LENGTH-SCALE DEPENDENCE OF VISCOPLASTIC PROPERTIES OF SILVER SINTER REVEALED BY INDENTATION TESTING AND MODELING

Abstract

This doctoral dissertation research focuses on using a combination of indentation testing and modeling to characterize the creep behavior of heterogeneous silver sinter at different temperatures, using multiple indenter sizes to interrogate length-scale effects. The measured steady-state creep deformation is characterized with three different modeling approaches, that rely on: (i) conventional deviatoric creep potential; (ii) pressure-sensitive Drucker-Prager creep potential; and (iii) length-scale dependent deviatoric creep potential. The creep flow rule for all three cases is Norton’s power-law creep. The materials in this study are from a family of sintered silver materials used for interconnects and die-attach in high-temperature electronics and for conductor traces in printed electronics. The dissertation focuses on identifying and quantifying the length-scale dependence presented by sintered materials due to their non-homogeneous morphology. Testing consists of constant-force indentations using spherical indenters of two different radii at three different temperatures: 25°C, 75°C, and 125°C. The indentation results were first analyzed using two different post-processing methods: an empirical approach with closed-form models (CFM) and a computational FEA approach based on classical continuum mechanics. Differences found between the CFM and numerical (FEA) analyses, while significant at room temperature, reduce with temperature. Both models reveal that indenters of different radii cause significantly different viscoplastic behavior. This dependence on tip radius increases with temperature The research was extended to examine two second-order influences of the metallic agglomerated phase and the discontinuous compliant phase of the microstructure of sintered silver on its viscoplastic behavior: (i) dependence on hydrostatic stress; (ii) dependence on microstructural length-scale. The aim of incorporating the pressure-sensitive modeling was to investigate what effect the intrinsic compressive hydrostatic stress in indentation tests might have on the measured viscoplastic properties. Results from using the Drucker-Prager creep model further confirmed the increasing dependence on length-scale with temperature. The length-scale dependence seen in all the above results is investigated and quantified with the help of a simplified strain-gradient viscoplastic model. This modeling approach is motivated by the conventional mechanism-based strain gradient (CMSG) model that is widely used in plasticity theory to quantify length-scale effects. The characteristic length-scale metric in this problem is presented by the agglomerate size distribution in the sintered material and is quantified in this study with ‘watershed analysis’ of cross-sectional features observed via electron microscopy. This discrete length scale is believed to cause the variations in the observed creep response when queried with indenters of different radii, because of the different strain gradients produced by the two different indenters. The length-scale dependence is incorporated in a strain-gradient viscoplastic constitutive model suitable for finite element modeling of deformation fields containing strong strain-gradients (e.g. in the die attach layer in microelectronics chip assembly). Finally, a procedure is proposed, to incorporate the scale-dependence in the empirical closed-form approach, currently available in the literature, for extracting viscoplastic properties from indentation tests. This approach provides corrected model constants for the strain-gradient viscoplastic model, using simple closed-form equations instead of expensive finite element modeling.