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47Combining vibration test with finite element analysis for the fatiguelife estimation of PBGA componentsY.S. Chen *, C.S. Wang, Y.J. YangDepartment of Mechanical Engineering, Yuan Ze University, 135, Yuan-tung Road, Chung-li, Taoyuan, TaiwanReceived 8 November 2007Available online 31 December 2007AbstractThe study develops a methodology that combines the vibration failure test, finite element analysis (FEA), and theoretical formulationfor the calculation of the electronic component’s fatigue life under vibration loading.A specially designed plastic ball grid array (PBGA) component with built-in daisy chain circuits is mounted on a printed wiring board (PWB) as the test vehicle for the vibration test. It is then excited by a sinusoidal vibration whose frequency equals the fundamental frequency of the test vehicle and tested until the component fails. Because the solder balls are too small for direct measurement of their stresses, FEA is used for obtaining the stresses instead.Thus, the real displacements in the vibration test are then inputted to the FEA model when performing the stress analysis.Consequently,the stress versus failure cycles (S–N) curve is constructed by correlating both the obtained stresses on the solder balls and the number of failure cycles in the vibration test. Furthermore, the Miner’s rule is applied in calculating the fatigue damage index for those test components when failed.Finally, a formula for the prediction of the component failure cycle is deduced from all these procedures studied. It is also examined later by firstly predicting the fatigue failure cycle of a component and then conducting a vibration test for the same component for the verification purposes. The field test results have proven to be consistent with predicted results.It is then believed that the methodology is effective in predicting component’s life and may be applied further in improving the reliability of electronic systems._ 2007 Elsevier Ltd. All rights reserved.1. IntroductionThe ball grid array (BGA) package has become a majorpackaging type in recent years, due to its high capacity forthe input/output (I/O) counts. Connections with outside circuits for these packages are normally through either the solder balls or pins under the package. This results in reliability issues, since there is a higher overall risk of failure given the large number of solder balls and pins.This problem has attracted much attention from researchers into the BGA component reliability in the past few years. The majority of research has focused 48on the thermal stress induced reliability issues because large quantities of heat are generated in such complicated high I/O circuit designs. This situation is uncontroversial for electronic devices used in motionless environments. However,for many real world applications, in addition to thermal stress, electronic systems are often subjected to dynamic loadings. The most familiar case is the vibration that is always encountered when the electronic product is transported from one place to another. However, for applications involving vehicles such as automobiles, ships, and aircrafts, vibration induced stresses are the dominant stresses and may not be ignored.In general, long term vibration loadings typically will cause IC component failure, and will definitely impact the reliability of electronic systems. Much experience with tracing the root causes of failure has shown that the solderjoints are probably the most stressed area and are the major failure locations in components under such dynamic loadings. In BGA components with tens, hundreds, or even thousands of solder balls, a disastrous failure may occur even when only one of these solder joints fails. This kind of problem is not unusual from our perspective, such as electronic module failures that leads to catastrophic loss of life and property in the avionics industry. Assuring the reliability of these solder balls is thus a critical concern especially for electronic devices used in the dynamic environment.Most electronic systems used in vibration environments are subjected to random instead of harmonic excitations.As a result, quality assurance of electronic devices usually uses random vibration as the test specification for acceptance tests, screening tests, and reliability qualification tests. Generally, this kind of test can be conducted only after the prototype is manufactured. This is generally feasible only after a period of time has passed, and is often seen as uneconomic in today’s fast-paced electronic technology markets. Thus, the establishment of an accurate and effective methodology for estimating of the fatigue life of components under vibration loading has become an urgentdemand.Previous research has already attempted to establish such a methodology. Wang [1–3] applied Manson’s work [4] on solder material fatigue properties to investigate theBGA solder joint fatigue life