Stochastic estimation of the number of fiber-break points in a CFRP by Markov process

References

• Phoenix SL, Beyerlein IJ. Distributions and size scalings for strength in a one-dimensional random lattice with load redistribution to nearest and next-nearest neighbors. Phys Rev E Stat Nonlin Soft Matter Phys. 2000;62:1622–1645.
   Web of Science ®Google Scholar
• Kawai M, Watanabe K, Hara E, et al. Effect of specimen size on longitudinal strength of unidirectional carbon/epoxy composite laminates (part 1, unnotched strength). Adv Compos Mater. 2019;28:53–71.
   Web of Science ®Google Scholar
• Rosen BW. Tensile failure of fibrous composites. Aiaa J. 1964;2:1985–1991.
   Google Scholar
• Zweben C. Tensile failure of fiber composites. Aiaa J. 1968;6:2325–2331.
   Google Scholar
• Curtin WA. Theory of mechanical properties of ceramic–matrix composites. J Amer Ceram Soc. 1991;74:2837–2845.
   Web of Science ®Google Scholar
• Goda K. Markov process analysis for the strength of ceramic matrix composites reinforced with continuous fibers. J Soc Mater SciJap. 2001;50:1–6. [ (re-recording in English) Materials Science Research International. 2002;8: 87–92].
   Google Scholar
• Harlow DG, Phoenix SL. The chain-of-bundles probability model for the strength of fibrous materials, I: analysis and conjectures. J Compos Mater. 1978;12:195–214. [ ibid. II: A numerical study of convergence. 1978;12: 314–334].
   Web of Science ®Google Scholar
• Suemasu H. An analytical study of probabilistic aspects of strength of unidirectional fiber reinforced composites under tensile loads. Trans JSCM. 1982;8:29–36.
   Google Scholar
• Pitt RE, Phoenix SL. Probability distributions for the strength of composite materials IV: localized load-sharing with tapering. Int J Fract. 1983;22:243–276.
   Web of Science ®Google Scholar
• Goda K. Application of Markov process to chain-of-bundles probability model and lifetime distribution analysis for fibrous composites. J Soc Mater SciJap. 1998;47:464–471. [ (re-recording in English) Materials Science Research International. 2001;STP-2:242–249].
   Google Scholar
• Goda K. A strength reliability model by Markov process of unidirectional composites with fibers placed in hexagonal arrays. Int J Solids Struct. 2003;40:6813–6837.
   Web of Science ®Google Scholar
• Goda K. Chapter 9. Toughened green composites: improving impact properties, Edited by Netravali AN. Adv Green Compos. 2018: Scrivener Publishing LLC. 211–246.
   Google Scholar
• Daniels HE. The statistical theory of strength of bundles of threads. Proc R Soc London. 1945;A183:405–435.
   Google Scholar
• Coleman BD. On the strength of classical fibres and fibre bundles. J Mech Phys Solids. 1958;7:60–70.
   Web of Science ®Google Scholar
• Hedgepeth JM. Stress Concentrations in Filamentary Structures. NASA Tech Note. 1961;D–882:1–30.
   Google Scholar
• Hedgepeth JM, Dyke PV. Local Stress Concentrations in Imperfect Filamentary Composite Materials. J Compos Mater. 1967;1:294–309.
   Google Scholar
• Wada A, Fukuda H. Approximate upper and lower bounds for the strength of unidirectional composites. Compos Sci Technol. 1999;59:89–95.
   Web of Science ®Google Scholar
• Oh KP. A Monte Carlo study of the strength of unidirectional fiber-reinforced Composites. J Compos Mater. 1979;13:311–328.
   Web of Science ®Google Scholar
• Kimpara I, Ozaki T, Takada S. Simulation on Tensile Failure Process of Unidirectional Hybrid FRP. J Soc Mater SciJap. 1985;34:280–285.
   Google Scholar
• Goda K, Fukunaga H. Considerations of the reliability of tensile strength at elevated temperature of unidirectional metal matrix composites. Compos Sci Technol. 1989;35:181–193.
   Web of Science ®Google Scholar
• Okabe T, Takeda N, Kamoshida Y, et al. A 3D shear-lag model considering micro-damage and statistical strength prediction of unidirectional fiber-reinforced composites. Compos Sci Technol. 2001;61:1773–1787.
   Web of Science ®Google Scholar
• Tanaka M, Hojo M, Hobbiebrunken T. Influence of non-uniform fiber arrangement on tensile fracture behavior of unidirectional fiber/epoxy model composites. Compos Interfaces. 2005;12:365–378.
   Web of Science ®Google Scholar
• Wang F, Chen ZQ, Wei YQ, et al. Numerical modeling of tensile behavior of fiber-reinforced polymer composites. J Compos Mater. 2010;44:2325–2340.
   Web of Science ®Google Scholar
• Wu Y, Zhang W, Wang S, et al. Prediction method of longitudinal tensile strength for unidirectional composites with interphase. J Reinf Plast Compos. 2013;32:540–546.
   Web of Science ®Google Scholar
• Goda K. The role of interfacial debonding in increasing the strength and reliability of unidirectional fibrous composites. Compos Sci Technol. 1999;59:1871–1879.
   Web of Science ®Google Scholar
• Goda K. Creep-rupture lifetime simulation of unidirectional metal matrix composites with and without time-dependent fiber breakage. Int J Plast. 2002;18:1729–1748.
   Web of Science ®Google Scholar
• Weibull W. A statistical distribution function of wide applicability. ASME J Ppl Mech. 1951;18:293–297.
   Web of Science ®Google Scholar
• Yoshida N, Hayashi H, Sakamoto H, et al. Special Issue/Inverse Problem. Math Sci. 1986;274:5–79.
   Google Scholar
• Karlin S. A first course in stochastic process. Sato K, Sato Y, translator;  1974:Sangyo-Tosho (in Japanese), 193-237, .
   Google Scholar
• Swolfs Y, Verpoest I, Gorbatikh L. Review: A review of input data and modelling assumptions in longitudinal strength models for unidirectional fibre-reinforced composite. Compos Struct. 2016;150:153–172.
   Web of Science ®Google Scholar
• Cox HL. The elasticity and strength of paper and other fibrous materials. Br J Appl Phys. 1952;3(3):302:72–79.
   Google Scholar
• Kelly A, Tyson WR. Tensile properties of fibre-reinforced metals: copper/tungsten and copper/molybdenum. J Mech Phys Solids. 1965;13:329–338.
   Web of Science ®Google Scholar
• Sawada Y, Nagai S, Kosaka T, et al. Evaluation of size effects in tensile strength of micro composites. Proc 37th Symp Jpn Soc Compos Mater. 2012;37: 73-74.
   Google Scholar
• Watanabe J, Tanaka F, Higuchi R, et al. A study of stress concentrations around fiber breaks in unidirectional CF/epoxy composites using double-fiber fragmentation tests. Adv Compos Mater. 2018;27:575–587.
   Web of Science ®Google Scholar
• Taketa I, Matsutani H. Effect of fiber length on the tensile strength of unidirectionally arrayed chopped strands. Adv Compos Mater. 2019;28:1–12.
   Google Scholar
• Weibull W. A statistical theory of strength of materials. Ingeniӧrsvetenskapsakademins. Handlingar. 1939;151:1–45.
   Google Scholar