... to the observed complex material behavior, the nonlinear mixed hardening Armstrong and Frederick model combined with the Perzyna viscoplastic law was chosen to fit the experimental data. This model was subsequently implemented into a commercial finite element code and used to simulate drop tests. Actual drop test...

...M. Dube; T. Kundu 20 03 2006 13 08 2009 17 11 2011 17 11 2011 compressibility elastoplasticity hardening solders viscoplasticity We respond to the technical content of the discussion as follows: 1 Discussant appears to have erroneously assumed...

... thermomechanical cyclic loading and accumulate damage in the elements. Plastic and viscoplastic damages are evaluated based on the plastic and viscoplastic work densities obtained through finite element. Constitutive properties are updated elementwise at each step of the process based on the state of damage...

... strains, the values of the material constants in the elasto-plastic-creep model proposed by the authors are determined. Simulations of the viscoplastic deformations of a Sn–3.0Ag–0.5Cu solder alloy are also conducted to verify the validity of the proposed method. copper alloys creep deformation...

... cyclic straining. solders electronics packaging materials testing deformation tin alloys silver alloys solder alloy time-dependent deformation nonproportional loading viscoplasticity constitutive model strain rate sensitivity dwell time The reliability of solder joints becomes...

...A. F. Fossum; P. T. Vianco; M. K. Neilsen; D. M. Pierce This paper summarizes the results of a program to construct an internal variable viscoplastic damage model to characterize 95.5Sn–3.9Ag–0.6Cu (wt.%) lead-free solder under cyclic thermomechanical loading conditions. A unified model is enhanced...

... at hot, a 10 min dwell at cold, and a 5–10° Celsius per minute ramp. Thermal cycling results show that Sn3.8Ag0.7Cu marginally outperforms SnPb for four different components under the studied test condition. In addition, the extensive detailed three-dimensional viscoplastic finite element stress...

... ) over a range of strain rates ( 10 − 5 to 10 − 3 / s ) under isothermal and thermomechanical conditions. Development of a unified viscoplastic constitutive model followed, taking into account the effects of the measured strain rate and temperature changes. The temperature rate effects are considered...

... computed. Under the Perzyna scheme, F = 0 at any step implies that the viscoplastic strain rate is zero. The steady-state asymptote for constant strain-rate tests is towards constant stress, i.e., nonzero viscoplastic strain-rate equal to the applied rate and thus, a corresponding nonzero F...

... material characteristics. The microstructure is often unstable, having significant effects on the flow behavior of solder joints at high homologous temperatures. Such complex behavior makes constitutive modeling an extremely difficult task. A viscoplasticity model unified with a thermodynamics-based damage...

... to provide an efficient numerical procedure of integration and iteration for calculating stress and other associated state variables within a strain-driven format. In particular, a novel Newton-Raphson iteration algorithm for the damage coupled constitutive material model involving von Mises viscoplastic...

...M. J. Heffes; H. F. Nied This paper examines the modeling of viscoplastic solder behavior in the vicinity of interfacial cracking for flip chip semiconductor packages. Of particular interest is the relationship between viscoplastic deformation in the solder bumps and any possible interface cracking...

... a constitutive model for solder which couples viscoplasticity with a unified damage theory. The unified damage theory is characterized by a damage surface in strain space which separates fatigue damage from inelastic damage. The damage evolution equations are derived within the framework of irreversible...

.... 01 November 2002 15 12 2003 soldering alloys fatigue chip scale packaging deformation thermal shock stress-strain relations viscoplasticity interface phenomena failure analysis Solder joint fatigue failure was one of the common failure mechanisms occurring in electronic...

... thermodynamic framework. The damage, as an internal state variable, is coupled with unified viscoplastic constitutive model to characterize the response of solder alloys. The damage-coupled viscoplastic model with kinematic and isotropic hardening is implemented in ABAQUS finite element package to simulate...

... observation, and cross section inspection. The corresponding 3-D finite element simulation was performed to analyze the effects of underfill on thermomechanical behavior. The viscoelasticity of underfill and the viscoplasticity of solder were considered in the 3-D simulations. The Coffin-Manson equation...

... absorption and diffusion through the polymeric underfill, and the resulting hygromechanical viscoplastic stress history. The simulations are combined with accelerated aging tests to assess in-service durability in hot, humid environments. Model predictions are compared with results of accelerated life tests...

...P. Davuluri; S. Shetty; A. Dasgupta; S. Young Efficient modeling strategies are developed to study thermomechanical durability of high I/O Ball Grid Array (BGA) packages, in order to facilitate virtual qualification and accelerated testing of component designs. A viscoplastic stress analysis...

...-structural stress fields. Micro-structural stress states are estimated under viscoplastic phenomena like grain boundary sliding, its blocking at second-phase particles, and diffusional creep relaxation. In Part II of this paper, the developed creep-fatigue damage model is quantified and parametric studies...

... tests at 60°C, strain rate = 0.1 , with different matrix deformation exponents In the present study, the unified viscoplastic constitutive model is proposed for 63Sn37Pb eutectic solders. The present model is capable of describing creep deformations. The grain sizes and phase sizes...