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36 The PCB Magazine • March 2015 2.5x larger than the current industry standard process average. As mentioned earlier, the challenge in reli- ability testing is correlating lab testing condi- tions to field use conditions. We know that tem- perature cycling causes thermal expansion and contraction that can induce mechanical stress- es [10–14] . Let's define stress as force per unit area that results from an applied load, and strain as the physical deformation response of a material to stress. Stress is driven by the large differences in the coefficient of thermal expansion (CTE) between the plated through-hole copper and the laminate in the X, Y, and Z-axis. Stress relax- ation and strain ratcheting occur during ther- mal cycling where tensile strength is reduced at peak thermal temperature, then increases as the electroplated copper is cooled. Cumulative strain then reduces elongation, and when the cumulative strain exceeds the critical strain, ductility exhaustion is reached and cracks occur. The faster the strain rate is applied, the quicker the critical strain is reached [14] . There are several failure theories used to explain these complex stresses; Von Mises stress has been used suc- cessfully [15] , but in-depth discussion in this area is beyond the scope of this paper. Of interest are the CTE values of the electroplated copper and the laminate below and above T g . Table 4 lists those CTEs; the laminate listed is a typical 180°C T g material. The coefficient of thermal expansion (CTE) is calculated as follows: Where: dl = the change in length of material in the direction being measured; l = overall length of the material in the di- rection being measured; dT = the change in temperature over which dl is measured. We can rearrange the formula to solve for dl: Let's look at an example of this by subject- ing a 3.81 mm (0.150") thick printed circuit board to a thermal stress per IPC TM-650 2.6.8E. We're interested in the expansion above T g , and in this case the laminate T g is 180°C with a CTE of 230 (Table 4), and a solder temperature of 288ºC. We can calculate the Z-axis expansion as follows: Calculating the out-of-plane elastic modulus is more challenging [16] . The result of the thermal stress is shown in Figure 5a. The mismatch of the CTEs causes significant stresses during ther- mal excursion, which is depicted in figures 5b and 5c. With accelerated testing, we increase the level of stress (e.g., amplitude in temperature cycling, voltage, or pressure) under which test units operate. A unit will fail when its strength drops below applied stress. Thus a unit at a high stress will generally fail more rapidly than it would have failed at low stress; hence we have accelerated its life [10] . There are several different accelerated test models one can choose from. The Coffin-Man- son relationship was originally developed as an empirical model to describe the effect that temperature cycling had on the failure of com- ponents in the hot part of a jet engine [10] . The Coffin-Manson model has been used success- fully to model crack growth in solder and other metals due to repeated temperature cycling as equipment is turned on and off [12]. The ge- neric form of this model is: Table 4: CTE of electroplated copper and a typical laminate. Feature RELIABILITy TESTING AND STATISTICS continues