Computer modeling of isothermal low-cycle fatigue of Pb-Sn solder joints

The low-cycle fatigue stress-strain hysteresis loops and Coffin-Manson (C-M) behavior of near-eutectic solder joints under isothermal conditions (300 K) in shear were modeled employing a plastic deformation constitutive equation combined with a fatigue crack growth rate (FCGR) equation. The constitutive equation is based on Dorn's high temperature creep equation, giving /spl gamma//spl dot//sub p/=AD/spl mu/b/kT [Sinh(/spl beta//spl tau///spl mu/)]/sup n/ where /spl gamma//spl dot/ is the plastic shear rate, D the appropriate diffusion constant, /spl mu/ the shear modulus, b the Burgers vector and /spl tau/ the shear stress. A, /spl beta/ and n are mechanism constants and kT has its usual meaning. The FCGR equation employed is based on the relationship experimentally determined by the authors, namely dA/sub c//dN=B/spl Delta/W/sub p//sup b/ where dAc/dN is the crack area growth rate and /spl Delta/W/sub p/ (=/spl Delta//spl tau//spl Delta//spl gamma//sub p/) is the plastic work per cycle. B and b are material constants. Reasonable agreement was found between the calculated and measured hysteresis loops and also the C-M behavior.<
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