Mechanical Engineering
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Item DURABILITY DISTRIBUTION ANALYSIS OF LEAD-FREE SOLDER JOINTS FOR PRINTED CIRCUIT BOARD APPLICATIONS(2023) Huang, Chien-Ming; Herrmann, Jeffrey; Mechanical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Fatigue models for predicting the cycles to failure of solder joints under temperature cycling situations have been discussed and developed for decades. However, most models were developed according to specific solder materials, components, and printed circuit boards in each research. There is no study to cluster and compare the fatigue models of solder joints through these different conditions. Therefore, the availability of the durability prediction of solder interconnections by using any of the available fatigue models can be unknown. On the other hand, current energy-based fatigue models for predicting the cycles to failure of the solder joint under thermo-mechanical loadings can only provide point estimates of the characteristic life or mean life. Nevertheless, the prediction of the fatigue life should be distributions with the uncertainties. Unfortunately, no study has been found that propagates the uncertainty of the cycles to failure, especially for the solder joints under temperature cycling. Therefore, the uncertainty propagation analysis of the cycles to failure is necessary to better estimate the distribution of the fatigue life of solder joint.The first part of this dissertation clusters and compares nine existing low-cycle energy-based fatigue models for different solder materials and components, and then analyzes major divergences between these studies. Moreover, the constants of the fatigue models are compared according to the divergences. Finite element simulation tool is applied to demonstrate the contributions of the factors on strain energy density and the variation on the predictions by applying these fatigue models. The results lead to conclusions with the advantages and limitations of using these available fatigue models for durability prediction of solder interconnections. These results provide insights that can help product designers understand and exploit the predictions of fatigue life while designing a printed circuit board and estimating its durability. In the end, precautions that can affect the prediction consistency of fatigue mode are provided for the engineers who will use these selected models or will develop their own models. The second part of this dissertation identifies 11 uncertain input variables, which can propagate the uncertainties, via basic mechanics theory. The eigenvector dimension reduction method and FEA simulation tool are employed to determine the distribution of the system response, which is the strain energy density. Then, the distribution of strain energy density is converted to the distribution of characteristic life (in cycles) by choosing the appropriate fatigue model from the first part of this dissertation. Finally, the distribution of cumulative distribution function of the fatigue life of solder joint is determined by taking the interval of characteristic life and specific shape parameters. In the end, this new uncertainty propagation approach can propagate the uncertainties from the material properties, geometries, and constitutive laws of the solder joint, as well as the uncertainties from strain energy density determination, low-cycle energy-based fatigue model selection, and the shape parameter from the field data in the selected fatigue life models.Item DEVELOPMENT OF FATIGUE MODELS FOR COPPER TRACES ON PRINTED WIRING ASSEMBLIES UNDER QUASI-STATIC CYCLIC MECHANICAL BENDING(2010) Farley, Daniel M; Dasgupta, Abhijit; Mechanical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)This dissertation investigates the fatigue durability of copper (Cu) traces on printed wiring assemblies (PWAs) under quasi-static cyclic mechanical flexure, using experimental results from a set of three-point bending fatigue tests, finite element (FE) modeling of the stresses generated during the cyclic bending tests, and response surfaces (RS) to facilitate iterative assessment of the model constants. Cyclic three-point bend tests were conducted on land grid array (LGA) components during this investigation. Failure analysis revealed the fatigue failure sites to be in the Cu traces, at the outer edge of the foot-print of the solder joint. A three-dimensional, elastic-plastic FE model simulating the event (based on a global and local modeling strategy) was used to determine the stresses and strains occurring at the failure site during the cyclic loading. Parametric studies were conducted to examine the influence of elastic-plastic constitutive behavior on the stress and strain states at the failure site. Results of the parametric studies were captured in compact meta-models, using polynomial response surfaces. The durability data was collected from the experiment and used in conjunction with these models, to develop a set of compatible constitutive and fatigue model constants that best fit the behavior observed. Since the loading was not fully reversed, a mean stress correction factor was needed. Existing correction methods, such as the modified Morrow model, were found to be deficient for tensile means stresses, due to high mean stresses predicted by classical constitutive models. A new correction model was proposed, based on a "tanh" term, which forced a saturation of the mean stress effect at higher stress levels for tensile means stresses. This saturation effect was also considered for compressive loading, termed the BCS model ("B" for "bounded" effect of the mean stresses), and compared with the standard unbounded model, termed the UCS model. A detailed iterative methodology was developed to iterate the Cu elastic-plastic constitutive model constants as well as the cyclic fatigue model constants needed to satisfy the observed durability behavior. This iterative model was based on the average strain values in cross section of the trace, at the failure site. The resulting fatigue model constants were termed the "averaged fatigue constants (AFCs). To further improve on the fatigue constants, the fatigue damage initiation and propagation behavior were considered separately, using a continuum damage mechanics method termed the successive initiation method. In this phase of the study, the constitutive model constants were those determined from the AFC model. This method uses an incremental damage growth concept rather than a classical fracture propagation concept, since there is distributed damage observed in the experiment. The resulting fatigue constants were termed the incremental fatigue constants (IFCs). Finally, the validity of the modeling approach and the developed AFC and IFC model constants are explored, using results from a published case study of four-point cyclic bend tests of leadless chip resistors (LCRs). The model appears to predict the results reasonably well.