A review and assessment of the interlaminar delamination problem com mon to layered composite materials is presented. The work covers calcula tion of interlaminar stresses from a homogeneous and microstructural material viewpoint as well as background information on the singularity problem. The observation of edge delamination and experimental efforts are discussed together with recent fracture mechanics studies. The conclu sions provides an assessment of the problem and suggestions for future investigation.
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References
1.
Tsuyoshi Hayashi , "Analytical Study of Interlaminar Shear Stresses in a Laminated Composite Plate,"Trans. Japan Society for Aeronautical Engineering and Space Sciences, Vol. 10 (1967), No. 17, p. 43.
2.
Tsuyoshi Hayashi and S. Sando, "Interlaminar Shear Stress Distribution in a Filament Wound Plate,"Proc. of International Symposium on Space Technology and Science, 8th, Tokyo, Japan, 25-30 Aug., 1969, pp. 291-302.
3.
A.H. Puppo and H.A. Evensen, "Interlaminar Shear in Laminated Composites Under Generalized Plane Stress,"J. Composite Materials, Vol. 4 (1970), pp. 204-220.
4.
Donald W.Oplinger, "Edge Effects in Angle Ply Composites," Report AMMRC TR 71-62, Army Materials and Mechanics Research Center, Watertown, Massachusetts, Dec. 1971.
5.
R. Byron Pipes and N.J. Pagano, "Interlaminar Stresses in Composite Laminates Under Uniform Axial Extension,"J. Composite Materials , Vol. 4 ( 1970), pp. 538-548.
6.
R. Byron Pipes, "Solution of Certain Problems in the Theory of Elasticity for Laminated Anisotropic Sytems," Ph.D. Dissertation, University of Texas at Arlington , 1972;
7.
see also "Interlaminar Stresses in Composite Materials," Report AFML-TR-72-18, Air Force Materials Laboratory, Wright-Patterson Air Force Base , Ohio, May 1972.
8.
N.J. Pagano and R. Byron Pipes, "The Influence of Stacking Sequence on Laminate Strength,"J. Composite Materials , Vol. 5 (1971), pp. 50-57.
9.
R.B. Pipes, B.E. Kaminski and N.J. Pagano, "Influence of the Free Edge upon the Strength of Angle-Ply Laminates,"Special Technical Publication 521, American Society for Testing and Materials, Philadelphia , 1973.
10.
N.J. Pagano , "On the Calculation of Interlaminar Normal Stress in Composite Laminate,"J. Composite Materials , Vol. 8 (1974), pp. 65-82.
11.
R.B. Pipes and N.J. Pagano, "Interlaminar Stresses in Composite Laminates - An Approximate Elasticity Solution,"J. Applied Mechanics , Vol. 41 (1974), pp. 668-672.
12.
Gary D. Renieri and Carl T.Herakovich, "Nonlinear Analysis of Laminated Fibrous Composites," Report VPI-E-76-10, Virginia Polytechnic Institute and State University, Blacksburg, Virginia , 1976.
13.
A.S.D. Wang and Frank W. Crossman , "Some New Results on Edge Effect in Symmetric Composite Laminates,"J. Composite Materials, Vol. 11 (1977), pp. 92-106.
14.
C.T. Herakovich, A. Nagarkar and D.A. O'Brien, "Failure Analysis of Composite Laminates with Free Edges," in Modern Developments in Composite Materials and Structures , J. R. Vinson, ed., The American Society of Mechanical Engineers (ASME), N.Y., 1979, pp. 53-66; also presented at the ASME Winter Annual Meeting, New York, 1979.
15.
N.J. Pagano , "Stress Fields in Composite Laminates,"Inter. J. Solids and Structures, Vol. 14 ( 1978), pp. 385-400.
16.
N.J. Pagano , "Free Edge Stress Fields in Composite Laminates,"Inter. J. Solids and Structures , Vol. 14 (1978), pp. 401-406.
17.
E.F. Rybicki, "Approximate Three-dimensional Stress Solutions for Some Laminated Plate Problems Using a Higher Order Equilibrium Finite Element Model, Part I. Preliminary Investigations," Report AFML-TR-70-201Air Force Materials Laboratory, Wright-Patterson Air Force Base, Ohio, 1970.
18.
E.F. Rybicki , "Approximate Three-Dimensional Solutions for Symmetric Laminates Under Inplane Loading,"J. Composite Materials, Vol. 5 (1971 ), pp. 354-360.
19.
S.S. Wang, Ph.D. Thesis, Hayden Memorial Library, Massachusetts Institute of Technology, Cambridge, Massachusetts , 1974.
