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Research Papers

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

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

School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907-2088

G. Subbarayan

School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907-2088ganeshs@purdue.edu

L. Nguyen

 National Semiconductor Corporation, Santa Clara, CA 95051

J. Electron. Packag 130(2), 021003 (Apr 15, 2008) (9 pages) doi:10.1115/1.2840057 History: Received January 05, 2007; Revised August 20, 2007; Published April 15, 2008

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.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

Different methods of incorporating irreversibility into the cohesive law: (a) unloading-reloading to and from origin (17), (b) unloading to origin, hysteretic reloading (18), and (c) variable slope unloading-reloading (19)

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Figure 2

Typical form of the Weibull PDF (left) and the traction-separation law derived from the Smith–Ferrante law (right). The forms are clearly very similar.

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Figure 3

Damage accumulation as a function of elongation ratio (18)

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Figure 4

(a) Test specimen dimensions; inset shows cross section of the solder joint. (b) Crack fronts obtained as a result of thermomechanical fatigue imposed on solder joints, followed by red dye penetration. Results shown for (from left to right) 411, 621 and 807 10mincycles between 0°C and 100°C. The images were processed and crack fronts measured using SCION IMAGE (26). The circles are approximations to the experimentally observed crack fronts (all dimensions in millimeters).

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Figure 5

Thermocouple measurements for top (exposed to ambient) and bottom (in contact with Peltier device) of specimen. These profiles were used as isothermal boundary conditions in simulation.

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Figure 6

Finite element model of a quarter of the specimen assembly and the refined mesh of the solder joint

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Figure 7

Plots of the evolution of (a) inelastic strains and (b) damage ahead of the crack tip over seven simulated fatigue cycles

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Figure 8

Comparison of experimentally observed and numerically predicted crack fronts

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Figure 9

Comparison of experimentally observed and numerically predicted crack fronts for different fatigue cycles. The white squares correspond to the first set of intact tie constraints ahead of the crack front. The red dye corresponds to the cracked area.

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Figure 10

Crack growth as a function of number of cycles showing a bilinear rate of growth with a transition in rate at normalized crack length of approximately 0.7

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Figure 11

The hybrid model shows excellent correlation between crack fronts observed experimentally and tracked via simulations (reproduced from Ref. 15)

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Figure 12

The computed rate of damage change for a crack locus along the centerline of the solder interconnection (15); the change in the rate of damage change from linear to exponential occurred at a normalized crack length of approximately 0.7 and corresponded to a change in fracture morphology from creep fatigue to shear overload (28)

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