# Research Paper

## **Abstract**

The objective of this research is to study the influence of morphology on fracture and debonding of silicon particles embedded in an Al-1%Si matrix. The fracture and deboning is caused by applied tensile and compressive cyclic loading conditions. Finite element method is used to study these effects to accurately represent particle geometry, particle interactions, and the stress-strain behavior of the aluminum matrix. A cluster of 4 to 8 silicon particle inclusion is chosen for the study over infinite array of inclusion or single isolated inclusion. Silicon particles are modeled with linear elastic constitutive relationship and matrix material using internal state variable cyclic plasticity model. A two level design of experiments method is used to test 16 sets of combination made with 7 variables; relative particle size, shape, spacing, configuration, alignment, grouping and matrix microporosity. Results of the study proves the dominance of shape and alignment during initial fracturing and debonding and spacing during later. Local intensification of stresses in induced by particle debonding in Al-1%Si matrix. This intensification of stresses is higher than that of particle fracture. Enhancement is spacing due to consecutive fracturing in the cluster turns out to be another dominant factor due to large local intensification of stresses.

## Methodology

Two level design of experiments method is used to study the effects of seven parameters at their chosen range of conditions is shown in Fig.1. A total of 16 significant combinations of the 7 morphological parameters at their extreme allowed conditions are chosen for the study, shown in the following design matrix in Table 1. The extremes for these parameters are based on micro-graphical observations from an A365 aluminum alloy study which constitutes silicon particles.Finite element cases were created for all 16 combinations with following assumptions; 1) Traces of other element are not considered in the model though that are generally present in the alloy to promote hardening and other casting properties. 2) The silicon particles are assumed to behave in an isotropic linear elastic. The Al matrix material is described using an internal state variable plasticity model with coupled micro void growth. 3) Temperature and strain rate dependence on the plasticity of the model were not considered. Experimental data regression is thoroughly used to generate constants for the model. In Fig 2, stress-strain model output is compared to experimental output for cycles 1, 2, and 10. A point of saturation is attained at the end of 10 cycles in both cases. Maximum tensile principal stress is an important study parameter which is the proposed cause of fracture in Si particles. Debonding is studied on the basis of hydrostatic stresses on particle matrix interface. The screening of the two significant parameters is listed under table 2