Advanced Metallization and Interconnect Systems for Ulsi by R. C. Ellwanger, S. Q. Wang

By R. C. Ellwanger, S. Q. Wang

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Indd 22 5/6/11 8:54:47 AM Understanding welding stress and distortion 23 physics of welding stresses and deformations. It involves a uniformly heated bar, as shown in Fig. 1. The axial stress corresponds to the stress in the welding direction. This simplified illustration corresponds to assuming that hot filler is added to the joint and the cold, surrounding material acts as a restraint. The heating up, softening and expansion of the surrounding material is ignored in this illustration. 1] where E is Young’s modulus and a is the thermal expansion coefficient of the welded material.

1 Prescribed heat flux Two FE approaches, prescribed heat flux or temperature, are exemplified. , 1984) is found to be useful. indd 46 5/6/11 8:55:02 AM Understanding welding stress and distortion 47 1985, 1986a, 1986b) and Lindgren (2006). Goldak et al. (1990) and Akhlagi and Goldak (2005) include some discussion of advanced weld pool models. Additional useful information can be found in the books by Radaj (1999, 2003). The heat input model is not a purely predictive method (Goldak, 1989), as the net heat input is unknown.

9 shows the staggered procedure. The thermal and mechanical calculations are performed in each time step but the heat conduction takes place at fixed geometry. Thus the updating of the geometry for the thermal analysis lags one time step behind. Thermal stress problems can usually be treated as quasistatic problems. Then the inertia forces are ignored in the mechanical analysis. This is also the case for welding processes with the exception of the strongly coupled problem of explosive welding where the deformation generates the heat.

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