Statistics of fracture for an elastic notched composite lamina containing Weibull fibers -Part I. Features from Monte-Carlo simulation

Engineering Fracture Mechanics

Volumn 57, Issue 2-3, 1997, Pages 241-265

  Beyerlein, Irene J ^a   Leigh Phoenix, S ^a  

^a Department of Obstetrics Gynecology   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; FRACTURE MECHANICS; FRACTURE TOUGHNESS; MONTE CARLO METHODS; SHEAR STRESS; STATISTICS; STRENGTH OF MATERIALS; WEIBULL DISTRIBUTION;

BREAK INFLUENCE SUPERPOSITION (BIS) TECHNIQUE; ELASTIC COMPOSITE LAMINA;

FIBER REINFORCED MATERIALS;

EID: 0031130886     PISSN: 00137944     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0013-7944(97)00012-x     Document Type: Article

References (65)

1. Baxenvanakis, C., Jeulin, D. and Renard, J., Fracture statistics of a unidirectional composite. Int. J. Fracture, 1995, 73, 149-181.
2. Steinbrech, R. W., R-curve behavior of ceramics. In Fracture Mechanics of Ceramics, Vol. 9. ed. R. C. Bradt et al. Plenum Press, New York, 1992.
3. Kreider, K. G. and Leverant, G. R., Boron fiber metal matrix composites by plasma spraying. AFML-TR-66-219, Air Force Materials Laboratory, 1966.
4. Lenoe, E. M., Micromechanics of boron filament reinforced aluminum composites. Symposium on Metal Matrix Composites, ASTM, 1967.
5. Rosen, B. W., Tensile failure of fibrous composites. AIAA J., 1964, 2(11), 1985-1991.
6. Friedman, E., A tensile failure mechanism for whisker reinforced composites. 22nd Annual Meeting of the Reinforced Plastics Division of the SPI, Washington, D.C., U.S.A., 1967.
7. Jones, W. F. and Goree, J. G., Fracture behavior of unidirectional boron/A1 composite laminates. Mech. Composite Mater., ASME AMD, 1983, 58, 171-178.
8. Herring, H. W., Lytzon, J. L. and Steele, J. H. Jr, Experimental observations of tensile fracture in unidirectional boron filament reinforced aluminum sheet. Metall. Trans., 1973, 4, 807-817.
9. Hedgepeth, J. M., Stress concentrations in filamentary structures. NASA TN D-882, 1961.
10. Hedgepeth, J. M. and Van Dyke, P., Local stress concentrations in imperfect filamentary composite materials. J. Compos. Mater., 1967, 1, 294-309.
11. Van Dyke, P. and Hedgepeth, J. M., Stress concentrations from single-filament failures in composite materials. Textile Res. J., 1969, 39, 618-626.
12. Fichter, W. B., Stress concentrations around broken filaments in a filament-stiffened sheet. NASA TN D-5453, 1969.
13. Goree, J. G. and Gross, R. S., Analysis of a unidirectional composite containing broken fibers and matrix damage. Engng Fracture Mech., 1979, 13, 563-578.
14. Goree, J. G. and Gross, R. S., Stresses in a three-dimensional unidirectional composite containing broken fibers. Engng Fracture Mech., 1980, 13, 395-405.
15. Fukuda, H. and Chou, T. W., An advanced shear-lag model applicable to discontinuous fiber composites. J. Compos. Mater., 1981, 15, 79-91.
16. Batdorf, S. B. and Ko, R., Use of shear lag for composite microstress analysis-rectangular array. AIAA J., 1985, 23(6), 926-930.
17. Rossettos, J. N. and Shishesaz, M., Stress concentration in fiber composite sheets including matrix extension. J. appl. Mech., 1987, 54, 723-724.
18. Hikami, F. and Chou, T. W., Explicit crack problem solutions of unidirectional composites: elastic stress concentrations. AIAA J., 1990, 28, 499-505.
19. Ochiai, S., Schulte, K. and Peters, P. W. M., Strain concentration factors for fibers and matrix in unidirectional composites. Comp. Sci. Technol., 1991, 41, 237-256.
