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Fatigue damage - poster

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  • 1. Fatigue damage modeling in solder joints A. Abdul-Baqi, P.J.G. Schreurs, M.G.D. Geers Eindhoven University of Technology, Section of Materials TechnologyIntroduction Results In the electronics industry, reliability of the IC package is Figure 3 shows the distribution of damage at different cycles. usually assessed by the integrity of its solder joint intercon- It is clear that damage starts at the interfaces with the sec- nects. The latter have the function of forming both electrical ond phase particles, as these were initially assigned the low- and mechanical connections between the silicon chip and the est stiffness. Later on, damage propagates to the upper and printed circuit board. Repeated switching of the electronic lower interfaces, then throughout the bump. device leads to fatigue damage of the solder joints. Progres- sive damage will eventually result in a device failure. N = 30 cycles N = 60 cyclesObjective The objective of this research is to model the fatigue damage process in a solder bump when subjected to cyclic loading. The model should describe the gradual degradation of the solder bump material and predict its life-time. N = 90 cycles N = 120 cyclesMethodology The solder bump shown in Figure 1 is modeled in plain strain. Cyclic loading is applied in terms of sinusoidal shear displacement which is prescribed incrementally. Cohesive zones are embedded at physical boundaries in the solder ma- terial, i.e. grain boundaries and interphase boundaries. In a first step, the material is idealized as a well-defined two- phase system (Figure 1). Figure 3: Damage distribution in the solder bump after different Ux loading cycles. Red lines indicate damaged cohesive zones. cz g1 0.6 4 czg2 2 F (N) 0.4 0.1 mm Deff czg3 0 x 0.2 −2 czg4 (b) (a) −4 0 0 20 40 60 80 100 120 0 20 40 60 80 100 120 0.1 mm N (cycles) N (cycles) Figure 1: Modeled geometry. Figure 4: The total damage in the solder bump (a) and the reaction A cohesive zone is a four-noded element (Figure 2) with zero force (b) versus the number of cycles. initial thickness (∆ = 0). Its constitutive behavior is speci- fied through a relation between the separation ∆α and a cor- The evolution of damage in the solder bump with the number responding traction Tα , with α being either the local normal of cycles is shown in Figure 4(a), where Deff is an average ef- (n) or tangential (t) direction in the cohesive zone plane. fective measure of damage in the entire bump. The reaction force shown in Figure 4(b) decreases as a result of the grad- continuum element ual loss of the overall stiffness of the bump. ∆ cohesive zone Conclusions continuum element The cohesive zone approach seems promising in modeling fatigue damage. For a quantitative comparison with experi- mental observations, a proper choice of cohesive and other Figure 2: Illustration of the cohesive zone. parameters in the model is required. A damage variable Dα is incorporated into the cohesive zone law to account for the gradual loss of stiffness [1]. The vari- able varies between (0) for damage-free cohesive zones and (1) for completely damaged zones. The rate of damage is References: taken to be proportional to the rate of separation and the cur- [1] R OE , K.L. AND S IEGMUND , T., 2003. An irreversible cohesive zone ˙ ˙ rent damage, i.e. Dα ∝ ∆α (1 − Dα ). model for interface fatigue crack growth simulation. Engineering Frac- ture Mechanics 70, 209–232. /department of mechanical engineering PO Box 513, 5600 MB Eindhoven, the Netherlands

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