Eur. Phys. J. Plus (2019) 134: 148
https://doi.org/10.1140/epjp/i2019-12475-7

Regular Article

The effect of the substitution on the failure process in heterogeneous materials: Fiber bundle model study

¹ LBGIM, Ecole Normale Supérieure, University Hassan II, Casablanca, Morocco
² LPMC, Faculty of sciences Ben M’sik, University Hasan II, Casablanca, Morocco
³ LPMC, University Chouaib Doukkali, El Jadida, Morocco
⁴ Centre régional des métiers d’éducation et de formation, Settat, Morocco

^* e-mail: sbiaai47@gmail.com

Received: 20 April 2018
Accepted: 15 December 2018
Published online: 15 April 2019

Abstract

This paper is devoted to study numerically the effect of the substitution on the failure process in composite materials and a comparison of failure damage between substituted and classical composite materials. Our investigations are made in the framework of the fiber bundle model (FBM) treated in the local load sharing rule (LLS). The system consists mainly of a collection of fiber type A, in which we substitute a small portion by fiber type B which is stronger than the initial type. Our simulation results show that the avalanche breaking is redistributed on two separated states due to the competition of the breakdown process between two fibers type A and B. However, the time t between two avalanche states decreases with the applied load. Moreover, the fraction of the inserted fiber type B is very small, the number of the broken fibers A (avalanche size) decreases. Despite their small number in the material, fibers B play an important role in protecting fibers A against system damage. This substitution disrupts and blocks the process of failure in the material which exhibits a greater resistance and toughness towards the applied load.