A Multiscale Damage Accumulation Theory for Solder Joint Failure

Bhate, D.; Mysore, Kaushik; Subbarayan, Ganesh

doi:10.1115/interpack2009-89399

Cited by 3 publications

(4 citation statements)

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“…Recent work proposed an information-theoretic failure model capable of describing damage accumulation and fatigue failure in ductile solids. 28,29 Characterization of damage accumulation of Sn-3.0Ag-0.5Cu test specimens during cyclic fatigue is ongoing, and we will report results from these tests as well as those on mixed solder alloys in the near future.…”

Section: Discussion Of Simulation Resultsmentioning

confidence: 97%

Constitutive Behavior of Mixed Sn-Pb/Sn-3.0Ag-0.5Cu Solder Alloys

Tucker

Chan

Subbarayan

et al. 2011

Journal of Elec Materi

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During the transition from Pb-containing solders to Pb-free solders, joints composed of a mixture of Sn-Pb and Sn-Ag-Cu often result from either mixed assemblies or rework. Comprehensive characterization of the mechanical behavior of these mixed solder alloys resulting in a deformationally complete constitutive description is necessary to predict failure of mixed alloy solder joints. Three alloys with 1 wt.%, 5 wt.%, and 20 wt.% Pb were selected so as to represent reasonable ranges of Pb contamination expected from different 63Sn-37Pb components mixed with Sn-3.0Ag-0.5Cu. Creep and displacementcontrolled tests were performed on specially designed assemblies at temperatures of 25°C, 75°C, and 125°C using a double lap shear test setup that ensures a nearly homogeneous state of plastic strain at the joint interface. The observed changes in creep and tensile behavior with Pb additions were related to phase equilibria and microstructure differences observed through differential scanning calorimetric and scanning electron microscopic cross-sectional analysis. As Pb content increased, the steady-state creep strain rates increased, and primary creep decreased. Even 1 wt.% Pb addition was sufficient to induce substantially large creep strains relative to the Sn-3.0Ag-0.5Cu alloy. We describe rate-dependent constitutive models for Pb-contaminated Sn-Ag-Cu solder alloys, ranging from the traditional time-hardening creep model to the viscoplastic Anand model. We illustrate the utility of these constitutive models by examining the inelastic response of a chip-scale package (CSP) under thermomechanical loading through finite-element analysis. The models predict that, as Pb content increases, total inelastic dissipation decreases.

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Section: Discussion Of Simulation Resultsmentioning

confidence: 97%

Constitutive Behavior of Mixed Sn-Pb/Sn-3.0Ag-0.5Cu Solder Alloys

Tucker

Chan

Subbarayan

et al. 2011

Journal of Elec Materi

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“…Through equilibrium thermodynamics and J 2 plasticity theory, it can be shown that the dissipation associated with plasticity is entropic dissipation. 17 Thus, for a material experiencing perfect plasticity, isotropic, and kinematic hardening, the entropy generation rate at a point is…”

Section: Maximum-entropy Principle and Probability Of A Microstructurmentioning

confidence: 99%

“…The following sections provide a brief summary of the development of the MEFM described in detail in Ref. 17.…”

Section: The Maximum-entropy Fracture Model (Mefm)mentioning

confidence: 99%

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Maximum-Entropy Principle for Modeling Damage and Fracture in Solder Joints

Chan

Subbarayan

Nguyen³

2011

Journal of Elec Materi

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A maximum-entropy fracture model (MEFM) is derived from concepts of information theory and statistical thermodynamics. Exploiting the maximumentropy principle enables life predictions for a structure in the presence of microstructural uncertainty. This single-parameter model relates the probability of fracture to accumulated entropic dissipation at a given material point. Using J 2 plasticity and equilibrium thermodynamics, entropic dissipation is related to inelastic dissipation. We demonstrate the MEFM by extracting the single damage accumulation parameter for Sn-3.8Ag-0.7Cu solder through cyclical fatigue testing. We then apply the model with the single parameter to numerically predict, in three dimensions, crack initiation and growth in Sn-3.8Ag-0.7Cu solder joints of a wafer-level chip-scale package (WLCSP). The simulated crack fronts are validated against experimentally observed crack fronts obtained by testing 64 packages under conditions identical to those used in the simulations. The model is shown to accurately predict the geometrical profile of the observed crack fronts, and the number of cycles corresponding to the observed crack profile to within 10% of the measured number of cycles.Key words: Maximum-entropy principle, information theory, microstructural uncertainty, lead-free solder, fatigue fracture INTRODUCTIONA variety of fatigue fracture models exist for solder joints at the present time. These include the most commonly used, but empirical Coffin-Manson relations, as well as the less frequently used, but nonempirical models based on fracture mechanics or continuum damage mechanics. The empirical Coffin-Manson models and their variants rely on an ability to predict life on the basis of conditions prevalent in an intact joint; that is, they do not track damage accumulation as well as the cracks that initiate and propagate as a result of the accumulated damage. The fracture mechanics models, particularly those based on linear elastic fracture mechanics (LEFM) 1 such as the Paris law, 2 rely on assumptions of small cracks relative to the geometry of the structures, small-scale yielding, and selfsimilar crack growth, all of which are untrue in solder joints. The continuum damage mechanics (CDM) models on the other hand often posit empirical constitutive and damage behavior in developing the failure model. 3,4 Related to the above, there are significant microstructural uncertainties present in solder joints, particularly in their lead-free variants. Lead-free solders composed of Sn-Ag-Cu are approximately 96 wt.% to 97 wt.% Sn and primarily consist of a few randomly orientated, large Sn grains. 5-9 It is well recognized at the present time that the mechanical properties and coefficient of thermal expansion (CTE) of Sn are anisotropic, inducing unique behavior in Sn-dominated lead-free solder joints. There are also suggestions in the literature that this anisotropy is a dominant determinant of

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Multiscale modeling for reliability assessment in microelectronic systems

Mysore

Subbarayan

2009

2009 IEEE International Electron Devices Meeting (IEDM)

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A Multiscale Damage Accumulation Theory for Solder Joint Failure

Cited by 3 publications

References 0 publications

Constitutive Behavior of Mixed Sn-Pb/Sn-3.0Ag-0.5Cu Solder Alloys

Constitutive Behavior of Mixed Sn-Pb/Sn-3.0Ag-0.5Cu Solder Alloys

Maximum-Entropy Principle for Modeling Damage and Fracture in Solder Joints

Multiscale modeling for reliability assessment in microelectronic systems

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