vibration testing and analysis of ball grid array package solder joints

Vibration Testing and Analysis of Ball Grid Array Package Solder Joints

Shaw Fong Wong*, Pramod Malatkar, Canham Rick, Vijay Kulkarni and Ian Chin Intel Technology Sdn. Bhd.

Lot 8, Jalan Hi-Tech 2/3, Kulim High Technology Park, 09000, Kulim, Kedah, Malaysia *Email: [email protected], Phone: +60-4-433-2941, Fax: +60-4-433-7581

Abstract A methodology to characterize and predict fatigue failure

of BGA package solder joints under vibration loading is presented. The results show that the board strain versus number-of-cycles-to-failure (or E-N) curve has a linear trend with little scatter in data points, similar to that of a classical fatigue theory using cyclic stress versus number-of-cycles-to-failure (or S-N) curves. Using finite element analysis (FEA), the solder joint stress was shown to be linearly correlated to the board strain. Therefore, board strain can indeed be used as an optimum engineering metric to study the fatigue of ball grid array (BGA) solder joints. In addition, the E-N curve approach was shown to be applicable to cyclic bend and cyclic shock loading conditions as well. The E-N curves of lead-free and leaded solder systems also have been generated and compared to demonstrate that the lead-free system has a better high-cycle fatigue performance. In addition, a fatigue-life prediction methodology based on the Miner’s cumulative damage theory is proposed. The effectiveness of this methodology was demonstrated with promising results through random vibration testing of actual motherboards. Finally, a novel approach to study solder joint reliability (SJR) under vibration loading at the system level, using a fatigue curve generated at the component level is presented.

Introduction Vibration testing and analysis of electronic packages for

SJR characterization is still in early stages of development, in comparison to other established reliability stress conditions, like temperature cycling, bend, and shock. The continuous reduction in the BGA package and solder ball dimensions is increasing the risk of solder joint failure under vibration loading. Current industry standards for vibration testing rely mainly on pass or fail functional test criterion, with limited knowledge of factors contributing towards the failure. Also, there is no measurement metric available that could be effectively used to monitor the fatigue of solder joints under vibration. Therefore, understanding SJR under vibration loading is gaining momentum. In this paper, a metric that can be successfully used to characterize fatigue life of BGA solder joints under vibration loading is proposed.

Various fatigue methodologies related to vibration have been presented in literature. Barker et al. proposed a generalized strain versus life approach in 1990. They combined the low- and high-cycle fatigue contributions from thermal and vibration stress conditions, respectively, to predict solder joint fatigue life by adopting Coffin-Manson equation and Miner’s damage rule [1]. Solomon used plastic strain range to plot various solder systems fatigue life from shear test results [2]. This was followed by the fatigue crack length method by Guo and Conrad. They used an optical microscope to measure directly the crack growth in the test

specimen [3]. A fatigue approach based on deflection amplitude was suggested by Chuang et al. to quantify the vibration fracture life of lead-tin and lead-free (tin-zinc) eutectic systems. In their study, samples were clamped at one end and the other end was equipped with a deflection sensor to measure the total deflection amplitude under resonant frequency [4]. Shi et al. utilized the strain-life approach to evaluate fatigue life. Both total and plastic strains were measured using a dynamic extensometer [5]. Liu et al. applied “Paris Law” towards high-cycle vibration fatigue life prediction, and their approach was quite similar to that of Chuang et al. A stroboscope and optical sensors were used to monitor crack propagation at solder joint interfaces [6]. To date, the most common and popular approach used to characterize fatigue in metals/alloys is the S-N curve approach [7]. To predict fatigue failure, Miner proposed a cumulative damage index (CDI) to represent the fraction of fatigue life that was used up in every stress cycle back in 1945. For aluminum test specimen, he showed that the average value of CDI is around one at failure [8]. Under random vibration input, the study by Wong et al. indicated failure when CDI has a value greater than or equal to 0.5 [9]. However, Steinberg [10] and Pang et al. [11] assumed failure for CDI value greater than 0.7. Although various fatigue methodologies have been suggested, those approaches were skewed towards lab-scale validation on homogeneous samples. Furthermore, application on real electronic packaging products was not fully addressed. No direct measurable engineering metric can be referred to characterize the fatigue life of a fully assembled BGA solder joints. However, an S-N curve like approach and Miner’s rule application were benchmarked from literature learning.

