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OCTOBER 2023 I PCB007 MAGAZINE 45 der joints to rigid components can be used. e relationship predicts that increasing strain will decrease the number of cycles to failure in a specific way. Within a certain tempera- ture range, increasing the temperature cycling range is a way of increasing the strain. In general, the acceleration model should be based on the rate-controlling step in the fail- ure process. In some cases, the rate will be determined by an Arrhenius type equation; for example, if diffusion is the rate-controlling process: where D = diffusion rate D o = diffusion constant E a = activation energy for the process K = Boltzmann constant and T 1 and T 2 and t 1 and t 2 are two temperatures and corresponding equivalent diffusion times. Note that even when temperature is an important factor, an Arrhenius relationship may not exist; in the preceding thermal cycling example, the failure rate is roughly propor- tional to (ΔT) 2 . Some acceleration models will be explored in the following sections. e limits of applicability of an accelera- tion model are as important as the model itself. Increasing or decreasing the temperature too much may promote new failure modes that would not occur in service or invalidate the quantitative acceleration relationship. For example, if the temperature is elevated above the glass transition temperature (Tg) of the board, the z-axis CTE increases sharply, and the modulus decreases. is may actually lessen the strains imposed on solder joints, but it may also promote plated through-hole fail- ures. Finite element modeling/analysis (FEM/ FEA) can be invaluable in developing and/or applying acceleration models for thermal and mechanical tests. Two-dimensional nonlinear modeling capability will usually be required in order to get meaningful results. Models can be constructed to estimate the stresses and strains in the material (e.g., the Cu in a PTH barrel or the solder in a surface-mount or through- hole joint) under operating conditions as well as under test conditions. ese estimates will be far more accurate than the simple models provided in this overview because they can account for the interactions between materi- als in a complex structure and both elastic and plastic deformation. 5. Design tests based on the acceleration models and accepted sampling procedures. Using the acceleration model and the service environment and life, select test conditions and test times that simulate the life of the prod- uct in a much shorter period of time. e sam- ple size must be large enough that it is possi- ble to determine whether the reliability goal (acceptable number of failures over the service life) has been met. 15 Ideally, the life distribution in the accelerated test should be determined, even when the test period must be extended to do so. 6. Analyze failures to confirm failure mode predictions. Since an accelerated test is based on the assumption that a particular failure mode in the accelerated test is the same one that occurs in service, it is important to con- firm by failure analysis that this assumption is valid. If the failure mode in the accelerated test is different from the one expected, several pos- sibilities should be considered. 1) e accelerated test is introducing a new failure mode different from the one that will occur in service. Usually, this means that the acceleration of one parameter (e.g., frequency, temperature, humidity) was too severe. 2) e initial determination of the dominant failure mode was incorrect. In this case, to understand the significance of the test