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 γ˙_p=ADμb/kT [Sinh(βτ/μ)]ⁿ where γ˙ is the plastic shear rate, D the appropriate diffusion constant, μ the shear modulus, b the Burgers vector and τ the shear stress. A, β 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_c/dN=BΔW_p^b where dAc/dN is the crack area growth rate and ΔW_p (=ΔτΔγ_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