Metalliques [Metallic Manufacturing Industry Scientific and Technical Research Center] (CRIF) on dimensioning of reinforced plastics, at the request of the industrial members of the Fabriplast Group of Fabrimetal. Previously published papers concerning this research are the following: -- "Relation entre 1'etat de polymerisation, la fatigue et le fluage dune resine epoxy renforcee au verre textile" [Relation between the State of Polymerization, Fatigue and Flow of a Fiberglass-Reinforced Epoxy Resin](CRIF Publication PL 1) — "Study for polymerization and curing of polyester and epoxy resins by the dilatometric and resistivimetric methods" (CRIF Publication PL 2) -- "Theoretical and experimental study of the technical constants of laminates" (CRIF Publication PL 3) *Numbers in the margin indicate pagination in the foreign text. 1 1I

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I This study, like the preceding ones, is the result of collaboration between various research organizations; -- the Centre Europeen de Recherches et Essais [European Research and Testing Center] (CERE) of the Fiberglass Division of Saint- Gobain Industries at Chambery manufactured the rest materials and participated in interpretation of the results; -- the Institut National des Sciences Appliquees [National Applied Sciences Institute] (INSA) of Lyon performed the calculations according to the finite element theory; -- the Laboratoire de Resistance des Materiaux [Materials Resistance Laboratory] of the University of Liege performed the tests and contributed to analysis of the results; and lastly, -- the CRIF, acting as scientific coordinator, exploited the results and assumed scientific and technical resplosibility for the work. The CRIF is very grateful to these various organizations, without whose assistance the research could not have been successfully concluded. 1. Pur2ose of `rests 12 At the time when work was being done as reported in the paper entitled "Theoretical and experimental study of the technical constants of laminates" [1), traction tests in directions other than principal directions were carried out on the same laminates. Since these tests were carried out in a conventional manner, the results cannot be directly exploited but must be corrected in order to take into account the coupling phenomenon between traction and shear. The purpose of this work is to analyze technical constants in oblique directions and Co demonstrate that it is possible to predetermine them theoretically with adequate precision. Correction coefficients have been determined, based on an approximate elastic theory, and verified for one type of laminate with an ex- 2

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I act theory utilizing finite elements. (It will be recalled that this method consists of cutting the structure under study into a finite number of areas with simple geometric shapes termed "finite elements" (in this case, rectangles) and subsequently rejoining these areas with the aid of a computer.) These coefficients take into account particularly the type of extensometer utilized and the geometric parameters of the test. 2. approximate Theory of Traction Tests in Oblique Directions /3 2.1 General As demonstrated by the generalization of Hooke's Law [11, a simple traction test on an anisotropic material induces not only normal deformation e, but also tangential deformations y. Reportedly there is coupling of traction and shear effects. e x S 1 S 12 Cy Sly S22 lrxy Sae Sze S1 6 vX S te 0 (^) See 0 This equation demonstrates that e and y xy are not non-existent when S 16 and S 26 are not zero. Experience also demonstrates clearly that warping occurs during a traction test to the extent allowed by the anchorage of the ends of the test piece (Figure 1) . Figure 1 illustrates the deformation of a test piece made of a material which is not symmetric with respect to thickness. If the material is symmetric, warping occurs only on the plane surface of the test piece (Figure 4) . ^f 3

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Conventional test equipment, designed for isotropic materials, does not allow the ends of the test pieces to be rotated. When traction tests of anisotropic materials are carried out using this equipment, parasitic moments are introduced which could invalidate the results. The following theory is intended to calculate the error introduced by this procedure, and to correct the values obtained,by means of a coefficient which, as will be shown, depends particularly on the type of extensometer utilized. Various types of extensometers exist, differing particularly with respect to the test piece attachment means. As shown in Figure 2 1 the relative position of the feelers can vary; the Type I extensometer has feelers placed on both sides of the test piece while the Type II extensometer has feelers only on one side. The Type I and Type II extensometers are located at the edge of the test piece. The Type III extensometer is similar to the Type II extensometer, but its feelers rest on one of the surfaces of the test piece. Lastly, the Type IV extensometer is an axially oriented strain gauge. 2.2 Traction Test Theory 2.2.1 Compatibility Equation The analytic solution of the problem is obtained by applying the theory of elasticity [2]. The reference axis orientation is illustrated in Figure 3. The following relations must be satisfied [4]; -- equilibrium equations: aQa T aX + axy = 0 (2) Lx + aTxy = 0 ay ax 4 .. t M ^ a k

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V -- deformation/displacement relations; xixu aY • ay au + aV Y Xy 77uX (3) the generalization of Hooke's Law: e S11 S12 SIG' C Ste S22 S26 Y XY Sib S26 S66 a (4) a TXY When the displacement terms in equations (3) are removed, deformations as a function of strain with relations (4) are subsequently expressed, and equations (2) are utilized to find the compatibility equation: 2 2 a s a s 2 a s (2S i2 + S 66 ) `x + S I I » 2 5 16 x 2 0X2 2 ay2 yaa•sa - 2S26 Y - p + S22 axayaX2 axay (5) The Sa j matrix is termed the matrix of flexibility. Utilizing the notation selected by Ashton and Whitney [4], flexibilities are expressed as functions of technical constants according to the following relations: F 5 x

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1 S11 E1 S22 - -1 Soo • Xx YY S12a+* xX e- Yi xX YY S, 6 K , 2-X X EXX nx EYY 2.2.2 Limit Conditions GXY (6) If one end of the test piece (x - 0) is held by rigid clamps, the limit conditions can be written in the following way: (0 ,Y ) R 0 3u 0.1) . 0 (7) V aY Since the edges cf the test piece are free, it follow.-: (x, ;b) r (X,±b) a 0 0 rXY (a) The analytic solution satisfying these conditions is extremely (:omplex, or even impossible. Equations (7) can be replaced by the following limit conditions which are partially justified by experience: 0 8u 0,0 V (0,0) K 0 aY V 0 au (R ► 0) 0 ay u (0,0) - 0 (9) u (tiro) = Cot where e 0 is a deformation proportional to the magnitude of the applied force P. 6

