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The implementation of novel material models in the microscale gives a deeper understanding of inner and intercrystalline effects of crystalline materials. For future works, this allows more precise predictions of macroscale models. Here, we present a finite gradient crystal plasticity theory which preserves the single crystal slip kinematics. However, the model is restricted to one gradient-stress, associated with the gradient of the accumulated plastic slip, in order to account for long range dislocation interactions in a physically simplified, numerically efficient approach. In order to model the interaction of dislocations with and their transfer through grain boundaries, a grain boundary yield condition is introduced. The grain boundary flow rule is evaluated at sharp interfaces using discontinuous trial functions in the finite element implementation, thereby allowing for a discontinuous distribution of the accumulated plastic slip. Simulations of crystal aggregates are performed under different loading conditions which reproduce well the size dependence of the yield strength. An analytical solution for a one-dimensional single slip supports the numerical results. [ABSTRACT FROM AUTHOR]

This work aims at the formulation of a gradient crystal plasticity model which incorporates some of the latest developments in continuum dislocation theory and is, at the same time, well-suited for a three-dimensional numerical implementation. Specifically, a classical continuum crystal plasticity framework is extended by taking into account continuous dislocation density and curvature field variables which evolve according to partial differential equations (Hochrainer et al., 2014; Ebrahimi et al., 2014). These account for dislocation transport and curvature-induced line-length production and have been derived from a higher-dimensional continuum dislocation theory. The dislocation density information is used to model work hardening as a consequence of dislocation entanglement. A composite microstructure is simulated consisting of a soft elasto-plastic matrix and hard elastic inclusions. The particles are assumed to act as obstacles to dislocation motion, leading to pile-ups forming at the matrix–inclusion interface. This effect is modeled using gradient plasticity with a simplified equivalent plastic strain gradient approach (Wulfinghoff et al., 2013) which is used here in order to allow for an efficient numerical treatment of the three-dimensional numerical model. A regularized logarithmic energy is applied which is intended to approximate the higher order gradient stress of the statistical theory of Groma et al. (2003). [ABSTRACT FROM AUTHOR]

A nonlinear homogenization scheme is applied to consider two classes of micromechanical problems, i.e. to estimate the grain size dispersion influence and to model phase transformation effects in steels. The macroscopic material behavior is described purely based on micro-mechanical constitutive models. The coarse graining procedure contains the classical bounds, i.e. mixture theories, as special cases and determines the macroscopic stress and the evolution of the microstructural variables. In the context of the grain size dependent flow behavior of polycrystals, a log-normal distributed grain size is assumed together with a grain size dependent local plastic behavior. The numerical results are well approximated by a simple analytical expression. It is found that grain size dispersion leads to a decrease of the material strength, especially for small mean diameters around one micron. In the context of phase transformation phenomena, the thermo-mechanically strongly coupled Greenwood-Johnson effect is considered. Here, temperature driven phase transformation under external applied stress below the yield stress is modeled that leads to plastic strains. The main result of the present work is, that based on the suggested nonlinear homogenization technique of Hashin-Shtrikman type a numerically effective modeling approach is given, that can be applied at the Gauss point level of structural finite element simulations. In contrast to FE2 schemes, full three-dimensional microstructures can be modeled effectively with standard computers. The simulation results presented in this work are in good agreement with the experimental data. [ABSTRACT FROM AUTHOR]

A viscoplastic strain gradient crystal plasticity theory based on the gradient of the equivalent plastic strain ∇γ eq is proposed. A grain boundary yield condition is introduced. The microstructural explanation of the Hall-Petch effect, accounting for notch-like stress concentrations at the grain boundary as a result of discrete slip bands, is reviewed. Periodic tensile test FEM simulation results illustrate the prediction of the numerical model. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

