Mathematical models, for the stress analyses of unidirectional end notch flexure and end notch cantilever specimens using classical beam theory, first, second, and third-order shear deformation beam theories, have been developed to determine the interlaminar fracture toughness of unidirectional composites in mode II. In the present study, appropriate matching conditions, in terms of generalized displacements and stress resultants, have been derived and applied at the crack tip by enforcing the displacement continuity at the crack tip in conjunction with the variational equation. Strain energy release rate has been calculated using compliance approach. The compliance and strain energy release rate obtained from present formulations have been compared with the existing experimental, analytical, and finite element results and found that results from third-order shear deformation beam theory are in close agreement with the existing experimental and finite element results.
Issue Section:
Technical Papers
1.
Williams
, J. G.
, 1988
, “On the Calculation of Energy Release Rates for Cracked Laminates
,” Int. J. Fract.
, 36
(2
), pp. 101
–119
.2.
O’Brien, T. K., 1982, “Characterization of Delamination Onset and Growth in a Composite Laminate,” Damage in Composite Materials, K. L. Reifsnider, ed., American Society for Testing and Materials, ASTM-STP-775, pp. 140–167.
3.
Carlsson, L. A., and Gillespie, Jr., J. W., 1989, “Mode II Interlaminar Fracture of Composites,” Application of Fracture Mechanics to Composite Materials, K. Friedrich, ed., Elsevier, Amsterdam, 6, pp. 113–157.
4.
Sela
, N.
, and Ishai
, O.
, 1989
, “Interlaminar Fracture Toughness and Toughening of Laminated Composite Materials: A Review
,” Composites
, 20
(5
), pp. 423
–435
.5.
Barret
, J. D.
, and Foschi
, R. O.
, 1977
, “Mode II Stress Intensity Factors for Cracked Wood Beams
,” Eng. Fract. Mech.
, 9
(3
), pp. 371
–378
.6.
Russell, A. J., and Street, K. N., 1982, “Factors Affecting the Interlaminar Fracture Energy of Graphite/Epoxy Laminates,” Progress in Science and Engineering of Composites, ICCM-IV, T. Hayashi et al., eds., Japan Society for Composite Materials, Tokyo, 1, pp. 279–286.
7.
Carlsson
, L. A.
, Gillespie
, Jr., J. W.
, and Pipes
, R. B.
, 1986
, “On the Analysis and Design of End Notch Flexure (ENF) for Mode II Testing
,” J. Compos. Mater.
, 20
(6
), pp. 594
–604
.8.
Carlsson, L. A., Gillespie, Jr., J. W., and Whitney, J. M., 1986, “Interlaminar Fracture Mechanics Analysis of the End Notched Flexure Specimen,” Proceedings of the American Society for Composites—First Technical Conference, Technomic Publishing Company, Lancaster, PA, pp. 421–433.
9.
Whitney, J. M., Gillespie, Jr., J. W., and Carlsson, L. A., 1987, “Singularity Approach to the Analysis of the End Notch Flexure Specimen,” Proceedings of the American Society for Composites—Second Technical Conference, Technomic Publishing Company, Lancaster, PA, pp. 391–398.
10.
Whitney, J. M., 1987, “Stress Analysis of the End Notch Flexure Specimen for Mode II Delamination of Composite Materials,” AIAA/ASME/ASCE/AHS 28th Structures, Structural Dynamics and Materials Conference, Part I, ASME, New York, pp. 676–681.
11.
Whitney
, J. M.
, and Sun
, C. T.
, 1973
, “A Higher Order Theory for Extensional Motion of Laminated Composites
,” J. Sound Vib.
, 30
(1
), pp. 85
–97
.12.
Whitney
, J. M.
, 1990
, “Analysis of Interlaminar Mode II Bending Specimens Using a Higher Order Beam Theory
,” J. Reinf. Plast. Compos.
, 9
(6
), pp. 522
–536
.13.
Reissner
, E.
, 1950
, “Variational Theorem in Elasticity
,” J. Math. Phys.
, 29
(1
), pp. 90
–95
.14.
Williams
, J. G.
, 1989
, “The Fracture Mechanics of Delamination Tests
,” J. Strain Anal.
, 24
(4
), pp. 207
–214
.15.
Hashemi
, S.
, Kinloch
, A. J.
, and Williams
, J. G.
, 1990
, “The Analysis of Interlaminar Fracture in Uniaxial Fibre-polymer Composites
,” Proc. R. Soc. London, Ser. A
, 427
(1872
), pp. 173
–199
.16.
Hashemi
, S.
, Kinloch
, A. J.
, and Williams
, J. G.
, 1990
, “Mechanics and Mechanisms of Delamination in a Poly(Ether Sulphone)-Fibre Composite
,” Compos. Sci. Technol.
, 37
(4
), pp. 429
–462
.17.
Wang
, Y.
, and Williams
, J. G.
, 1992
, “Corrections for Mode II Fracture Toughness Specimens of Composite Materials
,” Compos. Sci. Technol.
, 43
(3
), pp. 251
–256
.18.
Chatterjee
, S. N.
, 1991
, “Analysis of Test Specimens for Interlaminar Mode II Fracture Toughness, Part 1: Elastic Laminates
,” J. Compos. Mater.
, 25
(5
), pp. 470
–493
.19.
Zhou
, J.
, and He
, T.
, 1994
, “On the Analysis of the End Notched Flexure Specimen for Measuring Mode II Fracture Toughness of Composite Materials
,” Compos. Sci. Technol.
, 50
(2
), pp. 209
–213
.20.
Corleto
, C. R.
, and Hogan
, H. A.
, 1995
, “Energy Release Rates for the ENF Specimen Using a Beam on an Elastic Foundation
,” J. Compos. Mater.
, 29
(11
), pp. 1420
–1436
.21.
Davidson
, B. D.
, Kru¨ger
, R.
, and Ko¨nig
, M.
, 1995
, “Three Dimensional Analysis and Resulting Design Recommendations for Unidirectional and Multidirectional End Notched Flexure Tests
,” J. Compos. Mater.
, 29
(16
), pp. 2108
–2133
.22.
Ding
, W.
, and Kortschot
, M. T.
, 1999
, “A Simplified Beam Analysis of the End Notched Flexure Mode II Delamination Specimen
,” Compos. Struct.
, 45
(4
), pp. 271
–278
.23.
Pavan Kumar, D. V. T. G., 1999, “Interlaminar Fracture Toughness of Composites—Higher Order Shear Deformation Beam Theories,” Ph.D. thesis, Indian Institute of Science, Bangalore, India.
24.
Salpekar
, S. A.
, Raju
, I. S.
, and O’Brien
, T. K.
, 1988
, “Strain Energy Release Rate Analysis of the End Notch Flexure Specimen Using the Finite Element Method
,” J. Compos. Technol. Res.
, 10
(4
), pp. 133
–139
.25.
Sela
, N.
, Ishai
, O.
, and Banks-Sills
, L.
, 1989
, “The Effect of Adhesive Thickness on Interlaminar Fracture Toughness of Interleaved CFRP Specimens
,” Composites
, 20
(3
), pp. 257
–264
.26.
Gillespie
, Jr., J. W.
, Carlsson
, L. A.
, and Pipes
, R. B.
, 1986
, “Finite Element Analysis of the End Notch Flexure Specimen for Measuring Mode II Fracture Toughness
,” Compos. Sci. Technol.
, 27
(3
), pp. 177
–197
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