In this paper, a fatigue life prediction methodology based on Miner’s cumulative damage theory was developed and validated on fully loaded motherboards. Since it is impractical to measure the stress within the small BGA solder joint under vibration, board strain was used as the reference metric. The E-N curve was generated using a specific component-level vibration test setup, to aid in accurate estimation of strain and cycles to failure. This board also eliminated extraneous failure modes like pad crater and trace cracking. Data collected from the system-level random input test was used in conjunction with the E-N curve to validate the fatigue methodology. All of the tested boards went through failure analysis to confirm the failure modes and FEA was used to explain the failure trends. In addition, the effects of solder metallurgy on the fatigue life were validated. Finally, the universal applicability of the E-N curve approach to study fatigue failure under all mechanical loading conditions – Vibration, Cyclic Bend and Cyclic Shock were demonstrated. A novel approach to study solder joint reliability (SJR) under vibration loading at the system

1-4244-0985-3/07/$25.00 ©2007 IEEE 373 2007 Electronic Components and Technology Conference

level, using a fatigue curve generated at the component level is presented as well.

Setups and Methodology Component-Level Test Setup

A Dynamic Test Board (DTB) was designed and tested with an electro-dynamic vibration shaker. The DTB, shown in Figure 1(a), is an approximately 1.57mm thick, 305mm2 square board with only a BGA package mounted on it in the center. It was made up of typical FR4 printed circuit board material. The holes on the board, arranged in a circular pattern with constant distance, were used to secure the board onto a support plate using standoffs. The multiple holes enable obtaining different bend modes using the same board, by just changing the mount locations appropriately. The fine pitch BGA components were designed with a full daisy chain array of either lead-free with tin-silver-copper (SnAgCu) or leaded (SnPb) solder balls. Figure 1(b) shows the test board assembly on an electro-dynamic vibration shaker.

Figure 1: Vibration test setup: (a) a DTB mounted onto a fixture using eight standoffs, and (b) complete picture of the setup.

The potential failure modes in vibration loading are: (i) solder joint crack on board and/or package side, (ii) PCB trace crack close to package outer corners (especially when trace thickness is relatively small compared to the pad diameter), and (iii) pad crater on board side (normally with metal-defined pads). In order to focus on solder joint failure only, the other two failure modes were eliminated by adding the following design features in the corner areas of the board: thicker traces, redundant traces, and solder-mask defined (SMD) pads to ensure only BGA fatigue failure in all of the test boards. More detail on the impact of board design can be found in Malatkar, et al [12].

Under harmonic input, the board response would typically contain significant contribution from one or more modes. These are due to nonlinearities inherent in the system. In order to obtain a clean sinusoidal response, it would become necessary to minimize the impact of nonlinearities. For inputs beyond 5g (gravity acceleration), the nonlinear response was prominent, and hence the input g-level did not exceed 5g. Also, to avoid interaction between modes through internal resonance, the location of the standoffs (used to mount the board onto the shaker) was varied until the ratio of the first and second/third natural frequencies was away from 1:2 and 1:3 [13].

As discussed earlier, it is not feasible to characterize fatigue failure of solder joints using the S-N curve approach due to difficulty in measuring the solder joint stress during vibration. Instead, the board strain which is indicative of the severity of the solder joint stressing was used. Therefore, a board strain versus cycles-to-failure plot (or E-N curve) was developed. A 45° strain gage rosette was placed on the secondary side of every test board, underneath the package corner, to measure the localized bending strain as shown in Figure 2. Due to slight variations in the natural frequency and therefore the amplification of individual boards, it was necessary to directly measure the strain for every board tested. Each DTB was subjected to a sinusoidal input till failure by having a fixed G-level at a resonant frequency. The number of cycles to failure was calculated through the time to failure (in seconds) multiply with the input frequency (in Hz). Input G-levels from 0.75g to 4.0g were used to produce a range of board strain values. To monitor the connectivity of the solder joints, resistance of daisy chain structure in the package and board was recorded. A 100% increase in resistance was indicative of failure in one of the solder joints, as shown in Figure 3. The compressive principal strain (corresponding to tensile stress in solder joints) and number of cycles to failure data collected from all of the test boards was used to generate the E-N curve.

