D. Bhate

Constitutive Behavior of Sn3.8Ag0.7Cu and Sn1.0Ag0.5Cu Alloys at Creep and Low Strain Rate Regimes

Constitutive models for SnAgCu solder alloys are of great interest at the present. Commonly, constitutive models that have been successfully used in the past for Sn-Pb solders are used to describe the behavior of SnAgCu solder alloys. Two issues in the modeling of lead-free solders demand careful attention: 1) Lead-free solders show significantly different creep strain evolution with time, stress and temperature, and the assumption of evolution to steady state creep nearly instantaneously may not be valid in SnAgCu alloys and 2) Models derived from bulk sample test data may not be reliable when predicting deformation behavior at the solder interconnection level for lead-free solders due to the differences in the inherent microstructures at these different scales. In addition, the building of valid constitutive models from test data derived from tests on solder joints must de-convolute the effects of joint geometry and its influence on stress heterogeneity. Such issues have often received insufficient attention in prior constitutive modeling efforts. In this study all of the above issues are addressed in developing constitutive models of Sn3.8Ag0.7Cu and Sn1.0Ag0.5Cu solder alloys, which represent the extremes of Ag composition that have been mooted at the present time. The results of monotonic testing are reported for strain rates ranging from 4.02E-6 to 2.40E-3 s-1. The creep behavior at stress levels ranging from 7.8 to 52 MPa is also described. Both types of tests were performed at temperatures of 25degC, 75degC and 125degC. The popular Anand model and the classical time-hardening creep model are fit to the data, and the experimentally obtained model parameters are reported. The test data are compared against other reported data in the literature and conclusions are drawn on the plausible sources of error in the data reported in the prior literature.

Constitutive Models for Intermediate- and High-Strain Rate Flow Behavior of Sn3.8Ag0.7Cu and Sn1.0Ag0.5Cu Solder Alloys

In much of the existing research, SnAgCu solder alloys are characterized at low strain rates, typically in the 10-6 to 1 s-1 range. In this paper, we report experimental results and constitutive models for two popular SnAgCu solder alloys at intermediate and high strain rates, ranging from 10-2 to 103 s-1 at room temperature. These experiments were performed using two different experimental setups: a MTS 810 uniaxial compression tester, and a split-Hopkinson pressure bar. In conjunction with our previous work at lower strain rates (10-6 to 10-3 s-1), these results yield the plastic flow response of these solders over nine decades of strain rate, and demonstrate a remarkably consistent relationship between the yield stress and the strain rate over the entire nine decades. We also develop the Anand viscoplastic constitutive model, and demonstrate that fit parameters for the low-strain rate regime can be extrapolated to accurately predict the experimental response at high strain rates. Thus, the model presented here proffers the capability of modeling solder deformation under a wide range of loading conditions using most commercially available finite element (FE) programs. To illustrate the validity of the model parameters, we develop idealized FE models together with cohesive zone failure descriptions at the interface between the solder and the intermetallic compound. We demonstrate that when used in conjunction with appropriate failure models, the constitutive model developed here accurately captures the empirically observed shift in failure modes from bulk failure to interfacial failure under tensile loading at higher strain rates.

Aging-informed behavior of Sn3.8Ag0.7Cu solder alloys

Predicting reliability of solder joints requires a thorough understanding of solder constitutive behavior. Recent studies on SnAgCu solder alloys have reported that pre-test conditions of aging-time and aging-temperatures can be factors that significantly affect solder constitutive behavior. The results presented here are a part of ongoing efforts to construct constitutive models that can predict aging affects on behavior of SnAgCu solder alloys. In this work, creep test results on aged Sn3.8Ag0.7Cu samples are reported, and aging effects are discussed primarily on secondary creep behavior and on microstructure. Aging effects on primary creep are observed, and will be discussed, and modeled in a future work. Experiments to characterize behavior were carried out using double-lap shear tests on specimens specifically prepared to represent realistic microstructures, and mitigate effects of joint geometry, and stress heterogeneity during test conditions. Aging temperatures of -10deg C, 25deg C, 75deg C and 125deg C, and aging times of 15, 30, 60 and 90 days (at each aging temperature) were selected as different levels of factors in a statistically designed experiment. Previous studies have focused on developing constitutive models without due considerations to aging effects, the results presented herein augment aging-informed constitutive model development efforts that are currently in progress.