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i-^ 2.2,3 strain and Dis lacemcnt Expressions Since shear is indopendont of x, it can be posited; TXY R f (Y) (10) By integration in (2), it follows ZL 41 X --xf' (Y) + 0 (Y) 0 Y • h (x) (11) Taking into account the condition for compatibility (5) and preceding relations, we obtain; f (Y) " C o (Y2 . b2 S16 - 2 ----- C O Y 2 + C 1 y + C2 (12) 9 (Y) S11 h (x) 0 where C O , C 1 and C 2 are integration constants. From (4), (11) and (12), the strain and deformation expressions can be obtained quite easily; ^16 a x - 2C O xY - 2 .°P- C O Y 2 + C 1 Y + C2 S I1 Cy 0 22 O (Y - b ) TxY` C ex s 5 11 (-2Coxy + C1Y + C2) - 536 (13) S 16 C o (Y2 + b2) (14) C = S12 (-2C O xY C O Y 2 + C 1 Y + C 2 ) + S 26CO (y 2 - b2) - 2 51.1 Y xY = COY 2 + C1Y + C 2 ) + S6 6 C O (y 2 - b2) Sts (-2Coxy - 2 S16 S11 7 ^I

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-.I By integration, the following displacement expressions are found: U » S16Cox (Y 2 + b2) + Sl1x (C2 + ClY C Y) + Cs + (Sl602 - SooCW - Ca)Y + C OY° W6 2 Sl6 ClY Y 2 + C 2 # S12Y (» T ^1t COY + 6 26COY + ( Y 2» 3 b 2 )+ C 4 + o x Sl6C1y2 (l5) - CoxY) SlICIX2 Silcox, C x —s= + ^. s The integration constants are obtained by expressing the limit L_.^., conditions: 6 S 16 co 0 s 11t2 6b 2 (S11566 Sl6) + C I » Cot Co C 2 s (6 5661) 2 + Sl It`) Cos lIt, y 6 ( 1 6) C4 0 CS 0 2.2.4 Magnitudes Yielded by the Test The traction test allows determination of two technical constants: the modulus of elasticity and the Poisson coefficient of the material, while simultaneously recording the (C x , P) and (C y , C x ) or (C y r P) graphs. These measurements can be made without any particular difficulty for isotropic materials, regardless of the type of extensometer utilized. in the case of anisotropic materials, the field of deformation is not uniform, as shown in Figure 4, as charted for a flexible material utilizing equations (15) (E ll = 8 kg/mm 2 , E 22 = 0.5 kg/mm2 , v 12 = 0.5, V21 = 0.03125, G 12 = 0.2 kg/mm2 ) for elongation of co = 20 percent. 8

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7 Therefore, for these materials, it is necessary to examine more closely the magnitudes actually yielded by tile, measurement equipment. In the case of Figure 5, the test piece is fitted with a Type z extensometer (see Figure 2a) whose feelers are located at points A and B and with a transverse strain gauge whose ends are located at points C and D. Proceeding in the same manner as for isotropic materials, the magnitudes measured are the following; * AaX EXX e * X with* Pr P ^X S2 * v* ev xy ° eK (17) in fact, the values obtained (denoted by asterisks) aru^ not exact. The extensometer does not yield e x but (see Figure 5) does yield: /8 * u Q - uA e _2c _ x ` (18) Likewise, the transverse strain gauge yields: V - v D ey = ^ The expression of or* is written: b ^x = 'fie - n bOx- dy (19) (20) Therefore, the measured constants E* and vXy must be modified by correction coefficients, to be determined, such as; = 1*i-= i E XX ( - n ) EXX (21) v Xy =- E XX Saz =vX y P - ^) (22) i E t wq 9

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2.2.5 Correction Coefficients for the Modulus of Elasticity Let us consider the Type Z extensometer as shown in Figure 5. When a x is replaced in equation (20) by its expression (131, and relations (16) are taken into account, the expression of a* is written: S1G 2 S11 * S 06 QX CO b 2( .-_.- _ 2 ` S16 "T S11 / + ^ S16 1 R (23) The .00rdinates of extensometer feeler application points A and a are, ;:•espectively : A ( - c ; b) et B ( + c - b) [23a) When uA and u B are calculated by means of relation (15) and are replaced in equation (18), we obtain: b3 S12 r I ^11 - Isc S11 S IG S 66 S 11 S16 yielding: I ^X * * - S 11 (1 - nI) E XX o X S 66 - 2S1 6 -b (^2 )C=Co C 2) c ^ S1 S i I 2 S16 R2 S 11 (24) S11 S16 /9 (25) with the subscript "z" referring to a Type Z extensometer. Whence, when c* and a** are replaced by the above expressions: n - 8Sia + S 16 ( e2) S11 + 2 (S12+scc-2S^-1 )l (26) ' ' I - ( 6S 2 S11 cc + ^ S 11) - 4 Sic 'E. 10 e

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I If the extensometer is turned so that the feelers are at points ,A' and II', it then follows, in the same manner: x f3S1 6 - S16(-^- C2) Sib) -2 S11 + 2 ( S 12+ S66 (27) I S11 (6SG6 + YrS11) - 4 Sib Likewise, for a Type II extensometer: 8 Sib n Ii = 2 S I1(6566 + E' S I1) - 4 Sf6 r (28) The expression does not change if the extensometer is turned. For the strain gauge: 2 SIG n = 2 I S11(6S66 + S11) - 4 S16 ( 2 9) The Type TIT extensometer whose edges rest on the surface of the test piece should not be utilized for tests in oblique directions, since the edges thus rest along a line which will be warped, and the contact point of the feeler cannot be determined. Therefore, for this type of test, the extensometer should be located along the edge of the test piece. in summary, positing: a = 2 Si6 X2 /10 (30) Q = S IG (^ - (:2) S 11 1' j ( S 1?. + S66 = S 11 (6 S 66 +;- S 11) - 2 a 11 11

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the correction coefficient expressions become: 4a + Q nI F 4a n II s ^; 4a - Q n I F n IV = (31) 2.2.6 Correction Coeffi cient for the Poisson Coefficient If the test piece is fitted qith a transverse gauge as shown in Figure 6, the expression of ey is given by relation (19) in which the v are replaced by their expression (15): S11 Sib (32) Cy =- v xy Co = I 6S G6 b 2 + S 11 k' - d21 4 - With equation (23), C can be expressed as a function of a*: 0 * b S16 Co = ax ( 65 66 b 2 + S 11 whence: * 6S66 b2 + * e = - vXy a S11 6S 66 b 2 + S11 R 2 - 4 ^ 1 - b2 Positing: _ 4 S1 6 (7r 4 5 11 6 b2, (33) V - S16 S 11 9 2 - 4 d2 ^16 — Si6 (34) 1) e 1 S 11 ( 6 S 66 + S11b2)- 4 S216 12 (35) 1

