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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Bibliographic Details
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
Online Access:Get full text
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Summary: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.
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ISSN:1385-2000
1573-2738
DOI:10.1007/s11043-018-09406-9