International Journal of Damage Mechanics

This paper presents a micro-mechanistic approach for modeling fatigue damage initiation due to cyclic plasticity and cyclic creep in eutectic Pb-Sn solder. The issue of damage evolution is deferred to a future paper. Fatigue damage model due to cyclic plasticity is modeled with dislocation mechanics. A conceptual framework is provided to quantify the influence of temperature on fatigue damage due to cyclic plasticity. Damage mechanics due to cyclic creep is modeled with a void nucleation model based on micro-structural stress fields. Micro-structural stress states are estimated under viscoplastic phenomena like grain boundary sliding and its blocking at second phase particles, and diffusional creep relaxation. A conceptual framework is provided to quantify the creep-fatigue damage due to thermo-mechanical cycling.

This paper presents the development of a damage-coupled constitutive model to characterize the mechanical behavior of 63Sn-37Pb solder material under thermo-mechanical fatigue (TMF) loading. Based on the theory of damage mechanics, two internal state variables, known as the damage parameters, are introduced to characterize material degradation due to the change of material microstructures under load. Then, a damage effect tensor is proposed to define the effective stress for a damaged material. In general, there are two different kinds of damage accumulation depending upon the mode of loading: inelastic damage and fatigue damage. With the aid of irreversible thermodynamics, the damage evolution equations are established. A failure criterion is proposed based on the equivalent damage accumulation in materials. A test program to determine the material parameters is also presented.

The damage model is implemented in a finite element program ABAQUS through its user-defined material subroutine UMAT. The model is applied to predict the behavior for 63Sn-37Pb solder alloy under monotonic tensile loading, load-controlled tensile creep loading and strain-controlled fatigue loading. The behavior of a notched specimen under monotonic tensile loading is also examined. The predicted failure mode and maximum load agree well with those measured experimentally.

Concurrent vibration and thermal loading is commonly encountered in the service life of electronic packaging, such as in automotive, airplane, military and mobile electronic devices. Solder joint reliability has been a critical issue of the overall design of microelectronic devices. However, the contribution of vibration to thermal fatigue life of solder joints has rarely been investigated. Presently, vibration is taken as a loading case that only causes elastic material response. Literature is scarce on vibration plasticity and vibration caused fatigue for micron scale structures. The standard practice in the industry is to use Miner’s rule to calculate combined environment fatigue life. This study shows that using Miner’s rule for fatigue life under combined loading is inaccurate for micron scale solder joints. There are a number of constitutive models to simulate thermomechanical behavior of solder joints, yet few of these, if any, models are verified by test data obtained from actual microelectronics solder joints. The authors see the need of such tests for the purpose of better understanding of material behavior of micron scale solder joints under thermal and vibration loading and providing a solid basis for more accurate material modeling and fatigue life prediction. This paper reports observations from a series of concurrent thermal cycling and vibration tests on 63Sn/37Pb solder joints of an actual ball grid array (BGA) package. Moiré interferometry (MI) is used to measure the inelastic deformation field of solder joints with submicron resolution. A large capacity Super AGREE thermal chamber and a high acceleration electrodynamic shaker are assembled together to perform the concurrent cycling. The cyclic plasticity of solder joints and microstructure evolution are discussed and related to fatigue life prediction. The results obtained in this study agree with findings reported in the literature from micron scale material testing where it has been shown that “smaller is stronger.”

In the present paper we describe and demonstrate a computationally efficient technique for analyzing fracture mechanics problems in mixed linear-nonlinear systems. The technique combines the methodology of Rybicki and Kanninen for calculation of the energy release rate in fracture processes with a decomposition based analysis procedure recently proposed by Subbarayan and co-workers. The methodology will enable quick design decisions during the package development stages without significant loss of accuracy. The developed procedure is demonstrated on a hypothetical 5 × 5 array package. It is shown that on this representative package nearly 30% time savings (or a 150% speed-up) can be acheived in estimating the energy release rate at an accuracy loss of only 6.2%. Prior research has shown that the analysis time is nearly independent of package size, indicating unbounded speed-ups for larger package sizes.