20. Beyerlein, I. J., Phoenix, S. L. and Sastry, A. M., Stress concentrations around aligned fiber breaks in a unidirectional composite with an elastic-plastic matrix. Simulation of Materials Processing: Theory, Methods and Applications, NUMIFORM 95, ed. S. F. Shen and P. R. Dawson. AA Balkema Publishers, Netherlands, 1995, pp. 237-242.
21. Nairn, J. A., Fracture mechanics of unidirectional composites using the shear lag model - I. Theory. J. Compos. Mater., 1988, 22, 561-588.
22. Sastry, A. M. and Phoenix, S. L., Load redistribution near non-aligned fibre breaks in a two-dimensional unidirectional composite using break-influence superposition. J. Mater. Sci. Lett, 1993, 12, 1596-1599.
23. Beyerlein, I. J. and Phoenix, S. L., Stress concentrations around multiple fiber breaks in an elastic matrix with local yielding or debonding using quadratic influence superposition. J. Mech. Phys. Solids, 1996, 44, 1997-2039.
24. Zhou, S. J. and Curtin, W. A., Failure of fiber composites: a lattice Green function model. Acta. Metall. Mater., 1995, 43, 3093-3104.
25. Ibnabdeljalil, M. and Curtin, W. A., Size effects on the strength of fiber-reinforced composites. To appear in Int. J. Solids Structures, 1995.
26. Ibnabdeljalil, M. and Curtin, W. A., Strength and reliability of notched fiber-reinforced composites. Submitted to Acta Mater., 1996.
27. Reedy, E. D., Fiber stresses in a crack monolayer: comparison of shear-lag and 3-D finite element predictions. J. Compos. Mater., 1984, 18, 595-607.
28. Beyerlein, I. J., Phoenix, S. L. and Sastry, A. M., Comparison of shear-lag theory and continuum fracture mechanics for modeling fiber and matrix stresses in an elastic cracked composite lamina. Int. J. Solids Structures, 1996, 33, 2543-2574.
29. Nedele, M. R. and Wisnom, M. R., Three-dimensional finite element analysis of the stress concentration at a single fibre break. Comp. Sci. Technol., 1994, 51, 517-524.
30. Case, S. W. and Reifsnider, K. L., Micromechanical analysis of fiber fracture in unidirectional composite materials. Int. J. Solids Structures, 1996, 33, 3795-3812.
31. Marshall, D. B. and Cox, B. N., Tensile fracture of brittle matrix composites: influence of fiber strength. Acta Metall., 1987, 35, 2607-2619.
32. Bao, G. and Suo, Z., Remarks on crack-bridging concepts. Appl. Mech. Rev., 1992, 45, 355-366.
33. Cox, B. N., Carter, W. C. and Fleck, N. A., A binary model of textile composites - I. Formulation. Acta Metall. Mater., 1994, 42(10), 3463-3479.
34. Wells, J. K. and Beaumont, P. W. R., Crack-tip energy absorption processes in fibre composites. J. Mater. Sci., 1985, 20, 2735-2749.
35. Sastry, A. M., Calculation of stress concentrations in damaged composite solids for determining strength distributions. Ph.D. Thesis, Department of Aerospace and Mechanical Engineering, Cornell University, Ithaca, NY, 1994.
36. Larder, R. A. and Beadle, C. W., The stochastic finite element simulation of parallel fiber composites. J. Compos. Mater., 1976, 10, 21-31.
37. Oh, K., A Monte-Carlo study of the strength of unidirectional fiber-reinforced composites. J. Compos. Mater., 1979, 13, 311-328.
38. Manders, P. W., Bader, M. G. and Chou, T. W., Monte-Carlo simulation of the strength of composite fibre bundles. Fibre Sci. Technol., 1982, 17, 183-204.
39. Fukuda, H. and Kawata, K., On the strength distribution of unidirectional fibre composites. Fibre Sci. Technol., 1977, 10, 53.
40. Ochiai, S. and Osamura, K., Influences of interfacial bonding strength and scatter of fibre strength on tensile behavior of unidirectional metal matrix composites. J. Mater. Sci., 1988, 23, 886-893.
41. Goda, K. and Phoenix, S. L., Reliability approach to the tensile strength of unidirectional CFRP composites by Monte-Carlo simulation in a shear-lag model. Comp. Sci. Technol., 1994, 50, 457-468.