A Nonlinear Fracture Mechanics Approach to Modeling Fatigue Crack Growth in Solder Joints

Predicting the fatigue life of solder interconnections is a challenge due to the complex nonlinear behavior of solder alloys and the importance of the load history. Long experience with Sn-Pb solder alloys together with empirical fatigue life models such as the Coffin-Manson rule have helped us identify reliable choices among package design alternatives. However for the currently popular Pb-free choice of SnAgCu solder joints. designing accelerated thermal cycling tests and estimating the fatigue life are challenged by the significantly different creep behavior relative to Sn-Pb alloys. In this paper, a hybrid fatigue modeling approach inspired by nonlinear fracture mechanics is developed to predict the crack trajectory and fatigue life of a solder interconnection. The model is shown to be similar to well accepted cohesive zone models in its theoretical development and application and is anticipated to be computationally more efficient compared to cohesive zone models in a finite element setting. The approach goes beyond empirical modeling in accurately predicting crack trajectories and is validated against experiments performed on lead-free as well as Sn-Pb solder joint containing microelectronic packages. Material parameters relevant to the model are estimated via a coupled experimental and numerical technique.

Fatigue Crack Growth and Life Descriptions of Sn3.8Ag0.7Cu Solder Joints: A Computational and Experimental Study

The need for predicting fatigue life in solder joints is well appreciated at the present time. Currently, however, there are very few experimentally validated material parameters for popular SnAgCu alloys. Furthermore, the validity of Coffin-Manson life models, being empirical, also needs to be explored for these alloys which creep in a manner significantly different from SnPb solder alloys. In this paper, we present a modeling approach inspired by cohesive zone theory of modern fracture mechanics and Weibull distributions of material failure. The approach relies on the accurate estimation of inelastic strains at the crack tip estimated through finite element analysis, which are then used to make decisions on crack propagation. Like most popular cohesive zone models, the modeling approach presented here requires the estimation of two parameters. Unlike most cohesive zone models however, no special elements are needed in the finite element model and estimation of the parameters is more straightforward. We demonstrate the applicability of the modeling approach via the simulation of fatigue crack growth in Sn3.8Ag0.7Cu solder joints subjected to anisotropic thermal cycling. Anisotropic thermal cycling conditions were created experimentally using a simulated power cycling testing device and fatigue crack fronts were tracked at different life cycles using traditional dye-and-pry methods. The experiments were repeated for varying temperature profiles. Experimental results were coupled with numerical analysis to obtain fracture parameters for Sn3.8Ag0.7Cu. The model and the parameters were then validated by verifying their predictive ability against a variety of temperature profiles. In a separate study, the authors have developed a time hardening creep model for describing the behavior of Sn3.8Ag0.7Cu. The time hardening model accounts for primary and secondary creep and does not restrict itself to the assumption of steady state creep. The need for accurate estimation of inelastic strains in the finite element model is thus met using a valid constitutive model to describe solder creep behavior. The ability of the model to predict three dimensional crack fronts for a variety of fatigue loading environments, with sufficient accuracy, is a key result of this work.

A nonlinear fracture mechanics prespective on solder joint failure: going beyond the coffin-manson equation

Predicting the fatigue life of solder interconnections is a challenge due to the complex nonlinear behavior of solder alloys and the load history. Long experience with Sn-Pb solder alloys together with empirical fatigue life models such as the Coffin-Manson rule have helped us identify reliable choices among package design alternatives. However, for the currently popular Pb-free choice of SnAgCu solder joints, designing accelerated thermal cycling tests and estimating the fatigue life are challenged by the significantly different creep behavior relative to Sn-Pb alloys. In this paper, a hybrid fatigue modeling approach inspired by nonlinear fracture mechanics is developed to predict the crack trajectory and fatigue life of a solder interconnection subjected to both isothermal accelerated thermal and anisothermal power cycling conditions. The model is shown to be similar to well accepted cohesive zone models in its approach and application and is anticipated to be computationally more efficient in a finite element setting. The approach goes beyond empirical modeling in accurately predicting crack trajectories. It is argued that such non-empirical models that capture the physics of material degradation and failure can form the basis for determining meaningful Pb-free solder environmental testing conditions as well as the acceleration factors relative to field use

Effects of Dwell Time on the Fatigue Life of Sn3.8Ag0.7Cu and Sn3.0Ag0.5Cu Solder Joints During Simulated Power Cycling

Compared to Sn-Pb solder joints, our understanding of the fatigue of SnAgCu solder joints is far from complete. The challenges to achieving a complete understanding of SnAgCu solder joint fatigue arise partly from their significantly different creep behavior and vulnerability to micro structure evolution (aging). In this paper, we present results from thermal fatigue tests carried out with the help of a simulated power cycling tester. The test specimens were 1.27 mm pitch Ceramic Ball-Grid Array (CBGA) components with two lead-free solder alloy compositions - Sn3.8Ag0.7Cu and Sn3.0Ag0.5Cu. The components were subjected to hot dwells at 100degC for 10, 30 and 60 minutes to study the effect of dwell time on the fatigue life -a total of 48 components were tested. The resulting failure data was fit to a Weibull distribution. The packages were stored at room temperature prior to testing and the effect of the time of storage on the fatigue life was also studied. Finite element analyses were performed to study the effect of hot dwell time on the fatigue life of the CBGA component.

