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This paper presents a procedure for determining the elastoplastic parameters of phase-field fracture of sintered material. The material considered was sintered steel Astaloy™ Mo+0.2C of three densities: 6.5, 6.8 and 7.1 g/ cm 3 . The stress–strain curve and Wöhler curve, which are experimentally obtained, are utilized for validation of the numerical simulations. For modelling of damage evolution, a CCPF (Convergence check phase-field) algorithm was used as a numerical framework. During calibration of the numerical parameters, two-dimensional as well as three-dimensional modelling was used. A comparison of different fatigue degradation functions known from the literature is also made. To improve the efficiency of numerical simulations of fatigue behaviour, the cycle skip technique is also employed. [ABSTRACT FROM AUTHOR]

The paper proposes a novel staggered phase-field framework for modelling brittle and ductile fractures in monotonic and cyclic loading regimes. The algorithm consists of two mesh layers (displacement and phase field) and a single special-purpose, user-defined finite element, which controls global convergence of the coupled problem and passing of the solution variables between mesh layers. The proposed algorithm is implemented into FE software ABAQUS. For the problem of high cyclic fatigue, a cycle-skipping scheme is also introduced. The proposed methodology is verified on the usual benchmark examples. Small-strain theory is applied, but it has been demonstrated that extension to large strains is straightforward using only the ABAQUS built-in option. The efficiency and stability of the proposed framework was proven by comparison of computational time and the number of iterations per increment in the RCTRL scheme. [ABSTRACT FROM AUTHOR]

During the process of laser cladding IN718/WC composite coatings, the dissolution and metallurgical reaction of WC particles significantly influence the microstructures of the coatings. However, the limited experimental methods restrict direct observation and prevent a deep understanding of this complicated process. Therefore, a novel numerical model for the solidification process of IN718/WC composite coatings was proposed. The model was established with the coupled multi-phase-field model and lattice Boltzmann method. Different kinds of microstructure around WC particles were simulated by the model and verified by experiments. Subsequently, microhardness and wear tests were carried out to investigate the improved mechanical properties of IN718 coatings reinforced by WC particles. The results show that the cellular alloy reaction layer, IN718 grains, and eutectic structure are formed, in turn, around WC particles. The convection in the laser molten pool can induce double-tail-like or spindle-like WC convection diffusion bands. The hardness of these bands is higher than that of the IN718 matrix. More importantly, WC convection diffusion bands can inhibit the growth of columnar crystals, because the dissolved WC can decrease the freezing temperature of the melt. Finally, mechanical property tests show that WC particles increase the hardness of the coating and significantly improve its wear resistance. [ABSTRACT FROM AUTHOR]

A recently developed phase-field model for simulating diffusion-induced grain boundary migration (DIGM) is applied to binary Fe–Zn. The driving force for the boundary migration is assumed to come from the coherency strain energy mechanism suggested by Sulonen. The effect of the angle of the grain boundary with the surface on the velocity of the boundary migration is studied in detail. The simulation results compare favorably with experimental observations, such as the oscillatory motion of the grain boundary, velocity of the moving grain boundary during DIGM, and the maximum value of mole fraction of Zn at the surface after 20 h of heat treatment. [ABSTRACT FROM AUTHOR]

This study proposes a hydrogen-assisted fracture analysis methodology considering associated deformation and hydrogen transport inside a phase-field-based formulation. First, the hydrogen transport around a crack tip is calculated, and then the effect of hydrogen enhanced decohesion (HEDE) is modeled by defining the critical energy release rate as a function of hydrogen concentration. The proposed method is based on a coupled hydrogen mechanical damage under phase-field and implemented through a user subroutine in ABAQUS software. The test using compact tension (CT) sample is investigated numerically to study the hydrogen embrittlement on 45CrNiMoVA steel. Experimentally, the microstructural fracture presents a mixed brittle fracture mode, consisting of quasi-cleavage (QC) and intergranular (IG) fracture with hydrogen. This fracture mode is consistent with the suggested HEDE mechanism in the model. The simulation results show that hydrogen accumulates at the crack tip where positive hydrostatic stress is located. Moreover, the model estimates the initial hydrogen concentration through iterations. The simulated load-line displacement curves show good agreement with the experimental plots, demonstrating the predictive capabilities of the presented scheme. [ABSTRACT FROM AUTHOR]