Figure 2: Strain gage attached close to the package corner on the secondary side of board.

Figure 3: Electrical daisy chain in-situ monitoring of two different boards with different failure times (100% increment in electrical resistance).

374 2007 Electronic Components and Technology Conference

FEA Model Setup A detailed 3-D model consisting of the DTB, BGA

package and solder joints was modeled using ABAQUS*, a commercially available FEA software. Specifically, the component-level test setup (reference to Figure 1), was modeled and shown in Figure 4. The model was assembled using appropriate constraints and coupling equations [14]. Based on the high-cycle fatigue failures observed experimentally, linear material properties were assumed. The specific values used for the various material parameters were similar to the ones used by Loh and Garner [15]. In this study, the linear elastic, modal superposition method was adopted, as it was computationally efficient and yet yielded accurate results. The board and the package were optimally meshed using linear and quadratic elements. Mesh density was appropriately set to provide adequate resolution at locations of interest. A local model, illustrated in Figure 5, was also analyzed to verify the local solder joint stresses.

For validation and verification purposes, two different analyses were performed: harmonic and steady-state dynamic analyses. The former determines the model’s dynamic response as a function of frequency while the latter determines the steady-state time response at a predetermined excitation frequency. These analyses were preceded by a frequency extraction step that determines the natural frequencies and mode shapes in the frequency range of interest. Modes up to twice the highest frequency in the sweep range were extracted to ensure the contributions of higher modes were accounted for in the superposition technique.

Figure 4: FEA model of the DTB, BGA package and boundary conditions.

Figure 5: Solder joint used in: (a) global model and (b) local model.

System-Level Test Setup An ATX form factor mechanical test board (MTB), as

illustrated in Figure 6 was used for system level validation. By benchmarking DTB, the MTB also has the similar design features to ensure only solder joint failure is detected. Since the same BGA component was tested on DTB level, this BGA package was the only component monitored for the system level fatigue life prediction methodology validations. The accompanied heat sink of the component was purposely removed to allow meaningful comparison with DTB can be done at later stage. However, all other components (CPU with heat sink, connectors, etc.) were included on overall MTB assembly. A fixture plate mimicking an ATX chassis was designed and used for system level vibration testing. The board thickness used is approximately 1.57mm and assembled with SnAgCu solder system. Similar to DTB, board strain and daisy chain resistance were the two main metrics monitored. Initially, strain was measured at all four corners of the MCH. Due to the non-symmetric response induced by the proximity to the CPU thermal solution, one corner was found significantly higher consistently. Hence, for all subsequence tests, only the worst case corner was monitored.

Figure 6: A fully-loaded MTB secured to a fixture plate, prior to mounting onto the vibration table.

The fatigue life prediction methodology is based on the

Miner’s cumulative damage theory, which accounts for the damage accumulated over every stress cycle. As the boards are tested with random input, a methodology is needed to determine their strain components and also the number of occurrences (or cycles). To achieve this, rainflow cycle counting algorithm was used, which essentially determines the number of cycles ni at each strain level εi from the irregular strain history [16 &17]. Miner’s rule was then applied to determine the cumulative damage from the various strain components. Failure occurs when the cumulative damage equals (or exceeds) C, as given below:

CNn

Nn

Nn

=+++ ...3

3

2

2

1

1

(1)

where ni, obtained from the rainflow algorithm, corresponds to the number of cycles of the strain component εi in the board response and Ni, obtained from the E-N curve at the strain


level εi. C was experimentally found to be between 0.7 and 2.2, but for design purposes, it is usually assumed to be 1. Results and Discussions Component-Level Analysis: Fatigue Curves

