Electrical and mechanical behaviour of metal thin films with deformation-induced cracks predicted by computational homogenisation

Motivated by advances in flexible electronic technologies and by the endeavour to develop non-destructive testing methods, this article analyses the capability of computational multiscale formulations to predict the influence of microscale cracks on effective macroscopic electrical and mechanical material properties. To this end, thin metal films under mechanical load are experimentally analysed by using in-situ confocal laser scanning microscopy (CLSM) and in-situ four point probe resistance measurements. Image processing techniques are then used to generate representative volume elements from the laser intensity images. These discrete representations of the crack pattern at the microscale serve as the basis for the calculation of effective macroscopic electrical conductivity and mechanical stiffness tensors by means of computational homogenisation approaches. A comparison of simulation results with experimental electrical resistance measurements and a detailed study of fundamental numerical properties demonstrates the applicability of the proposed approach. In particular, the (numerical) errors that are induced by the representative volume element size and by the finite element discretisation are studied, and the influence of the filter that is used in the generation process of the representative volume element is analysed.

The Minimum Representative Volume Element Size for Coefficient of Thermal Expansion of Particle Reinforced Metal Matrix Composites

A 3D realistic microstructure based computational homogenization model is proposed, in order to determine the temperature dependent effective coefficient of thermal expansion of particle reinforced metal matrix composites The model employed three-dimensional realistic microstructures with different domain sizes, where particles had random shape, sharp edges and were randomly distributed. The unit cell microstructure based model and classical analytical models were also presented for comparison. As an illustration of the model, a 17% vol. SiCpreinforced 2124Al composite was investigated. Its minimum RVE size is found to beδ= 15, whereδis called the size ratio and defined by the ratio between the side length of microstructure and the mean particle radius.