20.
E.L. Stanton , "A Three-Dimensional Parametric Cubic Discrete Element Program for the Analysis of Composite Structures," Report MDC G5716 , McDonnell Douglas Astronautics Company-West, Huntington Beach, California, Jan. 1975.
21.
E.L. Stanton , L.M. Crain and T.F. Neu, "A Parametric Cubic Modelling System for General Solids of Composite Material," InterJ. Numerical Methods in Engineering, Vol. 11 (1977), pp. 653-670.
22.
Thomas F. Neu , "Finite Element Analysis of Edge Effects in Angle-ply Composite Laminates," NTIS publication AD-777 654, National Technical Information Service, Springfield, Virginia, 1974.
23.
S. Tang, "A Boundary Layer Theory - Part I: Laminated Composites in Plane Stress,"J. Composite Materials, Vol. 9 (1975), pp. 33-41.
24.
S. Tang and A. Levy, "A Boundary Layer Theory — Part II: Extension of Laminated Finite Strip,"J. Composite Materials, Vol. 9 (1975), pp. 42-50.
25.
Peter W. Hsu and Carl T.Herakovich, "Interlaminar Stresses in Composite Laminates - A Perturbation Analysis," Report VPI-E-76-1, Virginia Polytechnic and State University, Blacksburg, Virginia, 1976.
26.
P.W. Hsu and C.T. Herakovich , "Edge Effects in Angle-Ply Composite Laminates,"J. Composite Materials, Vol. 11 (1977), pp. 422-428.
27.
A.S.D. Wang , and Frank W.Crossman, "Calculation of Edge Stresses in Multi-Layer Laminates by Sub-Structuring,"J. Composite Materials, Vol. 12 ( 1978), pp. 76-83.
28.
James T. S. Wang and J.N. Dickson, "Interlaminar Stresses in Symmetric Composite Laminates,"J. Composite Materials , Vol. 12 (1978), pp. 390-402.
29.
Nicholas J. Salamon, "A Finite-difference Program for Stresses in Anisotropic, Layered Plates in Bending," NASA TN D-8059, National Aeroanutics and Space Administration, 1975.
30.
Nicholas J. Salamon, "Interlaminar Stresses in a Layered Composite Laminate in Bending,"Fibre Science and Technology, Vol. 11 ( 1978), pp. 305-317.
31.
Nicholas J. Salamon , "The Stress Distribution in Sandwich Beams in Uniform Bending,"presented at the American Society for Testing and Materials Symposium on Test Methods and Design Allowables for Fibrous Composites, Dearborn, Michigan, October, 1979.
32.
Sam Tang, "Interlaminar Stresses of Uniformly Loaded Rectangular Composite Plates,"J. Composite Materials, Vol. 10 (1976), pp. 69-78.
33.
J.R. Dana and R.M. Barker, "Three-Dimensional Analysis for the Stress Distribution Near Circular Holes in Laminated Composites," Report VPI-E-74-18, Virginia Polytechnic Institute and State University, Blacksburg, Virginia, 1974.
34.
Edmund F. Rybicki and David W. Schmuser, "Effect of Stacking Sequence and Lay-up Angle on Free Edge Stresses Around a Hole in a Laminated Plate Under Tension,"J. Composite Materials , Vol. 12(1978), pp. 300-313.
35.
Richard M.Barker, JonR. Dana and Charles W. Pryor, Jr. , "Three-Dimensional Analysis of Stress Concentration Near Holes in Laminated Composites," Report VPI-E-72-27, Virginia Polytechnic Institute and State University, Blacksburg, Virginia, 1972.
36.
Milton S. Hess , "The End Problem for a Laminated Elastic Strip - I. The General Solution,"J. Composite Materials , Vol. 3 (1969), pp. 262-280.
37.
Milton S. Hess , "The End Problem for a Laminated Elastic Strip - II. Differential Expansion Stresses,"J. Composite Materials, Vol. 3 (1969), pp. 630-641.
38.
Akhilesh C. Agarwal and Mark W. Huggins, "Differential Expansion in Elastic Laminates,"ASCE - J. of the Structural Division , Vol. 99 ( 1973), ST4, pp. 655-663.
39.
P.B. Grimado , "Interlaminar Thermoelastic Stresses in Layered Beams,"J. Thermal Stresses, Vol. 1 (1978), pp. 75-86.
40.
Ori Ishai, Dan Peretz and Naftali Galili, "Mechanical Behavior of Multimaterial Composite Systems," Report AD-A013 063National Technical Information Service, Springfield, Virginia, 1975.