The fatigue E-N curves were generated under vibration input using 45 test boards with SnAgCu BGA packages and 31 test boards with SnPb solder. The resultant E-N curves are plotted together in Figure 7. On a log-linear plot, all of the data points of a given solder material fall along a straight line, with a correlation coefficient (R2) of around 0.8. These E-N curves have characteristics of a classical high-cycle S-N curve and, thus, demonstrated that the board strain is a viable metric in studying solder joint fatigue life. The scatter in the data points is not significant, which suggested that the test setup and procedure were robust and provided repeatable data. It is also obvious from Figure 7 that the high-cycle fatigue performance of SnAgCu solder system under vibration loading is much better than SnPb solder system.

Figure 7: E-N curves of SnAgCu and SnPb solder systems under vibration.

In addition to vibration, boards under cyclic bend and cyclic shock loading conditions were tested. The detailed test setups and input conditions were described in [18]. Here the vibration results along with those obtained from the cyclic bend and cyclic shock tests were combined, to present a complete picture of the mechanical fatigue characteristics of SnAgCu and SnPb solder systems. For the case of SnPb solder system (Figure 8), all of the data points from vibration, cyclic bend and cyclic shock tests fell along a straight line in a log-log plot, with the R2 being 0.92. However, the SnAgCu data fell along two distinct lines: vibration and cyclic bend data along one line (R2 = 0.88) and the cyclic shock data on another line (R2 = 0.76), as illustrated in Figure 9. The reason for the two sets of lines seen in the fatigue behavior of SnAgCu system is potentially due to the different failure modes observed in cyclic bend and cyclic shock tests. The failure mode transitions from predominantly bulk solder failure in cyclic bend to completely inter-metallic compound (IMC) failure in cyclic shock. In other words, the strain rate seems to be dictating the failure modes and their transitions, as reported in [19]. This could be due to the dependency of bulk solder (ductile material) and IMC (brittle material) strength on the strain rate. At higher strain rates, tensile

strength of bulk solder seems to be higher than IMC, and therefore, there was a transition in failure mode. For more details on these failure analysis finding and discussions, refer to [18].

Figure 8: Mechanical fatigue curve of SnPb solder system.

Figure 9: Mechanical fatigue curves of SnAgCu solder system..

Figure 10: Cross-over (as indicated by arrow) in the SnAgCu and SnPb solder fatigue data points.

All the data points with the SnPb and SnAgCu solder systems are plotted together in Figure 10. Interestingly, the two sets of data points, with totaling 152 in number and spanning over ten million cycles to failure, cross over approximately between 1x102 to 1x103 ranges of the


normalized cycles-to-failure point. Below the cross-over point, comprising vibration and cyclic bend data, SnAgCu solder has a higher number of cycles to failure than SnPb solder. And above the cross-over point, comprising cyclic shock data, performance of SnPb solder is much better. Component-Level Analysis: Failure Analysis Results

Figure 11: Cross-section images of a solder joint indicating cracks on the board and package interfaces, along with their initiation locations and propagation directions.

Figure 12: Dye-and-pry images of package and board interfaces on the four corners solder joints. The dye material on board and package pads indicates the presence of a crack and also its propagation direction.

All of the test boards went through failure analysis (FA),

to verify the actual failure modes. Two FA methods, namely cross-sectioning and dye-and-pry (D&P), were used to determine the crack initiation location and direction of crack propagation under vibration loading. Majority of the samples had predominantly bulk solder failure, but in certain cases the crack also propagated through the IMC layer, especially in SnAgCu solder system. The common trends observed are as follows: (i) The crack always initiated near to bulk solder, right next to the solder resist, due to the high stress concentration generated at that location; (ii) The crack then propagated through the bulk or along the solder/IMC interface and/or through the IMC layer; and (iii) The direction of crack growth was along the package diagonal. On the board side, the cracks initiated and grew towards package center, whereas on the package side it grew away from package center. All these trends are illustrated in the cross-section images in

Figure 11 and the D&P images in Figure 12. This cracking behavior was further validated with FEA approach in the next section. FEA Model Analysis: Model Tuning and Validation

The FEA model was correlated for global behavior using experimental frequency-response function (FRF). The model was tuned based on the data collected by the accelerometer placed at the center of the BGA package. Figure 13 shows the FRF comparison between experiment results and FEA predictions. As tabulated in Table 1, a relatively good correlation between the natural frequencies with errors well within 10%. However, the comparison discovered a missing mode and minor disparity in the higher frequencies. These differences were attributed to the boundary conditions assumed in the model. For instance, the actual standoffs were elastic and influence the board response, but were assumed to be rigid in the FEA model.

