Multiscale thermoelastic analysis of random heterogeneous materials

Abstract

Abstract A methodology is presented for the multiscale thermoelastic analysis of random heterogeneous materials. Realistic random microstructures are generated for computational analyses using random morphology description functions (RMDFs) and their corresponding homogenized material properties obtained through the asymptotic expansion homogenization (AEH) method as described previously in Part I. Part II of the investigation concerns the computation of heat flux and stresses at the macro- and micro-scales for a heterogeneous body with random microstructure. The stresses at the microstructural level, coupled with appropriate material failure models, enable the realistic failure analysis of random media which in turn can be used to create useful initial failure envelopes at the macroscale for random materials. Initial failure envelopes are generated for metal/ceramic and metal/metal random heterogeneous materials using this direct micromechanical failure analysis methodology. The microscale and macroscale analysis tools are coupled together to perform a thorough and accurate multiscale analysis of random heterogeneous components. The proposed methodology is illustrated using two model problems. In the first model problem, a functionally graded Al / Al 2 O 3 beam with material composition that varies in the thickness direction is analyzed. In the second model problem, a functionally graded W/Cu component with bi-directional grading is subjected to a heat flux on a portion of its boundary and the corresponding macroscopic temperature, macroscopic average stresses, microscopic stress distribution and factor of safety are computed. In addition, a detailed investigation of failure at the microscale is performed at the critical location for representative random microstructures.