A multi-scale phase-field approach, which couples the mesoscopic crystallization with the microscopic orientation of chain segments and macroscopic viscoelastic melt flow, is proposed to study how the crystal growth of semi-crystalline polymers is affected by flows. To make the simulation feasible, we divide the problem into three parts. In the first part, a finitely extensible nonlinear elastic (FENE) dumbbell model is used to simulate the flow induced molecular structure. In the second part, formulas for estimating the density, orientation and aspect ratio of nuclei upon the oriented molecular structure are derived. Finally, in the third part, a massive mathematical model that couples the phase-field, temperature field, flow field and orientation field is established to model the crystal growth with melt flow. Two-dimensional simulations are carried out for predicting the flow effect on the crystal growth of isotactic polystyrene under a plane Poiseuille flow. In solving the model, a semi-analytical method is adopted to avoid the numerical difficult of a "high Weissenberg number problem" in the first part, and an efficient fractional step method is used to reduce the computing complexity in the third part. The simulation results demonstrate that flow strongly affects the morphology of single crystal but does not bring a significant influence on the holistic morphology of bulk crystallization. [ABSTRACT FROM AUTHOR]

The continuum decomposition of the Fe-Cr alloys from initial phase separation to steady-state coarsening with concentrations varying from 25 at % Cr and 30 at % Cr to 33 at % Cr aged at 750 K was studied by utilizing three-dimensional phase-field simulations. The dynamic stages of separation of nanoscale Cr-enriched α phase were distinguished by the evolution of the volume fraction, particle number density and the average particle radius of the α phase. The stage of steady-state coarsening was characterized with an equilibrium volume fraction and decreasing particle number density. The coarsening rate constant by linear fitting of the cube of average radius and aging time shows an increase with the increasing Cr concentration. The time exponents decrease from the growth and coarsening stage to the steady-state coarsening stage and show a dependence on the particles number density at different concentrations. The quantitative evolutions of α phase via nucleation growth and spinodal decomposition are theoretically helpful for understanding the microstructure evolution with aging time in Fe-Cr alloys. [ABSTRACT FROM AUTHOR]

Martensitic steels form a material class with a versatile range of properties that can be selected by varying the processing chain. In order to study and design the desired processing with the minimal experimental effort, modeling tools are required. In this work, a full processing cycle from quenching over tempering to mechanical testing is simulated with a single modeling framework that combines the features of the phase-field method and a coupled chemo-mechanical approach. In order to perform the mechanical testing, the mechanical part is extended to the large deformations case and coupled to crystal plasticity and a linear damage model. The quenching process is governed by the austenite-martensite transformation. In the tempering step, carbon segregation to the grain boundaries and the resulting cementite formation occur. During mechanical testing, the obtained material sample undergoes a large deformation that leads to local failure. The initial formation of the damage zones is observed to happen next to the carbides, while the final damage morphology follows the martensite microstructure. This multi-scale approach can be applied to design optimal microstructures dependent on processing and materials composition. [ABSTRACT FROM AUTHOR]

We give an overview of contributions made to the computational phase-field modelling of alloy solidification from the University of Leeds as part of the LiME project (EPSRC Advanced Manufacturing Hub in Liquid Metal Engineering). The broader look at the more salient features from our research allows the individual contributions to be seen in a wider context than can be seen from each contribution separately. We begin with a general introduction to phase-field and then reference the numerical issues that arise from the solution of the model before outlining contributions to phase-field modelling that we found most interesting or significant. These range from controlling and developing interface-width independent modelling; controlling morphology in both single and multiphase settings; generalising from single to multiphase models; and creating a thermodynamically consistent framework for modelling entropy flow and thereby postulating a temperature field consistent with the concepts of, and applicable in, multiphase and density-dependent settings. [ABSTRACT FROM AUTHOR]

