A gradient crystal plasticity theory for large deformations with a discontinuous accumulated plastic slip

Erdle, Hannes; Böhlke, Thomas

doi:10.1007/s00466-017-1447-7

Cited by 17 publications

(11 citation statements)

References 56 publications

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“…The user subroutine was developed at the Institute of Mechanics of Otto-von-Guericke-University Magdeburg, Germany. In the past, it was already applied for various materials under different loading cases [7,[16][17][18][19][20][21][22][23][24][25]. Subsection 2.1.1 presents a short description of the applied material model.…”

Section: Insensibility Of Phase Volume Ratios To Microstructure Position In Axisymmetric Fe Analysesmentioning

confidence: 99%

A Numerical Method to Improve the Representativeness of Real Microstructure Cut-Outs Applied in Finite Element Simulations

et al. 2021

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To improve the representativeness of a real microstructural cut-out for modeling purposes, a numerical method named as “boundary pixel color alteration (BPCA)” is presented to modify measured 2D microstructure cut-outs. Its physical background is related to the phase growth. For the application, the precondition is that the representativeness of the microstructure is already satisfied to a certain extent. This method resolves the problem that the phase composition of a small cut-out can have a large discrepancy to the real one. The main idea is to change the pixel color among neighboring pixels belonging to different phases. Our process simultaneously maintains most of the characteristics of the original morphology and is applicable for nearly all kinds of multi-phase or polycrystalline metallic alloys, as well. From our axisymmetric finite element (FE) simulations (ABAQUS ) applied with 2D real microstructures, it shows that the volume ratios of microstructural phases, as a function of the structure position to the symmetric axis, converge to phase area ratios in the 2D cut-out, even though the axisymmetric element volume is position dependent. A mathematical proof provides the reason for the aforementioned convergence. As examples to achieve real compositions and to numerically prove the aforementioned convergence, four different materials including multiphase polycrystals are implemented. An improvement of the predicted FE result is presented for the application of a modified microstructure (with a higher representativeness) compared to the original one.

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Section: Insensibility Of Phase Volume Ratios To Microstructure Position In Axisymmetric Fe Analysesmentioning

confidence: 99%

A Numerical Method to Improve the Representativeness of Real Microstructure Cut-Outs Applied in Finite Element Simulations

et al. 2021

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“…The velocity gradient tensor, L , can also be divided into elastic, e L , and inelastic, p L , parts (Dhala et al, 2019;Erdle and Böhlke, 2017;Fohrmeister et al, 2019): Due to experimentally observed accumulation of residual martensite (Kang et al, 2009), the volume fraction of each martensite variant can be divided into the reversible, rev   , and the irreversible, ire   , volume fractions. The total volume fraction of martensite is considered as the sum of eversible and irreversible parts (Ebrahimi et al, 2020).…”

Section: Definition Of Various Deformation Mechanisms In the Framework Of Thermodynamicsmentioning

confidence: 99%

Microstructure-based finite deformation modelling of super-elastic NiTi shape memory alloy considering various inelastic mechanisms

Ebrahimi¹,

Arghavani²,

Sohrabpour³

et al. 2020

Preprint

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In this study the mechanisms of transformation-induced plasticity (TRIP), detwinning-induced plasticity (DIP), and accumulation of residual martensite, are incorporated into a finite-deformation crystal plasticity model of NiTi SMA for the first time. The constitutive model is constructed at the single-crystal scale and also includes phase transformation and detwinning mechanisms. Using a proposed Helmholtz free energy, the driving forces for inelastic mechanisms are derived within the framework of thermodynamics. The constitutive model has been implemented in the Abaqus/Explicit finite-element program, using VUMAT subroutine to simulate a polycrystalline material. Considering various orientations for crystals, the effect of texture on tension-compression asymmetry is investigated. It is shown that different textures may cause stiffer, softer, or similar response in compression compared to tension. Due to the incorporation of the effect of residual martensite, the model provides accurate predictions of experimentally measured residual strain. The incorporation of the aforementioned inelastic deformation mechanisms is shown to accurately capture the key features related to cyclic loading. Finally, the effect of detwinning-induced plasticity in compressive cyclic loading of NiTi SMA is investigated. In strain-controlled cyclic compression-unloading tests DIP leads to a less negative peak stress and a more negative residual strain following several loading cycles.

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“…Inter-grain interaction modules from two theories are compared by Gottschalk et al [20]; Bayerschen et al [21]. Erdle and Böhlke [22] developed the continuum model of dislocation/grain boundary interaction based on the micromorphic strain gradient plasticity. We also mention the references [23][24][25][26][27][28][29] which use the same strain gradient plasticity.…”

Section: Introductionmentioning

confidence: 99%

Thermodynamic theory of dislocation/grain boundary interaction

Piao

2022

Continuum Mech. Thermodyn.

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The thermodynamic theory of dislocation/grain boundary interaction, including dislocation pileup against, absorption by, and transfer through the grain boundary, is developed for non-uniform plastic deformations in polycrystals. The case study is carried out on the boundary conditions affecting work hardening of a bicrystal subjected to plane constrained shear for three types of grain boundaries: (i) impermeable hard grain boundary, (ii) grain boundary that allows dislocation transfer without absorption, and (iii) grain boundary that absorbs dislocations and allows them to pass later.

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A gradient crystal plasticity theory for large deformations with a discontinuous accumulated plastic slip

Cited by 17 publications

References 56 publications

A Numerical Method to Improve the Representativeness of Real Microstructure Cut-Outs Applied in Finite Element Simulations

A Numerical Method to Improve the Representativeness of Real Microstructure Cut-Outs Applied in Finite Element Simulations

Microstructure-based finite deformation modelling of super-elastic NiTi shape memory alloy considering various inelastic mechanisms

Thermodynamic theory of dislocation/grain boundary interaction

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