Abstract

The paper presents a comprehensive formulation for the analysis of the stiffness and strength of fiber-reinforced composites with the matrix enhanced by adding elastic or shape memory alloy (SMA) spheroidal particles. The micromechanical model used to evaluate the stiffness tensor of the matrix with embedded particles is based on the Benveniste version of the Mori–Tanaka theory. In the case of a superelastic shape memory alloy particulate matrix, the stiffness of the particles depends on the martensitic fraction that is in turn affected by the state of stress within the particle. In this case an exact solution for the stiffness tensor of the composite material with elastic fibers and matrix and embedded SMA particles is developed combining the recent macromechanical solution for multi-phase composites with the inverse method of the analysis of SMA. In the particular case, this solution results in explicit formulae for the homogeneous material constants of a SMA particulate material subjected to axial loading. Upon the completion of the stiffness analysis the strengths of a fiber-reinforced material with the matrix containing elastic or SMA particles can be analyzed using the Eshelby solution for the stresses. As follows from numerical examples, elastic spherical particles added to the matrix of a fiber-reinforced composite significantly improve the transverse strength and stiffness of the material, even if the volume fraction of such particles is relatively small. The effect of elastic particles on the longitudinal strength and stiffness is less pronounced. It is also illustrated that the stress-induced transformation of superelastic SMA particles results in significant changes of the properties of SMA particulate composites.

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