A hybrid approach for the efficient computation of polycrystalline yield loci with the accuracy of the crystal plasticity finite element method

Direct experimental evaluation of the anisotropic yield locus of a given material, representing the zeros of the material's yield function in the stress space, is arduous. It is much more practical to determine the yield locus by combining limited measurements of yield strengths with predictions from numerical models based on microstructural features such as the orientation distribution function (ODF; also referred to as the crystallographic texture). For the latter, several different strategies exist in the current literature. In this work, we develop and present a new hybrid method that combines the numerical efficiency and simplicity of the classical crystallographic yield locus (CYL) method with the accuracy of the computationally expensive crystal plasticity finite element method (CPFEM). The development of our hybrid approach is presented in two steps. In the first step, we demonstrate for diverse crystallographic textures that the proposed hybrid method is in good agreement with the shape of the predicted yield locus estimated by either CPFEM or experiments, even for pronounced plastic anisotropy. It is shown that the calibration of only two parameters of the CYL method with only two yield stresses for different load cases obtained from either CPFEM simulations or experiments produces a reliable computation of the polycrystal yield loci for diverse crystallographic textures. The accuracy of the hybrid approach is evaluated using the results from the previously established CPFEM method for the computation of the entire yield locus and also experiments. In the second step, the point cloud data of stress tensors on the yield loci predicted by the calibrated CYL method are interpolated within the deviatoric stress space by cubic splines such that a smooth yield function can be constructed. Since the produced yield locus from the hybrid approach is presented as a smooth function, this formulation can potentially be used as an anisotropic yield function for the standard continuum plasticity methods commonly used in finite element analysis.

A ReaxFF potential for Al - ZnO systems

A reactive field force (ReaxFF) potential has been created in order to model the structural effects of low percentage dopant aluminium in a zinc oxide system. The potential’s parameters were fitted to configurations computed with Density Functional Theory (DFT): cohesive energies, binding energies and forces were all considered for bulk crystals, surface structures and ZnAl alloys. As a first application of the model, the energetic deposition (0.1 - 40 eV) of an aluminium atom onto the polar surface of a ZnO (000 ̄1) is considered. For low energies the Al atom attaches to two preferred sites on the surface but as the energy increases above ≈ 15 eV subplantation is preferred at near normal incidence, with high diffusion barriers between stable sites. At these energies, reflection of the Al atom occurs at incident angles above ≈ 55◦.

Simulating intergranular hydrogen enhanced decohesion in aluminium using density functional theory

Materials modelling at the atomistic scale provides a useful way of investigating the widely debated fundamental mechanisms of hydrogen embrittlement in materials like aluminium alloys. Density functional theory based tensile tests of grain boundaries (GBs) can be used to understand the hydrogen enhanced decohesion mechanism (HEDE). The cohesive zone model was employed to understand intergranular fracture from energies obtained in electronic structure calculations at small separation increments during ab initio tensile tests of an aluminium Σ11 GB supercell with variable coverages of H. The standard rigid grain shift test and a quasistatic sequential test, which aims to be faster and more realistic than the rigid grain shift method, were implemented. Both methods demonstrated the effects of H on the cohesive strength of the interface. The sequential method showed discrete structural changes during decohesion, along with significant deformation in general compared to the standard rigid approach. H was found to considerably weaken the GB, where increasing H content led to enhanced embrittlement such that, for the highest coverages of H, GB strength was reduced to approximately 20% of the strength of a pure Al GB - it is proposed that these results simulate HEDE. The possibility of finding H coverages required to induce this effect in real alloy systems is discussed in context by using calculations of the heat of segregation of H.

An integrated XFEM modeling with experimental measurements for optimizing thermal conductivity in carbon nanotube reinforced polyethylene

The present paper investigates the thermal properties of carbon nanotube reinforced polyethylene and specifically its potential as highly conductive material. To this end, an integrated approach is proposed combining both numerical and experimental procedures. First, in order to study conductive heat transfer in two-phase materials with imperfect interfaces, a detailed numerical model is developed based on the extended finite element method (XFEM), where material interfaces are modeled using the level set method. The thermal conductance at the interface of the carbon nanotubes and the polymer matrix is considered to be an unknown model parameter, the value of which is obtained by utilizing a series of experimental measurements of the composite material’s effective conductivity. The interfacial thermal conductance parameter value is inferred by calibrating the numerically predicted effective conductivity to the series of the corresponding experimental measurements. Once this parameter is estimated, the data-informed model is subsequently employed to provide reliable predictions of the effective conductivity of the composite for various weight fractions and configurations of carbon nanotubes in the parent material. Furthermore, microstructural morphologies that provide upper limits on the effective conductivity of the composite are identified via sensitivity analysis, demonstrating its potential as a highly conductive material.

