APPLICATIVE ELASTO-PLASTIC SELF CONSISTENCY MODEL INCORPORATING ESHELBY’S INCLUSION THEORY TO ANALYZE THE DEFORMATION IN HCP MATERIALS CONSISTING MULTIPLE DEFORMATION MODES

Author

Daniel Selvakumar Raja, Southern Illinois University CarbondaleFollow

Date of Award

12-1-2021

Degree Name

Doctor of Philosophy

Department

Engineering Science

First Advisor

Kweon, Soondo

Second Advisor

Chu, Tsuchin

Abstract

HCP materials are exceedingly being used as alloys and composites in several high strength light weight applications such as aerospace and aeronautical structures, deep sea maritime applications, and as biocompatible materials. To understand the deformation of HCP materials, reliable tools and techniques are required. One such technique is the Elasto-Plastic Self Consistency (EPSC) model. ESPC models use Eshelby’s Inclusion Theory as their basic formulation to model the strain experienced by a grain within a strained material sample. One of the oldest approximations (or models) used to model the grain’s strain within a strained sample is the Taylor’s Assumption (TA). TA assumes that each grain is strained to the same average value. EPSC models are different from the TA model since each grain modelled by the EPSC model would be strained to a different value. This is possible and obtained by solving an infinite domain boundary value problem. This key advantage of the EPSC model can therefore predict localized weak spots within material samples.EPSC models use the concept of eigen strain where the inhomogeneous grain is replaced with an equivalent inclusion. The technique proposed in this research is used to simulate uniaxial tension of rolled textured Magnesium. The number of deformation modes used in this research is seven. Both slipping systems and twinning systems are included in the simulation. The hardening phenomenon is described as a function of self-hardening as well as latent-hardening. As stated in (S. Kweon, 2020), modelling the interactive hardening requires a more robust numerical iterative technique. An improved robust iterative numerical technique is explained in (Daniel Raja, 2021) and (Soondo Kweon D. S., 2021). This research implements the equivalent inclusion theory in combination with the numerical iterative technique developed in the aforementioned papers.The report begins with the need for this research and advocates for the same. Then, the conceptional theories and the imaginary thought experiment performed by John D. Eshelby is presented. The concept of “Eigen Strain” which serves as the base work needed to understand and formulate the Equivalent Inclusion Theory is described in detail. The Equivalent Inclusion is then presented and developed. The concept of Green’s Function is presented and explained. These concepts serve as the building block for the derivation and calculation of the Eshelby Tensor which relates the concepts of eigen strain and constrained strain. The report concludes the theory section with the amalgamation of the ideas of the Green’s Function and Eigen Strain to develop the Eshelby Tensor for an Isotropic material as well as Anisotropic materials. In the following section, the unit cell accompanied with the deformation modes within the unit cell of an HCP material that are used in these simulations are presented. Following unit cell model, the crystal plasticity model which includes plastic deformation, hardening laws, and elastic deformation is elaborated. The results obtained from the simulation are presented and salient features are highlighted that are observed in the results. Lastly, the report concludes by pointing out key “take aways” from this research and identifies possible avenues for future research.Additionally, ten appendices are included towards the end of this report to enhance understanding of complicated derivations and solutions. Lastly, the author’s vita is included at the end of the report.