A homogenization-based five-step multi-scale finite element (FsMsFE) simulation framework is developed to describe the time-temperature-dependent viscoelastic behavior of 3D braided four-directional composites. The current analysis was performed via three-scale finite element models, the fiber/matrix (microscopic) representative unit cell (RUC) model, the yarn/matrix (mesoscopic) representative unit cell model, and the macroscopic solid model with homogeneous property. Coupling the time-temperature equivalence principle, multi-phase finite element approach, Laplace transformation and Prony series fitting technology, the character of the stress relaxation behaviors at three scales subject to variation in temperature is investigated, and the equivalent time-dependent thermal expansion coefficients (TTEC), the equivalent time-dependent thermal relaxation modulus (TTRM) under micro-scale and meso-scale were predicted. Furthermore, the impacts of temperature, structural parameters and relaxation time on the time-dependent thermo-viscoelastic properties of 3D braided four-directional composites were studied.
Purpose
This paper aims to investigate the creep properties of the bulks of low-Ag Cu/Sn-Ag-Cu-Bi-Ni/Cu micro solder joints from 298 to 358 K. The creep constitutive modelling was developed. Meanwhile, the creep mechanism of the bulks of Cu/Sn-Ag-Cu-Bi-Ni/Cu micro solder joints was discussed.
Design/methodology/approach
The creep properties of the bulks of low-Ag Cu/Sn-Ag-Cu-Bi-Ni/Cu micro solder joints from 298 to 358 K were investigated using the nanoindentation method.
Findings
The results of the experiments showed that the indentation depth and area increased with increasing temperatures. At the test temperature of 298-358 K, the creep strain rate of the bulks of the micro solder joints increases with the rising of the tested temperature. The values of creep stress exponent and activation energy calculated for the bulks of Cu/Sn-Ag-Cu-Bi-Ni/Cu micro solder joints were reasonably close to the published data. At the tested temperatures, dislocation climb took place and the dislocation climb motion was controlled by the dislocation pipe mechanism, and the second-phase particles enhancement mechanism played a very important role.
Originality/value
This study provides the creep properties of low-Ag Cu/Sn-Ag-Cu-Bi-Ni/Cu solder joints at different temperatures. The creep constitutive modelling has been developed for low-Ag Cu/Sn-Ag-Cu-Bi-Ni/Cu solder joints.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.