An Information Theoretic Argument on the Form of Damage Accumulation in Solids

An approach to modeling failure that is inspired by two experimentally observed facts is presented. These observations are: (1) cracks grow as the end result of a irreversible, dissipative process, and (2) fracture has an inherent lengthscale, timescale and/or spatial hierarchy influenced by the (possibly dynamically changing) microstructural state. The second of these facts enables one to view the seemingly deterministic cracks observed at higher levels of hierarchy as resulting from uncertain events at lower-levels of hierarchy associated with microstructural variations. A key mathematical result developed in Information Theory together with the maximum entropy principle of Statistical Mechanics is utilized to derive a form of damage that is “maximally non-committal” about microstructural uncertainty in lower levels of fracture hierarchy. The irrecoverable energy that is expended in the creation of new surfaces or in plastic dissipation is associated with the microstructural damage using continuum thermodynamics and J2 plasticity theory. The formulated result is shown to provide an exponential form of damage accumulation under constant dissipation rate, and a form similar to the popular Smith-Ferrante traction-separation law of cohesive zone models under conditions of decreasing dissipation rate. Finally, the model is validated through comparisons with experimental observations of damage accumulation during cyclic fatigue testing of solder alloys.

Singularities at Solder Joint Interfaces and Their Effects on Fracture Models

The problem of solder joint fatigue is essentially one of fatigue crack growth. However, little work has been done that enables fatigue life predictions by means of tracking the crack front and its growth. Most popular fatigue life models are empirical and therefore, limited in their applicability and in the insight they provide. Analytical fracture mechanics approaches such as the Paris law and the J-integral are of questionable validity due to the fact that several assumptions made in these approaches are not appropriate in the context of solder joint fatigue. Failure in solder joints involves large plastic deformation in a viscoplastic material along with crack growth which is not self-similar and is significantly large relative to the size of the joint. Accurate descriptions of crack growth in solder joints can thus be obtained only by means of an approach that includes (a) the complete constitutive behavior of solder and (b) a non-empirical failure model that does not make the limiting assumptions of small cracks or self-similar crack growth. One such promising approach is the hybrid damage modeling approach, which is inspired by cohesive zone modeling and Weibull functions. In this study, we focus on investigating the nature of the stress and strain behavior in solder joints and its effect on the hybrid model. We review well understood principles in elastic-plastic fracture mechanics and more recent work in cohesive zone modeling, that address the nature of the singular solutions at the crack tip and provide insight when dealing with the more complex problem of solder joint fracture. Using three dimensional finite element analysis of a chip scale package (CSP), we systematically examined the stress-strain behavior at the edge of the solder joint along the interface. The singular nature of the behavior manifests itself as mesh dependence of the predicted crack front shape and the cycles to failure. We discuss the conditions under which the predicted crack growth rate is of reasonable accuracy, by incorporation of a characteristic length measure. We validate predictions made by the hybrid damage modeling approach against a companion experimental study in which crack growth was tracked in packages subjected to accelerated thermal cycling. In the first part, we discussed the effects of choice of constitutive model (elasticity, deformation and incremental plasticity and creep) and finite deformation on the nature of the singularity at the crack tip and the resulting mesh sensitivity. We used a conventional crack-in-plate analysis to first study the effects and then investigate similar effects in the more complex problem of a solder joint. In the second part, presented here, a characteristic length is introduced in an attempt to mitigate the mesh dependence, and shown to improve results for the predictions of crack growth in both, the crack-in-plate and the solder joint models.

Rate-dependent behavior of Sn3.8Ag0.7Cu solder over strain rates of 10 −6 to 10 2 s −1

Solder joints are subjected to different loading conditions depending on the application environment. Desktop and server applications for example, involve thermomechanical fatigue loads at low-strain rates and the dominant mode of failure is creep fatigue. Mobile electronics applications on the other hand, are subject to dynamic stresses on the solder joint during impact. In our previous work, we developed a constitutive model based on mechanical test data at low strain rates. Experiments were carried out using double-lap shear test specimens of specially prepared solder assemblies over strain rate regimes of 10-6 to 10-3 s-1 [D. Bhate et al.]. In this work, the previous experimental results are augmented with tests performed at higher strain rates (10-3 to 102 s-1) at room temperature. These experiments were performed using two different experimental setups: a MTS 810 uniaxial compression tester and a Split Hopkinson Pressure Bar (SHPB). The experimental results demonstrate a remarkably consistent relationship between the yield stress and the strain rate over eight decades of strain rate! We also fit the data to viscoplastic constitutive models popularly available in commercial finite element programs. Although the constitutive models are built using data at low strain rate regimes, the model is shown to be a reasonable fit to the experimental data over the entire strain rate regime under consideration (10-6 to 102 s-1). The differences in observed behavior under compression and tension are discussed, along with a microstructural study of the samples used in the tests.