Constitutive Modelling On The Whole-life Ratcheting Behavior Of Low-temperature Sintered Nano-scale Silver Paste

For materials or structures subjected to cyclic stress with non-zero mean stress,a cyclic accumulation of inelastic deformation will occur,which is termed as ratcheting behaviors.In the field of electronic packaging,ratcheting effects would present in the link materials,due to the different coefficients of thermal expansion and temperatures between substrates and devices.The evolution of voids and cracks in the inner of paste would affect the accumulation of ratcheting behavior,thus the effects were adopted to describe the whole-life ratcheting effects of low-temperature sintered nano-scale silver paste as the link material.In this paper,damage-coupled constitutive model were introduced into describing whole-life ratcheting behavior,and implemented in FEA.The topics has significance in theory,high innovation and great practical application value.Euler radial return mapping was adopted to implement the stress update of OWAF model,the example proves that Euler radial return mapping was efficient and convergent in the stress update of constitutive model.Afterwards,damage-coupled constitutive model was obtained in the framework of thermal mechanics and continuum damage mechanics,and Arrhenius power low was introduced to modify the flow rule.On the basis of the experimental results of the uniaxial whole-life ratcheting of low-temperature sintered nano-scale silver paste.The decreases of elastic modulus of low-temperature sintered nano-scale silver paste was adopted to describe the damage rule during the ratcheting experiments.The evolution of damage is consists of three parts: i.e.,initial,stable,and tertiary stages.The initial stage is the shortest.The secondary stage is the longest part with a stable ratcheting strain rate.In the tertiary stage,the evolution of damage reaches a plateau,causing the fatigue fracture of the sintered silver film.In addition,the damage variable of D is about 0.35 when fatigue failure appears.Moreover,the evolution of damage presents the similar rule under the normalization procedure,and the ? function method can be simulated the evolution of damage accurately under different loading conditions.The Arrhenius power-low was introduced into the constitutive model to simulate the temperature-dependent tensile response of sintered silver film.The evolution of damage accelerate the accumulation of ratcheting strain,which are in good agreement with the experimental results.Furthermore,temperature-dependent ratcheting response of sintered silver film can be also described well by the proposed model.Fortran language was adopted to compile the subroutine,which implement the damage-coupled constitutive model in FEA.The evolution of damage and damagecoupled variables were implemented in the subroutine.The results calculated in FEA was obtained in one element.The results imply that it is good fit with the model results.The good fitness illustrates the accuracy of implementation in FEA.Afterwards,the overlap structure which nano-scale silver paste applied to link material was calculated in the ABAQUS with damage-coupled constitutive model.The calculated results illustrates that the ratcheting strain calculated by damage-coupled constitutive model is higher than no damage model evidently,due to the presence of damage variables.