Development and implementation of state variable based user materials in computational plasticity

Abstract

The Finite Element Method is a powerful tool that can be used to test, improve or better understand an industrially relevant problem. There are numerous Finite Element Analysis (FEA) software packages that operate either in the commercial, open source or research space. Di erent application speci c codes also have specialised model formulations. Most software packages have a comprehensive list of material models already implemented. If a di 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 ective implementation and testing of a user implemented material requires knowledge on the e 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 cation and implementation of existing computational plasticity models for use within FEA. The e ect of di erent strain formulation choices is rst illustrated and discussed using di erent sample problems. Three di erent FEA software packages are also compared before discussion and implementation of a general numerical framework for corotated hypo-elastoplasticity in isotropic and combined hardening. The numerical framework allows expansion to include di 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 cation is investigated 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 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 implemented. The recrystallisation and through thickness microstructural variation of a High Strength, Low Alloy (HSLA) steel are nally investigated during the process of industrial hot rolling or roughing simulations.