Research Papers

Singularities at Solder Joint Interfaces and Their Effects on Fracture Models

[+] Author and Article Information
D. Bhate, D. Chan

 Purdue University, West Lafayette, IN 47907

G. Subbarayan

 Purdue University, West Lafayette, IN 47907ganeshs@purdue.edu

L. Nguyen

 National Semiconductor Corporation, Santa Clara, CA 95051

J. Zhao, D. Edwards

 Texas Instruments, Dallas, TX 75243

J. Electron. Packag 132(2), 021007 (Jun 25, 2010) (10 pages) doi:10.1115/1.4001588 History: Received November 26, 2008; Revised December 02, 2009; Published June 25, 2010; Online June 25, 2010

In this study, we focus on investigating the nature of the stress and strain behavior in solder joints and their effect on the hybrid damage modeling approach, which is inspired by cohesive zone modeling and Weibull functions [Towashiraporn, , 2005, “A Hybrid Model for Computationally Efficient Fatigue Fracture Simulations at Microelectronic Assembly Interfaces,” Int. J. Solids Struct., 42(15), pp. 4468–4483]. 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, we systematically examine 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 incorporating 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.

Copyright © 2010 by American Society of Mechanical Engineers
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Figure 1

(a) Schematic of crack-in-plate problem selected for modeling purposes and (b) stress-strain response predicted by a Ramberg–Osgood model with exponents 9 and 17

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Figure 2

Finite element mesh used to model the crack-in-plate problem. Quarter symmetry was exploited and the mesh was locally refined at the crack tip until results approached an elastic singularity to within a reasonable error.

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Figure 3

Stress and strain fields ahead of the crack tip for elastic and deformation plasticity material models. Power-law fits were performed to estimate the order of the singularity for comparison with LEFM and HRR solutions. Inclusion of nonlinear geometry effects (finite deformation) has a great influence on the results of deformation plasticity, blunting both the stress and strain singularities.

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Figure 4

Stress and strain fields ahead of the crack tip for incremental plasticity (rate-independent) and time hardening creep material models modeled with nonlinear geometry effects included. Stresses are non-singular but strains have singular-like behavior at the crack tip.

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Figure 5

Various levels of mesh refinement used to study mesh dependence of fields ahead of the crack tip. Number of elements along the edges is indicated.

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Figure 6

Stress, strain, and inelastic dissipation fields ahead of the crack tip for the four different levels of mesh refinement shown in Fig. 5. Whereas the stress field does not show significant sensitivity to mesh refinement, the inelastic strain and dissipation fields do.

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Figure 7

Chip scale package finite element model utilizing one-eighth symmetry and package cross-section

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Figure 8

Four-joint alumina coupon solder specimen (dimensions in mm) used in Ref. 27 along with finite element model (quarter symmetric)

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Figure 9

Inelastic dissipation, shear stress, total equivalent inelastic strain, and change in total equivalent inelastic strain per cycle plotted as a function of normalized distance from the edge of the solder joint, where the crack is expected to initiate

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Figure 10

Total equivalent inelastic strain plotted as a function of normalized distance along the centerline of the alumina coupon solder joint specimen showing singular-like behavior of equivalent inelastic strain

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Figure 11

Mesh dependence of crack growth predictions after 1000 s using the subroutine in a transient finite element analysis. The elements in the lighter shade at the bottom-left corner indicate elements, where damage exceeds the critical value (defined here as 0.95); numerical results in Table 3.

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Figure 12

Crack front after 200 cycles as predicted by the hybrid model for joint meshes of various levels of refinement. The white curve is indicative of the crack front.

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Figure 13

(a) One of the many forms of the cohesive traction-separation law, which relates fracture work/energy per unit area to separation. (b) The use of a characteristic length can yield unrealistic results for elements that do not have aspect ratio close to unity (circled)

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Figure 14

Reduced sensitivity of equivalent inelastic strain and dissipation to mesh refinement after using characteristic length measure

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Figure 15

Crack growth predictions using subroutine after incorporation of characteristic length measure; numerical results in Table 3

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Figure 16

Crack growth predictions for two different levels of refinement compared with experimental data

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Figure 17

A comparison of simulated and experimentally observed crack fronts on the chip scale package obtained using the developed computational procedure



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