Study On Damage-Coupled Time-Dependent Multiaxial Constitutive And Fatigue Failure Model Of Electronic Packaging Solder Alloy

During electronic packaging processing or under service conditions, thermal mismatch among various materials often causes large inelastic strain and creep strain in solder joints. The significant deformation makes solder joints the weakest link in the entire electronic assembly. The failure of a single solder joint could make an entire electronic assembly inoperable. The major failure form of solder joints is thermal fatigue and fracture damage, and the deformation behavior and response of stress is very complex due to the complicated service conditions of solder joint. At the present time, the nonproportional cyclic deformation and fatigue failure behavior has been one of the key issues for the reliability and durability of solder joints. In recent years, many researchers have made a lot of experimental studies on the uniaxial cyclic deformation and fatigue failure behavior for solder. However, the investigations on the cyclic deformation and fatigue failure behavior under multiaxial nonproportional loading are relatively fewer. Most of the fatigue life prediction methods were still based on the classical fatigue models and these models cannot account for the degradation of solder material properties upon progressive load applications. The studies on the constitutive models and fatigue failure models based on the concept of damage mechanics mostly focused on the deformation and fatigue failure behavior under uniaxial loading. Moreover, with the development of computer technology, the cyclic deformation and fatigue behavior of engineering components can be simulated by using finite element programs (ABAQUS, ANSYS etc.). Unfortunately, the classical constitutive models in existing programs cannot relatively accurately describe the cyclic deformation behavior under complicated loading for some materials. So it is necessary to implement the new theoretical models into finite element programs and apply these models to simulate the cyclic deformation and fatigue failure behavior of engineering structures accurately. This will promote the application of the advanced theoretical models in structural analysis and life evaluation, and has great engineering application value. Therefore, it is necessary to carry out the experimental studies on the time-dependent cyclic deformation and fatigue failure behavior of solder alloy, and then to develop damage-coupled time-dependent multiaxial constitutive model and fatigue failure model, finally to implement the theoretical model into the finite element software. The study not only provides important theoretical basis, but also establishes foundation for theoretical model applied in engineering analysis and design.The following studies on solder alloy 63Sn-37Pb were carried out in this paper:1. A systemic experimental study was carried out on the cyclic deformation behavior and low cycle fatigue failure behavior of solder alloy 63Sn-37Pb under uniaxial and multiaxial strain loading. The basic characteristics of cyclic deformation and fatigue failure behavior under different strain rate, dwell time, loading shape, strain amplitude, different nonproportional strain path and its loading history were obtained by analyzing the experimental data, and this establishes foundation for the proposing of theoretical model. Furthermore, the low cycle fatigue test was carried out on simple structural specimen, so that the engineering applicability of the damage-coupled time-dependent multiaxial theoretical model used in the structure analyzing of solder alloy can be validated.2. Based on the experimental study, in the framework of irreversible thermal-dynamics and continuum mechanics, a new damage-coupled time-dependent multiaxial constitutive model and fatigue failure model under nonoproportional loading was developed based on the Sandia constitutive model and Yang's viscoplastic constitutive model. In the model, the damage evolution equation was defined and damage variable was intrudoced in the flow rule, the static recovery term and nonproportionality was introduced into the evolution equation of kinematic hardening. Correspondingly, a simple and reasonable method to determine the parameters of model was given. The comparison between the simulated and experimental results indicated that the developed theoretical model can not only describe the cyclic deformation and fatigue failure behavior of solder alloy 63Sn-37Pb under uniaxial and multiaxial loading satisfactorily, but also can predict the low cycle fatigue life of material accurately.3. The developed constitutive model and fatigue failure model was implemented into the finite element program ABAQUS by user subroutine UMAT. The internal variables were updated through the simplification and time discretization of the model and implicit stress integration algorithm, and then the consistent tangent module used in the equilibrium iteration was also deduced. The validation of the implementation was verified through the simulation of cyclic deformation behavior under different loading paths using finite element analysis.4. The developed theoretical model was used to predict the low cycle fatigue behavior under various nonproportional cyclic loading with finite element method, The comparison with experimental results indicated that the theoretical model can not only predict the response of loading and the incessant degradation of load with the cyclic number for solder structure, but also can predict the low cycle fatigue life. Moreover, the developed damage-coupled time-dependent multiaxial theoretical model can not only simulate the cyclic deformation and fatigue failure behavior of material specimen for sloder alloy, but also can predict complicated cyclic deformational behavior and low cycle fatigue behavior under nonoproportional loading paths. This work lays a foundation for the application of the theoretical model in fatigue failure analysis and also helpful to improve the analyzing method of reliability for electronic packaging solder joint.