Abstract
This paper presents an overview of a fracture-mechanics approach to some of the most frequently encountered matrix-dominated sublaminate cracks in epoxy-based composite laminates. By “sublaminate,” it is meant that the cracks are internal to the laminate, generally invisible macroscopically, but are much larger in size than those microcracks considered in the realm of micromechanics. The origin of sublaminate cracks is assumed to stem from the coalesence of natural material flaws (also microcracks), which occur under a certain favorable laminate stress condition. Thus, the modeling of the mechanisms of sublaminate crack initiation and propagation is essentially mechanistic and probabilistic in nature. Some specific results from several analytical/experimental investigations using graphite-epoxy laminates are presented and discussed in this paper.
References
1.
Tsai
, S. W.
and Hahn
, H. T.
, Introduction to Composite Materials
, Technomics
, Stanford, CT
, 1980
.2.
Starnes
, J. H.
and Rouse
, M.
, “Post-Buckling and Failure Characteristics of Selected Flat Rectangular Graphite-Epoxy Plates Loaded in Compression
,” Proceedings of the AIAA/ASME/ASCE/AHS, 22nd Structures, Structural Dynamics and Materials Conference
, American Society of Mechanical Engineers
, New York
, 1981
.3.
Starnes
, J. H.
and Williams
, J. G.
, “Failure Characteristics of Graphite-Epoxy Structural Components Loaded in Compression
,” NASA-TR-84552, NASA Langley Research Center
, Hampton, VA
, 1982
.4.
Waddoups
, M. E.
, Eisenmann
, J. R.
, and Kaminski
, B. E.
, “Macroscopic Fracture Mechanics of Advanced Composite Materials
,” Journal of Composite Materials
0021-9983, Vol. 5
, 10
1971
, p. 466.5.
Cruse
, T. A.
, “Tensile Strength of Notched Composites
,” Journal of Composite Materials
0021-9983, Vol. 7
, 04
1973
, p. 218.6.
Whitney
, J. M.
and Nuismer
, R. J.
, “Stress Fracture Criteria for Laminated Composites Containing Stress Concentrations
,” Journal of Composite Materials
0021-9983, Vol. 8
, 07
1974
, p. 253.7.
Cooper
, G. A.
and Kelly
, A.
, “Role of the Interface in the Fracture of Fiber-Composite Materials
,” Interfaces in Composites
, STP 452, American Society for Testing and Materials
, Philadelphia
, 1969
, p. 90.8.
Greszezuk
, L. B.
, “Theoretical Studies of the Mechanisms of the Fiber-Matrix Interface in Composites
,” Interfaces in Composites
, STP 452, American Society for Testing and Materials
, Philadelphia
, 1969
, p. 42.9.
Kelly
, A.
, “Interface Effects and the Work of Fracture of a Fibrous Composites
,” Proceedings of the Royal Society
, Vol. A-319
, 1970
, p. 95.10.
Phillips
, D. C.
and Tetelman
, A. S.
, “The Fracture Toughness of Fiber Composites
,” Composites
0010-4361, Vol. 3
, No. 5
, 09
1972
, p. 216.11.
Piggott
, M. R.
, “Theoretical Estimation of Fracture Toughness of Fibrous Composites
,” Journal of Material Science
, Vol. 5
, 1970
, p. 669.12.
Zweben
, C.
and Rosen
, B. W.
, “A Statistical Theory of Material Strength with Application to Composite Materials
,” Journal of Mechanics and Physics of Solids
0022-5096 https://doi.org/10.1016/0022-5096(70)90023-2, Vol. 18
, 1970
, p. 189.13.
Corten
, H. T.
, “Fracture Mechanics of Composites
,” Fracture
, Vol. 7
, H.
Liebowitz
, Ed., Academic Press
, NY
, 1972
, p. 676.14.
Wu
, E. M.
