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Stress update algorithm for the combined viscoplastic and plastic behaviours of single‐crystal superalloys
Author(s) -
Kindrachuk Vitaliy,
Fedelich Bernard
Publication year - 2011
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.3172
Subject(s) - viscoplasticity , finite element method , constitutive equation , tangent , plasticity , rate of convergence , strain rate , subroutine , quadratic equation , convergence (economics) , mathematics , materials science , algorithm , computer science , structural engineering , geometry , composite material , engineering , computer network , channel (broadcasting) , economics , economic growth , operating system
A crystallographic constitutive model is developed, which accounts for both rate‐sensitive and rate‐insensitive flow. Single‐crystal plasticity and viscoplasticity are the limiting cases of the model, so that it properly reflects the material response over a wide temperature range. A non‐linear dynamic recovery is included to properly describe ratchetting. We provide a robust integration scheme based on generalization of the return‐mapping algorithm and of the procedure for active set search. The implicit integration and consistent tangent are implemented through the UMAT subroutine in the ABAQUS finite element program. The capability of the model to account for both high and low strain rates is demonstrated in numerical examples. Finally, the stability of integration scheme and quadratic convergence of the global Newton–Raphson equilibrium iterations are demonstrated on the example of a notched bar under tension. Copyright © 2011 John Wiley & Sons, Ltd.