41.
Ori Ishai, Dan Peretz and Shlomit Gali, "Mechanical Behavior of Multimaterial Composite Systems. Interlaminar Behavior." Report AD-A032 011, National Technical Information Service , Springfield, Virginia, 1976.
42.
David B. Bogy , "Edge-Bonded Dissimilar Orthogonal Elastic Wedges Under Normal and Shear Loading,"J. Applied Mechanics, Vol. 35 ( 1968), pp. 460-466.
43.
D.B. Bogy, "On the Problem of Edge-Bonded Elastic Quarter-Planes Loaded at the Boundary,"Inter. J. Solids and Structures , Vol. 6 (1970), pp. 1287-1313.
44.
J. Dundurs , "Edge-Bonded Dissimilar Orthogonal Elastic Wedges Under Normal and Shear Loading - Discussion,"J. Applied Mechanics, Vol. 36 ( 1969), pp. 650-652.
45.
D.B. Bogy, "Two Edge-Bonded Elastic Wedges of Different Materials and Wedge Angles Under Surface Tractions,"J. Applied Mechanics , Vol. 38 (1971), pp. 377-387.
46.
A.J. Durelli and V.J. Parks, "Two Edge-Bonded Elastic Wedges of Different Materials and Wedge Angles Under Surface Tractions — Discussion,"J. Applied Mechanics, Vol. 39 (1972), p. 317.
47.
D.B. Bogy, "The Plane Solution for Anisotropic Elastic Wedges Under Normal and Shear Loading,"J. Applied Mechanics , Vol. 39 (1972), pp. 1103-1109.
48.
M.C. Kuo and D.B. Bogy, "Plane Solutions for the Displacement and Traction-Displacement Problems for Anisotropic Elastic Wedges,"J. Applied Mechanics , Vol. 41 (1974), pp. 197-202.
49.
M.C. Kuo and D.B. Bogy, "Plane Solutions for Traction Problems on Orthotropic Unsymmetrical Wedges and Symmetrical Twinned Wedges,"J. Applied Mechanics , Vol. 41 ( 1974), pp. 203-208.
50.
A.K. Rao, "Stress Concentrations and Singularities at Interface Corners,"Zeitschrift für angewandte Mathematik und Mechanki (ZAMM) Vol. 51 (1971) pp. 395-406.
51.
P.S. Theocaris , "The Order of Singularity at a Multi-Wedge Corner of a Composite Plate,"Inter. J. Engineering Science , Vol. 12 (1974 ), pp. 107-120.
52.
Pericles S.Theocaris, "Stress and Displacement Singularities Near Corners,"J. Applied Mathematics and Physics ((ZAMP), Vol. 26 (1975 ), pp. 77-98.
53.
P.S. Theocaris , "Stress Singularities in a Bi-Wedge,"Review Romanian Science Tech., Vol. 21 (1976), pp. 129-146.
54.
P.S. Theocaris and E.E. Gdoutos, "Stress Singularities at Equal Angle Biwedges and Two-Material Composite Half Planes with Rough Surfaces,"J. Applied Mechanics, Vol. 43 (1976), pp. 64-68.
55.
J.L. Swedlow , "Singularity Computations,"Inter. J. Numerical Methods in Engineering, Vol. 12 (1978), pp. 1779-1798.
56.
C.T. Herakovich , "On Thermal Edge Effects in Composite Laminates " Inter. J. Mechanical Sciences, Vol. 18 (1976), p. 129.
57.
A.S.D. Wang and Frank W.Crossman, "Edge Effects on Thermally Induced Stresses in Composite Laminates,"J. Composite Materials , Vol. 11 (1977), pp. 300-312.
58.
Frank W. Crossman and A.S.D. Wang, "Stress Field Induced by Transient Moisture Sorption in Finite-Width Composite Laminates,"J. Composite Materials, Vol. 12 (1978), pp. 2-18.
59.
Ronald D. Kriz, "Effect of Material Properties on Interlaminar Stresses in Angle-ply Composite Laminates," Report VPI-E-77-16, Virginia Polytechnic Institute and State University, Blacksburg, Virginia , 1977.
60.
Terence L. Waltz and Jack R. Vinson, "Interlaminar Stresses in Laminated Cylindrical Shells of Composite Materials," Report AD-A019 576 , National Technical Information Service, Springfield, Virginia, 1975.
61.
N.J. Pagano and E.F. Rybicki, "On the Significance of Effective Modulus Solutions for Fibrous Composites,"J. Composite Materials , Vol. 8 ( 1974), pp. 214-228.
