COMPOSITE MATERIALS: TESTING AND DESIGN (THIRD CONFERENCE) A conference sponsored by the AMERICAN SOCIETY FOR TESTING AND MATERIALS Williamsburg, Va., 21-22 March 1973 ASTM SPECIAL TECHNICAL PUBLICATION 546 C A Berg, F J McGarry, and S Y Elliott, coordinators List price $39.75 04-546000-33 AMERICAN SOCIETY FOR TESTING AND MATERIALS 1916 Race Street, Philadelphia, Pa 19103 Copyright by ASTM Int'l (all rights reserved); Sun Jan 21:27:58 EST 2016 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions a © by American Society for Testing and Materials 1974 Library of Congress Catalog Card Number: 70-185534 NOTE The Society is not responsible, as a body, for the statements and opinions advanced in this publication Printed in Baltimore, Md June 1974 Copyright by ASTM Int'l (all rights reserved); Sun Jan 21:27:58 EST 2016 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized Foreword The Third Conference on Composite Materials: Testing and Design was held 21-22 March 1973 in Williamsburg, Va Committee D-30 on High Modulus Fibers and Their Composites of the American Society for Testing and Materials sponsored the conference in conjunction with the Metallurgical Society of the American Institute of Mining, Metallurgical, and Petroleum Engineers and the American Society of Mechanical Engineers C A Berg, University of Pittsburgh, F J McGarry, Massachusetts Institute of Technology, and S Y EUiott, Douglas Aircraft Company, served as coordinators Most of the papers presented at the eight sessions are included in the volume which complements the first and second conference publications, ASTMSTP 460 and ASTMSTP 497, Composite Materials: Testing and Design Copyright by ASTM Int'l (all rights reserved); Sun Jan 21:27:58 EST 2016 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized Related ASTM Publications Composite Materials: Testing and Design (Second Conference), STP 497 (1972), $36.50 (04-497000-33) Analysis of the Test Methods for High Modulus Fibers and Composites, STP 521 (1973), $30.75 (04-521000-33) Applications of Composite Materials, STP 524 (1973), $16.75 (04-524000-33) Copyright by ASTM Int'l (all rights reserved); Sun Jan 21:27:58 EST 2016 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authori Contents Introduction Testing Methods Microbuckling of Lamina-Reinforced Composites—Z- B Greszczuk Theoretical Considerations Experimental Studies on Microbuckling of Lamina-Reinforced Composites Conclusions 26 Analysis of the Flexure Test for Laminated Composite Materials—/ M Whitney, C E Browning, and A Mair Analysis Transverse Shear Deformation Experimental Data Discussion Conclusions 30 31 36 38 40 42 Methods for Determining the Elastic and Viscoelastic Response of Composite Materials—Z) F Sims and J C Hatpin Validity of ±45 deg Laminate Test and Rail Shear Test Experimental Results Conclusions 46 48 56 60 Analysis, Testing, and Design of Filament Wound, Carbon-Carbon Burst Tubes-i? C Renter, Jr and T R Guess Analysis Numerical Results and Discussion Conclusions 67 69 75 82 Elastic Torsional Buckling of Thin-Walled Composite Cylinders—Z) E Marlowe, G F Sushinsky, and H B Dexter Analysis Specimens Torsional Tests Results and Discussion Future Work Conclusions 84 86 87 91 93 103 108 Analytical Treatments A Correlation Study of Finite-Element Modeling for Vibrations of Composite Material Panels—£ A Thornton and R R Clary Description of Correlation Study Discussion of Results Concluding Remarks Copyright Downloaded/printed University by by of 111 112 118 128 Probabilistic Concepts in Modeling the Tensile Strength Behavior of Fiber Bundles and Unidirectional Fiber/Matrix Composites—5 L Phoenix 130 Single-Fiber Tensile Strength Model 131 Generalized Fiber Bundle Strength Analysis 136 Probabilistic Tensile Failure Theories for Unidirectional Composites 143 Summary 149 Debonding of Rigid Inclusions in Plane Elastostatics—G P Sendeckyf Basic Equations Partially Bonded Elliptic Inclusion Analysis and Discussion of Results 152 154 155 159 On the Determination of Physical Properties of Composite Materials by a Three-Dimensional Finite-Element Procedure—S / Kang and G M Rentzepis 166 The Finite-Element Method 167 Computation of the Elastic Constants 172 Applications 174 The Unidirectional Fiber Composite 174 The Lamellar