【机械类毕业论文中英文对照文献翻译】结合振动测试与有限元分析估算PBGA元件的疲劳寿命
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【机械类毕业论文中英文对照文献翻译】结合振动测试与有限元分析估算PBGA元件的疲劳寿命,机械类毕业论文中英文对照文献翻译,机械类,毕业论文,中英文,对照,文献,翻译,结合,振动,测试,有限元分析,估算,PBGA,元件,疲劳,寿命
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附录： 结合振动测试与有限元分析估算PBGA元件的疲劳 寿命Y.S. Chen , C.S. Wang, Y.J. Yang*元智大学机械工程学系，台湾桃园中坜元东路135号。摘要该研究开发了一种方法，结合了振动故障测试，有限元分析（ FEA ） ，并且从理论上计算电子元件在振动载荷下的疲劳寿命。一种特别设计的塑料球栅阵列（ PBGA ）元件和内置菊花链电路一起安装在印刷电路板（板）做为振动试验的测试工具。然后用频率等于基本频率和试验测试器频率的正弦振动信号刺激它，直到的元件失效。由于焊球太小而不能直接测量其压力，用有限元分析代替获取压力。 因此，在进行应力分析时，振动测试的真正位移被输入到有限元模型。从而，获得的应力与失效周期（S-N）曲线与焊球压力和振动试验中失效周期的数值相关。此外，当测试元件失败时，Miner的定理适用于计算其疲劳损伤指数。最后，通过所有这些研究过程可以推导出一个适合估算元件故障周期的公式。而且在第一次估算一个元件的疲劳失效周期后，然后对同一元件进行了振动试验以验证估算。证明实地测试结果是符合预期结果的。可以相信该方法在预测元件疲劳寿命时是有效的，而且它可用于进一步提高电子系统的可靠性。版权归埃尔塞维尔有限公司所有，2007年。1 、导言 近年来由于其输入/输出（ I / O ）计数能力强，球栅阵列（ BGA ）封装，已成为一种主要的包装类型。通常是透过焊球或封装的引脚连接外部集成电路和这些封装。这样的结果是可靠性问题，因为大量焊球和引脚有一个较高的整体故障风险。自从研究人员深入到BGA元件的可靠性研究，这几年这个问题引起人们的注意。大多数研究都集中在热应力引起的可靠性问题，因为大部分热量是这种复杂的I / O 电路设计所产生的。电子设备在一动不动的环境中使用时这种情况是没有争议的。但是，许多现实应用中，除了热应力，电子系统常常受到动态载荷。最熟悉的例子是，电子产品从一个地方运到另一个地方时，总是会遇到振动。但是，由于应用涉及运输工具，如汽车，船舶，和飞机振动诱导应力是最主要的应力，并可能是不容忽视的。一般情况下，长期振动载荷通常是导致集成电路组件故障原因，电子系统的并必将影响可靠性。大量追查失效根源的经验表明，在这种动态载荷下，焊关节可能是最受压最大和部件的主要故障点。采用存在几十，几百，甚至数以千计焊球的BGA元件，即使只有其中一个焊点失效就可能会出现一个灾难性的失效。从我们的角度看种这问题是不寻常的，如在航空业，电子模块故障，将导致灾难性的生命和财产损失。因此确保这些焊球的可靠性，是动态环境中使用电子设备一的个关键问题。振动环境中使用的大多数电子系统受到随机波而不是谐波激励。其结果是，电子设备的质量保证，通常利用随机振动作为测试规范进行设计试验，筛选试验，可靠性鉴定测试。一般来说，这种测试可以只在原型制造进行。只有经过一段时间产品才被许可，在今天这种快节奏的电子技术市场这往往被视为是不经济的。因此，建立一个准确和有效的方法估算振动载荷中元件的疲劳寿命已成为一个紧迫需求。 以往的研究已经试图建立这种方法。王1-3 应用莉曼森关于焊接材料的疲劳性能的著作4研究BGA焊点在随机振动环境的疲劳寿命。王的研究结果表明，确定在随机振动载荷中的封装焊料的完整性时，验证模型是有效的。除了验证模型，理解振动载荷中元件的失败机理也是至关重要的。这个包括寻找失败的位置，并进一步改善电子元器件的薄弱环节。杨5,6使用了平面扫描正弦振动测试评估的可靠性，减少封装振动疲劳。封装模块的横截面失效测试表明，在振动载荷中疲劳失效总是发生在封装模块焊球的角落。王7 用PBGA装配和FCBGA装配进行了一系列振动疲劳试验，然后观察其失效模式差异。 然而，在现实负荷时，振动疲劳失效试验从容进行直到完成，都没观察到元件失效。在实验研究时，使用这种振动载荷很长一段时间是不切实际的。因此，为了在一个可以接受的期间内取得成果，该研究利用了情况最严重的振动共振载荷审查所有PBGA测试元件的疲劳寿命。此外，还应用了被广泛使用的疲劳模型，Miner的规则，来估计PBGA测试元件的疲劳寿命。在审查焊球的疲劳失效时， 压力和周期数据必须被记录下来。 不幸的是，在振动测试中大多数焊球太小，从而很难准确测量他们的应力。而是把震动测试的实际位移作为有限元分析的输入，间接地用有限元分析得到了这一数据。执行可靠性评估时，分析得到的焊球的这些应力就和振动试验的失效周期数值建立起了联系。2 、实验设置 为了知道什么时候远件失效，一特别设计的内置菊花链电路的PBGA组件被使用到振动试验中。组件和相应的菊花链电路如图1所示。该PBGA组件（35毫米-35毫米）上用共晶溶胶以1毫米间距安装0.6毫米直径的焊球。PCB是由203毫米长，63毫米宽，1.6毫米厚的FR4做成的。雏菊链电路连接PBGA上的所有焊料球，并串联在一起，其电阻在整个测试中被不断监测。在振动试验时一旦一个焊球发起裂纹，电阻将会增加。失效所定标准的研究遵行IPC标准8，通过检查菊花链电阻，是否超过初步电阻20 ，并连续发生 5次。数据采集系统是用来记录并计算出瞬时菊花链电阻。当电阻超过规定的失效电阻，且事件已连续录得五次，则认为元件实效并停止测试。为了执行振动疲劳寿命测试，PBGA组件和PWB组件用夹子的一边固定，而另一保持自由。