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Thermomechanical treatment of steel plays an important role in production, e.g., hot stamping. To capture the complex polymorphic material behavior of steel under thermal and mechanical loads, the usual approach in literature is to use a macroscopic phenomenological ansatz. In contrast, the aim of this work is to establish a more physically based two-scale model taking the material behavior of the different phases on the micro scale into account. The scale transition from macro scale to micro scale is performed by a nonlinear localization method of Hashin–Shtrikman type, which is based on a phase-wise constant stress polarization. The thermomechanical constitutive law is determined by both the phase transformation on micro scale and the temperature-dependent mechanical behavior of each phase. The mechanical behavior is based on a thermodynamical approach, i.e. introduction of a Helmholtz free energy for each phase and use of potential relations gained from the Clausius–Duhem (CD) inequality. The temperature-affected diffusionless evolution of the microstructure is modeled by both a Koistinen–Marburger (KM) consistent rate law and a suggested nonlinear extension of the KM model. The suggested transformation model leads to a better agreement with experimental results compared to the usually used approaches. The Johnson–Mehl–Avrami–Kolmogorov (JMAK) model is chosen to describe the diffusion driven phase transformation. After a parameter identification of the steel 42CrMo4 and a validation of the thermomechanical coupling, the influence of the latent heat, the transformation strain occurring during phase transformation, and the additional parameter arising in the homogenization scheme on the macroscopic behavior is investigated. [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]

The main purpose of this work is to develop a phenomenological model, which accounts for the evolution of the elastic and plastic properties of fcc polycrystals due to a crystallographic texture development and predicts the axial effects in torsion experiments. The anisotropic portion of the effective elasticity tensor is modeled by a growth law. The flow rule depends on the anisotropic part of the elasticity tensor. The normalized anisotropic part of the effective elasticity tensor is equal to the 4th-order coefficient of a tensorial Fourier expansion of the crystal orientation distribution function. Hence, the evolution of elastic and viscoplastic properties is modeled by an evolution equation for the 4th-order moment tensor of the orientation distribution function of an aggregate of cubic crystals. It is shown that the model is able to predict the plastic anisotropy that leads to the monotonic and cyclic Swift effect. The predictions are compared to those of the Taylor–Lin polycrystal model and to experimental data. In contrast to other phenomenological models proposed in the literature, the present model predicts the axial effects even if the initial state of the material is isotropic. [Copyright &y& Elsevier]

The purpose of the current work is the experimental investigation and modeling of Portevin–Le Châtelier (PLC) band development in AlMg3 aluminum alloys, in particular in AA5754. The experimental investigation employs both mechanical and thermal (infrared) radiation measurement methods. The former involve force, displacement, and strain measurements using strain gauges. The latter employ a high-speed infrared camera to capture PLC band trajectories and evolution. In addition, the critical strain for band nucleation, as well as band characteristics such as velocity, type, and strain state, have been determined. To model the experimental results, a modification of the Estrin–McCormick model (e.g., Estrin and McCormick, 1991) due to Böhlke et al. (2009) is employed. In this modification, the saturation value of the Cottrell–Bilby–Louat (CBL) contribution to the effective flow stress due to dynamic strain aging is not constant, but rather is assumed to be linearly dependent on the accumulated effective inelastic strain. This model is incorporated into a finite-element model for the experimental specimens constructed with the help of convergence and mesh-sensitivity studies. Using selected mechanical test data, model parameters for AA5754 are then identified. With the identified model, a number of comparisons between experimental results and model predictions are carried out for validation purposes. Attention is focused here in particular on aspects of PLC band nucleation and propagation. Nucleation behavior is studied in particular with respect to stress gradients. It was found that the stress gradient is not the main trigger for PLC band nucleation, and is less relevant with increasing strain. The comparison of experimental and simulation results for spatio-temporal strain patterns and stress distribution shows that strong stress drops are correlated with the start of longitudinal propagation of a fully evolved PLC band. Small oscillations between large stress drops during propagation of type B bands indicate the consecutive nucleation, propagation and disappearing of these bands. The transition region from normal to inverse behavior (decreasing strain rate) denotes the transition from type A to type B. A transition with increasing strain is observed both experimentally and in the simulation. For lower strain rates and higher strains, type C bands are observed as well. Generally speaking, the band velocity decreases with decreasing strain rate and increasing strain. On the other hand, the band strain is found to increase with increasing strain, and only slightly with increasing strain rate. Simulation and experimental results, generally, show very good agreement. [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: The effective material response of ductile metals containing spherical pores at volume fractions between 0.1% and 30% is investigated on a computational basis. Periodic hard core models of spherical voids are used in a Monte Carlo type finite element study. The objective of the study is the investigation of the pressure dependency of the deviatoric limit stress of the three-dimensional microstructures. In order to characterize the underlying morphology, the statistical properties of the unit cells are evaluated. The representativeness of the computational results is investigated. With respect to the local material response, the inelastic deformations within the unit cell are analyzed and compared for different types of boundary conditions. The computational results are related to existing analytical models and an extension of the Gurson–Tvergaard–Needleman model is proposed to overcome the observed discrepancies. The new model has only one additional parameter, and is found to efficiently predict the pressure dependency of the limit stress for all examined porosities. [Copyright &y& Elsevier]

In this work, we propose to use deep material networks (DMNs) as a surrogate model for full-field computational homogenization to inversely identify material parameters of constitutive inelastic models for short fiber-reinforced thermoplastics (SFRTs). Micromechanics offers an elegant way to obtain constitutive models of materials with complex microstructure, as these emerge naturally once an accurate geometrical representation of the microstructure and expressive material models of the constituents forming the material are known. Unfortunately, obtaining the latter is non-trivial, essentially for two reasons. For a start, experiments on pure samples may not accurately represent the conditions present in the composite. Moreover, the manufacturing process may alter the material behavior, and a subsequent modification is necessary. To avoid modeling the physics of the manufacturing process, one may identify the material models of the individual phases of the composite based on experiments on the composite. Unfortunately, this procedure requires conducting time-consuming simulations. In the work at hand, we use Deep Material Networks to replace full-field simulations, and to carry out an inverse parameter optimization of the matrix model in a SFRT. We are specifically concerned with the long-term creep response of SFRTs, which is particularly challenging to both experimental and simulation-based approaches due to the strong anisotropy and the long time scales involved. We propose a dedicated fully coupled plasticity and creep model for the polymer matrix and provide details on the experimental procedures. • We propose an inverse calibration method for the matrix model in a fiber reinforced thermoplastic. • A novel creep plasticity model is introduced. • Deep Material Networks are used to replace full-field micromechanical simulations. • Potential error sourced in the microstructure characteristics are investigated. • The approach is validated with creep tests in complimentary directions. [ABSTRACT FROM AUTHOR]

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]