Finite element implementation of non-unified visco-plasticity model considering static recovery

In order to examine relaxation behaviors of materials, static recovery term is always conducted in the backstress components for kinematic hardening in time-dependent plasticity model. Implicit integration algorithm for non-unified visco-plasticity model is derived. Plastic strain is divided into tw...

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Published in:	Mechanics of time-dependent materials Vol. 24; no. 1; pp. 59 - 72
Main Authors:	Yang, Menghao, Feng, Miaolin
Format:	Journal Article
Language:	English
Published:	Dordrecht Springer Netherlands 01.02.2020 Springer Nature B.V
Subjects:	Algorithms Characterization and Evaluation of Materials Classical Mechanics Computer simulation Convergence Cyclic loads Engineering Finite element method High temperature Iterative methods Mapping Materials recovery Mathematical analysis Mathematical models Nickel base alloys Numerical methods Plastic deformation Polymer Sciences Solid Mechanics Stiffness Strain Stress tensors Superalloys Tensors Time dependence Viscoplasticity Static recovery Return mapping Implicit integration algorithm Non-unified visco-plasticity model User subroutine
ISSN:	1385-2000, 1573-2738
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Abstract	In order to examine relaxation behaviors of materials, static recovery term is always conducted in the backstress components for kinematic hardening in time-dependent plasticity model. Implicit integration algorithm for non-unified visco-plasticity model is derived. Plastic strain is divided into two parts: the visco-plastic strain, which is calculated based on the viscosity function, and the steady strain which only depends on the equivalent deviatoric backstress. Using the Newton iterative strategy, two sets of equations for deviatoric stress and relative stress tensors are solved. Additionally, the return mapping method is applied in numerical method, and consistent tangent stiffness modulus is progressed for convergence in finite element analysis. The model is implemented into commercial software ABAQUS as user subroutine UMAT. Dwell experiments of nickel-based superalloy under strain-controlled cyclic loading with holding periods for relaxation at high temperature are selected to verify the method. The results indicate that the user subroutine attains convergence with good speed even at large increment, and the additional static recovery terms can improve the simulation for relaxation behaviors.
AbstractList	In order to examine relaxation behaviors of materials, static recovery term is always conducted in the backstress components for kinematic hardening in time-dependent plasticity model. Implicit integration algorithm for non-unified visco-plasticity model is derived. Plastic strain is divided into two parts: the visco-plastic strain, which is calculated based on the viscosity function, and the steady strain which only depends on the equivalent deviatoric backstress. Using the Newton iterative strategy, two sets of equations for deviatoric stress and relative stress tensors are solved. Additionally, the return mapping method is applied in numerical method, and consistent tangent stiffness modulus is progressed for convergence in finite element analysis. The model is implemented into commercial software ABAQUS as user subroutine UMAT. Dwell experiments of nickel-based superalloy under strain-controlled cyclic loading with holding periods for relaxation at high temperature are selected to verify the method. The results indicate that the user subroutine attains convergence with good speed even at large increment, and the additional static recovery terms can improve the simulation for relaxation behaviors.
Author	Feng, Miaolin Yang, Menghao
Author_xml	– sequence: 1 givenname: Menghao surname: Yang fullname: Yang, Menghao organization: State Key Laboratory of Ocean Engineering, School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University – sequence: 2 givenname: Miaolin orcidid: 0000-0003-2850-4254 surname: Feng fullname: Feng, Miaolin email: mlfeng@sjtu.edu.cn organization: State Key Laboratory of Ocean Engineering, School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University
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SubjectTerms	Algorithms Characterization and Evaluation of Materials Classical Mechanics Computer simulation Convergence Cyclic loads Engineering Finite element method High temperature Iterative methods Mapping Materials recovery Mathematical analysis Mathematical models Nickel base alloys Numerical methods Plastic deformation Polymer Sciences Solid Mechanics Stiffness Strain Stress tensors Superalloys Tensors Time dependence Viscoplasticity
Title	Finite element implementation of non-unified visco-plasticity model considering static recovery
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