然后用131赫兹的谐波刺激，即是测试工具的第一自然频率。振动振动筛上的测试组件的安装图如2所示。3 、应力分析 正如前面所述，振动试验是用来初步检查在指定下的元件的激励故障时间。然而，也有必要在进行元件的疲劳寿命评估时测试焊球的应力。在这项研究中，有限元分析用于PBGA元件焊球的应力分析，其边界条件的设定与振动试验所使用的相同。在有限元模型如图3所示，是用商业通信计算机软件ANSYS10.0构建的。对称有限元模型之所以被应用，是因为其有几何对称性和相应的边界条件。此外，边界条件的两个相边缘之一设置为固定，另一个保持活动以反映测试工具真正的优势条件。那些有限元模型中所使用的材料特性，其中包括那些板，焊球，衬底，芯片和成型化合物列出在表1中。它也指出，网格密度将对有限元分析的结果具有强烈影响。因此，应用该模型不同的网格密度的以审查分析结果频率的收敛性。图4的结果表明，一个焊球1152个要素已经汇聚总网。为了核查有限元模型，用模版检测方法检查测试工具的固有频率，然后比较其结果与那些从有限元分析的来的。图5显示了测试设置模态测试方法，这里试验样品是由夹子固定的，且其频率响应函数由所附加速计获得。图6描绘了的通过模态试验测试出的夹子的频率响应函数（FRF）。FRF上的前三个高峰表明，测试工具的前三个自然频率分别是在131赫兹，398赫兹和769赫兹。表2给出了模态试验和有限元分析自然频率的比较。如该表的最后一栏所示，相对于模态测试结果的所有的前三个自然频率错误率都在3 以内。一旦有限元模型被验证，该模型和进一步的分析就开始进行来研究振动激发下PBGA元件的响应。同样地如图7所示，为有限元分析模型的侧视图，表3所列位移谐波对夹子的两边发出频率为131赫兹的频率，以便产生响应。第一模式的模态形状相应地显示于图7。4 、讨论4.1 、发展中的S-N曲线为了建立共晶锡球的应力与疲劳失效周期曲线（S-N曲线），通过每次改变激励位移，共进行了6个不同的振动试验。所有的测试元件测试，直至他们菊花链电路已经失效，以及记录由此产生的故障周期。失效的溶胶焊球相应的应力，这时也通过谐波激励的有限元分析计算出来。表3 列出了一些实验失效周期和相应焊接球的最大压力。输入到混合器的相关的振动加速度和位移，也如上表中所列。可以通过这些曲线拟合实验数据，列出Eq（3）中的S-N曲线。Eq（1）和（2）是共晶焊料的曲线S-N，分别由曼森4和斯坦伯格9提供。当所有这三个曲线在图8绘制一起，我们观察到目前研究的曲线位于斯坦伯格曲线和曼森曲线之间。这个数字有趣的结果包括：具有一定的疲劳周期，斯坦伯格的应力曲线几乎位于其他两个的两倍。此外，该曲线与曼森曲线和目前研究的曲线比他们与斯坦伯格曲线更接近。重要的是要注意到，文献中所列两条曲线的所有结果都来自对焊锡材料本身的分析。然而，目前的研究测试的焊球位于实际元件中。正如Eq（1）和Eq（3）所示，在Manson曲线中压力和失败的周期的关系是，而在本研究中是。比较这两个公式，很明显，代表率曲线下降率的斜率几乎是一样的，只是各自的常数75.1和66.3 略有不同。这种微小的差异科学解释了为什么这两个结果非常接近。通过对比，相应的推导出斯坦伯格方程是，如Eq（2）所示。它有一个常系数109.6 ，远远大于梅森的或目前研究的。这意味着在相同的应力水平下，按Eq（2）计算的失效周期总始终是所有这三项研究中最高的。而且极小的斜率0.10也有利于解释为什么这个曲线并不像其他两个那样陡。 4.2 、振动载荷下焊球的应力分布基于有限元分析，振动负荷时元件上焊球的应力如图9所示，同时也显示了元件上焊球相应的物理布局。如有限元分析结果所示，可以检测出每一个焊球上的局部最大应力。此外，PNGA元件的每一列和行方向的焊球的最大应力位于角落。这就是说，焊球在这个位置承受最大压力，并应当用来判断失效。焊球的每一个列和行的压力，分别如图10和11所示。如图9所示，第一列的焊球的局部最大应力远高于第二列的。比如说，第一列焊球的最大的压力是13.79兆帕，但只第二列的只有有7.73兆帕。在所有这30个焊球中这些压力差异几乎增加了一倍（图10）。同样第一行和第二行的局部最大应力也表示在图11中，这两行的总体最大应力分别是13.79 MPa和11.78 MPa。但是，行之间的应力差别远远大于列之间的。比如说，前两个焊球压力比同一行其他的都高。除了最后一个外，第三个和其后的焊料球没有很大的差别。这是由于元件本身加强了整个组件的强度。4.3 、估计累积损伤指数（CDI） Mine的累积损伤指数被广泛应用于估计在不同的负载条件下的元件寿命。该方程可列为：这里是应力循环积累的实际值，是失效需要的周期，CDI代表累积损伤指数。当CDI等于1时，会出现故障。为了检查用曼森原理和先前的测试所的来的S-N曲线得是否适用于预测振动负荷下元件的使用寿命，设计了两套专门的实验对其进行验证。表4对实验进行了简要说明。同前实验一样，在这里振动筛再次用正弦位移激励。最低的三个应力如表3所示，即13.8兆帕、14.8兆帕、15兆帕，它们被选中再次振动试验，其持续较长一段时间后最终失效。对应于这三个应力水平，所需输入的激发位移分别是0.094毫米、0.099毫米和0.101毫米。详细的实验和相应CDI结果可以归纳如表4所示，用于测试设置1的应力水平等于13.8 MPa和15MPa。测试装置2 ，应力水平设置分别为14.8 MPa和15 MPa。通过Eq（4）所列的CDI计算确定失效，有必要由Eq（3）为这三个指定应力水平检查失效周期和每个现场测试的实际测试周期。相应的结果列在表4的最后一栏。值得注意的是，这两个计算出的CDI都恰好大约等于1。这同意这一事实在测试时元件已经被破坏。这些验证测试表明，Eq(3)推导出的S-N曲线在预测PBGA元件的疲劳寿命时是可靠的。5 、结论这项研究旨在结合实验和模拟测试预测电子元件振动疲劳寿命。