A gradient crystal plasticity theory is presented including a defect energy based on the gradient of an equivalent plastic strain measure. Preserving the single crystal slip kinematics, the gradient hardening contribution models dislocation long range interactions adding a back-stress term to the flow rule, similar to other gradient crystal plasticity theories. Owing to a reduced number of four nodal degrees of freedom the finite element implementation can handle systems consisting of an increased number of grains (compared to other theories) without elaborate or costly computer systems. Emphasis is put on the enhancement of the power law material subroutine. The associated implicit Euler scheme is optimized based on an improved starting value for the Newton scheme. Three-dimensional simulations illustrate that the proposed algorithm facilitates significantly larger time steps compared to the standard Newton scheme. (© 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

Multi-phase materials often times consist of constituents with high contrasts in phase-specific mechanical properties. Here, even after homogeneous plastic deformation phase-specific residual stresses develop that may affect the components behaviour in service. For numerical simulation of phase-specific residual stresses, knowledge of the particular phase-specific strain hardening behaviour is essential. In this study, the strain hardening of ferrite and austenite in cold rolled duplex stainless steel of type X2CrNiN23-4 is investigated. By means of X-ray diffraction, the phase-specific load partitioning and residual stress evolution are analysed for uniaxial load application in three directions within the sheets plane, taking into account the sheet metals phase specific anisotropy. In order to assess the necessity for experimental determination of anisotropic phase specific behaviour, the strain hardening parameters, derived from only one loading direction, are implemented in a mean-field approach for prediction of phase-specific stresses. A simplified simulation approach is applied that only considers macroscopic plastic anisotropy and results are compared to experimental findings. For all investigated loading directions, it was observed that austenite is the high-strength phase. This load partitioning behaviour was confirmed by the evolution of phase-specific residual stresses as a result of uniaxial elasto-plastic loading. With the simplified and fast numerical approach, satisfying results for prediction of anisotropic phase-specific (residual) stresses are obtained. [ABSTRACT FROM AUTHOR]

Abstract: Based on a slip gradient crystal plasticity theory, cf. [1], an analytical, one dimensional solution for the plastic slip is discussed with respect to a homogeneous stress state. Multislip is considered in a bicrystal with two slip systems in each grain. The orientation of the grains is accounted for by the choice of a free energy based on the grain boundary Burgers tensor, cf. [2]. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

An equivalent plastic strain gradient theory, cf. [1], is extended by a GB flow rule, that accounts for the misorientation of adjacent grains. In contrast to previous works, the grain boundary (GB) resistance against plastic flow is not treated as a constant parameter. Therefore, in the work at hand, the grain boundary dislocation density (GBD), cf. [2], is used as a measure for geometrical mismatch between all glide system orientations of two adjacent grains. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

The applicability of a strain gradient crystal plasticity model to size effects observed on microwires in torsion experiments is discussed. Finite Element simulations of simplified cylindrical grain aggregations are presented and the resulting overall mechanical response is compared to experimental data for gold from the literature. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

This article discusses a conceptual problem of gradient plasticity theories including a scalar plastic field variable, the Laplacian of which enters the yield criterion. Since the plastic field variable is assumed a scalar, it contains no information on the direction of the plastic flow. The work at hand demonstrates that even arbitrarily small perturbations can determine the direction of the plastic deformation in many formulations, which is considered an unphysical behavior. In this sense, the solution is not stable with respect to the boundary conditions. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

The deformation in polycrystals is often heterogenous, e.g. due to grain size dependent hardening. In a semi-analytical representative volume element (RVE), a log-normal distributed grain size is assumed together with a grain size dependent local plastic behavior. The numerical results are well approximated by a simple analytical expression. The effect of the homogenization comparison stiffness on the transient behaviour is explained using a simplified localization equation. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

A one-dimensional strain gradient plasticity model is reviewed in the context of Finite Element Method (FEM) solvability. It is found that under certain conditions specified the resulting system of two coupled partial differential equations in space and time leads to a symmetric global stiffness matrix. This is achieved upon standard weak form approach and yields a favorable system for an efficient numerical solution. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

