Development of Fatigue Models for Copper Traces on Printed Wiring Assemblies under Quasi-static Cyclic Mechanical Bending

Title of Document: DEVELOPMENT OF FATIGUE MODELS FOR COPPER TRACES ON PRINTED WIRING ASSEMBLIES UNDER QUASI-STATIC CYCLIC MECHANICAL BENDING. Daniel M Farley, Doctor of Philosophy, 2010 Directed By: Professor Abhijit Dasgupta Department of Mechanical Engineering 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 threedimensional, 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. DEVELOPMENT OF FATIGUE MODELS FOR COPPER TRACES ON PRINTED WIRING ASSEMBLIES UNDER QUASI-STATIC CYCLIC MECHANICAL BENDING.