Multi-phase transformations at large strains – Thermodynamic framework and simulation

Mahnken, Rolf; Wolff, Michael W.; Schneidt, Andreas; Böhm, Michael

doi:10.1016/j.ijplas.2012.05.009

Cited by 40 publications

(28 citation statements)

References 49 publications

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“…Macroscopic simulation of the interaction between PT and plasticity in different samples, based on macroscopic (averaged) constitutive equations was presented in Levitas and Zarechnyy (2010a,b); Sitko and Skoczen (2012); Mahnken et al (2012). Discrete dislocation plasticity combined with the nucleation and growth of elliptic M plates with the prescribed aspect ratio have been presented in Shi et al (2010).…”

Section: Introductionmentioning

confidence: 99%

Interaction between phase transformations and dislocations at the nanoscale. Part 2: Phase field simulation examples

Javanbakht

Levitas

2015

Journal of the Mechanics and Physics of Solids

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The complete system of phase field equations for coupled martensitic phase transformations (PTs), dislocation evolution, and mechanics at large strains is presented. Finite element method (FEM) is utilized to solve this system for two important problems. The first one is related to the simulation of shear strain-induced PT at the evolving dislocation pile-ups in a nanosized bicrystal. Plasticity plays a dual part in the interaction with PT. Dislocation pile-ups produce strong stress tensor concentrators that lead to barrierless martensite (M) nucleation. On the other hand, plasticity in the transforming grain relaxes these stress concentrators suppressing PT. The final stationary M morphology is governed by the local thermodynamic equilibrium, either at the interfaces or in terms of stresses averaged over the martensitic region or the entire grain. This is very surprising because of strong heterogeneity of stress fields and is in contrast to previous statements that phase equilibrium conditions do not enter the description of strain-induced PTs. The second problem is devoted to martensitic plate propagation through a bicrystal during temperature-induced PT. For elastic growth (without dislocations) and a large thermal driving force, a complex transformation path with plate branching and direct and reverse PTs is observed, which still ends with the same stationary nanostructure as for a smaller driving force and a traditional transformation path. Sharp grain boundary arrests plate growth at a relatively small driving force, exhibiting an athermal friction. For elastoplastic growth, the generation of dislocations produces athermal friction and arrests the plate below some critical driving force, leading to a morphological transition from plate to lath M. The width of the martensitic plate increases in comparison with elastic growth * Corresponding author. Email address: vlevitas@iastate.edu, tel. (515)-294-9691 (V. I. Levitas) 2 due to internal stress relaxation. Plate growth is accompanied by the nucleation of dislocations within M and remaining in M, the nucleation of dislocations at the tip of a plate and spreading them in austenite (A), and passing some dislocations through M, then through a M-A interface, and then through A. Due to the existence of a stationary equilibrium M nanostructure and concentration for each temperature, for a large enough observation time one observes athermal, rate-and time-independent kinetics, even while local kinetics is rate dependent. In the final structure, most dislocations are in M despite its having a yield strength three times larger than for A, which is consistent with experiments.

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Section: Introductionmentioning

confidence: 99%

Interaction between phase transformations and dislocations at the nanoscale. Part 2: Phase field simulation examples

Javanbakht

Levitas

2015

Journal of the Mechanics and Physics of Solids

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“…The relations (15.1) and (15.3) result from the Clausius-Duhem inequality by standard arguments, see e.g. [10]. The following inequalities are sufficient for validity of the Clausius-Duhem inequality (12.2):…”

Section: Constitutive Frameworkmentioning

confidence: 95%

A multi-mechanism model for cutting simulations based on the concept of generalized stresses

Cheng

Mahnken

2015

Computational Materials Science

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Abstract. Based on the concept of generalized stresses as proposed by Gurtin [6] and Forest [4], we extend an existing model for strain rate-and temperature-dependent asymmetric plastic material behaviour accompanied by phase transformation with a gradient term of phase fraction. To this end a chemical variable, representing the austenite volume fraction, is treated as an extra degree of freedom, and the influence of its first gradient will be studied. A generalized principle of virtual power is postulated involving generalized stresses and used to derive the constitutive equations. The bulk model is formulated within a thermodynamic framework. For the scenario of a cutting process we have a martensite-austenite-martensite transformation. Finally, a cutting simulation is investigated to test our model and the different mechanisms are illustrated.

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“…austenite, martensite) may differ about 1% (see e.g. [85,86]). In some cases, if high accuracy is required, this small differences may cause distortion of workpieces.…”

Section: (Vi) Interfaces Of Type S-ii In Spatial Representationmentioning

confidence: 99%

“…The Thomas derivative of the position vector x equals to the vectorial normal velocity (w γ · n γ )n γ (see (86)). Therefore, we get…”

Section: (I)mentioning

confidence: 99%

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Continuous bodies with thermodynamically active singular sharp interfaces

Wolff

Böhm

2016

Mathematics and Mechanics of Solids

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The subject of this comprehensive study is the general (mathematical) modeling of sharp (i.e. two-dimensional) interfaces without and with their own thermodynamical activity. We provide essential tools for the modeling of body-interface systems. Important items of the kinematics of singular (moving) interfaces as well as balance equations at interfaces will be addressed. Problems connected with material representation will be discussed. Special interfacial balances for mass, impulse, angular momentum, energy, mass of a tracer and of entropy will be considered including the discussion of special cases. As an illustrative example, a continuous model for a body with loss of material (e.g. due to mechanical treatment) will be developed in the framework presented.

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Multi-phase transformations at large strains – Thermodynamic framework and simulation

Cited by 40 publications

References 49 publications

Interaction between phase transformations and dislocations at the nanoscale. Part 2: Phase field simulation examples

Interaction between phase transformations and dislocations at the nanoscale. Part 2: Phase field simulation examples

A multi-mechanism model for cutting simulations based on the concept of generalized stresses

Continuous bodies with thermodynamically active singular sharp interfaces

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