As an anode material for lithium-ion batteries, amorphous silicon offers a significantly higher energy density than the graphite anodes currently used. Alloying reactions of lithium and silicon, however, induce large deformation and lead to volume changes up to 300%. We formulate a thermodynamically consistent continuum model for the chemo-elasto-plastic diffusion-deformation behavior of amorphous silicon and it’s alloy with lithium based on finite deformations. In this paper, two plasticity theories, i.e. a rate-independent theory with linear isotropic hardening and a rate-dependent one, are formulated to allow the evolution of plastic deformations and reduce occurring stresses. Using modern numerical techniques, such as higher order finite element methods as well as efficient space and time adaptive solution algorithms, the diffusion-deformation behavior resulting from both theories is compared. In order to further increase the computational efficiency, an automatic differentiation scheme is used, allowing for a significant speed up in assembling time as compared to an algorithmic linearization for the global finite element Newton scheme. Both plastic approaches lead to a more heterogeneous concentration distribution and to a change to tensile tangential Cauchy stresses at the particle surface at the end of one charging cycle. Different parameter studies show how an amplification of the plastic deformation is affected. Interestingly, an elliptical particle shows only plastic deformation at the smaller half axis. With the demonstrated efficiency of the applied methods, results after five charging cycles are also discussed and can provide indications for the performance of lithium-ion batteries in long term use. [ABSTRACT FROM AUTHOR]

Highlights: [•] A gradient crystal plasticity theory based on the gradient of an equivalent plastic strain is proposed. [•] The theory includes a grain boundary yield criterion. [•] A numerically efficient implementation is outlined. [•] The proposed model is able to capture the size effect in micro-specimens. [•] The material parameters are successfully fitted to the experiments of copper micro-wires from literature. [ABSTRACT FROM AUTHOR]

Abstract: Two-phase composites, which consist of polycrystalline -iron and copper particles, are studied mechanically under large plastic deformation. Due to the significant difference of the yield stress in the iron and the copper phase in which the slip system geometry is also dissimilar, a high heterogeneity and anisotropy characterize the plastic deformation behaviour. In this work, an elasto-viscoplastic material model is applied in finite element simulations, whereas the macroscopic material behaviour is established based on constitutive equations of the single crystal. Due to the natural spatial character of the slip system mechanisms of crystal plasticity, the numerical calculation must be performed fully 3D. However, since it is hardly possible to determine the grain geometry of a real material in 3D without destroying the sample by slicing or the like, real 2D cross-sections have been modelled and extended to the third dimension in an axisymmetric way producing an annular pattern, which comes closer to reality than a 2D structure. Numerical predictions include the grain deformation behaviour, the flow behaviour, the crystallographic texture, and the local strain in Fe–Cu composites. In particular, a quantitative study is performed for the mean value of the local strain in both phases, which shows a good agreement with the experimental result for the Fe17–Cu83 composite under tension. [Copyright &y& Elsevier]

The onset of nonlinear effects in metals, such as plasticity and damage, is strongly influenced by the heterogeneous stress distribution at the grain level. This work is devoted to studying the local stress distribution in fcc polycrystals using FFT-based solvers. In particular, we focus on the distribution of shear stresses resolved in the slip systems as the critical driving force for plastic deformations. Specific grain orientations with respect to load direction are investigated in the linear elastic regime and at incipient plastic deformations based on a large ensemble of microstructures. The elastic anisotropy of the single crystal is found to have a crucial influence on the scatter of the stress distribution, whereas the Young's modulus in the respective crystal direction governs the mean stress in the grain. It is further demonstrated that, for higher anisotropy, the shear stresses deviate from the normal distribution and are better approximated by a log-normal fit. Comparing the full-field simulations to the Maximum Entropy Method (MEM), reveals that the MEM provides an excellent prediction up to the second statistical moment in the linear elastic range. In a study on the spatial distribution of shear stresses, the grain boundary is identified as a region of pronounced stress fluctuations and as the starting point of yielding during the elastic–plastic transition. • Large-scale (200 realizations) FFT-based investigation of local stress distribution. • Statistical variance of stresses in a grain increases for higher anisotropy. • Local shear stress distributions are not exact Gaussian normal distributions. • Elastic MEM predicts grain stress means and covariances close to full-field results. • Plastification starts close to the grain boundary, expanding inwards from there. [ABSTRACT FROM AUTHOR]