Micromechanics-based damage model for liquid-assisted healing

Abstract

This work presents a damage evolution framework including liquid-assisted healing. The model incorporates contributions from void size, void pressure, surface tension and liquid pressure. Experimental motivation for the damage-healing model is provided with in-situ melting experiments, where the evolution of the void distribution under monotonic tension is illustrated. The damage evolution is based on nucleation and growth of voids, which are modeled in a unified creep and plasticity framework. The proposed damage formulation introduces a void collective, which computes the void distribution in the material and allows to describe void collapse using the Rayleigh-Plesset equation. The necessary conditions for healing are discussed with use of model results. Particularly, the role of external load during healing, the dependence on liquid viscosity and surface tension are investigated.

Analysis of Sn-Bi Solders: X-ray Micro Computed Tomography Imaging and Microstructure Characterization in Relation to Properties and Liquid Phase Healing Potential

“…The microstructural and morphology descriptors reported in the present work allow a discussion of several mechanical properties in the semi-solid state, with the eutectic phase still being liquid [ 35 , 36 ]. Under these conditions, the residual strength of the solder joint is an important measure to estimate tolerable external forces.…”

“…Theoretical considerations of liquid-assisted healing reported in References. [ 35 , 36 ] suggest that external compressive deformation is a driving force for liquid-assisted healing. This effect is limited by the tendency of void formation under semi-solid compression, which has been investigated for Al-Cu alloys [ 54 , 55 , 56 ].…”

“…The theoretical considerations of liquid-assisted healing in References. [ 35 , 36 ] discussed the role of local material transport for void healing. It was mentioned that the local resistance against material transport will lead to a deviation of the theoretical healing efficiency.…”

“…The elasto-plastic response of Sn-Ag-Cu solders after aging was studied by Maleki et al [ 26 , 29 ] and highlighted the possibility to compute the stress-strain response from tomography data. Besides these reported studies on thermal and mechanical behavior, other properties also depend on the microstructural morphology, such as semi-solid deformation [ 30 , 31 , 32 ], hot tearing [ 33 , 34 ] or liquid phase healing [ 35 , 36 ]. These properties have not been reported in literature for Sn-Bi alloys and it is the aim of the present work to provide the essential parameters to enable such studies.…”

Modelling of Void Collapse with Molecular Dynamics in Pure Sn

“…Healing in metals has recently gained attention as an innovative concept to reduce mechanical damage [1]. A micromechanical model was reported to formulate the liquid-assisted healing of a void collective, which is based on the Rayleigh-Plesset (RP) equation [2]. Molecular dynamics (MD) simulations can potentially provide a better understanding of processes on the nano-scale.…”