in a random vibration environment.Wang’s results indicated that the validated model is effective in determining the integrity of the PBGA solder joints during random vibration loading. In addition to validating models, understanding failure mechanisms for the components under vibration loading is also crucial. This includes both finding the failure location and further improvement of weak areas in electronic components.Yang [5,6] used the out-of-plane sweep sinusoidal vibration test to assess the reliability of the PBGA assembly against vibration fatigue. Examination of cross-sections of the failed PBGA modules showed that fatigue failure always 49occurred at the corner solder balls of the PBGA module under the vibration loading. Wang [7] conducted a series of vibration fatigue tests both with a PBGA assemblyand an FCBGA assembly and then observed the differences in their failure modes.However, with the realistic loading, a vibration fatigue failure test will always take time to complete before the failure on the component is observed. In experimental studies,it is impractical to use such field vibration loadings for a long period of time. Therefore, to obtain the results within an acceptable period, the study utilized the most severe situation of vibration resonance loading in examining the fatigue life of all PBGA test components. Additionally, a widely used fatigue model, Miner’s rule, is also used to estimate the fatigue life of the PBGA components.In any examination of fatigue failure for solder balls,stress and cycles to failure data must be recorded. Unfortunately,most solder balls are too small for accurate measurement of their stresses during vibration tests. Instead, this data is obtained indirectly from finite element analysis (FEA) by taking the real displacements in the vibration test as the input for the analysis. To perform the reliability assessment, these analyzed stresses on the solder balls arethen correlated with the number of failure cycles in the vibration test.2. Experimental set-upsIn order to trace when the component has been failed, a specially designed PBGA component with a built-in daisy chain circuit is used in the vibration test. The component and the corresponding daisy chain circuits are shown inFig. 1. The PBGA component, 35 mm 35 mm, is mounted with 0.6 mm diameter solder balls of eutectic solder in 1 mm pitch. The PCB is made of FR4 and is 203 mm in length, 63 mm in width, and has a thickness of 1.6 mm. The daisy chain circuit connects all the solder balls on the PBGA in series with a certain resulting resistance that is monitored constantly throughout the test.Once a crack is initiated in one of the solder balls duringthe vibration test, the resistance will increase. The failure criterion as set in the study follows the IPC standard [8] by checking the daisy chain resistance when it exceeds the initial resistance by 20%, and occurring consecutivelyfive times. A data acquisition system is used to record and calculate the instantaneous daisy chain resistance.When the resistance exceeds the defined failure resistance,and five occurrences have been recorded consecutively, thecomponent is then considered as having failed and the test is stopped.To perform the vibration fatigue life test, the PBGA component and PWB assembly is mounted on the shaker with one of the two opposite edges clamped while the other is kept free. It is then excited with a harmonic displacement of 131 Hz, that is, the first natural frequency of the testvehicle. The set-up of the test component on the vibration shaker is shown in Fig. 2.503. Stress analysisAs described previously, the vibration test is used primarily to check the time to failure for the component under a specified excitation. However, it is also necessary to check the stresses on the solder balls when conducting a fatigue life assessment of the components. In this study, FEA is used for the stress analysis of the solder balls on the PBGA components, with boundary condition settings identical to those used in the vibration test. The FEA model as presented in Fig. 3 is constructed with the commercial computersoftware ANSYS 10.0. The symmetric FEA model of the test board is utilized because of the symmetry both in the geometry and the corresponding boundary conditions.Also, the boundary conditions for one of the two opposite edges are set as clamped and the other is left free to reflect the real edge conditions of the test vehicle. The material properties used in this FEA model, including those of the PWB, solder balls, substrate, chip and molding compound are listed in Table 1. It is also noted that the mesh density will have a strong impact on the FEA results.Consequently, variations in mesh densities are applied in the model in order to examine the convergence of the analyzed frequency results. Fig. 4 shows that the resultshave already converged with a total mesh of 1152 elements on a single solder ball.For verification of the FEA model, the