Composite 180 The Short-Fiber Composite 180 Discussion 186 Laminate Strength—A Direct Characterization Procedure—£" M Wu and J K Scheublein 188 Basic Procedures for Establishing Laminate Failure Criterion 189 Experimental Results and Discussion 202 Summary and Conclusion 206 Experimental Studies Stress-Rupture Behavior of Strands of an Organic Fiber/Epoxy Matrix— T T Chiao, J E Wells, R L Moore, and M A Hamstad Experimental Results Analysis and Discussion Conclusions 209 210 213 214 223 Effect of Temperature and Strain Rate on the Tensile Properties of Boron-Aluminum and Boron-Epoxy Composites—Z) A Meyn Materials Test Procedures Results Discussion Conclusions 225 226 226 227 235 235 Methods of Fiber and Void Measurement in Graphite/Epoxy Composites—£" alley, D Roylance, and N Schneider 237 Materials 238 Copyright Downloaded/printed University by by of Experimental Methods Discussion of Results Conclusions 239 244 248 Evaluation of Experimental Methods for Determining Dynamic Stiffness and Damping of Composite Materials—C W Bert and R R Clary 250 Experimental Techniques 251 Free Vibration 252 Pulse Propagation 254 Forced Vibration Response 257 Application to Composite-Material Structures 260 Conclusions 263 Environmental Effects Effect of Salt Water and High-Temperature Exposure on Boron-Aluminum Composites—// E Dardi and K G Kreider 269 Salt Exposure 271 High-Temperature Exposure 275 Conclusions 280 Effects of Moisture on the Properties of High-Performance Structural Resins and Composites—C E Browning and J T Hartness 284 Materials and Experimental Procedures 285 Results and Discussion 288 Conclusions 302 Materials Parameters that Govern the Erosion Behavior of Polymeric Composites in Subsonic Rain Environments—G F Schmitt, Jr Apparatus Description Polymeric Composites Erosion Behavior Discussion and Conclusions 303 304 306 322 Lightning Protection for Composites—// T Clark 324 Evaluation of Candidate Coatings 325 Evaluation of Coatings on Boron/Epoxy Substrates 328 Evaluation of Coating Schemes on an F-4 Rudder 330 Evaluation of Coatings on a Simulated Boron/Epoxy Empennage Structure 330 Conclusions 339 Fatigue and Fracture Behavior Torsional Fatigue Behavior of Unidirectional Resin Matrix Composites— R C Novak 345 Experimental Procedure 346 Results and Discussion 349 Conclusions 358 vii Copyright by ASTM Int'l (all rights reserved); Sun Jan 21:27:58 EST 2016 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized Geometric and Loading Effects on Strength of Composite Plates with Cutouts-iJ E Rowlands, I M Daniel, and J B Whiteside 361 Orthotropic Stress Analysis 362 Laminates 363 Geometric and Loading Effects 364 Summary and Conclusions 373 Crack-Tip Deformation Measurements Accompanying Fracture in Fibrous and Laminar Composites—/ H Underwood Procedures Discussion of Results Summary 376 377 380 391 Uniaxial, Biaxial, and Fatigue Properties of Polyester Fiber Glass—L H Irwin, R A Dunlap, and P V Compton Materials Specimen Preparation for Test Laboratory Testing Data Analysis and Test Results Discussion of Results Conclusions 395 396 397 399 400 403 407 Interlaminar Shear Fatigue Characteristics of Fiber-Reinforced Composite }A2Atx\a\s—R Byron Pipes 419 Interlaminar Shear Fatigue Results 423 Fiber Tension and Interlaminar Shear Fatigue 427 Conclusions 430 Wear Properties Mechanical and Physical Properties of Advanced Composites—PV T Freeman and G C Kuebeler 435 Mechanical Properties 436 Physical Properties 446 Thermal Properties 448 Discontinuous Fiber Composites 450 Cost Considerations 451 Applications 454 Conclusions 454 Evaluation of Graphite Fiber Reinforced Plastic Composites for Use in Unlubricated Sliding Bearings—7? D Brown and W R Blackstone 457 Test Equipment 459 Bearing Specimens 460 Test Results 461 Discussion 468 Conclusions 474 Wear of Glass Fiber Reinforced Composite Material—^ L Ward 477 Experimental Procedure 478 Experimental Results 480 Discussion 492 viii Copyright by ASTM Int'l (all rights reserved); Sun Jan 21:27:58 EST 2016 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized Metallic Composites Effect of Filament-Matrix Interdiffusion on the Fatigue Resistance of Boron-Aluminum Composites—/ R Hancock and G G Shaw 497 Materials 498 Experimental 498 Results 500 Discussion 504 Conclusions 505 