Effect of Simulation Methodology on Solder Joint Crack Growth Correlation and Fatigue Life Prediction

A generalized solder joint fatigue life model for surface mount packages was previously published in Refs [1,2]. The model is based on correlation to measured crack growth data on BGA joints during thermal cycling. It was subsequently discovered by Anderson et.al. that the ANSYS 5.2 finite element code used in the model had an error in its method for calculating plastic work [3]. It was shown that significant error in life prediction could result by using a recent version of the code where the bug has been fixed. The error comes about since the original crack growth constants were derived based on plastic work calculations that had the bug. In this paper, crack initiation and growth constants are recalculated using ANSYS 5.6. In addition, several other model related issues are explored with respect to the crack growth correlations. For example, 3D slice models were compared to quarter symmetry models. Anand’s constitutive model was compared with Darveaux’s constitutive model. It was shown that the crack growth rate dependence on strain energy density always had an exponent of 1.10 +/0.15. This is in the range of the original correlation, so the accuracy of relative predictions should still be within +/25%. However, the accuracy of absolute predictions could be off by a factor of 7 in the worst case, if the analyst uses a modeling procedure that is not consistent with that used for the crack growth correlation. The key to good accuracy is to maintain consistency in the modeling procedure. Introduction Analytical models in engineering have several practical uses: 1) rapid design optimization during the development phase of a product, 2) predicting field use limits, and 3) failure analysis of product returned from the field or failed in a qualification test. The solder joint fatigue model presented here was first published in Ref [1]. An outline of the procedure to predict fatigue life is shown schematically in Figure 1. The model utilizes finite element analysis to calculate the inelastic strain energy density accumulated per cycle during thermal or power cycling. The strain energy density is then used with crack growth data to calculate the number of cycles to initiate a cracks, and the number of cycles to propagate cracks through a joint. In reference [2], more work was presented regarding sensitivity of the life prediction to the FEA procedure. As a result, the procedure was modified slightly to include volume averaging of the strain energy values near the joint interface. The model has been successfully applied to TSOP, CQFP, CBGA, PBGA, and power hybrid packages [1,2,4-9]. Calculate Strain Energy Density Accumulated per Cycle Calculate Number of Cycles to Crack Initiation Calculate Crack Growth Rate Calculate Fatigue Life Based on Joint Length Figure 1. Solder joint fatigue life prediction method. It was subsequently discovered by Anderson et.al. that ANSYS 5.5.2 and earlier versions of the finite element code had an error in their method for calculating plastic work [3]. Even though there had generally been good correlation to measured results, it was shown that significant error in life prediction could result by using a recent version of the code where the bug has been fixed (e.g. ANSYS 5.5.3 and later versions). The error comes about since the original crack growth constants were derived based on plastic work calculations that had the bug. In this paper, crack initiation and growth constants are recalculated using ANSYS 5.6. In addition, several other model related issues are explored with respect to the crack growth correlations. Several recommendations are made so the analyst can get accurate results more efficiently. Constitutive Relations Since solder is above half of its melting point at room temperature, creep processes are expected to dominate the deformation kinetics. Steady state creep of solder can be expressed by a relationship of the form [10-12] dεs dt = Css[sinh(ασ)] n exp( -Qa kT ) (1) where dεs/dt is the steady state strain rate, k is Boltzmann's constant, T is the absolute temperature, σ is the applied stress, Qa is the apparent activation energy, n is the stress exponent, α prescribes the stress level at which the power law dependence breaks down, and Css is a constant. Steady state creep data for 62Sn36Pb2Ag solder joints is shown in Figure 2.