Development and Implementation of State Variable Based User Materials in Computational Plasticity

336 Pages·2016·18.92 MB·English

Development and Implementation of State Variable

Based User Materials in Computational Plasticity

Gerhardus J. Jansen van Rensburg

© University of Pretoria
© University of Pretoria
Development and Implementation of State Variable
Based User Materials in Computational Plasticity

by

Gerhardus J. Jansen van Rensburg

This thesis is submitted in partial ful(cid:28)llment of the requirements for the degree

Philosophiae Doctor (Mechanical Engineering)

in the

Faculty of Engineering, the Built Environment and Information Technology

University of Pretoria

Pretoria

South Africa

2016

© University of Pretoria
© University of Pretoria
Abstract

Title: Development and Implementation of State Variable

Based User Materials in Computational Plasticity

Author: Gerhardus Jacobus Jansen van Rensburg

Supervisors: Prof. S. Kok

Dr. D.N. Wilke

The Finite Element Method is a powerful tool that can be used to test, improve or bet-
ter understand an industrially relevant problem. There are numerous Finite Element

Analysis(FEA)softwarepackagesthatoperateeitherinthecommercial, opensourceor

research space. Di(cid:27)erent application speci(cid:28)c codes also have specialised model formu-

lations. Most software packages have a comprehensive list of material models already

implemented. If a di(cid:27)erent material model is required, some form of user material can
often be implemented and linked to the software package.
In some cases the e(cid:27)ective implementation and testing of a user implemented ma-
terial requires knowledge on the e(cid:27)ect and handling of strain formulations, element

technologies and the desired material behaviour. With sophisticated material models

available in the research space, this thesis focuses on the identi(cid:28)cation and implemen-

i

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tation of existing computational plasticity models for use within FEA.
The e(cid:27)ect of di(cid:27)erent strain formulation choices is (cid:28)rst illustrated and discussed
using di(cid:27)erent sample problems. Three di(cid:27)erent FEA software packages are also com-

pared before discussion and implementation of a general numerical framework for coro-

tated hypo-elastoplasticity in isotropic and combined hardening. The numerical frame-

work allows expansion to include di(cid:27)erent, more sophisticated hardening behaviour by
simply altering the scalar equation used to update the von Mises yield surface.
The Mechanical Threshold Stress (MTS) material model is implemented within the
hypo-elastoplastic numerical framework. Material parameter identi(cid:28)cation is investi-

gated using linear regression on data followed by numerical optimisation. The MTS

model is a rate and temperature dependent state variable based material model. The

model is tuned to (cid:28)t imperfect cemented carbide data in compression, where material

test frame compliance or some eccentricity caused inhomogeneous deformation through
the test section of the specimen. The characterised model is then used on a sample
problem to investigate the plastic deformation in the cemented carbide anvils during
the High Pressure, High Temperature (HPHT) synthesis of diamond.

Further extensions, built on the dislocation density based modelling theory of the

MTS model, are investigated by selecting an alternate form of the state dependent

variable. A dislocation density ratio is used instead of the original stress like variable
in the MTS model. The evolution of this internal state variable is altered, along with
additional state dependent variables, to include additional deformation and thermal
mechanisms. The model extensions in the case of rate and temperature dependent

cyclic deformation as well as multiple waves of recrystallisation are discussed and im-

plemented. The recrystallisation and through thickness microstructural variation of a

High Strength, Low Alloy (HSLA) steel are (cid:28)nally investigated during the process of

industrial hot rolling or roughing simulations.

© University of Pretoria
© University of Pretoria
© University of Pretoria
To my wife Lize,

my parents,

family and friends,

for all their love and support.

© University of Pretoria
Acknowledgements

IwouldliketothanktheAdvancedMathematicalModellingcompetencyareaforgiving

me the opportunity and funding to do my Ph.D. I would like to thank my manager

Dr. Onno Ubbink in particular as well as my research supervisors at the University of

Pretoria, Prof. Schalk Kok and Dr. Nico Wilke for their insights and suggestions.

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