Keywords: ceramic matrix composites, thermal residual stresses, particle swarm optimization, harmony search algorithm, microstructure modelling, finite element analysis.

The thermal residual stresses induced in ceramic matrix composites (CMCs) with multilayered interphases when cooling down from the processing temperature have a significant influence on the mechanical behavior and lifetime of such composite structures. Experimentally [1] or analytically [2], many researchers have studied the effect of thermal residual stresses in CMCs. However, efforts to optimize the distribution of thermal residual stresses in the multi-layered interphases and matrix of the CMCs have not yet been made systematically.

The objective of this work is to minimize the thermal residual stresses of the CMCs by controlling the thicknesses of multi-layered interphases. The non-linear and non-differentiable nature of this optimization problem induces difficulty in using classical deterministic approaches for solutions. To solve this non-linear optimization problem a particle swarm optimization (PSO) algorithm [3] is used. The solution approach combines two numerical analyses:

(a) The unit cell finite element models of unidirectional CMCs with multi-layered interphases are generated and a finite element analysis is realized in order to determine the thermal residual stresses. (b) A PSO algorithm is interfaced with the finite element code to find an optimal design and thereby significantly reduce the thermal residual stresses within the CMCs. The classical PSO algorithm is modified to satisfy the variable limits of the optimization problem.

The optimization study is finally carried out on a unidirectional silicon carbide (SiC) fiber reinforced silicon carbide (SiC) ceramic matrix composite with four layers of interphases. The interphases consist in alternating sub-layers of pyrocarbon (PyC) and SiC. Our goal is to obtain optimal interphases thicknesses which minimize the thermal residual stresses generated upon cooling from processing (1000°C) to room (25°C) temperatures. Satisfactory results are obtained. Considering most previous applications of the PSO for composites one can state that they are focused on ply thicknesses and orientation angle optimization of composites laminates [4]. The present work extends the applicability of the PSO algorithm to CMCs.

1

H. Mei, "Measurement and calculation of thermal residual stress in fiber reinforced ceramic matrix composites", Composites Science and Technology, 68, 3285-3292, 2008. doi:10.1016/j.compscitech.2008.08.015

2

P. Vena, "Thermal residual stresses in graded ceramic composites: a microscopic computational model versus homogenized models", Meccanica, 40, 163-179, 2005. doi:10.1007/s11012-005-3064-3

3

J. Kennedy, R.C. Eberhart, "Particle swarm optimization", Proceedings of the IEEE international conference on neural networks, 4, 1942-1948, 1995. doi:10.1109/ICNN.1995.488968

4

N. Chang, W. Wang, W. Yang, J. Wang, "Ply stacking sequence optimization of composite laminate by permutation discrete particle swarm optimization", Structural and Multidisciplinary Optimization, 41, 179-187, 2010. doi:10.1007/s00158-009-0417-x

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