Laser-induced forward transfer for high-viscosity—of Pa·s—pastes differ from standard LIFT processes in its dynamics. In most techniques, the transference after setting a great gap does not modify the shape acquired by the fluid, so it stretches until it breaks into droplets. In contrast, there is no transferred material when the gap is bigger than three times the paste thickness in LIFT for high-viscosity pastes, and only a spray is observed on the acceptor using this configuration. In this work, the dynamics of the paste have been studied using a finite-element model in COMSOL Multiphysics, and the behavior of the paste varying the gap between the donor and the acceptor substrates has also been modeled. The paste bursts for great gaps, but it is confined when the acceptor is placed close enough. The obtained simulations have been compared with a previous work, in which the paste structures were photographed. The analysis of the simulations in terms of speed allows for predicting the burst of the paste—spray regime—and the construction of a printability map regarding the gap between the substrates. [ABSTRACT FROM AUTHOR]

In this work, a small-strain phase-field model is presented, which is able to predict crack propagation in systems with anisotropic brittle and ductile constituents. To model the anisotropic brittle crack propagation, an anisotropic critical energy release rate is used. The brittle constituents behave linear-elastically in a transversely isotropic manner. Ductile crack growth is realised by a special crack degradation function, depending on the accumulated plastic strain, which is calculated by following the J 2 -plasticity theory. The mechanical jump conditions are applied in solid-solid phase transition regions. The influence of the relevant model parameters on a crack propagating through a planar brittle-ductile interface, and furthermore a crack developing in a domain with a single anisotropic brittle ellipsoid, embedded in a ductile matrix, is investigated. We demonstrate that important properties concerning the mechanical behaviour of grey cast iron, such as the favoured growth of cracks along the graphite lamellae and the tension–compression load asymmetry of the stress–strain response, are covered by the model. The behaviour is analysed on the basis of a simulation domain consisting of three differently oriented elliptical inclusions, embedded in a ductile matrix, which is subjected to tensile and compressive load. The material parameters used correspond to graphite lamellae and pearlite. [ABSTRACT FROM AUTHOR]

Degradation, damage evolution, and fatigue models in the literature for various engineering materials, mostly metals and composites, are reviewed. For empirical models established under the framework of Newtonian mechanics, Gurson–Tvergaard–Needleman (GTN) type model, Johnson-Cook (J-C) type damage model, microplasticity model, some other micro-mechanism based damage models, and models using irreversible entropy as a metric with an empirical evolution function are thoroughly discussed. For Physics-based models, the development and applications of unified mechanics theory is reviewed. [ABSTRACT FROM AUTHOR]

Heat treatment has a significant impact on the microstructure and the mechanical properties of Al-Mg-Si alloys. The present study presents a first Phase-Field modelling approach on the recrystallisation and grain growth mechanism during annealing. It focuses on the precipitate fraction, radius, and Mg-Si concentration in the matrix phase, which are used as input data for the calculation of the yield strength and hardness at the end of different ageing treatments. Annealing and artificial ageing simulations have been conducted on the MultiPhase-Field based MICRESS@ software, while the ThermoCalc@ software has been used to construct the pseudo-binary Al-Mg phase-diagrams and the atomic-mobility databases of MgxSiy precipitates. Recrystallisation simulation estimates the recrystallisation kinetics, the grain growth, and the interface mobility with the presence/absence of secondary particles, selecting as annealing temperature 400 °C and a microstructure previously subjected to cold rolling. The pinning force of secondary particles decelerates the overall recrystallisation time, causing a slight decrease in the final grain radius due to the reduction of interface mobility. The ageing simulation examines different ageing temperatures (180 and 200 °C) for two distinct ternary systems (Al-0.9Mg-0.6Si/Al-1.0Mg-1.1Si wt.%) considering the interface energy and the chemical free energy as the driving force for precipitation. The combination of Phase-Field and the Deschamps–Brechet model predicted the under-ageing condition for the 180 °C ageing treatment and the peak-ageing condition for the 200 °C ageing treatment. [ABSTRACT FROM AUTHOR]