The validation and tuning process also involved comparing the mode shapes. The modes shapes from FEA and experimental modal analysis (EMA) had remarkably good correlation throughout the entire frequency range of interest. Figure 14 shows the excellent graphical matching between the 1st and 5th modes of the DTB mode shapes. Furthermore, the board strain response obtained from the model with the experimental strain gage measurements for various input G levels was compared. Figure 15 illustrates the good matching of the in-plane board strain time history between experiment and FEA for sinusoidal input of 1.0g in time history plots.

Figure 13: Experimental and FEA FRF comparison at 0.1g sinusoidal input.

Table 1: Comparison between experimental and FEA natural frequencies

Frequency (Hz) Mode

Experiment FEA % Difference

1 78.8 75.4 -4.35% 2 126.9 137.3 +8.17% 3 297.5 306.4 3.00% 4 328.5 - - 5 367.3 370.1 +0.78% 6 447.6 432.1 -3.47% 7 470.3 462.3 -1.69% 8 487.5 500.3 +2.64%

Crack propagates within bulk solder

Crack initiation inbulk solder

Crack propagation direction

Crack propagates within bulk solder

Crack initiation inbulk solder

Crack propagation direction


Figure 14: Mode shape matching between EMA and FEA for: (a) 1st mode and (b) 5th mode.

Figure 15: Comparison of DTB strain response between FEA prediction and experimental values for a sine input of 1.0g. FEA Model Analysis: Solder Joint Stress and FA Trends

As discussed in previous sections, fatigue fracture through the bulk solder adjacent to the IMC is the common failure found in solder joints subjected to vibration loading. Figure 16 shows the cross-section view of a typical solder joint fatigue failure and the FEA prediction of the maximum principal stress vectors on the board and package interfaces. The FEA prediction of the crack initiation location and direction of crack propagation matched exactly with that observed in experimental FA results. In addition, the maximum principal stress contour from FEA was in agreement with D&P images in Figure 17. Again, similar trends between experiment and FEA were observed.

Besides, the FEA model has established the relationship between the in-plane board strain and the stress generated at the corner most BGA solder joints. The board strain and solder joint stress values were recorded for different acceleration levels while keeping the input frequency fixed at the 1st natural frequency. From Figure 18, it is clear that the board strains and solder joint stresses are linearly correlated and this was observed in [15]. This linear relationship justifies the use of board strain as a metric to study BGA package

solder joint fatigue and allow translation of the E-N curve into S-N curve in future works.

Figure 16: Cross-section image indicating crack initiation and propagation direction along with FEA prediction of maximum principal stress vector.

Figure 17: Matching between stress contour plots and dye-and-pry images from FA on the package and board interfaces.

Figure 18: Relationship between maximum solder joint stress and in-plane board strain.


Methodology Validation and System-Level Analysis The methodology validation activity was divided into two

parts. Firstly, the same setup of the DTB was subjected to random vibration input. The random power-spectral density was kept constant over a wide range of frequency, where the average acceleration (in root mean square, gRMS) level was varied for different board samples to obtain different time to failure values. All tests were run until failure as determined by 100% change in the daisy chain resistance. Strain data was collected at 1000 scans per second for the entire duration of test. The second part of methodology validation activity also used random input, but this time tested with the MTB configuration.

The rainflow distributions for every response strain history obtained from the DTB and MTB random input tests were determined using a MATLAB* script [20]. The Miner’s sum values obtained for the two different tests are tabulated in Tables 2 and 3. The average Miner’s sum obtained from the six DTB and eleven MTB boards are 1.13 and 1.55, respectively.