62.
J.M. Whitney and C.E. Browning, "Free-Edge Delamination in Tensile Coupons,"J. Composite Materials , Vol. 6 (1972), pp. 300-303.
63.
N.J. Pagano and R. Byron Pipes, "Some Observations on the Interlaminar Strength of Composite Laminates,"Inter. J. Mechanical Sciences, Vol. 15( 1973 ), pp. 679-688.
64.
R. Byron Pipes , "Interlaminar Strength of Laminated Polymeric Matrix Composites," Report AFML-TR-76-82, Air Force Materials Laboratory, Wright-Patterson Air Force Base, Ohio , 1973.
65.
Alexander Harris and Oscar Orringer, "Investigation of Angle-Ply Delamination Specimen for Interlaminar Strength Test" J. Composite Materials, Vol. 12 ( 1978), pp. 285-299.
66.
J.M. Whitney , "Free-Edge Effects in the Characterization of Composite Materials," in Analysis of the Test Methods for High Modulus Fibers and Composites, ASTM STP 521, American Society for Testing and Materials, Philadelphia, 1973 , pp. 167-180.
67.
Assa Rotem and Zri Hashin, "Failure Modes of Angle Ply Laminates,"J. Composite Materials, Vol. 9 ( 1975), pp. 191-206.
68.
K.L. Reifsnider , E.G. Henneke and W.W. Stinchcomb, "Defect-Property Relationships in Composite Materials," Report AFML-TR-76-81, Part II, Air Force Materials Laboratory, Wright-Patterson Air Force Base , Ohio, 1977.
69.
N.J. Pagano and L.M. Lackman, "Prevention of Delamination of Composite Laminates,"AIAA Journal , Vol. 13 (1975), pp. 399-401.
70.
O. Ishai, D. Peretz and S. Gali, "Direct Determination of Interlaminar Stresses in Polymeric Adhesive Layer,"Experimental Mechanics, Vol. 17 (1977), pp. 265-270.
71.
A.Y.C. Lou and J.D. Walter, "Interlaminar-shear-strain Measurements in Cord-Rubber Composites,"Experimental Mechanics , Vol. 18 (1978), pp. 457-463.
72.
E.F. Rybicki , D.W. Schmueser and J. Fox, "An Energy Release Rate Approach for Stable Crack Growth,"J. Composite Materials , Vol. 11 ( 1977), pp. 470-487.
73.
E.F. Rybicki and M.F. Kanninen, "A Finite Element Calculation of Stress Intensity Factors by a Modified Crack Closure Integral,"Engineering Fracture Mechanics, Vol. 9 (1977), pp. 931-938.
74.
S.S. Wang and H.T. Wang, "Interlaminar Crack Growth in Fiber Reinforced Composites During Fatigue " J. Engineering Materials and Technology , Vol. 101 (1979), pp. 34-41.
75.
I.M. Daniel , R.E. Rowlands and J.B. Whiteside, "Effects of Material and Stacking Sequence on Behavior of Composite Plates with Holes,"Experimental Mechanics, Vol. 14 ( 1974), pp. 1-9.
76.
L.A. Marcus and W.W. Stinchcomb , "Measurement of Fatigue Damage in Composite Materials,"Experimental Mechanics , Vol. 15 (1975), pp. 55-60
77.
. J.M. Whitney and R.Y. Kim, "Effect of Stacking Sequence on the Notched Strength of Laminated Composites," Report AFML-TR-76-177, Air Force Materials Laboratory, Wright-Patterson Air Force Base , Ohio, 1976.
78.
I.M. Daniel , "Behavior of Graphite/Epoxy Plates with Holes under Biaxial Loading,"Experimental Mechanics , Vol. 20 (1980), pp. 1-8.
79.
Robert L. Spilker and S.C. Chou, "Edge Effects in Symmetric Composite Laminates: Importance of Satisfying the Traction-Free-Edge Condition,"J. Composite Materials, Vol. 14 (1980), pp. 2-20.
80.
N.J. Pagano, Air Force Materials Laboratory, Wright-Patterson Air Force Base, Ohio, private communication, 1980.
81.
Eric Reissner , "Note on the Theorem of the Symmetry of the Stress Tensor,"J. Mathematics and Physics , Vol. 23 (1944), pp. 192-194.
82.
Giuseppe Gricoli , Mathematical Theory of Elastic Equilibrium (Recent Results, Academic Press, Inc., New York, 1962, Chapter X.
83.
A. S. D. Wang, Drexel University, Philadelphia, private communication, 1979.