Partially relaxed energy potentials for the modelling of microstructures – application to shape memory alloys

Bartel, Thorsten; Menzel, Andreas

doi:10.1002/gamm.201210005

Cited by 3 publications

(1 citation statement)

References 48 publications

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“…Taking into account complex interactions at the micro-scale-such as specific microstructure arrangements and twin formations-leads to reliable micromechanical material models, such as the ones presented in, e.g., [6,7,8,9,10,11,12,13,14]. However, a possible disadvantage of such precise modelling approaches might be the high computational costs that usually accompany the detailed capturing of microstructural material effects.…”

Section: Introductionmentioning

confidence: 99%

A Thermodynamically Consistent Finite Strain Micro-Sphere Framework for Phase-Transformation

Ostwald¹,

Bartel²,

Menzel³

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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Section: Introductionmentioning

confidence: 99%

A Thermodynamically Consistent Finite Strain Micro-Sphere Framework for Phase-Transformation

Ostwald¹,

Bartel²,

Menzel³

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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Computationally-efficient modeling of inelastic single crystal responses via anisotropic yield surfaces: Applications to shape memory alloys

Hartl

Kiefer

Schulte

et al. 2018

International Journal of Solids and Structures

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A kinematically-enhanced relaxation scheme for the modeling of displacive phase transformations

Bartel

Kiefer

Buckmann

et al. 2014

Journal of Intelligent Material Systems and Structures

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In this contribution, a micro-mechanically motivated, energy relaxation-based constitutive model for phase transformation, martensite reorientation and twin formation in shape memory alloys is proposed. The formulation builds on an idealized parametrization of the austenite-twinned martensite microstructure through first-and second-order laminates. To estimate the effective rank-one convex energy density of the phase mixture, the concept of laminate-based energy relaxation is applied. In this context, the evolution of the energetic and dissipative internal state variables, that describe characteristic microstructural features, is computed via constrained incremental energy minimization. This work also suggests a first step towards the continuous modeling of twin formation within the framework of energy relaxation and can be viewed as a generalization of earlier models suggested by Bartel and Hackl (2009) and Bartel et al. (2011). More specifically, in the current model the orientation of martensitic variants in space is not pre-assigned. Variants are rather left free to arrange themselves relative to the martensite-martensite interface in an energy-minimizing fashion, where, however, it is assumed that they form crystallographically-twinned pairs. The formulation also eliminates the need to introduce specific expressions for the Bain strains in each of the martensitic variants, by relating them to a master variant and utilizing the information about their absolute orientation. The predictive capabilities of the proposed modeling framework are demonstrated in several representative numerical examples. In the first part of the results section, the focus is placed on purely energetic analysis, and the particular influence of the different microstructural degrees of freedom on the relaxed energy densities and the corresponding stress-strain responses is investigated in detail. In the second part, macro-homogeneous uniaxial strain and shear loading cases are analyzed for the dissipative case. It is shown, that the proposed model, which, compared to purely phenomenological macro-scale models, has the advantage of strong micro-mechanical motivation, is capable of qualitatively predicting central features of single crystal shape memory alloy behavior, such as the phase diagram in stress-temperature space, and pseudo-elastic and pseudo-plastic responses, while simultaneously providing valuable insight into the underlying micro-scale mechanisms.

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Partially relaxed energy potentials for the modelling of microstructures – application to shape memory alloys

Cited by 3 publications

References 48 publications

A Thermodynamically Consistent Finite Strain Micro-Sphere Framework for Phase-Transformation

A Thermodynamically Consistent Finite Strain Micro-Sphere Framework for Phase-Transformation

Computationally-efficient modeling of inelastic single crystal responses via anisotropic yield surfaces: Applications to shape memory alloys

A kinematically-enhanced relaxation scheme for the modeling of displacive phase transformations

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