natural frequencies of the test vehicle are examined experimentally with the modal testing method and the results are then compared with those from the FEA. Fig. 5 shows the test set-up of the modal testing method where the test sample is fixed by its two opposite edges and its frequency response function is acquired with the attached accelerometer. Fig. 6 depicts the frequency response function (FRF) of the clamped test board as obtained through the modal testing.The first three peaks on the FRF indicate that the first three natural frequencies of the test vehicle are at 131 Hz,398 Hz, and 769 Hz, respectively. Table 2 gives the comparison of the natural frequencies as found both in the modal testing and FEA. As listed in the last column of the table for the error percentages relative to those of modal testing results, all the first three natural frequencies are all within 3%.Once the FEA model is verified, further analysis with the model is then carried out to investigate the responses of the PBGA component under vibration excitation. As shown in Fig. 7 for the side view of the FEA model, the harmonic displacements as listed in Table 3 are imposed on both sides of the clamped edges with an exciting frequency of 131 Hz so that resonance will occur. This will accelerate the occurrence of component failure and savetime on the test.The corresponding modal shape of the first mode is shown in Fig.7.4. Discussions514.1. Developing the S–N curveIn order to build the stress versus fatigue failure cycles curve (S–N curve) for the eutectic solder ball, the vibration test was conducted for a total of six different exciting specifications by varying the excitation displacement each time. All the test components are tested until their daisy chain circuits have been failed, and the resulting failure cycles are recorded. The corresponding stresses on the failed solder balls are then calculated through the harmonic excitation analysis in FEA.Table 3 lists the number of experimental failure cycles and the corresponding maximum stresses on the solder balls. The relating accelerations and equivalent displacements inputted to the shaker are also listed in the table.The S–N curve as listed in Eq. (3) can be worked outthough the curve fitting of these experimental data. Eqs.(1) and (2) are the S–N curves of the eutectic solder as offered by Manson [4] and Steinberg [9], respectively.r 66:3 N_0:12 e1Tr 109:6 N_0:10 e2Tr 75:1 N_0:12 e3TWhen all these three curves are plotted together in Fig. 8, it is observed that the curve of the current study is located between the curves of Steinberg’s and Manson’s. Interesting findings on this figure include: with a certain fatigue cycle,the stress for Steinberg’s curve is located almost twice asthose of the other two. Further, the curves both for Manson’s and the current study are closer to each other than they are to Steinberg’s. It is important to note that the two curves as listed in the literatures all result from analyzingthe solder material itself. However, the solder balls tested in current study are located on actual components.As noted both in Eq. (1) and Eq. (3), the relationship between the stresses and failure cycles is r = 66.3 N_0.12 in Manson’s, and is r = 75.1 N_0.12 in the current study.When comparing these two formulae, it is apparent that the quotient which represents the descent rate of the curve are nearly identical, differing only marginally in their respective constants of 75.1 and 66.3. This narrow difference explains why these two results are so close. By contrast,the corresponding equation as deduced from Steinberg is r = 109.6 N_0.10 as listed in Eq. (2). It has aconstant coefficient of 109.6, much larger than Mason’sor the current study. This implies that the calculated fatigue cycles of Eq. (2) are invariably the highest among all the three studies when under the same stress level. Additionally,the slightly smaller quotient of _0.10 also helpsexplain why this curve is not as steep as the other two.4.2. Stress distribution of the solder balls under vibration52loadingBased on the FEA analysis, the stresses of the solder balls on the component when under vibration loading are shown in Fig. 9, which also displays the corresponding physical layout of the solder balls around the component. As shown in the FEA results, the local maximum stresses on each of the solder balls can also be examined. In addition, the global maximum stress is located on the corner solder balls in each of the column and row-directions on the PBGA component. That is to say, the solder ball at this location undergoesthe most stressed condition and should be used for the failure determination. The stresses for each of the columns and rows of the solder balls are shown in Figs. 10 and 11,respectively. As shown in Fig. 9, the local maximum stresses on the solder balls in column one are much higher thanthose of column two. For example, the largest stress is 13.79 MPa on the first solder ball of column 1, but is only 7.73 MPa on the first solder ball on column 2. These stress differences are almost doubled (Fig. 10) among all the thirteen solder balls. Similarly, the local maximum stresses for each of the solder balls in row 1 and row 2 are shown inFig. 