The role of dissipation regarding the concept of purely mechanical theories in plasticity

Prahs, Andreas; Böhlke, Thomas

doi:10.1016/j.mechrescom.2021.103832

Cited by 4 publications

(3 citation statements)

References 26 publications

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“…It is shown in Prahs & Böhlke [46] that the bulk material is dissipation free within a purely mechanical framework, i.e. scriptDred=0.…”

Section: Gradient Crystal Plasticity Frameworkmentioning

confidence: 99%

“…This is equivalent to the assumption that the entire plastic work is stored inside the material. The assumptions of the purely mechanical theory in Prahs & Böhlke [46] are that the specific free energy can be additively decomposed into a mechanical and a thermal contribution, that the temperature is constant in space and time and that heat supplies are not present. With the assumption of a vanishing dissipation, a yield criterion function φα≤0 is defined for each slip system in order to characterize plastic flow.…”

Section: Gradient Crystal Plasticity Frameworkmentioning

confidence: 99%

“…[48]. In the following, based on the work of Prahs & Böhlke [46], dissipation free grain boundaries are considered for the purely mechanical framework which means again that the inelastic work is stored as defect energy in the grain boundaries. Consequently, the presented framework considers only energetic dislocation grain-boundary interactions, while neglecting the dissipative mechanisms, e.g.…”

Section: Gradient Crystal Plasticity Frameworkmentioning

confidence: 99%

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Analytical investigation of a grain boundary model that accounts for slip system coupling in gradient crystal plasticity frameworks

Erdle

Böhlke

2023

Proc. R. Soc. A.

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In this work, a physically based dislocation theory of plasticity is derived within an extended continuum mechanical context. An orientation-dependent grain boundary flow rule is introduced for the modelling of dislocation pile-up at grain boundaries and dislocation transmission through grain boundaries. With the conventional grain boundary modelling approach according to Gurtin (Gurtin. 2008 J. Mech. Phys. Solids 56 , 640–662. ( doi:10.1016/j.jmps.2007.05. 002 )) the single-crystal consistency check for the limit case of adjacent grains that hold no misorientation is not satisfied. In order to overcome this modelling shortcoming, a slip system coupling based on a geometric measure of slip system compatibility is introduced. In order to investigate the grain boundary modelling approaches, the analytical solution of a three-phase periodic laminate is used to study the interactions of dislocations and grain boundaries within the gradient crystal plasticity framework. With the developed grain boundary model two grain boundary states, i.e. microhard and microcontrolled, are observed for misaligned grains. This allows the modelling of slip activation at grain boundaries based on the dislocation pile-up stress.

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“…It is shown in Prahs & Böhlke [46] that the bulk material is dissipation free within a purely mechanical framework, i.e. scriptDred=0.…”

Section: Gradient Crystal Plasticity Frameworkmentioning

confidence: 99%

Section: Gradient Crystal Plasticity Frameworkmentioning

confidence: 99%

Section: Gradient Crystal Plasticity Frameworkmentioning

confidence: 99%

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Analytical investigation of a grain boundary model that accounts for slip system coupling in gradient crystal plasticity frameworks

Erdle

Böhlke

2023

Proc. R. Soc. A.

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A multiphase-field approach to small strain crystal plasticity accounting for balance equations on singular surfaces

Prahs,

Schöller,

Schwab

et al. 2023

Comput Mech

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An implementation of the crystal plasticity theory in the context of the multiphase-field method provides a numerically efficient tracking of evolving grain boundaries, modeled as diffuse interfaces. In literature, several approaches exist for the implementation of the plastic material behavior within the diffuse interface, based on interpolation, homogenization, or the mechanical jump conditions. Among these, only the jump condition approach exhibits an intrinsic relationship to the sharp interface (SI) theory. Therefore, in the work at hand, the implementation of the crystal plasticity theory within the jump condition approach, referred to as phase-specific plastic fields approach (PSPFA), is discussed in detail. The PSPFA is compared to the interpolation approach, referred to as common plastic fields approach (CPFA), using three-dimensional benchmark simulations of a bicrystal set-up. The comparison reveals that the PSPFA and SI coincide convincingly regarding the accumulated plastic slip and the Mises stress. In contrast, a significant deviation of CPFA and SI is observed both quantitatively and qualitatively, not only within the diffuse interface region, but throughout the complete simulation domain. A variation of the interface width illustrates that this observation can be transferred to the normal components of the total strain, even for smaller interface widths. Consequently, a quantitative estimate of the plastic material behavior, which is crucial for the prediction of the dynamic behavior of grain boundaries, is only provided by the PSPFA. The application of the crystal plasticity in the context of PSPFA to more complex microstructures is illustrated with respect to a periodic honeycomb-structure and an octotuple.

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Microstructure evolution accounting for crystal plasticity in the context of the multiphase-field method

Kannenberg,

Schöller,

Prahs

et al. 2023

Comput Mech

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The role of grain boundaries (GBs) and especially the migration of GBs is of utmost importance in regard of the overall mechanical behavior of polycrystals. By implementing a crystal plasticity (CP) theory in a multiphase-field method, where GBs are considered as diffuse interfaces of finite thickness, numerically costly tracking of migrating GBs, present during phase transformation processes, can be avoided. In this work, the implementation of the constitutive material behavior within the diffuse interface region, considers phase-specific plastic fields and the jump condition approach accounting for CP. Moreover, a coupling is considered in which the phase-field evolution and the balance of linear momentum are solved in each time step. The application of the model is extended to evolving phases and moving interfaces and approaches to strain inheritance are proposed. The impact of driving forces on the phase-field evolution arising from plastic deformation is discussed. To this end, the shape evolution of an inclusion is investigated. The resulting equilibrium shapes depend on the anisotropic plastic deformation and are illustrated and examined. Subsequently, evolving phases are studied in the context of static recrystallization (SRX). The GB migration involved in the growth of nuclei, which are placed in a previously deformed grain structure, is investigated. For this purpose, three approaches to strain inheritance are compared and, subsequently, different grain structures and distributions of nuclei are considered. It is shown, how the revisited method contributes to a simulation of SRX.

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The role of dissipation regarding the concept of purely mechanical theories in plasticity

Cited by 4 publications

References 26 publications

Analytical investigation of a grain boundary model that accounts for slip system coupling in gradient crystal plasticity frameworks

Analytical investigation of a grain boundary model that accounts for slip system coupling in gradient crystal plasticity frameworks

A multiphase-field approach to small strain crystal plasticity accounting for balance equations on singular surfaces

Microstructure evolution accounting for crystal plasticity in the context of the multiphase-field method

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