, “Application of Fracture Mechanics to Anisotropic Plates
,” Journal of Applied Mechanics
0021-8936, Vol. 34
, No. 4
, 12
1967
, p. 967.15.
Kanninen
, M. F.
, Rybicki
, E. F.
, and Brinson
, H. F.
, “A Critical Look at Current Applications of Fracture Mechanics to the Failure of Fiber-Reinforced Composites
,” Composites
0010-4361, Vol. 8
, No. 1
, 01
1977
, p. 17.16.
Wang
, A. S. D.
, Crossman
, F. W.
, and Law
, G. E.
, “Interlaminar Failure in Epoxy-Based Composite Laminates
,” Proceedings of the 29th MFPG Symposium on Advance Composites-Design and Applications
, National Bureau of Standards
, Washington, DC
, 1979
, p. 255.17.
Wang
, A. S. D.
and Law
, G. E.
, “An Energy Method for Multiple Transverse Cracks in Graphite-Epoxy Laminates
,” in Modern Developments in Composite Materials and Structures
, J.
Vinson
, Ed., American Society of Mechanical Engineers
, New York
, 1979
, p. 17.18.
Wang
, A. S. D.
and Crossman
, F. W.
, “Initiation and Growth of Transverse Cracks and Edge Delamination in Composite Laminates: Part 1. An Energy Method
,” Journal of Composite Materials
0021-9983, supplementary volume, Vol. 14
, No. 1
, 1980
, p. 71.19.
Crossman
, F. W.
, Warren
, W. T.
, Wang
, A. S. D.
, and Law
, G. E.
, “Initiation and Growth of Transverse Cracks and Edge Delamination in Composite Laminates: Part 2. Experimental Correlation
.” Journal of Composite Materials
0021-9983, supplementary volume, Vol. 14
, No. 1
, 1980
, p. 88.20.
Wang
, A. S. D.
, “Growth Mechanisms of Transverse Cracks and Ply-Delamination in Composite Laminates
,” Proceedings of the ICCM-III
, Vol. 1
, Paris, 1980
, p. 170.21.
Crossman
, F. W.
and Wang
, A. S. D.
, “The Dependence of Transverse Cracks and Delamination on Ply Thickness in Graphite-Epoxy Laminates
,” Damage in Composite Materials
, STP 775, American Society for Testing and Materials
, Philadelphia
, 1982
, pp. 118
-139
.22.
Wang
, A. S. D.
and Crossman
, F. W.
, “Fracture Mechanics of Sublaminate Cracks
,” technical report, Contract F49620-79-C-0206, Air Force Office of Scientific Research
, Washington, DC, 08
1982
.23.
Griffith
, A. A.
, “The Phenomena of Rupture and Flow in Solids
,” Philosophical Transactions of the Royal Society
, Vol. A-221
, London, 1920
, p. 163.24.
Irwin
, G. R.
, “Fracture Dynamics
,” Fracture of Metals
, American Society of Metals
, Cleveland, OH
, 1948
, p. 147.25.
Orowan
, E. O.
, “Fundamentals of Brittle Behavior of Metals
,” Fatigue and Fracture of Metals
, W. M.
Murray
, Ed., Wiley and Sons
, NY
, 1950
, p. 139.26.
Muskhelishvili
, N. I.
, Some Basic Problems From the Mathematical Theory of Elasticity
, Noordhoff
, Holland
, 1953
.27.
Sneddon
, I. N.
, “Integral Transform Methods
,” Methods of Analysis and Solutions of Crack Problems
, Noordhoff
, Holland
, 1973
, p. 315.28.
Lekhnitsky
, S. G.
, Theory of Elasticity of an Anisotropic Elastic Body
, Holden-Day
, San Francisco, CA
, 1963
.29.
Rice
, J. R.
, “A Path Independent Integral and Approximate Analysis of Strain Concentration by Notches and Cracks
,” Journal of Applied Mechanics, Transactions of the American Society of Mechanical Engineers
, Vol. 9
, 06
1968
, p. 379.30.