11. The overall maximum stresses in each of these two rows are 13.79 MPa and 11.78 MPa, respectively. However, the stress variations between rows are much greater than those between the columns. For example, the first two solder balls have much higher stresses than the rest of the solderballs in the same row. The stresses on the third solder ball and thereafter do not appear to vary significantly, with the exception of the last solder ball. This is due to the contribution of the component body itself to the reinforcement of the strength of the whole package assembly.4.3. Estimation of the cumulative damage index (CDI)The Miner’s cumulative damage index is widely used to estimate component life under different loading conditions.The equation can be listed as:CDI ?n1N1 tn2N2 t . . . e4Twhere ni is the actual number of stress cycles accumulated,Ni is the number of cycles required for a failure, and CDI stands for the cumulative damage index. When CDI is equal to one, failure will occur.In order to check whether the S–N curve as derived previously from the test data with the combination of the Miner’s rule together are applicable for the prediction ofthe component life under the vibration loading, two sets of specially designed 53experiments are conducted for verifi-cation purposes. The experimental specifications are summarized in Table 4. As the same in the previous experiments, the vibration shaker is excited again here by a sinusoidal displacement. The last three lower stress levels as shown in Table 3, i.e. 13.8 MPa, 14.8 MPa, and 15 MPa, are selected for the vibration test again so that the components will last longer for a certain period of time before finally failing. Corresponding to these three stress levels, the excitation displacements required for inputs to the PWB are 0.094 mm, 0.099 mm, and 0.101 mm, respectively.The details of the experiments and corresponding CDI results can be summarized in Table 4. As shown in thetable, stress levels equal to 13.8 MPa and 15MPa were used for test set 1. While in test set 2, stress levels are set as 14.8 MPa and 15 MPa, respectively. To determine the component failure through CDI calculation as listed inEq. (4), it is necessary to check the failure cycle (Ni) fromEq. (3) for each of these three designated stress levels,and the actual test cycle (ni) in each of the field tests. The corresponding results are listed in the last column of Table 4. It is noteworthy that both of the two calculated CDI’sare happened to be roughly equal to one. This agrees with the fact that the component damage has been induced during the physical test. These verification tests have shown that the S–N curve as derived in Eq. (3) is reliable in predicting the fatigue life of PBGA components.5. ConclusionsThe study seeks to predict the vibration fatigue life of electronic components by combining both empirical and simulation tests. The major difficulty in conducting this kind of investigation is the measurement of failure stresseson the solder balls. A further problem encountered is the determination of proper material properties for the analysis purposes. However, the presented methodology offers an alternative method to overcome these difficulties. Based on the results of this study, it can be concluded that:1. By using a series of simulation and experimental processes, the S–N curve for the solder balls of PBGA component may be obtained. The accuracy of the derived stress-failure cycle relations is compared with data from the literatures and even verified further in the failure tests. The results have shown that the model is accurate enough for fatigue life prediction.2. Examination of the stress distribution among all the solder balls shows that the maximum stress occurs on the solder ball located at the corner of the PBGA component. Detailed inspection shows that the local maximumstress on each of the solder balls is located at the interface between the solder balls and the printed circuit board.References54[1] Wong TE, Reed BA, Cohen HM, Chu DW. Development of BGAsolder joints vibration fatigue life prediction model. In: IEEE electronic components and technology conference; 1999. p. 149–54.[2] Wong TE, Palmieri FW, Reed BA, Fenger HS, Cohen HM, TeshibaKT. Durability/reliability of BGA solder joints under vibration environment. In: IEEE electronic components and technology conference;2000. p. 1083–8.[3] Wong TE, Palmieri FW, Fenger HS. Under-filled BGA solder joints vibration fatigue damage. In: Proceedings of 2002 inter society conference on thermal phenomena in electronic systems (ITHERM2002); 2002. p. 961–6.[4] Manson SS. Fatigue: a complex subject – some simple approximations.Exp Mech 1965;5:202–3.[5] Yang QJ, Pang HLJ, Wang ZP, L