Deformation Texture Evolution in Flat Profile AlMgSi Extrusions: Experiments, FEM, and Crystal Plasticity Modeling

In the present work, the deformation textures during flat profile extrusion from round billets of an AA6063 and an AA6082 aluminium alloy have been numerically modeled by coupling FEM flow simulations and crystal plasticity simulations and compared to experimentally measured textures obtained by electron back-scatter diffraction (EBSD). The AA6063 alloy was extruded at a relatively low temperature (350°C), while the AA6082 alloy, containing dispersoids that prevent recrystallization, was extruded at a higher temperature (500°C). Both alloys were water quenched at the exit of the die, to maintain the deformation texture after extrusion. In the center of the profiles, both alloys exhibit a conventional β-fiber texture and the Cube component, which was significantly stronger at the highest extrusion temperature. The classical full-constraint (FC)-Taylor and the Alamel grain cluster model were employed for the texture predictions. Both models were implemented using the regularized single crystal yield surface. This approach enables activation of any number and type of slip systems, as well as accounting for strain rate sensitivity, which are important at 350°C and 500°C. The strength of the nonoctahedral slips and the strain-rate sensitivity were varied by a global optimization algorithm. At 350°C, a good fit could be obtained both with the FC Taylor and the Alamel model, although the Alamel model clearly performs the best. However, even with rate sensitivity and nonoctahedral slip systems invoked, none of the models are capable of predicting the strong Cube component observed experimentally at 500°C.publishedVersio

Towards high-throughput microstructure simulation in compositionally complex alloys via machine learning

The coupling of computational thermodynamics and kinetics has been the central research theme in Integrated Computational Material Engineering (ICME). Two major bottlenecks in implementing this coupling and performing efficient ICME-guided high-throughput multi-component industrial alloys discovery or process parameters optimization, are slow responses in kinetic calculations to a given set of compositions and processing conditions and the quality of a large amount of calculated thermodynamic data. Here, we employ machine learning techniques to eliminate them, including (1) intelligent corrupt data detection and re-interpolation (i.e. data purge/cleaning) to a big tabulated thermodynamic dataset based on an unsupervised learning algorithm and (2) parameterization via artificial neural networks of the purged big thermodynamic dataset into a non-linear equation consisting of base functions and parameterization coefficients. The two techniques enable the efficient linkage of high-quality data with a previously developed microstructure model. This proposed approach not only improves the model performance by eliminating the interference of the corrupt data and stability due to the boundedness and continuity of the obtained non-linear equation but also dramatically reduces the running time and demand for computer physical memory simultaneously. The high computational robustness, efficiency, and accuracy, which are prerequisites for high-throughput computing, are verified by a series of case studies on multi-component aluminum, steel, and high-entropy alloys. The proposed data purge and parameterization methods are expected to apply to various microstructure simulation approaches or to bridging the multi-scale simulation where handling a large amount of input data is required. It is concluded that machine learning is a valuable tool in fueling the development of ICME and high throughput materials simulations.publishedVersio

Regularized Yield Surfaces for Crystal Plasticity of Metals

The rate-independent Schmid assumption for a metal crystal results in a yield surface that is faceted with sharp corners. Regularized yield surfaces round off the corners and can be convenient in computational implementations. To assess the error by doing so, the coefficients of regularized yield surfaces are calibrated to exactly interpolate certain points on the facets of the perfect Schmid yield surface, while the different stress predictions in the corners are taken as the error estimate. Calibrations are discussed for slip systems commonly activated for bcc and fcc metals. It is found that the quality of calibrations of the ideal rate-independent behavior requires very large yield-surface exponents. However, the rounding of the corners of the yield surface can be regarded as an improved approximation accounting for the instant, thermal strain-rate sensitivity, which is directly related to the yield-surface exponent. Distortion of the crystal yield surface during latent hardening is also discussed, including Bauschinger behavior or pseudo slip systems for twinning, for which the forward and backward of the slip system are distinguished