Table 2: Miner’s sum calculated using DTB strain response data.

Test Input gRMS Miner’s Sum 1.5 0.55 1.8 0.25 1.8 3.39 2.1 1.13 2.1 0.72

Component-level random input test

using DTB

2.1 0.71

Table 3: Miner’s numbers calculated using MTB strain response data.

Test Input gRMS Miner’s Sum 1.0 0.87 1.0 0.29 1.5 0.69 1.5 0.39 2.0 1.18 2.0 1.73 2.0 4.04 2.5 1.38 2.5 3.83 2.5 1.35

System-level random input test

using MTB

2.5 1.34 To get an idea of the variation in the E-N curve data

points, Miner’s sum for those boards were computed using the following formula:

curve

test

NN

M = (2)

where, Ntest denotes the actual number of cycles to failure for a given DTB from the test and Ncurve represents the predicted number of cycles to failure calculated using the measured strain of the DTB in the E-N curve relationship. Interestingly, the average Miner’s sum obtained from the 45 DTB boards used in the E-N curve generation is 1.52.

A pictorial summary of the Miner’s sum from the three sets of testing (DTB with sine input, DTB with random input, and MTB with random input) is illustrated in Figure 19. Apparently, the variation in Miner’s sum calculated using the proposed methodology based on the data from the random input tests of DTBs and MTBs was well within the variation seen in the sine tests. This clearly demonstrates that the proposed methodology is very effective in predicting fatigue failure accurately at the system level.

Figure 19: Distribution of Miner’s sum for all test cases. Besides, an interesting trend in all of the DTBs and MTBs

boards tested under random vibration was also observed. The Miner’s sum was entirely influenced by the higher strain components, even though their occurrence in the overall response was much lesser than the smaller strain components. Figure 20 shows a joined plot of the rainflow distribution and Miner’s sum contribution of the various strain components. The design implication of this is that if a system can be designed to reduce largest and most damaging strain components, then the BGA fatigue life can be greatly increased. It was also observed that the Miner’s sum for greater inputs (gRMS levels) was higher. This could be due to the difference in the strain state (or shape) of the board between the sine and random test cases. In addition, the current Miner’s sum calculation is not scalable. In other words, board strain data needs to be collected during the entire duration of the test (resulting in a large data file). This is being attributed to potential nonlinear response in the random vibration tests, due to the presence of high strain components. These issues will be addressed in future studies.

Figure 20: The rainflow distribution and Miner’s sum contribution plots.


Conclusions A component-level E-N curve approach was proposed to

characterize BGA package solder joint fatigue under vibration input. The specific designed test setup led to a linear E-N curve indicating the robustness of this metrology. This also validated the use of board strain as a metric to study solder joint fatigue. The linear relationship between the solder joint stress and board strain, obtained through FEA, further confirmed the use of board strain as an optimum engineering metric to monitor the severity of solder joint stressing. FEA was also successfully employed to explain the location of crack initiation and direction of crack propagation, on the board and package interfaces, as observed in experiments. The comparison of SnAgCu and SnPb fatigue curves clearly indicated the better performance of SnAgCu solder system under high-cycle fatigue test. However, this trend was reversed in low-cycle fatigue, where SnPb solder has superior fatigue resistance. The cross-over of SnAgCu and SnPb fatigue curves and the role played by strain rate in dictating the failure mode were also demonstrated. A fatigue-life prediction methodology, based on Miner’s rule was proposed and validated with reasonably good results using MTBs mimic to real motherboards. This methodology also holds the potential to be used seamlessly between all mechanical loading scenarios – Vibration, Cyclic Bend and Cyclic Shock.