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I and utilizing relation (25), the expression of e** becomes: 11 C = - S 11 t 1 0 v XY a e* xy xy (1 e n) X vX y ( 1 - ^) vXY with 1 - _ T T (37) (38) The n to be taken into consideration is clearly that one corresponding to the type of extensometer utilized to measure e*. 3. Comparison of the Approximate Theory and the Finite Element Theory /12 3.1 General In their publication "Deplacements, deformations et contraintes dans les materiaux elastiques anisotropes" [Displacements, Deforv-1tions and Strains in Anisotropic Elastic Materials] [3], R.M. Courtade et al. deal with the elaboration of the strain/deformation relation for an anisotropic elastic material, based on a procedure of calculations utilizing finite elements. As illustrated in Figure 6, this method allows limit conditions which are slightly different from those set forth in Section 2.2.2. Since this system is not symmetric with respect to the y-axis = 2, in the case of the Type II extensometer, the results differ depending on whether the extensometer is placed to the left (at AB) or to the right (at A'B') of the test piece (Figure 6). 13

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.--R--- 3.2 Compari^don of Correction Coefficients Found by the Two Theories These coefficients were calculated for a plate (1B in Table 11) with the following characteristics: Resin: rigid polyester Reinforcement: unidireotional (23% glass by volume) R = 100 mm Ell 1914 kg/mm2 b = 10 mm E 2 2 = 639 kg/mm2 C = 25 mm 0.327 v12 = d = 5 mm G12 = 257 kg/mm2 As shown in Table 1, the two theories yield correction coeffici- /13 ents which are relatively close, except in the case of the Type 11 extensometer. These deviations principally result from limit conditions which are not the same in the two cases. The deviations for the (1 coefficients are somewhat more significant. This comparison allows us to conclude that the approximate theory is sufficiently correct to be utilized in a study of the influence of geometric parameters on test conditions. 4. Influence of Geometric Test Parameters on the Correction Coeffi- 14 cients 4.1 General The influence of geometric parameters on the values of correction coefficients was studied for a material with the following characteristics: E f = 7000 kg/mm 2 ; v f = 0.25; Em = 395 kg/mm 2 ; v m = 0.35; p =0.23. These characteristics are those of Plate 1B in Table 11. r z 14 t r M ,

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Moreover, the T 1 parameter will vary, being proportional to the quantity of fibers lying in direction 1. Thus, if T 1 = 1, the laminate is unidirectional; if T 1 = 0.5 1 the laminate is balanced and bidirectional.; and, if T = 0 1 the fibers all lie in direction 2. The i symbols utilized for dimensions are defined in Figure 4 and Figure S. 4.2 Influence of the Type of Extensometer and of Tj Figure 7 illustrates for different values of T 1 the variation of different correction coefficients as functions of the angle a formed by the principal direction 1 of the material with the x-axis of the test piece (Figure 3). The geometric parameters selected for these calculations are those utilized for the tests, i.e.: R = 100 mm; b = 10 mm, with c = 25 mm for the Type I and Type II extensometers and c = 5 mm for the axial strain gauge. It can be seen that the coefficients with respect to the Type I extensometer are the most significant. Then follow (1 - n II) and LL5 nIV). With respect to the strain gauge, the latter is relatively (1 - weak. The correction factor (1 - f) for the Poisson coefficient is also small. It can also be seen that when T 1 = 1, the greatest absolute value of these coefficients is obtained when angle 8 = 250. 4.3 Influence of the Length of the Test Piece The curves shown in Figure 8 were calculated for T 1 = Ire = 22.50 and b = 10 for different values of c, with k being variable. It should be noted that with respect to Type I extensometers, the (1- n I) coefficients do not converge towards 1, contrary to supposition. This indicates that even if the test piece is quite long, a correction factor should be utilized with this type of extensometer. The other factors converge rapidly towards 1. 15

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F- 4 — 4.4 Influence of the Length of the Extensometer Measurement Base Figure 9 illustrates the influence of the relation cA on the value of the (1 - n i ) and (1 -- n i ) coefficients. The other coefficients are not affected. The curves shown in Figure 9 were obtained for Z = 100 mm, b = 10 mm, T = 1 and 0 = 22.5 0 . In addition, Figure 9 i shows the homologous curved obtained utilizing the finite element method. 4.5 Influence of the Lengthh of the Strain Gauge Measuring ey Figure 10 illustrates the influence of the relation d/b on the (1 - *) factor with respect to the Poisson coefficient. This curve was also obtained for T l = 1, 8 = 22.5°, b = 10 mm and R = 100 mm, with d being variable. 5. Choice of a Type of Extensometer 16 Study of the influence of geometric parameters allow p conclusions to be drawn concerning the type of extensometer and the dimensions of test pieces to be utilized in traction tests in oblique directions. Working conditions must be those under which the correction coefficients are the smallest. As noted above (Section 2.2.5), in order to measure e x , the Type II extensometer located on the surface of the test piece should not be utilized. The Type I extensometer utilized for tests should also be eschewed, since the corresponding correction coefficients do not converge towards 1 (see Figure 8). For measurement of e x , the two best types of extensometer are Type II and Type IV. Strain gauges are the most suitable to the extent that the operator is in complete control of their method of utilization on plastic materials. To measure e y , it is preferable to utilize a strain gauge whose length is as nearly as possible equal to the width of the test piece. In any case, the value of the (1 coefficient is always very close i to 1. I' 16 F' f