Strength contributions from precipitates

A theory for the strength contribution from precipitates is developed based on the statistical particle-size and shape distributions and the corresponding obstacle strengths. The generic case of spherical precipitates and the special case of needle-shaped precipitates in the 6xxx aluminium alloy series are considered. It is accounted for that the largest precipitates are stronger and at the same time, intersect a larger number of slip planes than the smaller ones. For a considered peak aged AA6082, the improved model gives a 59% higher strength, which fits the experiments well without the need of previously introduced calibration parameter for the mean effective particle spacing in the slip plane

Regularized Yield Surfaces for Crystal Plasticity of Metals

The rate-independent Schmid assumption for a metal crystal results in a yield surface that is faceted with sharp corners. Regularized yield surfaces round off the corners and can be convenient in computational implementations. To assess the error by doing so, the coefficients of regularized yield surfaces are calibrated to exactly interpolate certain points on the facets of the perfect Schmid yield surface, while the different stress predictions in the corners are taken as the error estimate. Calibrations are discussed for slip systems commonly activated for bcc and fcc metals. It is found that the quality of calibrations of the ideal rate-independent behavior requires very large yield-surface exponents. However, the rounding of the corners of the yield surface can be regarded as an improved approximation accounting for the instant, thermal strain-rate sensitivity, which is directly related to the yield-surface exponent. Distortion of the crystal yield surface during latent hardening is also discussed, including Bauschinger behavior or pseudo slip systems for twinning, for which the forward and backward of the slip system are distinguished

Spin and vorticity with vanishing rigid-body rotation during shear in continuum mechanics

A long-standing challenge in continuum mechanics has been how to separate shear deformation and corresponding shape changes from the rotation of a continuum. This can be obtained by a new decomposition of the spin tensor, i.e. of the skew part of the velocity gradient, into two parts, where one of them vanishes during shear flows. The same decomposition applies to the vorticity vector. In both cases, the two spin components are interpreted as generating plastic shear deformation and rigid body rotation. In continuum plasticity theories, the suggested rotational part of the spin tensor can be applied to avoid spurious behavior of the objective Lie derivatives of second order tensors, e.g. of the stress tensor. It provides a history-independent spin corresponding to a time-averaged angular velocity of the rotating line segments in a small homogeneous volume. In fluid mechanics, the new spin component can be used to quantify vortexes in shear flows and turbulent structures, and it provides a sound interpretation and generalization of the Δ and swirling-strength criteria for visualization of vortices

Bauschinger effect modelled by yield surface distortions

A model for distorting the yield surface by flattening the part in the reverse of the loading direction, is suggested. As the basis for the distortion, the model applies a pair of second-order back-stress tensors of similar type as in kinematic hardening models. The yield-surface formulation provides a flattening and shrinkage of a given first-order homogeneous yield surface in the reverse directions of the back-stress tensors. The mathematical formulation is based on similar ideas as the HAH (homogeneous yield function-based anisotropic hardening) model, for which the calibration of the equivalent stress-strain curve is independent of the Bauschinger part of the model. Severe mathematical and numerical challenges of the HAH model are pointed out, but are avoided in the new model. Furthermore, the yield surface doesn't have to contain the origin, and the r-value is conserved in stress reversals

Precipitation of Non-Spherical Particles in Aluminum Alloys Part I: Generalization of the Kampmann–Wagner Numerical Model

Particles precipitated during aging treatments often have non-spherical shapes, e.g., needles or plates, while in the classical Kampmann–Wagner Numerical (KWN) precipitation model, it is assumed that the particles are of spherical shape. This model is here generalized resulting in two correction factors accounting for the effects induced by the particles’ non-spherical shape on their growth kinetics. The first one is for the correction of the growth rate. It is derived from the approximate solution of the diffusion problem on spheroidal coordinate and verified by the three-dimensional numerical solutions for cuboid particles. The second factor is for the energetic correction due to the particle surface curvature. It is derived from chemical potential equality (or Gibbs energy minimization principle) at equilibrium for non-spherical particles and provides a correction factor for the Gibbs–Thomson effect. In the accompanying paper, the two correction factors are implemented into a multi-component KWN modeling framework, and the resulting improvements on the model’s predictive power are demonstrated.submittedVersio