A hybrid adaptive finite element phase‐field method for quasi‐static and dynamic brittle fracture

2019 ◽  
Vol 120 (9) ◽  
pp. 1108-1125 ◽  
Author(s):  
Fucheng Tian ◽  
Xiaoliang Tang ◽  
Tingyu Xu ◽  
Junsheng Yang ◽  
Liangbin Li
Keyword(s):  
Finite Element ◽  
Brittle Fracture ◽  
Phase Field ◽  
Field Method ◽  
Phase Field Method ◽  
Adaptive Finite Element ◽  
Dynamic Brittle Fracture

DiffCode: A System for the Simulation of Diffusion Driven Phase Evolution in Solids

2015 ◽  
Author(s):  
Subramanya Sadasiva ◽  
Ganesh Subbarayan
Keyword(s):  
Finite Element ◽  
Phase Field ◽  
Solder Joints ◽  
Three Dimensional ◽  
Phase Evolution ◽  
Field Method ◽  
Phase Field Method ◽  
Adaptive Finite Element ◽  
Finite Element Code ◽  
Void Evolution

Diffusion is an important mechanism for failure inducing phenomena in many applications. The common Pb-free solder alloys used in the current generation of electronics packages are complex multiphase multicomponent materials. As the scale of the solder joint decreases, it becomes increasingly important to account for the effect of surface phenomena such as grain boundary evolution, surface diffusion and interfacial reactions in the mechanics of the solder joints. The dynamics of these diffusion driven interfacial phenomena are affected by the state of stress and the electric current in the solid. The primary challenges to modeling the dynamics of evolution are the tracking of the interface while satisfying the boundary conditions for the bulk problem. In previous work, the authors utilized the phase field method in conjunction with a commercial finite element code to study the effect of stress and electrical fields on the diffusion driven evolution of voids in solder interconnects. The utilization of commercial tools for the simulation of the stress, electrical and thermal fields allowed for the use of pre-existing meshes and allowed the study of electromigration failure in assemblies of solder joints. However, the use of commercial tools can be expensive and the options for parallel simulation are limited, restricting the size and complexity of the simulations. In this work, the authors describe DiffCode, a parallel adaptive finite element code for three-Dimensional simulation of electromigration and stress migration driven failure due to void evolution and growth in solder as well as line interconnects using the phase field method. Several illustrative two-dimensional and three-dimensional electromigration driven void evolution simulations are demonstrated using the code.

Phase Field Modeling of Brittle Fracture Based on the Cell-Based Smooth FEM by Considering Spectral Decomposition

2020 ◽  
pp. 2050016 ◽  
Author(s):  
Fan Peng ◽  
Wei Huang ◽  
Y. E. Ma ◽  
Z. Q. Zhang ◽  
Yao Zhang
Keyword(s):  
Brittle Fracture ◽  
Phase Field ◽  
Spectral Decomposition ◽  
Strain Tensor ◽  
Phase Field Model ◽  
Field Method ◽  
Phase Field Method ◽  
Constitutive Response ◽  
Order Stress ◽  
Effective Phase

The spectral decomposition of the strain tensor is an essential technique to deal with the fracture problems via phase field method, and some incorrect results may be obtained without it. A novel phase field model for brittle fracture is developed based on cell-based smooth finite element (CS-FEM) and the spectral decomposition is taken into account. In order to describe the nonlinearity behaviors which contain the varied stress and elastic constitutive response caused by spectral decomposition. A second-order stress tensor and a fourth-order constitutive tensor based on decomposition of strain tensor are derived. A fundamental framework of CS-FEM is established to solve the phase field fracture problems, implemented by user-defined element (UEL) subroutine of ABAQUS software. The proposed model is validated by a typical Mode II crack, and the results show that the derived tensors are effective. Phase field parameter, CS-FEM parameter and mesh inhomogeneity are investigated to provide some useful suggestion for further development. Some classical numerical examples are solved by using the present model. The studies demonstrate that the proposed method can successfully overcome mesh distortion; the number of smooth cell does not show influences on the accuracy. Moreover, some results show that this method has the advantage over the standard FEM in convergence and computing efficiency.

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