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A transverse extensometer may also be utilizers. in such tests, the Q/b ratio should be at least 20 in order to yield virtually negligible correction coefficients. 6. Test Results Compared to the Puck Theory 17 6.1 Test Method The tests were carried out under the following conditions and with the equipment listed: -- test piece dimensions: see Figure 11 -- test equipment: Tinius Olsen UEH Dynamic -- feeler displacement speed: 1.25 mm/minute -- extensometer: Tinius Olsen with 50 mm measurement base -- strain gauge: TML Type Pl 10; 10 mm load cell: Tinius Olsen 3 t. 6.2 Materials Tested The materials tested were the same as those utilized in report [1]. The composition of these materials is given in Table II and their glass content is given in Table III. 6.3 Test Results Test results are summarized in Table IV, where they are compared with the values obtained utilizing the Puck theory [1]. Table IV illustrates, respectively: -- the type of reinforcement: U unidirectional U + M unidirectional + mat BE balanced bidirectional BE + M balanced bidirectional + mat B bidirectional B + M bidirectional + mat 17 ,I

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--- the angle 0 defined in Figure 3 and ---- the theoretical values of EPuck vPuck --- the experimental values E* and v* with the deviation in percent from theoretical values --• the corrected experimental values E eXp and v exp with the deviation in percont from the Puck theory 7. Conclusions /,^5 As shown in Table IV, the deviations obtained between the Puck theory and the experiments are satisfactory (less than 15%) in a majority of cases for measurement of the modulus of elasticity. Moreover, utilization of correction coefficients more often than not brought the measured value close to the theoretical value. The deviations observed are slightly more important than they are for the principal directions, particularly for unbalanced laminates. This is due to the fact that only three tests were made for the latter directions, while five tests were made for the principal directions. Therefore, in the former case, the mean is less representative. Some of the deviations obtained for Poisson coefficients are quite large, as was the case for the principal directions [1). These large deviations are probably attributable to faulty attachment of the gauge to the test piece or to parasitic errors introduced into the measurement system. This has led us to conceive of a systematic study of the use of gauges on plastic materials. This study will be carried out in the next few months. It is in fact important to answer the question raised by an author: "Do we measure strain when we measure strain?" Current work indicates that somet',mes this question must be answered in the negative, and it is absolutely essential to resolve this problem if we are to obtain a better understanding of the behavior of reinforced plastics. 18

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1. Acknowledgements 26 We are deeply thankful to Madame R.M. Courtade, Ph.D., engineer at the Institut National. des .Sciences Appliques [National. Applied Sciences Institute) (INSA) of Lyon, who, with the aid of her finite element program, resolved for us the problem of the deformation of anisotropic test pieces. our thanks are also due to Mr. Manera, engineer at the Centre Europeen de Recherche et Essais [European Research and Testing Center] (CERE) of the Fiberglass Division of Saint-Gobain Industries for his much-appreciated assistance and always constructive criticism. Lastly, we thank the Belgian industrial members of the Fabriplast Group of Fabrimetal for the assistance and encouragement they always gave our work, and particularly Mr. Arlians and Mr. Vivile, the president and secretary, respectively, of Fabriplast. f 19

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REFERENCES 27 1. Lacrosse, B., Massonnet, C., Viatour, G. and Vidouse, F., "Theoretical and Experimental Study of the Technical Constants of Laminates" (CR1F PL 3, June 1972) 2. Pagano, N.J. and Halpin, J.C., "Influence of End Constraint in the Testing of Anisotropie Bodies", J.Com2.Mat, 2 1 18 (1968) 3. Courtade, R.M., Lemaire, M. and Cubaud, J.C., "Deplacements, deformations et contraintes dans les materiaux elastiques anisotropes" [Displacements, Deformations and Strains in Anisotropic Elastic Materials], Verre Textile/Plastiques Renforees [Fiberglass/ Reinforced Plastics], June 1973 4. Ashton, J.E. and Whitney, J.M., Theory of Laminated Plates, Technomic Publishing Co. [n.d.] 20 F ik

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Table I. Comparison of the correction coeff ciento y i e 1 do d by tr lie t w 0 them riev 0__._, 22,68 45 67,5° Coeffi Appxox.^rirtii;e Devia- Approx. , Finito l5eviv Tprox, ri nite !1 viFicient theory Itelement tl^n t jeory, lement.ti n theory elements t on 1 - n 1 1,2844 1 ► 3?17 2,80 1,1446 0,8356 0,8430 0,67 0,9993 0,9941 - 0052 1 - n , 0,6172 0,6448 4,30 1 - n11 0,9508 0,8435 - 12,70 0 ► 9900 1 - n1 l 0,9 1,08 1,1231 15,30 0,9900 1 - n i v 0,9077 0 ► 9951 0,70 0,9975 w w N W w w w w N- N w w M w w w w N- N N w N N -^ w s N w ww w w M 4 w N w f.- w- N M N N w w w M s Nw w w M N NN -iRN N N 1,1521 0,92 1=07 1,0076 0,68 0,9249 - 7 0 00 1,0000 0,9935 - 0,65 1,0699 7,50 1,0000 1,0082 0,81 0,9986 0,11 1,0000 1 1 0001 0,01 1 - t1 1 1 1399 1 1 2280 7,25 0,9827 1,0521 6,60 1,2844 1 ► 4558 11,80 1 - r , 0,6172 0,7116 13,30 0,8323 0,9007 7,59 0,9813 1,0374 5,40 - 3' 11 0 1 9500 0,9860 0,9070 0,10 0,9820 1 i O374 5,30 1 0 1 9300 - 2,15 1 - i1' 1 0,9508 1,2372 23,10 0,91160 6,70 1 - t 1V 0,9877 1,0987 10,10 0,9935 t , r F. 1,1441 13,82 0,9820 1,0521 1,0672 6,91 0,9820 1,0423 5,80 C 2))

