Creep behavior due to interface diffusion in unidirectional fiber-reinforced metal matrix composites under general loading conditions: a micromechanics analysis

Abstract

In this paper, the creep behavior due to interface diffusion in unidirectional fiber-reinforced metal matrix composites under general transverse loading conditions is studied. A micromechanics model is adopted to estimate the average stresses in fibers, which is demonstrated to be of reasonable accuracy by comparing with finite element analysis. The creep deformation due to interface diffusion is characterized by a tensor-form creep strain rate, which is related to the components of average stress in fibers and possesses incompressibility. The derived creep strain tensor is then introduced into fibers as eigenstrain to estimate the effect of creep strain on stress redistribution in composites. Eventually, the macroscopic creep strain of composites under constant external loads and the stress relaxation at fixed displacements due to interface diffusion are calculated by the incremental creep analysis procedures based on the average field theory. The effects of loading conditions on the overall creep behavior are examined in detail. Results of this study show that under the fixed strain condition, the initial biaxial stress ratio actually varies rather than remains unchanged during the stress relaxation process. In both constant stress and constant strain conditions, stresses in fibers have a propensity to approach hydrostatic stress state, thus suppressing the interface diffusion. These findings were not reported in previous researches and may bring new understanding on diffusion-induced creep deformation in metal matrix composite materials.

Appendix

For isotropic materials, the elastic stiffness C is expressed in the following $6 \times 6$ matrix form:

$$\begin{aligned} {\mathbf{C}}=\left[ \begin{array}{c@{\quad }c@{\quad }c@{\quad }c@{\quad }c@{\quad }c} {\lambda +2\mu }&{} \lambda &{} \lambda &{} &{} &{} \\ \lambda &{} {\lambda +2\mu }&{} \lambda &{} &{} {\left[ 0 \right] _{3\times 3} }&{} \\ \lambda &{} \lambda &{} {\lambda +2\mu }&{} &{} &{} \\ &{} &{} &{} \mu &{} 0&{} 0 \\ &{} {\left[ 0 \right] _{3\times 3} }&{} &{} 0&{} \mu &{} 0 \\ &{} &{} &{} 0&{} 0&{} \mu \\ \end{array} \right] , \end{aligned}$$

(A1)

where $\mu =E/[2(1+\nu )]$ and $\lambda =2\mu \nu /(1-2\nu )$.

Unidirectional fiber-reinforced metal matrix composites under general transverse loading condition is treated as a plain strain problem in this study. The Eshelby tensor for a long fiber (plane strain) is expressed as

$$\begin{aligned} \mathbf{S}=\left[ \begin{array}{c@{\quad }c@{\quad }c@{\quad }c@{\quad }c@{\quad }c} {A(5-4\nu )}&{} {A(4\nu -1)}&{} {4A\nu }&{} &{} &{} \\ {A(4\nu -1)}&{} {A(5-4\nu )}&{} {4A\nu }&{} &{} {\left[ 0 \right] _{3\times 3} }&{} \\ 0&{} 0&{} 0&{} &{} &{} \\ &{} &{} &{} {1/4}&{} 0&{} 0 \\ &{} {\left[ 0 \right] _{3\times 3} }&{} &{} 0&{} {1/4}&{} 0 \\ &{} &{} &{} 0&{} 0&{} {A(3-4\nu )} \\ \end{array} \right] , \end{aligned}$$

(A2)

where $A=1/[8(1-\nu )]$.