Improving the durability and sustainability of concrete structures has been driving the enormous number of research papers on self-healing mechanisms that have been published in the past decades. The vast developments of computer science significantly contributed to this and enhanced the various possibilities numerical simulations can offer to predict the entire service life, with emphasis on crack development and cementitious self-healing. The aim of this paper is to review the currently available literature on numerical methods for cementitious self-healing and fracture development using Phase-Field (PF) methods. The PF method is a computational method that has been frequently used for modeling and predicting the evolution of meso- and microstructural morphology of cementitious materials. It uses a set of conservative and non-conservative field variables to describe the phase evolutions. Unlike traditional sharp interface models, these field variables are continuous in the interfacial region, which is typical for PF methods. The present study first summarizes the various principles of self-healing mechanisms for cementitious materials, followed by the application of PF methods for simulating microscopic phase transformations. Then, a review on the various PF approaches for precipitation reaction and fracture mechanisms is reported, where the final section addresses potential key issues that may be considered in future developments of self-healing models. This also includes unified, combined and coupled multi-field models, which allow a comprehensive simulation of self-healing processes in cementitious materials. [ABSTRACT FROM AUTHOR]

The complex failure mechanisms of glass laminates under in-plane loading conditions is modelled within the framework of phase-field strategy. Laminated glass is widely used for structural purposes due to its safe post-glass-breakage response. In fact, the combination of several glass plies bonded together with polymeric interlayers allows overcoming the brittleness of the glass and to reach a pseudo-ductile response. Moreover, the post-breakage behaviour of the laminate is strictly correlated by the mechanical properties of the constituents. Ruptures may appear as cracks within the layers or delamination of the bonding interface. The global response of a glass laminate, validated against experimental results taken from the literature, is carried out by investigating a simplified layup of two glass plies connected by cohesive interfaces through an interlayer. Delamination of the adhesive interface is described, and crack patterns within the materials are fully described. Finally, the proposed approach put the basis for future comparisons with results of experimental campaign and real-life applications. [ABSTRACT FROM AUTHOR]

The distribution homogeneity of grain size affects the fluidity of the semi-solid slurry, which in turn affects the properties of the casting. One key factor affecting grain size uniformity resides in the nucleation number, which has been studied thoroughly, while the other factor is temperature gradient which has not been investigated yet. In this study, the microstructure evolutions under certain temperature gradients are investigated by experiment and simulation using a two-dimensional quantitative phase-field (PF) model. A parallel and adaptive mesh refinement algorithm is adopted to solve the nonlinear phase-field equations. The results indicate that temperature gradient can affect the size distribution of microstructure in the semi-solid slurry prepared by the SEED process. A higher temperature gradient (in the range of 0.230~0.657 °C/mm) along the radial direction is beneficial to the homogeneity of the grain size in a slurry. [ABSTRACT FROM AUTHOR]

3C-SiC is a promising material for low-voltage power electronic devices but its growth is still challenging. Heteroepitaxy of 3C-SiC on Si micrometer-sized pillars is regarded as a viable method to achieve high crystalline quality, minimizing the effects of lattice and thermal expansion mismatch. Three-dimensional micro-crystals with sharply-faceted profiles are obtained, eventually touching with each other to form a continuous layer, suspended on the underlying pillars. By comparing experimental data and simulation results obtained by a phase-field growth model, here we demonstrate that the evolution of the crystal morphology occurs in a kinetic regime, dominated by the different incorporation times on the crystal facets. These microscopic parameters, effective to characterize the out-of-equilibrium growth process, are estimated by a best-fitting procedure, matching simulation profiles to the experimental one at different deposition stages. Then, simulations are exploited to inspect the role of a different pillar geometry and template effects are recognized. Finally, coalescence of closely spaced crystals ordered into an hexagonal array is investigated. Two possible alignments of the pattern are compared and the most convenient arrangement is evaluated. [ABSTRACT FROM AUTHOR]