PSI - Issue 61

Necdet Ali Özdür et al. / Procedia Structural Integrity 61 (2024) 277–284 N.A. O¨ zdu¨r et al. / Structural Integrity Procedia 00 (2024) 000–000

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1. Introduction

Magnesium has been the subject of an intense research activity that aims to develop an understanding of and to possibly predict the idiosyncrasies in its mechanical attributes. Starting from the crystal scale, the di ff erence between activation energies of slip and twin deformation mechanisms (Agnew and Duygulu (2005)) and the profusely activated tensile twin mechanism (Christian and Mahajan (1995)) yield an extremely anisotropic plastic deformation. On the macroscopic scale, tensile twin is auto-catalytic, causing an avalanche of twinning across the sample. This type of macroscopic localized plastic deformation (Lu¨ders banding) is particularly sharp in rolled Magnesium (Aydıner and Telemez (2014); Kapan et al. (2017); Shafaghi et al. (2020); Erman et al. (2023)). Since twinning completely reorients a portion of the crystal, it has a convoluted interaction with other deformation mechanisms, which further adds to the complexity of the material behavior. Due to the heterogeneous and anisotropic deformation of Magnesium, it is di ffi cult to predict its behavior consis tently in a wide range of environments. Hence, the scope of material models are restricted in terms of physical fidelity. Mean-field, self-consistent formulations like Wang et al. (2013) try match the overall stress-strain behavior by mod eling intra-grain deformation mechanisms and various aspects of twinning. Among full-field modeling attempts with finite elements and spectral solutions, Zhang and Joshi (2012); Mareau and Daymond (2016) employ various phe nomenological treatments of twinning in an attempt to achieve mechanical fidelity, while Homayonifar and Mosler (2012); Chang and Kochmann (2015); Husser and Bargmann (2019) also consider the evolution of the texture. Most models homogenize the abrupt twinning activity with a volume fraction parameter; this treatment of twinning is called ”pseudo-slip”. More recent models with discrete twin implementations (e.g., Cheng and Ghosh (2017)) aim to better capture the morphological details of twinning and local plasticity though they are computationally more expensive. While these crystal plasticity models are able to capture certain aspects of the mechanical behavior of Magnesium, for a large portion of them, thermal behavior (and thus temperature comparisons) is irrelevant, unless they impose a temperature-dependent formulation such as Hollenweger and Kochmann (2022). In fact, most models lack the necessary mathematical structure to produce temperature information. In this context, the main goal of this work is to introduce an additional methodology to validate crystal plasticity models by incorporating temperature measurements. Similar to Eisenlohr et al. (2012), the dissipated energy during the deformation will be measured by an infrared (IR) camera. Synchronously collected stress and strain data allows the calculation of plastic work (and power). The stored and dissipated components of plastic work are thus experimentally obtained, yielding the main comparison point with a thermomechanical model, similar to the in the sense to the thermomechanical analysis done by Seghir et al. (2010). In this study, the model that is employed to make this comparison is a thermo-viscoplastic variational model, cast in the variational framework initially devised by Ortiz and Stainier (1999) for viscoplastic constitutive relations and later revised by Yang et al. (2006); Stainier and Ortiz (2010) to incorporate thermomechanical coupling.

Fig. 1. (a) Experiment setup, components 1-9 are referred to in the text; (b) representation of hot rolled plate and the most prominent unit cell; (c) prepared specimen with dummy sample; (d) pole figure of the plate, indicating sharp rolling texture.