Analytical Solution for the Stress Field around a Hard Spherical Particle in a Metal Matrix Composite Incorporating Size and Finite Volume Effects

An analytical solution is presented for the stress field around an elastic spherical particle embedded in a finite elastic—plastic metal matrix subjected to hydrostatic tension. The formulation is based on a strain gradient plasticity theory and a unit cell of finite dimensions, and the resulting solution incorporates the size and finite volume effects. The counterpart solutions based on classical elasticity and plasticity are reduced from the current solution, and the solution for that of an elastic spherical particle embedded in an infinitely large elastic—plastic matrix is obtained as a special case. The newly derived solution can capture the particle size effect and account for composites with both dilute and non-dilute particle distributions, unlike existing analytical models. The stress concentration factor on the particle/matrix interface, which depends on the particle size and volume fraction, is determined by directly applying the current solution. Numerical results quantitatively show that the stress concentration factor increases as the particle volume fraction increases and the strain-hardening level of the matrix material decreases. Also, these results reveal that the stress concentration factor decreases with decreasing particle size at the micron scale, thereby predicting the particle size effect.