其主要困难在于测量焊球的失效应力。另一个遇到的问题是确定用于分析材料的固有性能。然而，现有的理论提供了可供选择的方法来克服这些困难。基于研究的结果，可以得出结论认为： 1 、通过一系列的模拟与实验，可以获得PBGA元件上焊球的S-N曲线。获得的应力-实效循环关系的准确性和文献数据进行了比较，甚至做了进一步的失效测试进行核实。结果表明，用该模型预测疲劳寿命是足够正确的。 2 、对所有焊接求进行的应力分布的测试表明，最大应力发生在PBGA元件焊球的角落。详细结果表明，每个焊球上的最大局部应力位于焊球与印刷电路板之间的接触面上。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 components 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 (SN) 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 Miners 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 components 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 on 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 todays 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 13 applied Mansons work 4 on solder material fatigue properties to investigate theBGA solder joint fatigue life in a random vibration environment.Wangs 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 occurred 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, Miners 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. 2.3. 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. Discussions4.1. Developing the SN curveIn order to build the stress versus fatigue failure cycles curve (SN 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 SN curve as listed in Eq. (3) can be worked outthough the curve fitting of these experimental data. Eqs.(1) and (2) are the SN 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 Steinbergs and Mansons. Interesting findings on this figure include: with a certain fatigue cycle,the stress for Steinbergs curve is located almost twice asthose of the other two. Further, the curves both for Mansons and the current study are closer to each other than they are to Steinbergs. 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 Mansons, 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 Masonsor 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 vibrationloadingBased 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 Miners 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 SN curve as derived previously from the test data with the combination of the Miners rule together are applicable for the prediction ofthe component life under the vibration loading, two sets of specially designed experiments 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 CDIsare 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 SN 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
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