DOI: https://doi.org/10.15587/2313-8416.2018.146636

### Method of the reliability calculation of orthotropic composite materials with random defects

Roman Baitsar, Roman Kvit

#### Аннотация

An algorithm for the reliability calculating of stochastically defective orthotropic composite materials under conditions of a complex stress state is described. The criterion of maximum macroscopic stresses for a composite with arbitrarily oriented cracks with a predominant orientation in the direction of reinforcement is considered. The distribution function of the composite failure loading is obtained. The calculation is carried out and diagrams are constructed for the dependence of the test material sample probability of fracture on the applied loading for different number of cracks and structural heterogeneity

#### Ключевые слова

reliability; orthotropic composite material; probability of failure; distribution function; failure loading

PDF (English)

#### Литература

Barbero, E., Fernández-Sáez, J., Navarro, C. (2000). Statistical analysis of the mechanical properties of composite materials. Composites Part B: Engineering, 31 (5), 375–381. doi: https://doi.org/10.1016/s1359-8368(00)00027-5

Dirikolu, M., Aktas, A., Birgoren, B. (2002). Statistical analysis of fracture strength of composite materials using Weibull distribution. Turkish Journal of Engineering and Environmental Sciences, 26 (1), 45–48.

Sakin, R., Ay, İ. (2008). Statistical analysis of bending fatigue life data using Weibull distribution in glass-fiber reinforced polyester composites. Materials & Design, 29 (6), 1170–1181. doi: https://doi.org/10.1016/j.matdes.2007.05.005

Kolios, A. J., Proia, S. (2012). Evaluation of the Reliability Performance of Failure Criteria for Composite Structures. World Journal of Mechanics, 02 (03), 162–170. doi: https://doi.org/10.4236/wjm.2012.23019

Khoroshun, L. P., Nazarenko, L. V. (2013). Deformation and Damage of Composites with Anisotropic Components (Review). International Applied Mechanics, 49 (4), 388–455. doi: https://doi.org/10.1007/s10778-013-0578-6

Balasubramanian, M. (2016). Statistical analysis of tensile strength and elongation of pulse TIG welded titanium alloy joints using Weibull distribution. Cogent Engineering, 3 (1). doi: https://doi.org/10.1080/23311916.2016.1239298

Naresh, K., Shankar, K., Velmurugan, R. (2018). Reliability analysis of tensile strengths using Weibull distribution in glass/epoxy and carbon/epoxy composites. Composites Part B: Engineering, 133, 129–144. doi: https://doi.org/10.1016/j.compositesb.2017.09.002

Kvit, R., Krupka, Z. (1997). Determination of the orthotropic composite materials strength statistical characteristics. Bulletin of the Lviv Polytechnic State University. Physical and Mathematical Sciences, 85–87.

Serensen, S., Zaitsev, G. (1982). Bearing capacity of thin-walled structures made of reinforced plastics with defects. Kyiv, 295.

Deliavskyi, M., Kvit, R. (1992). Macro-stress distribution near crack-like defects in anisotropic micro-inhomogeneous body under flat deformation and longitudinal displacement. Physicochemical Mechanics of Materials, 2, 50–54.

Korolyuk, V., Skorokhod, A., Portenko, N., Turbin, A. (1985). A manual on probability theory and mathematical statistics. Moscow, 640.

Kvit, R. (2000). A statistical approach to the assessment of the reliability of structural materials. Bulletin of the Lviv Polytechnic National University. Physical and Mathematical Sciences, 93–96.

Vytvytsky, P., Popina, S. (1980). Strength and criteria of brittle fracture of stochastically defective bodies. Kyiv, 186.

Sih, G. C., Liebowitz, H. (1975). Mathematical theory of brittle fracture. Fracture. Vol. 2. Moscow, 83–203.

#### Пристатейная библиография ГОСТ

Barbero E., Fernández-Sáez J., Navarro C. Statistical analysis of the mechanical properties of composite materials // Composites Part B: Engineering. 2000. Vol. 31, Issue 5. P. 375–381. doi: https://doi.org/10.1016/s1359-8368(00)00027-5

Dirikolu M., Aktas A., Birgoren B. Statistical analysis of fracture strength of composite materials using Weibull distribution // Turkish Journal of Engineering and Environmental Sciences. 2002. Vol. 26, Issue 1. P. 45–48.

Sakin R., Ay İ. Statistical analysis of bending fatigue life data using Weibull distribution in glass-fiber reinforced polyester composites // Materials & Design. 2008. Vol. 29, Issue 6. P. 1170–1181. doi: https://doi.org/10.1016/j.matdes.2007.05.005

Kolios A. J., Proia S. Evaluation of the Reliability Performance of Failure Criteria for Composite Structures // World Journal of Mechanics. 2012. Vol. 02, Issue 03. P. 162–170. doi: https://doi.org/10.4236/wjm.2012.23019

Khoroshun L. P., Nazarenko L. V. Deformation and Damage of Composites with Anisotropic Components (Review) // International Applied Mechanics. 2013. Vol. 49, Issue 4. P. 388–455. doi: https://doi.org/10.1007/s10778-013-0578-6

Balasubramanian M. Statistical analysis of tensile strength and elongation of pulse TIG welded titanium alloy joints using Weibull distribution // Cogent Engineering. 2016. Vol. 3, Issue 1. doi: https://doi.org/10.1080/23311916.2016.1239298

Naresh K., Shankar K., Velmurugan R. Reliability analysis of tensile strengths using Weibull distribution in glass/epoxy and carbon/epoxy composites // Composites Part B: Engineering. 2018. Vol. 133. P. 129–144. doi: https://doi.org/10.1016/j.compositesb.2017.09.002

Kvit R., Krupka Z. Determination of the orthotropic composite materials strength statistical characteristics // Bulletin of the Lviv Polytechnic State University. Physical and Mathematical Sciences. 1997. P. 85–87.

Serensen S., Zaitsev G. Bearing capacity of thin-walled structures made of reinforced plastics with defects. Kyiv, 1982. 295 p.

Deliavskyi M., Kvit R. Macro-stress distribution near crack-like defects in anisotropic micro-inhomogeneous body under flat deformation and longitudinal displacement // Physicochemical Mechanics of Materials. 1992. Vol. 2. P. 50–54.

A manual on probability theory and mathematical statistics / Korolyuk V. et. al. Moscow, 1985. 640 p.

Kvit R. A statistical approach to the assessment of the reliability of structural materials // Bulletin of the Lviv Polytechnic National University. Physical and Mathematical Sciences. 2000. P. 93–96.

Vytvytsky P., Popina S. Strength and criteria of brittle fracture of stochastically defective bodies. Kyiv, 1980. 186 p.

Sih G. C., Liebowitz H. Mathematical theory of brittle fracture. Fracture. Vol. 2. Moscow, 1975. P. 83–203.

Copyright (c) 2018 Roman Baitsar, Roman Kvit

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ISSN 2313-8416 (Online), ISSN 2313-6286 (Print)