42. Gurvich, M. R. and Pipes, R. B., Strength size effect of laminated composites. Comp. Sci. Technol., 1995, 55, 93-105.
43. Lienkamp, M. and Schwartz, P., A Monte Carlo simulation of the failure of a seven fiber microcomposite. Comp. Sci. Technol., 1993, 46, 139-146.
44. Phoenix, S. L. and Smith, R. L., A comparison of probabilistic techniques for the strength of fibrous materials under local load-sharing among fibers. Int. J. Solids Structures, 1983, 19, 479-496.
45. Phoenix, S. L., Schwartz, P. and Robinson IV, H. H., Statistics for the strength and lifetime in creep-rupture of model carbon/epoxy composites. Comp. Sci. Technol., 1988, 32, 81-120.
46. Duxbury, P. M. and Leath, P. L., The failure probability and average strength of disordered systems. Submitted to Phys. Rev. Lett., 1995.
47. Leath, P. L. and Duxbury, P. M., Fracture of heterogeneous materials with continuous distributions of local breaking strengths. Phys. Rev. B., 1994, 49, 14905-14917.
48. Duxbury, P. M., Kim, S. G. and Leath, P. L., Size effect and statistics of fracture in random materials. Mater. Sci. Engng, 1994, A176, 25-31.
49. Herrmann, H. J. and Roux, S. (eds), Statistical Models for the Fracture of Disordered Media. Elsevier Science, 1990.
50. Herrmann, H. J., Hanson, A. and Roux, S., Fracture of disordered elastic lattices in two dimensions. Phys. Rev. B., 1989, 39(1), 637-648.
51. Roux, S., Hanson, A. and Hinrichsen, E. L., Multifractality of conductance jumps in percolation. Phys. Rev. B., 1991, 43(4), 3601-3612.
52. Suo, Z., Ho, S. and Gong, X., Notch ductile-to-brittle transition due to localized inelastic band. J. Engng Mater. Technol., 1993, 115, 319-326.
53. Wells, J. K. and Beaumont, P. W. R., Debonding and pull-out processes in fibrous composites. J. Mater. Sci., 1985, 20, 1275-1284.
54. Sutcu, M., Statistical fibre fracture and single crack behavior in uniaxially reinforced ceramic composites. J. Mater. Sci., 1988, 23, 928-933.
55. Sutcu, M., Weibull statistics applied to fiber failure in ceramic composites and work of fracture. Acta Metall., 1989, 37, 651-661.
56. Budiansky, B. and Amazigo, J. C., Notched strength of ceramic composites: long fibers, stochastic, short fibers. Presented at IUTAM Symposium on Nonlinear Analysis of Fracture, University of Cambridge, 3-7 September 1995.
57. Watson, A. S. and Smith, R. L., An examination of statistical theories for fibrous materials in the light of experimental data. J. Mater. Sci., 1985, 20, 3260-3270.
58. Lawn, B., Fracture of Brittle Solids, 2nd edn. Cambridge University Press, NY, U.S.A., 1993.
59. Corten, H. T., Fracture mechanics of composites. In Fracture, Vol. VII, ed. H. Liebowitz. Academic, NY, U.S.A., 1972, pp. 676-769.
60. Beaumont, P. W. R. and Phillips, D. C., Tensile strengths of notched composites. J. Compos. Mater., 1967, 6, 32-46.
61. Kawashima, T., Okamoto, H., Yamamoto, H. and Kitamura, A., Grain size dependence of the fracture toughness of silicon nitride ceramics. J. Ceram. Soc. Jpn, 1991, 99, 1-4.
62. Mitomo, M., Toughening of silicon nitride ceramics by microstructural control. Proc. Sci. Engng Ceram., Ceram. Soc. Japan, Tokyo, 1991, pp. 101-107.
63. Nose, T. and Kubo, H., Influence of grain morphology of the sintered body on the fracture toughness of ceramic materials. Am. Ceram. Soc. 43rd Pacific Coast Region Meeting, Seattle, WA, U.S.A., 14-L-90P, 1990.
64. 4 Ceramics, ed. M. J. Hoffmann and P. Gunter. Kluwer, Boston, MA, U.S.A., 1994, pp. 87-100.
65. Jogota, A. and Bennison, S. J., Element breaking rules in computational models for brittle fracture. To appear in Model Simul. in Mater. Sci. Engng, 1995.