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^Ikl Table 11. Plate compooi,f ion 51) (E * 274 kg/mm = v a 01,366) Resins : P a flexible polyester (Palatal 11 B «rigid polyester (Stratyl 0) (E w 395 kg/W ; v » Ot350) Ex rigid epoxy (Ciba LY55C) (E = Plate No. Type of Brand Name reinforcement 342 kg/mm 2 v - 0,294) Gr/m2 Number of Method of layers manufacture 1 P Satin Porcher 716his 200 17 Press 5 P Satin Porcher 716bis 200 6 Mat Govctex PI q 12 450 3 if 9 P Satin Tissaverre 158 308 11 11 P Taffetas Tissaverre 249 200 16 17 P Satin Tissaverre 158 4 512 450 3 Mat Gevetex 1-1 308 18 P 249 200 6 Taffetas Tissaverre Mat Gevetex M 512 450 3 19 Mat 512 450 4 P Gevetex M 23 1) Preformed 25 Spray up 1 8 directional Verester 29 5 B Catching rov, Cotton 5283 9 B Taffetas Verester 39 13 B Serge Veret or 131 17 B Mats M1.100.P23 21 B Mats M4.400.P3 25 B Unidir. Verester 29 Mats M1.100.P23 29 B Taffotas Verester 39 F;at M1.100,P23 30 8 Serge Verester 131 Mat M1.100.P23 31 8 Spray up 34 B Preformed 36 B Mat Gevetex M512 „ Spray up 400 5 Contact 420 4 500 4 470 4 450 3 450 3 if 400 2 450 2 500 2 450 2 470 2 450 2 Spray up Presse 450 4 38 B Satin Porcher 716bis 17 40 B Taffetas Tissaverre 249 200 200 16 44 B Satin Tissaverre 158 308 11 48 B Satin Porcher 716bis 200 6 Mats Gevetex M 512 450 3 52 B Taffetas Tissaverre 249 200 6 Mat Gevetex M 512 450 3 53 B Satin Tissaverre 158 308 4 Mat Gevetex M 512 450 3 1 E Satin Tissaverre 158 308 Presse 11 it 3 E Satin Porcher 716bis 17 200 5 E Taffetas Tissaverre 249 200 16 7 E Unidir. Verester 764 9 E Taffetas Verester 39 t a L 610 3 Contact If 500 4

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Table III. Glass contents T - Glass content by weight Glass content by volume M I: 2 Glass content per square meter (m ) Plate No. T M 1 P 61.46 5 P 51.29 9 P 61.80 13 P 64.06 17 P 53.40 18 P 56.42 19 P 41.92 23 P 37.32 25 P 26.69 1 B 38.88 5 B 33.84 9 B 41.92 13 B 42.67 17 8 26.86 21 B 24.73 25 B 32.87 29 B 38.52 30 8 35.87 31 B 31.11 34 B 37.09 36 B 39.82 38 B 59.44 40 B 63.95 44 B (111.59 48 B 51.97 52 B 53.70 53 B 52.48 1 E 61.48 3 E 60.98 5 E 62.40 7 E 42.49 9 E 45.39 k r L, m gr/ml +'.426 3274 0.315 2361 0.44"1 3270 0.455 3432 0.337 2545 0.362 2708 0.249 1854 0.219 1637 0.147 1638 0.23 2106 0.19 1642 0.24 1999 0.25 2235 0.14 1253 0.13 1147 0.19 1517 0.23 1748 0.20 1828 0.18 1221 0.21 1598 0.22 1727 0.40 3057 0.45 3404 0.43 3241 0.32 2438 0.33 2548 0.32 2475 0.41 3241 0.41 3287 0.42 3380 0.25 1883 0.26 2058 A3

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U)1 r 1 '{ m I + O to Ul 1 Vl ; 1 1 0 1 W 1 W 1 W 1 i A N O IA N I A N 1 to 171 .r. N i ,1i 1. 1'fi K H 0. n 0 0 V N Q 1 1 to Ol A N I 1O CT .p N i to N O I in N Q I Ut N O I C) V Ul N O I O t7 Ut a V to N O I V cP :1-1 a e O to 'p A in O O In O O cm y0 in O a O o 0 I N N N 1 r+ 1 N I H 1 VI w In m N O I to N V Cn 0) n N I N Cn N 1 V t0 W t V 04 M I N '81 00 V Sn O cn in p in o m N N NI N 1 Ul O N! co 00 N 01 Cn W I 'J Ul N V to IUl Ul Ul W ci, I I-' m O N W 1 A. A V1 OO to 00 1 fn t0 N I 171 W W Cn N 1 A A w Cn I A w V w .N^ I 1 1 1 I I N N N 1 N N I N I N N I 0 w 1 N N I H N I Ul O N I V N W I W 00 N 1 N O OD V Cn I V Ol N O I Cn N Cn Cn V 1 m Cl,l 1 Ul A NI A O N 1 0 0) W 1 V w N 0) to 1 Cn A N W M Cn H V I Cn co w co O tD W I of rn N I 0) W W 0) N I V cn V N ID Ol N W O 1 0 I 1 1 1 1 1 I 1 1 I 1 1 1 I 1 1 1 1 f 1 1 I 1 1 1 1 I 1 1 to 1 N ^mC7 b (D 1 n 1 1 I 1 1 1 1 1 X N• I H N N I N I H I N W N I N 1 N N mrt I w H 1 lO N N 1 Q1 O N I N W Od l 1p A N N A I Ol Cn O M W IA Ul N H 1 Sn A 0 1A CO 1-^ 1^ O O I 0) O V i-' A l 00 CO 00 10 O to 1 1 I I 1 1 I 1 1 1 i i i i i 1 1 t I 1 I H N N I N I N NI /-• 1 (n N 1 r l A Imr ^. 1 X P) 1 ^.1. H i N ! y\C O ro H N 1 H N I j m 1 Ul In C)1 1 V O W 1 co to N 1 O N Cn V 0) 1 V Cn A O 1 0) A Ol Cn V rD V 1 Cn w NI A Cn H I O N W I CP Ul V V 40 1 UI Ul in V i Cn A O In Cn w 1 00 ON to I O N W I G) H H 1 V N A to N I 'V W W W I to N t0 W a - b 1 1 1 I I i i i t0 I N ct m rn i c I 1 1 1 1 1 1 1 I I I 1 1 nc j• 0 1 I I I I 1 1 1 ! 1 t t i I m I O I 0 N I H I H I /-N N N N I N N I N X I N H N N N I tD A N I Cn A H I N L" CO I t0 Ln N O A l Cn Ul W N W I ^A C71 Vl N ^p to m 1 L', 41 O 1 4- 'CO %+ I in 1J O 1 IT, iO H 'g. .A I M 'N V VW I V in in rn 1 1 I i I 1 1 I I 1 1 1 1 1 1 I I I 1 t in i- JA 1 ^• X Pi I O O\q 1 a ct O 0 O O l p O O i 0 O O 1 0 O O O O i 0 O O O O i 0 O C7 p O ms+ I w I v I I v i w i a W N 1 0 H W W N I r%) A W N N C /.e I C)1 W N I o W N I A W H I W CJ N t0 1 V A V co I N N O N O r-^ 1 N O A I O 1 CT 1 co Cn V I N Cn w w Ul Cl I 10 A U7 I W ()1 N I V V C)1 I to A W OV W I co t)1 W W I `J 1 I 1 I 1 to N N N 1p I o O o O 0 1 C) 0 0 1 0 CD O O o 1 o o p i p o p I o C) cm c o N C* rl 1 A W +1-+ ° I A W H I A W N 1 W N N N IV 1 0 N N W W I N W A N 1 C) CO V I O Ln Cn 1 Ul W to I N Co -1 V W I to •P Cn Co N Ito Ul m N m 0 1 to N Ul I V 00 N 1 Cn 00 N I t0 O G, N w l A O A Ul O I V UI H '71 Y't I 1 1 I I I I I i i i i i Ul I ct tn^ i n 1" m 1 1 1 1 1 1 I 1 1 1 1 I 1 1 1 I C X 1 }^'1' O I N N I N I w H I H N w I N H N rt I !"• I w p 1 Cn N O H 00 1 0 Cn ^! H w I 01 O V I W A O I 41 W O 1 0 N H fll 1 OA N 1 Ul tO A I V Cn N I ya O H O O I ^' P 1 I 1 I I 1 I I I I "CO l0 O 'm VI N A O C "^ H I O pro 1 0 1 0 O O t 0 O O 1 0 O O 1 0 ) O O O 1 0 O O O O 1 0 C) O O N 1 0 N W yF• W I N, Cl .A N H ipC I A N N I A N N I A W H I W W N N 1 C) C O V I O V Cl I Cn A W I N H to Cnto W I to W O to N I t0 N O N O X Ul I V Cn I A Cn 'J N O I 'V V A Ul Cn 'p 1 LO Cn N 1 cn A H 1 tO CO V W 1 I I 1 1 I 1 1 1 1 1 C^ I I 1 I I I I C 1.1. 1 ^ 1 ^ ^ I 1 ( 1 ^ I 1 I roG pnc' 1 ^ I 1 I N W H I N W 1 1 N N N I N N N 1 N 1 I-1i 1 Cn A V I W U1 O I Ol t71 O 1 0 A N O to 1 I 1 1 H X 1 Cn H .-• W co 1 0 N N N W 'I7 0 1 1. C"^ I co 41 N 1 Cn tO A i v ^! N 1 0 Ul w w O 1 m O N a 1 I 1 i 1 I I 1 1 1 1 1 1 1 1 f 1 I 1 1 k( I ^ I g y Fb^ t' 1 m V o.i 1 N V .P m N' t 1 X 1 1 X O\O 1 I I I H I 1 O I j O