Bucci
, R. J.
, Paris
, P. C.
, Landis
, J. D.
, and Rice
, J. R.
, “J-Integral Estimation Procedures
,” Fracture Toughness
, Part II, STP 514, American Society for Testing and Materials
, Philadelphia
, 1972
, p. 40.31.
Irwin
, G. R.
, “Fracture
,” Handbuch der Physik
, Vol. 5
, Spinger-Varlag
, Berlin
, 1958
, p. 551.32.
Rybicki
, E. F.
and Kanninen
, M. F.
, “A Finite Element Calculation of Stress Intensity Factors by a Modified Crack-Closure Integral
,” Engineering Fracture Mechanics
0013-7944 https://doi.org/10.1016/0013-7944(77)90013-3, Vol. 9
, 1977
, p. 931.33.
Wang
, A. S. D.
and Crossman
, F. W.
, “Some New Results on Edge Effects in Symmetric Composite Laminates
,” Journal of Composite Materials
0021-9983, Vol. 11
, 01
1977
, p. 92.34.
Raju
, I. S.
and Crews
, J. H.
, “Three Dimensional Analysis of [0/90]s and [90/0]s Laminates with a Central Circular Hole
,” Composites Technology Review
, Vol. 4
, No. 4
, Winter, 1982, p. 116
-124
.35.
Spilker
, R. L.
and Chou
, S. C.
, “Edge Effects in Symmetric Composite Laminates: Importance of Satisfying the Traction Free Edge Condition
,” Journal of Composite Materials
0021-9983, Vol. 14
, 01
1980
, p. 2.36.
Wang
, S. S.
and Choi
, I.
, “Boundary Layer Effects in Composite Laminates
,” Journal of Applied Mechanics
0021-8936, Part 1 and Part 2, Vol. 49
, No. 3
, 09
1982
, p. 541.37.
Isida
, M.
, “Method of Laurant Series Expansion for Internal Crack Problems
,” Methods of Analysis and Solutions of Crack Problems
, G. C.
Sih
, Ed., Noordhoff
, Holland
, 1973
, p. 56.38.
Whitcomb
, J. D.
, Raju
, I. S.
, and Goree
, J. G.
, “Reliability of the Finite Element Method for Calculating Free Edge Stresses in Composite Laminates
,” Computers and Structures
, Vol. 15
, No. 1
, 1982
, p. 23.39.
Cullen
, J. S.
, “Mode-I Delamination of Unidirectional Graphite Epoxy Composite Under Complex Load Histories
,” M.S. thesis, Texas A&M University
, College Station, TX, 1981
.40.
Williams
, D.
, “Mode-I Transverse Cracking in an Epoxy and a Graphite Fiber Reinforced Epoxy
,” M.S. thesis, Texas A&M University
, College Station, TX, 1981
.41.
Wilkins
, D. J.
, “A Comparison of the Delamination and Environmental Resistance of a Graphite-Epoxy and a Graphite-Bismaleimade
,” NAV-GD-0037, Naval Air System Commission
, Washington, DC, 09
1981
.42.
Wilkins
, D. J.
, Eisenmann
, J. R.
, Camin
, R. A.
, Margolis
, W. S.
, and Benson
, R. A.
, “Characterizing Delamination Growth in Graphite-Epoxy
,” Damage in Composite Materials
, STP 775, American Society for Testing and Materials
, Philadelphia
, 1982
, pp. 168
-183
.43.
Vanderkley
, P. S.
, “Mode-I and Mode-II Delamination Fracture Toughness of an Unidirectional Graphite-Epoxy Composite
,” M.S., thesis, Texas A&M University
, College Station, TX, 1981
.44.
Bascom
, W. D.
, Cottington
, R. L.
, and Thomas
, C. O.
, “Fracture Design Criteria for Structural Adhesive Bonding—Promise and Problems
,” Naval Engineering Journal
, Vol. 88
, No. 4
, 08
1976
, p. 73.45.