For future work, extension of the E-N curve approach to socket solder joints is planned. The fatigue-life prediction methodology would be used to study the fatigue failure under combined vibration, cyclic bend and/or cyclic shock loading conditions. Additionally, the FEA model would be further developed to identify package and board design parameters that significantly impact solder joint fatigue life, and in turn come up with design solutions to improve fatigue resistance. Also included in the plan are some fundamental studies on different solder metallurgy to reason out the trends seen in the fatigue curves of SnAgCu and SnPb solder systems. Acknowledgments

The authors would like to acknowledge the help received from Troy Pringle, Lee Chek Loon, Lew Huey Ling, Jose Chavarria, Rick Brewer and Tozer Bandorawalla in fatigue curve generation, failure analyses and methodology development. Special thanks to Luke Garner, Loh Wei Keat, Rick Williams, Pardeep Bhatti and Intel management for their support and encouragement. References 1. Barker, D. et al, “Combined Vibrational and Thermal

Solder Joint Fatigue – A Generalized Strain versus Life Approach,” Journal of Electronic Packaging, Vol. 112 (1990), pp. 129-134.

2. Solomon, H. D., “Low Cycle Fatigue of Sn96 Solder with Reference to Eutectic Solder and High Pb Solder,” Transactions of ASME, Vol. 113 (1991), pp. 102-108.

3. Guo, Z. and Conrad, H., “Fatigue Crack Growth Rate in 63Sn37Pb Solder Joints,” Journal of Electronic Packaging, Vol. 115 (1993), pp. 159-164.

4. Chuang, C. M., Lui, T. S. and Chen, L. H., “The Characterization of Vibration Fracture of Pb-Sn and Lead

Free Sn-Zn Eutectic Solders,” Journal of Electronic Materials, Vol. 30 (2001), pp. 1232-1240.

5. Shi, X. Q. et al, “Low Cycle Fatigue Analysis of Temperature and Frequency Effects in Eutectic Solder Alloy,” International Journal of Fatigue, Vol. 22 (2000), pp. 217-228.

6. Liu, X. et al, “Experimental Study and Life Prediction on High Cycle Vibration Fatigue in BGA Packages,” Microelectronics Reliability, Vol. 26 (2006), pp. 1128-1138.

7. Suresh, S., Fatigue of Materials, Cambridge University Press (Cambridge, 1992), pp. 126-140.

8. Miner, M. A., “Cumulative Damage in Fatigue,” ASME Journal of Applied Mechanics, Vol. 12 (1945), pp. A159-A164.

9. Wong, T. E. et al, “Development of BGA Solder Joint Vibration Fatigue Life Prediction Model,” 49th Electronic Component Technology Conf, 1999.

10. Steinberg, D. S., Vibration Analysis for Electronic Equipment, Wiley (New York, 2000).

11. Pang, H. L. J. et al, “Vibration Fatigue Analysis for FCOB Solder Joints,” 54th Electronic Component Technology Conf, 2004.

12. Malatkar, P. et al, “Pitfalls An Engineer Needs To Be Aware Of During Vibration Testing,” Proc 56th Electronic Components and Technology Conf, San Diego, CA, May. 2006.

13. Nayfeh, A. H., Nonlinear Interactions, Wiley (New York, 2000).

14. ABAQUS User Manual (version 6.5), ABAQUS Inc., 2005.

15. Loh, W. K. and Garner, L. J., “Solder Joint Reliability Prediction of Flip Chip Packages Under Shock Loading Environment,” InterPACK, San Francisco, CA, July. 2005.

16. Dowling, N. E., Mechanical Behavior of Materials, 2nd Edition, Prentice Hall (New Jersey, 1999), pp. 404-408.

17. Annual Book of ASTM Standards, Vol. 03.01, ASTM E 1049-85 (Reapproved 1997), Standard practices for cycle counting in fatigue analysis, 2003.

18. Pringle, T. D. et al, “Solder Joint Reliability of BGA Package under End-User Handling Test Conditions,” to be presented at 57th Electronic Components and Technology Conf, Reno, NV, May. 2007.

19. Darveaux, R. et al, “Interface Failure in Lead Free Solder Joints,” 56th Electronic Components and Technology Conf, San Diego, CA, May. 2006.

20. Nieslony, A., “Rain Flow Counting Method,” http://www.mathworks.com/matlabcentral/files/3026/content/index.html, 2005.

*Other brands and names are the property of their respective owner.