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I3y 4 m 1 1 1 Ul 1 VI 1 (V 1 1 I 1 W I N I tD 1 lII I Ul I i w i co i w i m i m i I I 1 1 1 I t ^ I 1 1.,. .^11 1 .A N I .A N i .G>' N 1 .A N 1 4^- N 1 .A N 1 Vl N O 1 Vl N O I tll N O I Vt N O 1 VI N O I Vt N 1 ^ 1 V 1 I r 1 t 1 0 to 0 1 0 Cn of C) to CO 1 0 Ul 01 0 Ul 01 0 t» 1 1 1 I 1 1 I r M M I Y Y Y I r M I H .1 r Y Y I Y r I Y W Ul 1 Y W Ul 1 w O r I V lD W I C7 W to I O W 1 O) r O 1 tD .P W I M W W I P Vl N 1 CT 00 to I^ Vl .P N N 1 (T Ul V V D) 1D Vl U/ w Ul -J O Y U) 1 1 1 •-{ L- 1 1 1 I 1 I i I Y r 1 •^ I Y Y Y I r Y I Y r l r Y N I M Y I r Ul .P 1 0 M Q) 1 V O M I to O w l w V N I M .J'+ Im 1 O v_ _ Fy 1 M t 1 w Y i W I tU l ^'^ O fn i ro i 'v i w} 1 1 I tD 1 ^ ^ , ^.a I A N 1 n N I d^- N O O I V1 N O I CJl N C7 1 C1l N O I 1 1 '"^'' CO 1 G Ul W 1 0 Ul 01 CO W Q 1 1 1 7C m Y I r N 1 r N 1 t- Y N UO 'O to 1 10 N C) I co N O I Y cn Y \ C A I W m CT I to X* ca 1 to W W n CT 1 H 4^ CT 1 to O u V 4^- W F)^ 1 ' -^---- I 1 1 1 ^, N I Y Y N I N I Y r N m r I N CT N 1 V t0 m I W co W I N En V 1 O O Xi 1 to M M 1 Ul N ^ I W 00 Y I t0 Ut 4A 1 OS) O O 1 .LA tt) 4. 1 'W H W ;7 M w W 1 CO N C) 1 W .A 0 1^ r to 1 N CO I-' 1 M 4) 1 0 1 1 1 1 10 1 1 E I I I I I I I 1 i 1 1 1 ( 1 1 t 1 1 I 1 1 1. 1 1 I 1 1 I Y 1 1-1 I r N I N N r I H to 1 W W N 1 V V N ^ 14 Y N I N 1--^--i 1 I 1 ,^ C: I I I ( I I 1 1 1 1 ^ Nt ! 1 I P) I N Y I N N I M M Y mx 1 C+ N I tp CT Q) i V1 N N Y11 O1 r l 0 N O I N tT IA I V tD 01 1 0 ^P N .1 W CT1 O 1.1^ w I W Ul i N cn 6 1 tO O w i 4 N t)1 i t0 Ul to i %, yA C) I IT w .tom I yP t0 N I W p- N i W p Rl 0 1 I 1 1 I I I It 1 I 1 I 1 1 I I 1 1 1 1 I I 1 1 1 1 1 I 1 L 1 1 1 I 1 1 1 1 >♦ ry N 1 (D 1 I 1 X L.^^ 1 I 1 i^ 1 1 I r - I I t C7 0^0 • 1 1 I I Y M YI Y Y Y I Y I M Y N l r r N I r N l r r N to rn Y I r r I I r W .Fa 1 0 .P al I V 10 r l 10 lD W i W W r,,%),l r p r I N O N I V .J:a O I W W W \ 0 . 1 N CO V1 CO W .la 1 lD CT 1 .P1 WA O .A 1 co C)) CD 1 O I V al 07 vX al CJ) .P r 1to 1 m Ul W 1 00 N O 1 W 00 O; JP 1 N .A t0 1 W .A N 1 14 N N 'V N N O V LO 4A M 1 Y 1 1 I 1 I 1 ! ! t ! 1 t I 1 1 1 I 1 1 ^ I 1 1 ; I I + I 1 ; 1 I 1 I I r I N I N r l r N I 1 I m ct 1 1 I '9 u. I 1 I ^ ``^ 1 ; I I ^ I 1 ^ I 1 ^ m w I N 1-^ I N Y t r r r 1 W C71 N t tO O) O) I U1 N l r O 1 0 W O I N W 117 I V O 0) 1 0 r N I W N O X I V 1 1 I 1 I w 1 E 1 I. a I N VW O 1 4.0 F-+ W 1 V O Ul 1 to W W I Y N O I cn A .A R 4P .P VN I W Ul r I Y CT ^A ^m 0 1 1 1 1 I t 1 I I 1 1 1 I 1 1 I 1 I 1 1 1 I I I I I 1 1 1 1 1 I I 'I 1 1 X 1 1 I ^^ I 1 I X I I I 1 ! 1 O o\Q O t I I 1 0 O 0 1 0 O O 1 0 O O 1 0 O O 1 0 O O! O O O 1 0 O O i 0 O O ,^ O 0 1 0 1 I 1 I ^ 1 F 1 I I I C I 4? W N I W W N I .A W NI Ul w H I Ul W r l Ul W H 1 m .P r l C) 4P r l Ul W r I O N N) ItO N N I O N N I O CT N 1 N CQ r l C) CT r f 0 Ul r I N CO .P 0 co Y I N t 0 4P CT 1 to -? N W I N r O) 1 W N O) 1 CO Ul Ul 7c V 1 .A co co I V t0 M I O) N .A I (J) 1 1 1 1 I I I I I 1 0 0 0 1 0 O 0 1 0 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 0 1 0 O O C 0 1 0 ^p W r l Ul I Y I Ul W r l P W ^' i CT W r l .A W r rt 1 W 4P N I W W N I w W 1-' Ln 4 1 Ul r. N I N CT V 1 t0 VI U1 I M O) .P 1 Y O Ul 1J rI v Q) W 1 0 Y r 1 U1 tD Ul 4h 1 C) U1 N I .J^ O) WI O r V1 t 0 v N I CO CT .{^ 1 M V O) 1 r W Ol I O N V 1 O LO 1 1 1 1 1 1 1 1 ^ 1 ^ 1 1 1 1 1 1 I I 1 1 1 1 1 1 1 1 ! 1 1 1 1 1 r N I N r r l •A 1 H 1 N I r N I V .1- .C+ I O H O I t)1 W CT IF 1 1"I' 1 .A H H I W H O) I W U) V I ID O .A I H U) O) I W Ul 1 1 1 1 1 1 .^ ro 1 1 1 n w, 1 1 1 1 1 I I 1 I ^ I N N r l r 1 r C 1 O tD 1 0 V V I V CT W 1^ W V t Ul O W I V N V N I fp N P t U> V 00 1 O) In ^I ! I I 1 I 1 I I I 1 1 1 1 1 I 1 1 I 1 I I I I 1 1 t 1 1 1 1 1 1 1 1 1 1 I +-- 1 I 1 I 1 1 1 I I x ^, 1 1 I I 1 1 C) o\o 1 1 I O I O O 0 1 0 O O 1 O O Sc)1 O 0 1 0 O 0 1 0 O 0 1 0 O 0 1 0 O 0 1 0 O O I W W N I W w N I W w Inr 1 W r 1In W W H I 4 A H J Q) W 1-1 1 .A N r r I Ul V I t0 W Ul I CT Y O) r I V CC) w 1 0 Ul H' I Ul tO Vl 'XD 1 Ul ^4 N I N N w .A I Y Ul 1^ I O N I 4P V W I O CT Ul 1 0 to N 1 00 4A 4N O 0) I Y H m I O O) V I O co Ul O 1 CT I 1 1 1 I 1 1 1 I 1 1 t I 1 1 1 I I 1 I I 1 I I 1 1 1 1 I 1 I I t 1 1 1 1 1 I Y H I N r l .A 1 H I N N I I I I 1 1 I 'O d 1 C ro 1 1 1 I 1 1 I ! 1 1 f'1 I I I ^ N' I N H! N I H N ^C 1 IU (T I W N v I tD co 4, 1 r Y O) 1 W O) N 1v 41 .i-+ 1 0 v O 1 CJ7 t0 o, x C.1. 1 .A N H I W O I JP .A tD 1 0 to V I V .P W 1 .A CO V I Ut V W I V r W I 00 N 4 1 Ul O CO I M N 1 1 1 I I I 1 I I 1 1 1 1 1 I 1 1 1 1 1 I 1 1 I 1 I I 1 1 1 t I 1 I 1 1 1 1 1 I 1 I 1 I t 1 I 1 ^ I 1 I 1 1 1 X I-I• I I I 1 1 1 1 1 1 C:) 25-