The Notched Tensile Behavior of Metal Matrix Composites—A^ M Prewo 507 Experimental 508 Results and Discussion 509 Conclusions 520 Reinforcement of Metals with Advanced Filamentary Composites—C T Herakovich, J G Davis, and H B Dexter 523 Applications of Composite Reinforced Metals 524 Tensile Behavior of Boron/Epoxy Reinforced Metals 528 Concluding Remarks 541 Comparison of the Mechanical Behavior of Filamentary Reinforced Aluminum and Titanium Alloys—/ / Toth 542 Experimental Procedures 544 Results and Discussion 546 Summary and Conclusions 558 Plastic Deformation Processing and Compressive Failure Mechanism in Aluminum Composite Materials—il/ Chang and E Scala 561 Analytical Studies 563 Analytical Models and Calculated Results 564 Comparison with Experiments 571 Conclusions 575 Aircraft Applications Tolerance of Advanced Composites to Ballistic Damage—£" F Olster and P A Roy 583 Materials 584 Test Procedure 584 ' Test Results 587 Analytical Investigation 593 Conclusions 603 Analysis of Filament-Reinforced Spherical Pressure Vessels—F P Gerstle, Jr Introduction and Material Modeling Governing Equations Estimation of the Reinforcing Laminate Stiffnesses and Strengths Solution of Equations 604 605 607 608 613 ix Copyright by ASTM Int'l (all rights reserved); Sun Jan 21:27:58 EST 2016 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized 660 COMPOSITE MATERIALS (THIRD CONFERENCE) FIG 8b-Closeup showing damage resultingfront2-lb steel ball dropped from ft the centerline The resultant damage was a small 0.080 in deep indentation over an area of 3/4 in diameter Radiographic and ultrasonic tests indicate that a debond occurred over an approximate area in, in diameter with no breakage of fibers Following the accidental damage test the tube was subjected to a torque of 31 500 Ib'in No signs of damage (or audible sounds) were evident Holding a reduced load of 10 000 lb*in., the tube was impacted with a fully tumbled 30-caliber AP round at 1671 fps No load "drop off" was observed The load was then removed As shown in Fig 9, the entrance and exit damage is typical of an all-metal construction, and is limited to approximately 33 percent of the circumference and \% in along the length Each layer of metal petaled individually, with the boron either adhering to metal or completely detaching itself in a random manner Tube No was finally tested to failure, where at 20 000 Ib'in the metal tore at an angle of approximately 80 deg from the centerline This failure is shown in Fig 10 The No tube, as shown in Table 1, was subjected to similar testing A ballistic test using a 30-caliber ball round at muzzle velocity resulted in a relative small area of damage, as shown in Fig 11 A ball drop test resulted in similar damage to that shown for tube No Conclusions The strength to weight ratio of the hybrid construction compares favorably with all-aluminum and all-composite designs Although the test data are limited, the retention of approximately 2/3 the ultimate strength is, to say the least, very encouraging In the accidental drop test, minimal damage occurred, and in the Copyright by ASTM Int'l (all rights reserved); Sun Jan 21:27:58 EST 2016 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized FIGGE ETAL ON HELICOPTER DRIVE SHAFTS 661 FIG 9a-Entry damage of the hybrid torque tube FIG 9b-Exit damage of the hybrid torque tube FIG 9c—Damage resulting from ballistic perforation Copyright by ASTM Int'l (all rights reserved); Sun Jan 21:27:58 EST 2016 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized 662 COMPOSITE MATERIALS (THIRD CONFERENCE) FIG lO-Final failure of the ballistically damaged hybrid torque tube FIG il-View looking down axis of tube showing damage incurred when perforated by a 30-caliber ball round ballistic test a metallike failure was evident The hybrid concept appears to offer significant resistance to impact; however, further tests are required on thinner sections In view of other system advantages, such as conventional metal-tometal attachments and least volume of high-cost composite, the system appears very attractive Copyright by ASTM Int'l (all rights reserved); Sun Jan 21:27:58 EST 2016 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized / Tirosh ' and C A Berg ^ Experimental Stress Intensity Factor