Solder Creep-Fatigue Analysis by an Energy-Partitioning Approach

Abstract

This study explores the possibility of using a unified theory of creep-fatigue, similar to the Halford-Manson strain-range partitioning method, for examining the effect of cyclic temperature range on fatigue life, over a wide range of temperatures. Other investigators have attempted similar techniques before for solder fatigue analysis. The present study is different since it proposes an energy-partitioning technique rather than strain-partitioning to examine the dependence of solder fatigue behavior on temperature dependent changes in the relative amounts of plastic and creep strains. The solder microstructure also dictates creep behavior but is assumed to be a given invariant parameter in this study. In other words, this study is targeted at as-cast microstructures and does not address post-recrystallization behavior. A sample solder joint of axisymmetric configuration, commonly found in leaded through-hole mounting technology, is analyzed with the help of nonlinear finite element methods. The strain history is determined for constant-amplitude temperature cycling with linear loading and unloading, and with constant dwells at upper and lower ends of the cycle. Large-deformation continuum formulations are utilized in conjunction with a viscoplastic constitutive model for the solder creep-plasticity behavior. Relevant material properties are obtained from experimental data in the literature. The results show significant amounts of rachetting and shakedown in the solder joint. Detailed stress-strain histories are presented, illustrating the strain amplitude, mean strain and residual stresses and strains. For illustrative purposes, the hysteresis cycles are partitioned into elastic, plastic and creep components. Such partitioned histories are essential in order to implement either the Halford-Manson strain-range partitioning technique or the energy-based approach suggested here, for analyzing the creep-fatigue damage accumulation in solder material. This study also illustrates the role and utility of the finite element method in generating the detailed stress-strain histories necessary for implementing the energy partitioning approach for creep-fatigue damage evaluation. Solder life prediction is presented as a function of cyclic temperature range at a given mean temperature.

Measuring intrinsic elastic modulus of Pb/Sn solder alloys

“…Quite a few researchers have developed constitutive models to simulate the stress-strain response of the Pb/Sn solder alloys (Adams, 1986;Basaran and Chandaroy, 1998;Basaran and Chandaroy, 1997;Basaran and Tang, 2002;Chandaroy and Basaran, 1999;Dasgupta et al, 2001;Dasgupta et al, 1992;Rhode and Swearengen, 1980;Frear et al, 1995;Hacke et al, 1997;Kashyap and Murty, 1981;Knecht and Fox, 1990;Lau et al, 1987;Pan, 1991;Riemer, 1990;Subrahmanyan et al, 1989;Zubelewicz, 1993;Guo et al, 1991;Ling and Dasgupta, 2000;Wong et al, 1997;Tang and Basaran, 2001) and many others. The values of elastic modulus researchers use in these publications vary between 9 and 48 GPa.…”

A modified energy-based low cycle fatigue model for eutectic solder alloy

“…In contrast, it is much easier to calculate energy density from the low cycle hysteresis loops for any types of solder joints under test (7). Therefore, in recent years, energy-based low cycle fatigue models have been increasingly used for solder alloys (7)(8)(9). These models are not so well established as the strain-based ones, and some researchers (10) even expressed doubt on whether energy density is a true parameter governing fatigue life of solder alloy.…”

“…However, it is practically very difficult to obtain a single plastic strain value in a solder joint because of the complex stress state (6). In contrast, it is much easier to calculate energy density from the low cycle hysteresis loops for any types of solder joints under test (7). Therefore, in recent years, energy-based low cycle fatigue models have been increasingly used for solder alloys (7)(8)(9).…”

Solder joint reliability of plastic ball grid array with solder bumped flip chip

“…The elasto-plastic constitutive relations of eutectic solder are adopted from Frear et al (1994). It should be noted that, for the stress analysis of solder joints, there are various approaches in the literature, for instance, visco-plastic (creep) analysis (Darveaux and Banerji, 1992), energy partition method (Dasgupta et al, 1992), and fracture mechanics (Pao, 1992). All aforementioned models are more sophisticated than the elasto-plastic analysis.…”