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I CIl 1 j 1 1 O P-h .n 1 w 't1» 4JP I (^ 1.J j O 1'1' 1 ro w of .r, N 1 to al .r>. N 1 ^n rn .r. N '^ O N N q O U1 113 C^ ^ c,^ V tIt N A vl 14 O (h O w C) 1 q Cn 1 1 ^ CA L" CD I Co w C) Ln O +' 1 1 r-1 tD H H I M M M H I M m M H o to N M) I W N H . Ca to 1 4 f^ m 0 t to •O H W Q N N) Cl N I q q (71 H lD I V c^Dw In to X. 'O+ G co N N v 4*.^ N M N ^ W I -r" W Co co X. I n I .-J 1 cr, I N J 1 to co to Co I ti MI-+ to ~ toI M to M to M tt7 W •P to M 1 •A a- to Ul N 1 vt co H C7 W m J. M •P4 .r+ Ul N 1 U1 to Cn to CO 1 W w W CT 0) ^ Ih I 1 1 l i I c3 ( N i J me 1 l i ) c IJ, I H M H I H 77 W H H O O i)1 I W(^+ Ul W N I M M H H C*1, C^ V to I V•R Cn N Ol v+1 I V w O) M ' 1 1 i I 1 `J. 1-3 N I U1 vl Ul (Jl N p ' x N I M •n,' cD I C7 1 b o\° H H 1.. 1 H H H M %'r to C) to N •.T 1 H H H H 1 H q Ul 1C) I M H C)) UO to to m w V m V H I •F• CT W 0 to m H of to V 1 to TC I i I I I 1 I M i M W N Ul N I H CU .t'a .P M X 11+ (o V N vl cn I W •F• W Ul to -J 1 IJ N I 1 I r 1 I 1 N I U1 O M (.n '^. (D V -4 M I Ul H m a 0) ^ X f ;3 'q 0 .vTlf^" O i I 1 t I i n F^-1• ct M M i rP^l ^^ p N N I Cn W N Cn N MCI 1 X 1 P, n 1 X ^• 1 1 M I C) o\° 1 O I O (:7 C7 C7 C) I C7 C CJ C? q 1 C.1 C., 1 C;) O G? 1 H W FQ W N I N N W W N I IV C•: W N w C) o) a Ul 1 C] to to J'. C.) C of i C ) w to CJ H C W I N 411 t— -J IV I p W .P V Op n Cb co 01 W I I O O O C) CJ I O t:l I . M N W W N 1 t^ N .tom N N 0 M I tt) to ) 7S I rl c^ O I f? O G? O G + 1 W W W I M W X. IV M C N V " 1 -•J UI -U.- to • N U1 UI IV Cn CJ I (:J 01 N W O 1 I 1 I N W w N I V W I H 1 I 1 I 1 1 I W 7v, h'• 1 -1 I ()1 M U1 Crt l0 CO r • Ol W I H IV M •h Ul I L^j. ^I N N W I Ch 41 C•1 -,J Cl) I CO q W W JS C'^ VUl M N N WI r• I 1 Ii I O C^ n q f7 1 0 (D N W W W I r• W -A U) N (D M CCI W 47 N I •/-• 4y tY1 W Ul Ul 1 ttl to CTI. CT M W O I 1, to 1 1 1 1 I 1 N N I I I X { CD i.J1 11 C^ 1 , q 1 °\° C) q CD ) ID O O q C W CO N I IJ OD •A H A X fn O W I H to lL. N O 'a 1 1 C ro 1 ^ 1 I 1 1 I 1 C ^^ 1 f) h•• 1-+ I U1 H .-• U1 C F 1 CA Cn G) 1 rn M CIl OO CD 1 H H N M U1 ID l0 ••! 1 Ul I t V N W I H W I 1 1 I 1 I 1 1 .. I X I H. X. V O) I CD CA N Ul A •v O 1 (DG 1 X I IJ. 1 X 1 C) o\° I O I J7

