Correlation and diffusion breaking in the failure process of composite materials

Abstract

Abstract Fiber bundle model is one of the important statistical and theoretical physics approaches to investigate the fracture and breakdown of heterogeneous material extensively used both by the engineering and physics community. In this paper, using the correlation function and its properties, we study the diffusion of the failure process in composite materials that consist of a set of with randomly oriented fibers loaded by an external constant total load. The investigation is based on fiber bundle model where the fibers are randomly oriented; each fiber is subject only the cosine component of the external load, and when it fails, its load is shared by surviving neighboring fibers according to the local load sharing rule (LLS). The failure process ensures an advancing interfacial fracture and the areas of the damaged regions increases with time until a final crack of material. By using the correlation function of the fraction of broken fibers, we study the diffusion properties of micro crack created in the composite materials. The results show that the correlation decreases exponentially with time and decreases with both of applied load and temperature. We calculate then the effective diffusion coefficient cracks which increase exponentially with applied load and linearly with the temperature. The failure time tf of the materials decrease with temperature as a power law. Obtained results are compared with the one of the classical model consist of a set of parallel fibers.