Measurements in Orthotropic Composites REFERENCE: Tirosh, J and Berg, C A., "Experimental Stress Intensity Factor Measurements in Orthotropic Composites," Composite Materials: Testing and Design (Third Conference), ASTM STP 546, American Society for Testing and Materials, 1974, pp 663-673 ABSTRACT: A new experimental technique is presented for studying the toughness of anisotropic plane bodies The technique is based upon the Path Independent Integral concept (Rice, 1968) where a strain energy distribution is line-integrated (via a string of strain gages) along a convenient path which yields the singular behavior of the cracked body The use of this technique is demonstrated for an isotropic (aluminum) plate and an orthotropic (fiber glass/epoxy) composite with favorable agreement with the analytical and numerical (finite elements) counterpart solutions KEY WORDS: composite materials, stress intensity, toughness, calibration, anisotropy, orthotropism, finite elements, strain energy methods, fiber glass reinforced plastics, strain gages In the engineering application of linear fracture mechanics to the prediction of strength and life of cracked structures, a knowledge of the crack tip stress intensity factor is essential This information along with the fracture toughness of the structural material (that is, the critical stress intensity factor) are prerequisite to such prediction To avoid, in practice, a hazardous operation with a structure by excessive crack growth, local failure, etc., the calculated stress intensity factor should not exceed the toughness value by a safe margin This concept is now widely used by designers and amplified by a large volume of publications Presently available collections of stress intensity factors (for example, Paris and Sih[i]^) are confined to simple specified geometries and to ' Faculty of Mechanical Engineering, Technion-lsrael Institute of Technology, Haifa, Israel * Department of Mechanical Engineering, University of Pittsburgh, Pittsburgh, Pa ^ The itaUc numbers in brackets refer to the list of references appended to this paper 663 Copyright 1974 b y A S I M International Copyright by Downloaded/printed University of ASTM by Washington Int'l www.astm.org (all (University rights of reserved); Washington) Sun pursuant Jan to Licen 664 COMPOSITE MATERIALS (THIRD CONFERENCE) (mostly) traction boundary conditions rather than the more common displacement boundary conditions which are encountered in standard laboratory tests Few solutions of stress intensity factors in non-isotropic bodies are also offered in the literature [i,) (1) where F is an arbitrarily preselected curve which surrounds the notch tip shown in Fig The path P starts from the lower flank of the crack and proceeds counter-clockwise to the upper flank, as shown in Fig CRACK FIG 1-/4 path integral r around the crack tip and a path integral r* along the contour, having identical J values Copyright by ASTM Int'l (all rights reserved); Sun Jan 21:27:58 EST 2016 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized TIROSH AND BERG ON ORTHOTROPIC COMPOSITES 665 Consider a cracked orthotropic plate with a cartesian coordinate system in the principal orthotropic directions, namely with " " as:'c-axis and " " asj-axis The stress-strain relation has the form: ail fli2 fl2 ^2 _0 0 Ox Oy ^6 (2) Oxy where U2J_ Hi 1^2 ^1 £,2 Ml2 and El and £"2 are the tension moduli, ju the shear modulus, and Ut Poisson's ratio For a body such as this one (cracked along the negative x-axis) Griffith's strain-energy release rate function, G, was presented by Sih and Liebowitz[6] for the three distinct modes of separation; opening, in-plane sliding, and out of plane sliding modes They obtained for plane stress V2 G, = (3a) s/2E Kil_ (3b) G2 = Eiy/2 Km' (3c) G , =• 2(}Xi3H23f' where K\, K\i, and Km are the conventional stress-intensity factors associated with these three basic modes The fundamental physical equivalence between the functional defined by the " / integral" and the overall strain-energy release rate was proved by Rice [5] to yield / = ( G i +G2 +G3) (3d) The sum of the stress-intensity factors lend themselves conveniently to direct evaluation via the / value rather than via the strain energy release rate Summing Copyright by ASTM Int'l (all rights reserved); Sun Jan 21:27:58 EST 2016 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized 666 COMPOSITE MATERIALS (THIRD CONFERENCE) Eqs 3fl, 3b, and 3c, the final formula of J, in terms of the K's and the elastic parameters, is: For the isotropic case [£"1 = ^2 = 2IJL(1 + I*), MI = Mi - M2 ] Eq reduces to: J=(Ki^+Ku^)lE+KniHi+i>)IE (5) which is the well-known energy release rate formula in the isotropic case [7,5] For cases of plane deformation Km vanishes For these cases, rearranging Eq 4, the expressions/i(£'i £'2)''^^//Tl^ for the opening mode and/2^'i/A'ii^ for the sliding mode, may be expressed as material constants: -Kr ^'-\rT-\ ^'^ where, for abbreviation a = (E,/E,)y^ and ) P= (7) (EJ(2(li2)''^l2)J Numerical and Experimental Evaluations In this section the Mode I stress intensity factor Ki is determined for the prenotched orthotropic specimen of Fig subjected to uniform vertical displacement along its top and bottom horizontal edges The orthotropic axes of the material are assumed to lie in the vertical and horizontal directions Thus Ki will be the only nonvanishing stress-intensity factor to be found at the notch tip In view of the path-independence of the / integral, a counter-clockwise path may be taken so as to follow the contour of the specimen from the lower to the upper flank of the notch as shown by the dashed line in Fig By choosing this particular line of integration the only nonvanishing contribution of / for a uniform grip displacement is that of the energy distribution along the free vertical edges of the specimen The resulting integral is: '=2[ ( W(b- c,y)dy + f W{-c,y)dy] 0-' hJ (notationin Fig 2) (8) Copyright by ASTM Int'l (all rights reserved); Sun Jan 21:27:58 EST 2016 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized TIROSH AND BERG ON ORTHOTROPIC COMPOSITES 667 In a case of nonuniform grip displacement acting on the edges of the specimen as shown in Fig 2, the following additional term must be added to the right side of Eq8: Ax b-c -dx (9) The elastic stress and strain distributions^ were determined numerically using a conventional finite-element method such as that referred to by Marcal and King [7] The procedure is explained in some detail in Refs and The results were used for the energy-density contour integration of Eq Denoting by Aj, the length of the ith element along the contour then the line integral is lumped according to: (10) and the overall value o f / i s determined by summation TAU(x,h) Ittta^ t ,t,t,t,t AW(b-c,yi) —-c - \ CRACK b-3C FTTTTTTTTT T FIG 2~Energy distribution (.schematic) along the path shown in Fig in case of uniform prescribed traction The rectangular net is the finite elements used for the numerical calculation of the stress and strain throughout the body * On the assumption that small-scale plasticity near the crack has a negligible effect on the elastic solution in more remote zones Copyright by ASTM Int'l (all rights reserved); Sun Jan 21:27:58 EST 2016 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized 668 COMPOSITE MATERIALS (THIRD CONFERENCE) The strain distribution along the contour was experimentally measured with a string of strain gages mounted close to the free edge of the specimen as shown in Figs 3a and 3b Since the material on this path undergoes uniaxial tension, the energy density is calculated in a straightforward manner by using the measured values of the strain and the elastic modulus [replacing aiyi) in Eq 10 by its equivalent E'eiyi)] > so that AJi=-E€y^(yi)Ayi (10a) The total value of / is obtained as the area under the curve of the square of the measured strain along each free edge, on both sides of the specimen, as indicated by Eq IOH and illustrated in Fig Evaluation of the Method In order to evaluate the proposed method for determination of the stress intensity factor, two examples were considered For the first case a sp'ecimen of isotropic material was considered for which analytical results are available In the second case a specimen of an orthotropic material, in which the crack is aligned with the axes of orthotropy, was considered For this case no solution for Ki FIG 3a-The arrangement of the strain gages along the path of integration Copyright by ASTM Int'l (all rights reserved); Sun Jan 21:27:58 