Assessment of four strain energy decomposition methods for phase field fracture models using quasi-static and dynamic benchmark cases

Strain energy decomposition methods in phase field fracture models separate strain energy that contributes to fracture from that which does not. However, various decomposition methods have been proposed in the literature, and it can be difficult to determine an appropriate method for a given problem. The goal of this work is to facilitate the choice of strain decomposition method by assessing the performance of three existing methods (spectral decomposition of the stress or the strain and deviatoric decomposition of the strain) and one new method (deviatoric decomposition of the stress) with several benchmark problems. In each benchmark problem, we compare the performance of the four methods using both qualitative and quantitative metrics. In the first benchmark, we compare the predicted mechanical behavior of cracked material. We then use four quasi-static benchmark cases: a single edge notched tension test, a single edge notched shear test, a three-point bending test, and a L-shaped panel test. Finally, we use two dynamic benchmark cases: a dynamic tensile fracture test and a dynamic shear fracture test. All four methods perform well in tension, the two spectral methods perform better in compression and with mixed mode (though the stress spectral method performs the best), and all the methods show minor issues in at least one of the shear cases. In general, whether the strain or the stress is decomposed does not have a significant impact on the predicted behavior.

Pinning of dislocations in disordered alloys: effects of dislocation orientation

The current interest in compositionally complex alloys including so called high entropy alloys has caused renewed interest in the general problem of solute hardening. It has been suggested that this problem can be addressed by treating the alloy as an effective medium containing a random distribution of dilatation and compression centers representing the volumetric misfit of atoms of different species. The mean square stresses arising from such a random distribution can be calculated analytically, their spatial correlations are strongly anisotropic and exhibit long-range tails with third-order power law decay (Geslin and Rodney 2021; Geslin et al. 2021). Here we discuss implications of the anisotropic and long-range nature of the correlation functions for the pinning of dislocations of arbitrary orientation. While edge dislocations are found to follow the standard pinning paradigm, for dislocations of near screw orientation we demonstrate the co-existence of two types of pinning energy minima.

Parallel-GPU-accelerated adaptive mesh refinement for three-dimensional phase-field simulation of dendritic growth during solidification of binary alloy

In the phase-field simulation of dendrite growth during the solidification of an alloy, the computational cost becomes extremely high when the diffusion length is significantly larger than the curvature radius of a dendrite tip. In such cases, the adaptive mesh refinement (AMR) method is effective for improving the computational performance. In this study, we perform a three-dimensional dendrite growth phase-field simulation in which AMR is implemented via parallel computing using multiple graphics processing units (GPUs), which provide high parallel computation performance. In the parallel GPU computation, we apply dynamic load balancing to parallel computing to equalize the computational cost per GPU. The accuracy of an AMR refinement condition is confirmed through the single-GPU computations of columnar dendrite growth during the directional solidification of a binary alloy. Next, we evaluate the efficiency of dynamic load balancing by performing multiple-GPU parallel computations for three different directional solidification simulations using a moving frame algorithm. Finally, weak scaling tests are performed to confirm the parallel efficiency of the developed code.

Machine learning-assisted high-throughput exploration of interface energy space in multi-phase-field model with CALPHAD potential

Computational methods are increasingly being incorporated into the exploitation of microstructure–property relationships for microstructure-sensitive design of materials. In the present work, we propose non-intrusive materials informatics methods for the high-throughput exploration and analysis of a synthetic microstructure space using a machine learning-reinforced multi-phase-field modeling scheme. We specifically study the interface energy space as one of the most uncertain inputs in phase-field modeling and its impact on the shape and contact angle of a growing phase during heterogeneous solidification of secondary phase between solid and liquid phases. We evaluate and discuss methods for the study of sensitivity and propagation of uncertainty in these input parameters as reflected on the shape of the Cu6Sn5 intermetallic during growth over the Cu substrate inside the liquid Sn solder due to uncertain interface energies. The sensitivity results rank σSI,σIL, and σIL, respectively, as the most influential parameters on the shape of the intermetallic. Furthermore, we use variational autoencoder, a deep generative neural network method, and label spreading, a semi-supervised machine learning method for establishing correlations between inputs of outputs of the computational model. We clustered the microstructures into three categories (“wetting”, “dewetting”, and “invariant”) using the label spreading method and compared it with the trend observed in the Young-Laplace equation. On the other hand, a structure map in the interface energy space is developed that shows σSI and σSL alter the shape of the intermetallic synchronously where an increase in the latter and decrease in the former changes the shape from dewetting structures to wetting structures. The study shows that the machine learning-reinforced phase-field method is a convenient approach to analyze microstructure design space in the framework of the ICME.

VQE method: a short survey and recent developments

The variational quantum eigensolver (VQE) is a method that uses a hybrid quantum-classical computational approach to find eigenvalues of a Hamiltonian. VQE has been proposed as an alternative to fully quantum algorithms such as quantum phase estimation (QPE) because fully quantum algorithms require quantum hardware that will not be accessible in the near future. VQE has been successfully applied to solve the electronic Schrödinger equation for a variety of small molecules. However, the scalability of this method is limited by two factors: the complexity of the quantum circuits and the complexity of the classical optimization problem. Both of these factors are affected by the choice of the variational ansatz used to represent the trial wave function. Hence, the construction of an efficient ansatz is an active area of research. Put another way, modern quantum computers are not capable of executing deep quantum circuits produced by using currently available ansatzes for problems that map onto more than several qubits. In this review, we present recent developments in the field of designing efficient ansatzes that fall into two categories—chemistry–inspired and hardware–efficient—that produce quantum circuits that are easier to run on modern hardware. We discuss the shortfalls of ansatzes originally formulated for VQE simulations, how they are addressed in more sophisticated methods, and the potential ways for further improvements.

