Effects of the Unified Viscoplastic Formulation and Temperature Terms on the Thermomechanical Behavior of Soldering Materials

Solder materials are critical packaging compounds and due to usually weakest melting temperature among packaging constitutive materials, thus, they are frequently subjected to a multitude of physical phenomena: creep, fatigue and combined hardening effects. The complexity and interaction of such factors must be considered in suitable way in the mechanical behavior modeling using the appropriate material behavior laws. The choice of the mechanical model depends on several factors such as the complexity of constitutive equations to be integrated, the availability and suitability of implementation in the FE codes, the number of parameters to be identified, the capability of the model to represent the most common physical features of the material... Following these observations and in order to deal with these critical remarks, comparisons between the most common unified viscoplastic models should be done in the local and finite element levels for the decision upon the most efficient model. That is the aim of this paper with application to a tin based solder token as the test material. Thermoviscoplastic modeling of solders Two ways of reasoning are in general followed by researchers in the modeling efforts. In one side, available models with few material parameters are preferred because they are in generally predefined and available in the FE codes, which is leading to less identification and computation efforts but the price is a weak correlation with some material experimental data. This is acceptable in some cases based on the resemblance, the complexity of the long-term behavior of some commonly used solders, the low level of applied loadings and also the most important objective which is the lifetime prediction of the solder. We can include Anand [1] and the separated viscoplastic models [2] among these categories. On the other point of view, and inspite of the complexity of their constitutive equations, some kind of unified viscoplastic such as McDowell [3], Basaran et al. [4] Wei et al. [5] Chaboche [6] are “painfully” implemented in the FE codes by suitable integration algorithms. They also present a huge number of parameters but can describe the majority of the material physical mechanisms such creep, relaxation, Bauschinger effects, cyclic hardening, ratcheting,...These models are also suitable for complex and combined loadings such as thermal, in-phase and out-of-phase thermomechanical fatigue [7], nonproportional loadings,...they may offer the possibility of fatigue model coupling or damage model incorporation in the constitutive equations themselves leading to a realistic follow-up of the degradation of the material [8]. Based on these facts, the aim of this work is limited to the comparison of some of these models. So we present firstly a brief description of the chosen models i.e. Anand, McDowell and Chaboche unified viscoplastic models. Next, we describe the experimental tests and identification model. Then, comparisons of the numerical results issued from shear and relaxation tests are made and finally a comparison is done using finite element simulation for assembled structure. Description of the studied laws The unified viscoplastic models are usually formulated using two kinds of equations: flow law which represents the inelastic strain rate variation and a set of evolution equations for describing the variation of the state variables. The flow law reflects the inelastic deformation of metals with respect to the stress and temperature levels. Then, its formulation is mainly related to the high temperature creep mechanisms such dislocation climb and dislocation glide, creep dislocation, etc [9]. The state variables could be kinematic hardening, isotropic hardening and damage of the material. In the evolution equation and in order to represent accurately the hardening/softening effects, hardening, dynamic and thermal static recovery terms are employed. Hardening represents purely the resistance to plastic deformation and it is proportional to the inelastic strain rate. Dynamic recovery terms are used for the thermally activated mechanisms which acts especially at high temperature and serves in certain manner to take into account the dislocation annihilation during deformation. Static thermal recovery terms dominate when time-dependent effects such creep and relaxation are strongly present. So, it reduces shear stresses due to dislocation interactions (hardening) and isotropically dispersed material defects. Anand viscoplastic model. The model presents only one scalar state variable denoted by s for isotropic hardening effects [10] or « deformation resistance ». The scalar form of the model is expressed as follows: 1/ exp sinh m in G Q A B R T s                       (1) Where A and B are material parameters, Q is the activation energy, m is the strain rate sensitivity, RG is the gas constant, and T is the absolute temperature, respectively. A simple form of the evolution equation of s is defined as 0 1 . 1 ; 1 * * a in s s s h sign a s s                      (2)