Wang
, A. S. D.
, Kishore
, N. N.
, and Feng
, W. W.
, “On Mixed-Mode Fracture in Off-Axis Unidirectional Graphite-Epoxy Composites
,” Proceedings of the ICCM-IV
, Vol. 1
. Japan Society of Composite Materials
, Tokyo
, 1982
, p. 599.46.
Bader
, M. G.
, Bailey
, J. E.
, Curtis
, P. T.
, and Parvizi
, A.
, “The Mechanisms of Initiation of Development of Damage in Multi-Axial Fiber-Reinforced Plastics Laminates
,” Mechanical Behavior of Materials
, ICM-3, Vol. 3
, 1979
, p. 227.47.
Aveston
, J.
and Kelly
, A.
, “Theory of Multiple Fracture of Fibrous Composites
,” Journal of Material Science
, Vol. 8
, 1973
, p. 352.48.
Reifsnider
, K. L.
and Masters
, J. L.
, “Investigation of Characteristic Damage States in Composites Laminates
,” ASME Paper No. 78-WA-AERO-4, American Society of Mechanical Engineers
, New York
, 1978
.49.
Juvinall
, R. C.
, Stress, Strain and Strength
, McGraw Hill
, NY
1967
, p. 346.50.
Wang
, A. S. D.
, Chou
, P. C.
, Lei
, C. S.
, and Bucinell
, “Cumulative Damage Model for Advanced Composite Materials
,” final report, Contract F33615-80-C-5039, Air Force Wright Aeronautical Laboratory
, Dayton, OH, 08
1983
.51.
Chou
, P. C.
, Wang
, A. S. D.
, and Miller
, H. R.
, “Cumulative Damage Model for Advanced Composite Materials
,” AFWAL-TR-82-4083, U.S. Air Force Wright Aeronautical Laboratory
, Dayton, OH
, 1982
.52.
Pipes
, R. B.
and Pagano
, N. J.
, “Interlaminar Stresses in Composite Laminates Under Uniform Axial Tension
,” Journal Composite Materials
, Vol. 4
, 10
1970
, p. 538.53.
Bjeletich
, J. G.
, Crossman
, F. W.
, and Warren
, W. J.
, “The Influence of Stacking Sequence on Failure Modes in Quasi-Isotropic Graphite-Epoxy Laminates
,” Failure Modes in Composites—IV
, American Institute of Metallurgical Engineers
, Washington, DC
, 1979
.54.
Rodini
, B. T.
and Eisenmann
, J. R.
, “An Analytical and Experimental Investigation of Edge Delamination in Composite Laminates
,” in Fibrous Composites in Structural Design
, E. M.
Lenoe
, Ed., Pleum Press
, NY
, 1978
, p. 441.55.
Law
, G. E.
, “Fracture Analysis of [+25/90n]s Graphite-Epoxy Composite Laminates
,” Ph.D. thesis, Drexel University
, Philadelphia, 1981
.56.
Wang
, A. S. D.
and Slomiana
, M.
, “Fracture Mechanics of Delamination—Initiation and Growth
,” NADC-TR-79056-60, Naval Air Development Center
, Warminster, PA
, 01
1982
.57.
Crossman
, F. W.
, Warren
, W. J.
, and Wang
, A. S. D.
, “Influence of Ply Thickness on Damage Accumulation and Final Fracture
,” Proceedings of the Symposium on Mechanics of Composite Materials and Structures
, American Society of Mechanical Engineers
, New York, Boston, MA
, 11
1983
, p. 215.58.
Wang
, A. S. D.
, Kishore
, N. N.
, and Li
, C. A.
, “A Three Dimensional Finite Element Analysis of Contoured Interlaminar Cracks
,” NADC-TR-84018-60, Naval Air Development Center
, Warminster, PA
, 10
1983
.
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