Size dependent creep deformation of elastically constrained compliant metallic joints

Abstract

The present study proposes a novel method to predict the size dependent creep behavior of bi-material joints formed by constraining a creep compliant metal, such as Sn, having varied thickness ranging from 1.4 mm to 170 µm, between stiff elastic substrates, such as Cu. A dramatic reduction in the secondary or minimum creep rate was observed with decrease in joint thickness. Finite element (FE) analysis using continuum formulations attributed this strengthening to the geometric constraints imposed by Cu, which increases the triaxiality in the joints and hence reduces the effective stress. While FE results were in close agreement with experiment in thick joints, it significantly overpredicted the creep rate of miniature joints. Further, orientation imaging revealed that microstructure varied with length scale, from bulk Sn with multiple grains to miniature joints having a few grains. The additional strengthening was captured using dislocation-based crystal plasticity (CP) creep modeling of Sn-Cu joints by incorporating this microstructural length scale, in addition to the geometric constraints. CP simulations revealed that orientation anisotropy of Sn and the constraints imposed by substrates on dislocation motion lead to higher strength in the miniature joints. Using the insights from FE and CP modeling a unified length scale sensitive model, incorporating both geometric or continuum and microstructural factors, was developed that can accurately predict the creep response of the joints of macro and meso length scale.