Sweep-tracing algorithm: in silico slip crystallography and tension-compression asymmetry in BCC metals

Direct Molecular Dynamics (MD) simulations are being increasingly employed to model dislocation-mediated crystal plasticity with atomic resolution. Thanks to the dislocation extraction algorithm (DXA), dislocation lines can be now accurately detected and positioned in space and their Burgers vector unambiguously identified in silico, while the simulation is being performed. However, DXA extracts static snapshots of dislocation configurations that by themselves present no information on dislocation motion. Referred to as a sweep-tracing algorithm (STA), here we introduce a practical computational method to observe dislocation motion and to accurately quantify its important characteristics such as preferential slip planes (slip crystallography). STA reconnects pairs of successive snapshots extracted by DXA and computes elementary slip facets thus precisely tracing the motion of dislocation segments from one snapshot to the next. As a testbed for our new method, we apply STA to the analysis of dislocation motion in large-scale MD simulations of single crystal plasticity in BCC metals. We observe that, when the crystal is subjected to uniaxial deformation along its [001] axis, dislocation slip predominantly occurs on the {112} maximum resolved shear stress plane under tension, while in compression slip is non-crystallographic (pencil) resulting in asymmetric mechanical response. The marked contrast in the observed slip crystallography is attributed to the twinning/anti-twinning asymmetry of shears in the {112} planes relatively favoring dislocation motion in the twinning sense while hindering dislocations from moving in the anti-twinning directions.

Quantum cluster algorithm for data classification

We present a quantum algorithm for data classification based on the nearest-neighbor learning algorithm. The classification algorithm is divided into two steps: Firstly, data in the same class is divided into smaller groups with sublabels assisting building boundaries between data with different labels. Secondly we construct a quantum circuit for classification that contains multi control gates. The algorithm is easy to implement and efficient in predicting the labels of test data. To illustrate the power and efficiency of this approach, we construct the phase transition diagram for the metal-insulator transition of VO2, using limited trained experimental data, where VO2 is a typical strongly correlated electron materials, and the metallic-insulating phase transition has drawn much attention in condensed matter physics. Moreover, we demonstrate our algorithm on the classification of randomly generated data and the classification of entanglement for various Werner states, where the training sets can not be divided by a single curve, instead, more than one curves are required to separate them apart perfectly. Our preliminary result shows considerable potential for various classification problems, particularly for constructing different phases in materials.

Surface stress calculations for nanoparticles and cavities in aluminum, silicon, and iron: influence of pressure and validity of the Young-Laplace equation

This study is dedicated to the determination of the surface energy and stress of nanoparticles and cavities in presence of pressure, and to the evaluation of the accuracy of the Young-Laplace equation for these systems. Procedures are proposed to extract those quantities from classical interatomic potentials calculations, carried out for three distinct materials: aluminum, silicon, and iron. Our investigations first reveal the increase of surface energy and stress of nanoparticles as a function of pressure. On the contrary we find a significant decrease for cavities, which can be correlated to the initiation of plastic deformation at high pressure. We show that the Young-Laplace equation should not be used for quantitative predictions when the Laplace pressure is computed with a constant surface energy value, as usually done in the literature. Instead, a significant improvement is obtained by using the diameter and pressure-dependent surface stress. In that case, the Young-Laplace equation can be used with a reasonable accuracy at low pressures for nanoparticles with diameters as low as 4 nm, and 2 nm for cavities. At lower sizes, or high pressures, a severely limiting factor is the challenge of extracting meaningful surface stress values.

From mechanism-based to data-driven approaches in materials science

A time-honored approach in theoretical materials science revolves around the search for basic mechanisms that should incorporate key feature of the phenomenon under investigation. Recent years have witnessed an explosion across areas of science of a data-driven approach fueled by recent advances in machine learning. Here we provide a brief perspective on the strengths and weaknesses of mechanism based and data-driven approaches in the context of the mechanics of materials. We discuss recent literature on dislocation dynamics, atomistic plasticity in glasses focusing on the empirical discovery of governing equations through artificial intelligence. We conclude highlighting the main open issues and suggesting possible improvements and future trajectories in the fields.

Slip-free multiplication and complexity of dislocation networks in FCC metals

During plastic deformation of crystalline solids, intricate networks of dislocation lines form and evolve. To capture dislocation density evolution, prominent theories of crystal plasticity assume that 1) multiplication is driven by slip in active slip systems and 2) pair-wise slip system interactions dominate network evolution. In this work, we analyze a massive database of over 100 discrete dislocation dynamics simulations (with cross-slip suppressed), and our findings bring both of these assumptions into question. We demonstrate that dislocation multiplication is commonly observed on slip systems with no applied stress and no plastic strain rate, a phenomenon we refer to as slip-free multiplication. We show that while the formation of glissile junctions provides one mechanism for slip-free multiplication, additional mechanisms which account for the influence of coplanar interactions are needed to fully explain the observations. Unlike glissile junction formation which results from a binary reaction between a pair of slip systems, these new multiplication mechanisms require higher order reactions that lead to complex network configurations. While these complex configurations have not been given much attention previously, they account for about 50% of the line intersections in our database.