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Figure 1, Deformation of an Anisotropic Test Piece Q8

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RgjtOD'0M'L'Ty Or t, pAGh is POOR CL 111- 4 1 RA b, — ow r - CL cu to 4--) (D Ei 0 LO Ql W 0 co E-i CN; a) 4+„ Elo rq 'I; a 9 'I

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X / 1 ^ ; i I f f F^ ti r b I I I i b Figure 3. Orientation of Reference Axes „y0

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CL x m a^ rd d N O l U O N cd N N O •r°i H U H N O U a ^, .r-I n^ K U U is U O 4-i rd .r{ N I cd N 4-i O r O .H T Fi z O cd O 4-i F^+ O f~ 4-i O N .ri A C^ N U Cd ^^' II m H N N bD -H P4, rA ,^ 1

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P Q b 4 P b I Fisure 5. 'hest Piece .3o!

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X t.r Utilized by the Finite Elementeo33 r Figure 6. Limit Conditions N N

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Ii^l 1,00 1 1.00 a, 1251 .°ks s ;0.05 10 X210 ^ 30 / ^,% d0 '' 00 1,001 7! °q0 no go 0 n^ 075 OM 1^1 1,50i C 125 p0 J . r + ^4,:,, p0 0 ,y ^^: . ! 1 . 01 10 26 30 °^ 6p^ 60 70 .,,. 00 ti J^^ 0 15 ^J I l! b0 Figure 7, Influence of the Type 1.411 10 20 00 40 00 00 70 00 901! 6025 t a^^r Y,10e? #, t,+pa9J m 7.0015 A 0,901 111Y 1.01 10 20 90 40 50 00 70 00 90 11 1.00 •- , ..r„•-^ ^-a 1„a7e ^ •• ^. tl^O1Q ^. °,+^ =. T,la50 •Tl4 as ,.;f'^v 0.00 LJO15 '•^ Tp04p. 0.n0 I•y 1,00 Oe 1.02 t,+! Y .0 ^ ^,.. , I, p 1 1 J T, n0 50 p s"^ T^^.,+Q.50 1100 ! 10 20 30 40 50 00 70 00 00 0 0199 of Extensometer and of T on Correction Coefficients i 34 1

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r^ m^ a ,! (n) §,_! a% q , 610 i ^ }\ ^. ,\ \ ^® : ea ^ n / 7/ \2^ 01 ^K .\ ^ ..... .. o,^ \. ^\ ! i wn to & | ! ^ ^: O.E. '0i ^ :C9, e. ,,'it (7^) 2, 50 ® a Qo : ° k , 0,90 0 0105 Uo op (b) \ ( . }}! {< ^ ~ Rf .., .^ .. 5 . d( \ / K p^ `'#,9 2 a m . » , ± / * ^ Figure 8, Influence of the Length of the Ieot Piece ^.^ r ^ ^ ^3s

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1.11 0.1 Oo2 C) 2 O 0.1 0.2 I 0,3 0.4 0.5 Approximate Theory Fl.nite Elements 0.5 C -- # 0.3 0.4 *- T Figure 9. Influence of the Length of the Extensometer Measuiament Base .36 L

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w LO z cd Q) IIle a^ cd 0 t^ a^ a 4 Eln w a a^ 4-) r" Q w U (D r-1 4-^ H r-i d.) 6D q-{ w ) n l'J T- O 37

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s! e! i. f1{ 1 I f' ,1 10 r7 I , i f' r `! I" 1 I l ► 0 0 ° N . Figure 11. Test Piece Dimensions (in mm) F r F;.