EST 2016 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized TIROSH AND BERG ON ORTHOTROPIC COMPOSITES 669 (*) FIG ib-Prepared specimens of Al 7075-T6 (a) and of fiber gkss/epoxy (b) for "J integral" evaluation other than the numerical scheme[9] used here is available An orthotropic specimen of fiber glass reinforced epoxy was used in experiments to determine Ki via the methods discussed here Isotropic Case Consider a singly notched isotropic specimen with £'=10X 10*psi and 1^= 1/3, under uniform traction T= 1000 psi, and crack length C= in The numerical solution [9] yields / = 0.73[psi-in.] (11) Considering this isotropic case as a limit of the more general orthotropic expression of the / integral (Eq 4), one obtains from (7) that a = 1, and |3 = The corresponding normalized / integral is Jy/E^W^/Ki^ = Accordingly, the stress intensity factor is identical to Eq which is Ki = {JEf^ = 2.75 ksiVlrT (11a) Copyright by ASTM Int'l (all rights reserved); Sun Jan 21:27:58 EST 2016 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized 670 COMPOSITE MATERIALS (THIRD CONFERENCE) z Grip D / D X / / / D D ; I \ o I A* I 8 Al 7075-T6 Fiber glass /epoxy ^ \ \ \ \ A \ Grip I 10 60 70 Longitudinal strain (squared) t^ 20 30 40 50 [lO'*] FIG \-Experimental strain measurement (on both faces of the cracked sheets) in Al 7075-T6 sheet and fiber glass/epoxy sheet in uniform grip displacement under the same nominal load P The area between the best-fitted line and the specimen represents the energy line integral along this edge For further comparison, the stress-intensity factor is obtained from the analytical solution given by Paris and Sih[i]: Ki = -yTimf"- (12) where is a tabulated geometrical correction factor For the present case = 1.73, ( [ i ] , p.44),hence ii:i=2.95-ksiVm (13) For plane strain conditions, using the / value from Eq 11 one gets Ki = [JElil - v^)] '/^ = 2.92-ksix^ It is seen that all three results with traction boundary conditions are in good agreement (error percent) Copyright by ASTM Int'l (all rights reserved); Sun Jan 21:27:58 EST 2016 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized TIROSH AND BERG ON ORTHOTROPIC COMPOSITES 671 Tests with uniform grip displacement were carried out with aluminum sheet (Al 7075-T6) Typical strain distributions along the unnotched free edge are presented in Fig It has been repeated for several load levels to substantiate the linear nature of K with respect to load As mentioned, the / value has been calculated from the area under the curve of measured strain values (gages were mounted on both sides of the specimen to check whether bending is involved in the test) The only known analytical counterpart solution is due to Bowie and Neal[iO] Although it is based on imposing uniform displacement boundary conditions ("constrained edges") as encountered in the laboratory test, it has been presented in terms of the resulting normal load which is usually recorded in most tensile testing machines Comparisons between experimental and analytical results are presented in Fig Orthotropic Case Consider an orthotropic specimen (unidirectional glass fiber/epoxy composite) with the following elastic properties: £"2 (along the fibers) El (transverse the fibers) Gi2 i'i2(>i'2i) = 4.75 X 10* psi =1.38 X 10* psi = 0.375 X 10* psi =0.32 - — I — — I — I — I — I — I — I — I — — I — — A Experimental o Experimental Fiber glass/epoxy Theoretical AL7075-T6 (Bowie and Neol) Numerical (finite elements with J integral) T-s/c Nominal Traction times the square root ksi v^n of the crack length FIG 5—Uniform grip displacement test Experimental results versus (a) analyticalisotropic sheet {Al 7075-T6), (b) numerical-orthotropic sheet (fiber glass/epoxy) Copyright by ASTM Int'l (all rights reserved); Sun Jan 21:27:58 EST 2016 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized 672 COMPOSITE MATERIALS (THIRD CONFERENCE) The / integral values for various grip displacement were determined by the finite-element numerical technique, and the associated nominal load was calculated A uniform mesh, as shown in Fig 2, was utilized The experimental procedure was the same as for the isotropic case The notch was cut perpendicular to the direction of the fibers A minor change is associated with Eq lOfl, where the