Solidification and grain formation in alloys: a 2D application of the grand-potential-based phase-field approach

Solidification is a significant step in the forming of crystalline structures during various manufacturing and material processing techniques. Solidification characteristics and the microstructures formed during the process dictate the properties and performance of the materials. Hence, understanding how the process conditions relate to various microstructure formations is paramount. In this work, a grand-potential-based multi-phase, multi-component, multi-order-parameter phase-field model is used to demonstrate the solidification of alloys in 2D. This model has several key advantages over other multi-phase models such as it decouples the bulk energy from the interfacial energy, removes the constraints for the phase concentration variable, and prevents spurious 3rd-phase formation at the two phase interfaces. Here, the model is implemented in a finite-element-based phase-field modeling code. The role of various modeling parameters in governing the solidification rate and the shape of the solidified structure is evaluated. It is demonstrated that the process conditions such as temperature gradient, thermal diffusion, cooling rate, etc., influence the solidification characteristics by altering the level of undercooling. Furthermore, the capability of the model to capture directional solidification and polycrystalline structure formation exhibiting various grain shapes is illustrated. In both these cases, the process conditions have been related to the growth rate and associated shape of the dendritic structure. This work serves as a stepping stone towards resolving the larger problem of understanding the process-structure-property-performance correlation in solidified materials.

Energy quadratization Runge-Kutta method for the modified phase field crystal equation

In this paper, we propose high order and unconditionally energy stable methods for a modified phase field crystal equation by applying the strategy of the energy quadratization Runge–Kutta methods. We transform the original model into an equivalent system with auxiliary variables and quadratic free energy. The modified system preserves the laws of mass conservation and energy dissipation with the associated energy functional. We present rigorous proofs of the mass conservation and energy dissipation properties of the proposed numerical methods and present numerical experiments conducted to demonstrate their accuracy and energy stability. Finally, we compare long-term simulations using an indicator function to characterize the pattern formation.

Synergetic effect of Si addition on mechanical properties in face-centered-cubic high entropy alloys: A first-principles study

High-entropy alloys (HEA) have been receiving increased attention for their excellent mechanical properties. Our recent study revealed that Si-doped face-centered cubic (FCC) HEAs have great potential to improve both strength and ductility. Here, we carried out first-principles calculations in cooperation with Monte Carlo simulation and structural factor analysis to explore the effect of Si addition on the macroscopic mechanical properties. As a result, Si addition increased the local lattice distortion and the stacking fault energy. Furthermore, the short-range order formation in Si-doped alloy caused highly fluctuated stacking fault energy. Thus, the heterogeneous solid solution states in which low and high stacking fault regions are distributed into the matrix were nucleated. This unique feature in Si-doped FCC-HEA induces ultrafine twin formation in Si-doped alloys, which can be a dominant factor in improving both strength and ductility.

Impact of a strong temperature gradient on grain growth in films

The migration of grain boundaries and, therewith, the phenomenon of grain growth depend strongly on the annealing temperature. Generally, higher temperatures are associated with higher mobilities of the boundaries and therewith faster microstructural coarsening. In the present study, the influence of a strong temperature gradient on grain growth in thin films is investigated. To that aim, a modified three-dimensional Potts model algorithm is employed, where the annealing temperature changes with the thickness of the sample taking grain boundary mobility and energy into account. The resulting drag effect has serious consequences for the temporal and spatial evolution of the grain microstructure.

Dislocation transport using a time-explicit Runge-Kutta discontinuous Galerkin finite element approach

A time-explicit Runge-Kutta discontinuous Galerkin (RKDG) finite element scheme is proposed to solve the dislocation transport initial boundary value problem in 3D. The dislocation density transport equation, which lies at the core of this problem, is a first-order unsteady-state advection-reaction-type hyperbolic partial differential equation; the DG approach is well suited to solve such equations that lack any diffusion terms. The development of the RKDG scheme follows the method of lines approach. First, a space semi-discretization is performed using the DG approach with upwinding to obtain a system of ordinary differential equations in time. Then, time discretization is performed using explicit RK schemes to solve this system. The 3D numerical implementation of the RKDG scheme is performed for the first-order (forward Euler), second-order and third-order RK methods using the strong stability preserving approach. These implementations provide (quasi-)optimal convergence rates for smooth solutions. A slope limiter is used to prevent spurious Gibbs oscillations arising from high-order space approximations (polynomial degree ≥ 1) of rough solutions. A parametric study is performed to understand the influence of key parameters of the RKDG scheme on the stability of the solution predicted during a screw dislocation transport simulation. Then, annihilation of two oppositely signed screw dislocations and the expansion of a polygonal dislocation loop are simulated. The RKDG scheme is able to resolve the shock generated during dislocation annihilation without any spurious oscillations and predict the prismatic loop expansion with very low numerical diffusion. These results demonstrate the robustness of the scheme.

Mesoscopic scale simulation and wear investigation of self-lubricating fabric liner based on representative volume element

As the self-lubricating layer of self-lubricating spherical plain bearings, fabric liner shows obvious heterogeneous anisotropic characteristics, so it is a technical difficulty to predict its wear properties. In this paper, the continuous wear of self-lubricating fabric liner was simulated based on the mesoscopic scale wear model. The macroscopic wear properties of the fabric liner were characterized by establishing a representative volume element (RVE), and subsequently imposing periodic boundary restrictions (PBCs) on periodic surfaces. In order to avoid excessive mesh distortion, voxel grids meshing method was used, and then continuous wear of the heterogeneous material was realized by adjusting node coordinates and combining nodes. Detailed comparison between simulation prediction results and wear test data of fabric liner was made. The good correlation of the results confirmed that the mesoscopic scale wear model could be used in accurately predict the tribological performance of fabric composite.