appropriate value of Young's modulus Ei or £"2 is inserted according to the direction which undergoes extension in the test In the present tests E2 was used in Eq lOa One set of results is shovm in Fig The values of Ki which are evaluated this way agree favorably with the numerical results given in Fig Conclusions The suggested experimental procedure offers a method for determining stress intensity factors in isotropic as well as orthotropic bodies It consists of evaluating the / integral via a string of strain measurements along an appropriate path One test in which the strains are measured is sufficient for J evaluation and determination of the associated K factor This is in contrast to the usual compliance calibration method which requires a series of tests, with different incremental crack lengths in order to obtain a K value In addition, crack extension in fibrous composite is difficult to detect and to control, so that the simpUcity of the suggested technique is attractive The main drawbacks of the suggested method are (a) the relatively expensive and time-consuming preparation procedure, and (b) the nonsimple application to cases other than uniform grip displacement The latter limitation is not inherent to the method, but due to the technical difficulties of measuring the term (9) in the / integral In the absence, to date, of means for analytical determination of the stress intensity factors for an anisotropic specimen,^ the reliability of the proposed procedure is difficult to assess All that can be said at present is that the success obtained with isotropic specimens encourages one to apply the method to orthotropic specimens as well Acknowledgments This work was initiated at Massachusetts Institute of Technology, Department of Mechanical Engineering, under a contract with Celanese Research Company (New Jersey) Extension of the work was carried out at the Technion—Israel Institute of Technology, with the financial support of the Research and Development Foundation, Ltd., Contract No 030-213 ' An exception is given in a recent work by Bowie and Freese[i7] Their numerical solution is limited, however, to traction boundary conditions Copyright by ASTM Int'l (all rights reserved); Sun Jan 21:27:58 EST 2016 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized TIROSH AND BERG ON ORTHOTROPIC COMPOSITES 673 References [1] Paris, P C and Sih, G C, "Stress Analysis of Craclcs," Fracture Toughness Testing and Its Applications, ASTM STP 381, American Society for Testing and Materials, 1965, pp 43-51 [2] Brown, W F., Jr., and Strawley, J E "Plain Strain Crack Toughness Testing," ASTM STP 410, American Society for Testing and Materials, 1966 [i] Lubahn, J D., "Experimental Determination of Energy Release Rate, Proceedings, American Society for Testing and Materials, Vol 59,1959, pp 885-890 [4\ Bueckner, H F., "Propagation of Cracks and Energy of Elastic Deformation, Transactions, American Society of Mechanical Engineers, Vol 80,1958, pp 1225-1232 [5] Rice, J R., "A Path Independent Integral and the Approximate Analysis of Strain Concentration by Notches and Cracks," Journal of Applied Mechanics, Vol 35, 1968, pp 379-386 [6] Sih, G C and Liebowitz, H., "Mathematical Theories of Brittle Fracture," Ch in Fracture, Vol 11, H Liebowtiz, ed Academic Press, 1969, pp 67-190 [7] Marcal, P V and King, I P., "Elastic-Plastic Analysis for 2-D Stress System by the Finite Element Method," International Journal of Mechanical Sciences, Vol 4,1967, pp 143-155 [8] Chan, S K., Tuab, I S., and Wilson, W K., "On the Finite Element Method in Linear Fracture Mechamcs," Engineering Fracture Mechanics, Vol 2, 1970, pp 1-17 [9] Tirosh, J., Carson, J W., and Berg, C A., "Stress Intensity Factors by the Finite Element tJLethoA," Israel Journal of Technology, Vol 10,1972, pp 265-270 [10] Bowie, O L and Neal, D M., "Stress Intensity Factors for Single Edge Cracks in Rectangular Sheet with Constrained Ends," technical report, Army Materials Research Agency, TR-65-20,1965 [11] Bowie, O L and Freese, C E., "Central Crack in Plane Orthotropic Rectangular Sliest," International Journal of Fracture Mechanics, 1972, pp 49-58 Copyright by ASTM Int'l (all rights reserved); Sun Jan 21:27:58 EST 2016 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized