arXiv subjects

J. Segurado

Publications and source records attributed to J. Segurado.

At least 19 recordsLinked to original sources

arXiv2026

A Correction Method for Crack Area Overestimation in Phase-Field Fracture

Phase-field fracture models are known to overestimate the crack area, a discrepancy that compromises the accuracy of fracture predictions. This issue stems from the diffuse crack representation and numerical artifacts, such as strain localization, where the phase-field variable artificially saturates across finite elements. Existing correction strategies, including mesh-dependent factors and skeletonization algorithms, have significant limitations. Mesh-based corrections are often unreliable for unstructured meshes, while skeletonization can be complex and inaccurate for intricate crack topologies, especially in three dimensions. This paper introduces a novel and robust framework to correct this overestimation. Our approach is founded on the principle of energy equipartition, where the energy contributions from the phase-field and its gradient are equal as the length-scale parameter approaches zero. Since numerical artifacts primarily affect the phase-field term while leaving the gradient term largely unperturbed, we propose that the crack area can be accurately approximated as twice the gradient-dependent energy. This method is inherently mesh-independent and readily applicable to the entire domain, including 3D simulations. The proposed methodology is validated against benchmarks with analytical solutions and compared with established methods like skeletonization to demonstrate its accuracy. It is then applied to complex geometries with curvilinear crack paths and evaluated in a three-dimensional simulation.

cond-mat.mtrl-sci↗

arXiv2025

A Phase-Field Approach to Fracture and Fatigue Analysis: Bridging Theory and Simulation

This article presents a novel, robust and efficient framework for fatigue crack-propagation that combines the principles of Linear Elastic Fracture Mechanics (LEFM) with phase-field fracture (PFF). Contrary to cycle-by-cycle PFF approaches, this work relies on a single simulation and uses standard crack propagation models such as Paris' law for the material response, simplifying its parametrization. The core of the methodology is the numerical evaluation of the derivative of a specimen's compliance with respect to the crack area. To retrieve this compliance the framework relies on a PFF-FEM simulation, controlled imposing a monotonic crack growth. This control of the loading process is done by a new crack-control scheme which allows to robustly trace the complete equilibrium path of a crack, capturing complex instabilities. The specimen's compliance obtained from the PFF simulation enables the integration of Paris' law to predict fatigue life. The proposed methodology is first validated through a series of benchmarks with analytical solutions to demonstrate its accuracy. The framework is then applied to more complex geometries where the crack path is unknown, showing a very good agreement with experimental results of both crack paths and fatigue life.

cond-mat.mtrl-sci↗

arXiv2024

Martensite decomposition kinetics in additively manufactured Ti-6Al-4V alloy: in-situ characterisation and phase-field modelling

Additive manufacturing of Ti-6Al-4V alloy via laser powder-bed fusion leads to non-equilibrium $\alpha'$ martensitic microstructures, with high strength but poor ductility and toughness. These properties may be modified by heat treatments, whereby the $\alpha'$ phase decomposes into equilibrium $\alpha+\beta$ structures, while possibly conserving microstructural features and length scales of the $\alpha'$ lath structure. Here, we combine experimental and computational methods to explore the kinetics of martensite decomposition. Experiments rely on in-situ characterisation (electron microscopy and diffraction) during multi-step heat treatment from 400$^{\circ}$C up to the alloy $\beta$-transus temperature (995$^{\circ}$C). Computational simulations rely on an experimentally-informed computationally-efficient phase-field model. Experiments confirmed that as-built microstructures were fully composed of martensitic $\alpha'$ laths. During martensite decomposition, nucleation of the $\beta$ phase occurs primarily along $\alpha'$ lath boundaries, with traces of $\beta$ nucleation along crystalline defects. Phase-field results, using electron backscatter diffraction maps of as-built microstructures as initial conditions, are compared directly with in-situ characterisation data. Experiments and simulations confirmed that, while full decomposition into stable $\alpha+\beta$ phases may be complete at 650$^{\circ}$C provided sufficient annealing time, visible morphological evolution of the microstructure was only observed for $T\geq\,$700$^{\circ}$C, without modification of the prior-$\beta$ grain structure.

physics.app-ph↗

arXiv2023

Efficiency and accuracy of GPU-parallelized Fourier spectral methods for solving phase-field models

Phase-field models are widely employed to simulate microstructure evolution during processes such as solidification or heat treatment. The resulting partial differential equations, often strongly coupled together, may be solved by a broad range of numerical methods, but this often results in a high computational cost, which calls for advanced numerical methods to accelerate their resolution. Here, we quantitatively test the efficiency and accuracy of semi-implicit Fourier spectral-based methods, implemented in Python programming language and parallelized on a graphics processing unit (GPU), for solving a phase-field model coupling Cahn-Hilliard and Allen-Cahn equations. We compare computational performance and accuracy with a standard explicit finite difference (FD) implementation with similar GPU parallelization on the same hardware. For a similar spatial discretization, the semi-implicit Fourier spectral (FS) solvers outperform the FD resolution as soon as the time step can be taken 5 to 6 times higher than afforded for the stability of the FD scheme. The accuracy of the FS methods also remains excellent even for coarse grids, while that of FD deteriorates significantly. Therefore, for an equivalent level of accuracy, semi-implicit FS methods severely outperform explicit FD, by up to 4 orders of magnitude, as they allow much coarser spatial and temporal discretization.

cond-mat.mtrl-sci↗

arXiv2022

An implicit FFT-based method for wave propagation in elastic heterogeneous media

An FFT-based algorithm is developed to simulate the propagation of elastic waves in heterogeneous $d$-dimensional rectangular shape domains. The method allows one to prescribe the displacement as a function of time in a subregion of the domain, emulating the application of Dirichlet boundary conditions on an outer face. Time discretization is performed using an unconditionally stable beta-Newmark approach. The implicit problem for obtaining the displacement at each time step is solved by transforming the equilibrium equations into Fourier space and solving the corresponding linear system with a preconditioned Krylov solver. The resulting method is validated against analytical solutions and compared with implicit and explicit finite element simulations and with an explicit FFT approach. The accuracy of the method is similar to or better than that of finite elements, and the numerical performance is clearly superior, allowing the use of much larger models. To illustrate the capabilities of the method, some numerical examples are presented, including the propagation of planar, circular, and spherical waves and the simulation of the propagation of a pulse in a polycrystalline medium.

math.NA↗

arXiv2022

A generalized line tension model for precipitate strengthening in metallic alloys

A generalized line tension model has been developed to estimate the critical resolved shear stress in precipitation hardened alloys. The model is based in previous line tension models for regular arrays of either impenetrable or shearable spherical precipitates that were expanded to take into account the effect of the elastic mismatch between the matrix and the precipitates. The model parameters are calibrated from dislocation dynamics simulations that covered a wide range of precipitate diameters and spacing as well as of the mismatch in elastic constants. This model is extended to deal with random arrays of monodisperse spherical precipitates by changing the geometrical parameters of the model by the averaged ones corresponding to the random distributions. The model predictions were in good agreement with the critical resolved shear stresses obtained from dislocation dynamics simulations of random spherical precipitates distributions for both impenetrable and shearable precipitates, providing a fast and accurate tool to predict precipitate strengthening in metallic alloys.

cond-mat.mtrl-sci↗

arXiv2021

Adaptation and validation of FFT methods for homogenization of lattice based materials

An FFT framework which preserves a good numerical performance in the case of domains with large regions of empty space is proposed and analyzed for its application to lattice based materials. Two spectral solvers specially suited to resolve problem containing phases with zero stiffness are considered (1) a Galerkin approach combined with the MINRES linear solver and a discrete differentiation rule and (2) a modification of a displacement FFT solver which penalizes the indetermination of strains in the empty regions, leading to a fully determined equation. The solvers are combined with several approaches to smooth out the lattice surface, based on modifying the actual stiffness of the voxels not fully embedded in the lattice or empty space. The accuracy of the resulting approaches is assessed for an octet-lattice by comparison with FEM solutions for different relative densities and discretization levels. It is shown that the adapted Galerkin approach combined with a Voigt surface smoothening was the best FFT framework considering accuracy, numerical efficiency and h-convergence. With respect to numerical efficiency it was observed that FFT becomes competitive compared to FEM for cells with relative densities above 7%. Finally, to show the real potential of the approaches presented, the FFT frameworks are used to simulate the behavior of a printed lattice by using direct 3D tomographic data as input. The approaches proposed include explicitly in the simulation the actual surface roughness and internal porosity resulting from the fabrication process. The simulations allowed to quantify the reduction of the lattice stiffness \rev{as well as to resolve the stress localization of 50% near large pores.

cond-mat.mtrl-sci↗

arXiv2021

An FFT-based approach for Bloch wave analysis: application to polycrystals

A method based on the Fast Fourier Transform is proposed to obtain the dispersion relation of acoustic waves in heterogeneous periodic media with arbitrary microstructures. The microstructure is explicitly considered using a voxelized Representative Volume Element (RVE). The dispersion diagram is obtained solving an eigenvalue problem for Bloch waves in Fourier space. To this aim, two linear operators representing stiffness and mass are defined through the use of differential operators in Fourier space. The smallest eigenvalues are obtained using the implicitly restarted Lanczos and the subspace iteration methods, and the required inverse of the stiffness operator is done using the conjugate gradient with a preconditioner. The method is used to study the propagation of acoustic waves in elastic polycrystals, showing the strong effect of crystal anistropy and polycrystaline texture on the propagation. It is shown that the method combines the simplicity of classical Fourier series analysis with the versatility of Finite Elements to account for complex geometries proving an efficient and general approach which allows the use of large RVEs in 3D.

cond-mat.mtrl-sci↗

arXiv2021

An FFT framework for simulating non-local ductile failure in heterogeneous materials

The simulation of fracture using continuum ductile damage models attains a pathological discretization dependence caused by strain localization, after loss of ellipticity of the problem, in regions whose size is connected to the spatial discretization. Implicit gradient techniques suppress this problem introducing some inelastic non-local fields and solving an enriched formulation where the classical balance of linear momentum is fully coupled with a Helmholtz-type equation for each of the non-local variable. Such Helmholtz-type equations determine the distribution of the non-local fields in bands whose width is controlled by a characteristic length, independently on the spatial discretization. The numerical resolution of this coupled problem using the Finite Element method is computationally very expensive and its use to simulate the damage process in 3D multi-phase microstructures becomes prohibitive. In this work, we propose a novel FFT-based iterative algorithm for simulating gradient ductile damage in computational homogenization problems. In particular, the Helmholtz-type equation of the implicit gradient approach is properly generalized to model the regularization of damage in multi-phase media, where multiple damage variables and different characteristic lengths may come into play. In the proposed iterative algorithm, two distinct problems are solved in a staggered fashion: (i) a conventional mechanical problem via a FFT-Galerkin solver with mixed macroscopic loading control and (ii) the generalized Helmholtz-type equation using a Krylov-based algorithm combined with an efficient pre-conditioner. The numerical implementation is firstly validated. Finally, the robustness and efficiency of the algorithm is demonstrated in the simulation of failure of complex 3D particle reinforced composites characterized by millions of degrees of freedom.

cs.CE↗

arXiv2021

Dislocation dynamics prediction of the strength of Al-Cu alloys containing shearable $θ''$ precipitates

The critical resolved shear stress of an Al 4 wt. \% Cu alloy containing a homogeneous distribution of $θ''$ precipitates was determined by means of dislocation dynamics simulations. The size distribution, shape, orientation and volume fraction of the precipitates in the alloy were obtained from transmission electron microscopy observations while the parameters controlling the dislocation/precipitate interactions (elastic mismatch, transformation strains, dislocation mobility and cross-slip probability, etc.) were calculated from atomistic simulations. The precipitates were assumed to be either impenetrable or shearable by the dislocations, the latter characterized by a threshold shear stress that has to be overcome to shear the precipitate. The predictions of the simulations in terms of the critical resolved shear stress and of the dislocation/precipitate interaction mechanisms were in good agreement with the experimental results. It was concluded that the optimum strength of this alloy is attained with a homogeneous distribution of $θ''$ precipitates whose average size ($\approx$ 40 nm) is at the transition between precipitate shearing and looping. Overall, the dislocation dynamics strategy presented in this paper is able to provide quantitative predictions of precipitate strengthening in metallic alloys.

cond-mat.mtrl-sci↗

arXiv2020

Multiscale modelling of precipitation hardening in Al-Cu alloys: dislocation dynamics simulations and experimental validation

The mechanisms of dislocation/precipitate interactions were analyzed in an Al-Cu alloy containing a homogeneous dispersion of $θ'$ precipitates by means of discrete dislocation dynamics simulations. The simulations were carried out within the framework of the discrete-continuous method and the precipitates were assumed to be impenetrable by dislocations. The main parameters that determine the dislocation/precipitate interactions (elastic mismatch, stress-free transformation strains, dislocation mobility and cross-slip rate) were obtained from atomistic simulations, while the size, shape, spatial distribution and volume fraction of the precipitates were obtained from transmission electron microscopy. The predictions of the critical resolved shear stress (including the contribution of solid solution) were in agreement with the experimental results obtained by means of compression tests in micropillars of the Al-Cu alloy oriented for single slip. The simulations revealed that the most important contribution to the precipitation hardening of the alloy was provided by the stress-free transformation strains followed by the solution hardening and the Orowan mechanism due to the bow-out of the dislocations around the precipitates.

cond-mat.mtrl-sci↗

arXiv2019

A coupled model of diffusional creep of polycrystalline solids based on climb of dislocations at grain boundaries

A continuum theory based on thermodynamics has been developed for modeling diffusional creep of polycrystalline solids. It consists of a coupled problem of vacancy diffusion and mechanics where the vacancy generation/absorption at grain boundaries is driven by grain boundary dislocations climb. The model is stated in terms of general balance laws and completed by the choice of constitutive equations consistent with classical non-equilibrium thermodynamics. The kinetics of diffusional creep is derived from physically-based mechanisms of climb of dislocations at grain boundaries, thus introducing a dependence of diffusional creep on the density and mobility of boundary dislocations. Several representative examples have been solved using the finite element method and assuming representative volume elements made up of an array of regular-shaped crystals. The effect of stress, temperature, grain size, and grain boundary dislocation mobility is analyzed and compared with classical theories of diffusional creep. The simulation results demonstrate the ability of the present model to reproduce the macroscopic stress and grain size dependence observed under both diffusion and interface controlled regimes as well the evolution of this dependency with the temperature. In addition, the numerical implementation of the model allows to predict the evolution of microscopic fields through the microstructure.

cond-mat.mtrl-sci↗

arXiv2019

Simulation of the Hall-Petch effect in FCC polycrystals by means of strain gradient crystal plasticity and FFT homogenization

The influence of grain size on the flow stress of various FCC polycrystals (Cu, Al, Ag and Ni) has been analyzed by means of computational homogenization of a representative volume element of the microstructure using a FFT approach in combination with a strain gradient crystal plasticity model. The density of geometrically necessary dislocations resulting from the incompatibility of plastic deformation among different crystals was obtained from the Nye tensor, which was efficiently obtained from the curl operation in the Fourier space. The simulation results were in good agreement with the experimental data for Cu, Al, Ag and Ni polycrystals for grain sizes > 20 microns and strains < 5% and provided a physical explanation for the higher strengthening provided by grain boundaries in Al and Ni, as compared with Cu and Ag. The investigation demonstrates how the combination of FFT with strain gradient crystal plasticity can be used to include effect of grain boundaries in the mechanical behavior of polycrystals using realistic representative volume elements of the microstructure.

cond-mat.mtrl-sci↗

arXiv2019

Effect of slip transmission at grain boundaries in Al bicrystals

The effect of slip transfer on the deformation mechanisms of Al bicrystals was explored using a rate-dependent dislocation-based crystal plasticity model. Three different types of grain boundaries (GBs) were included in the model by modifying the rate of dislocation accumulation near the GB in the Kocks-Mecking law, leading to fully-opaque (dislocation blocking), fully-transparent and partially-transparent GBs. In the latter, slip transmission is only allowed in pairs of SS in neighbour grains that are suitably oriented for slip transfer according to the Luster-Morris parameter. Modifications of the GB character led to important changes in the deformation mechanisms at the GB. In general, bicrystals with fully-opaque boundaries showed an increase in the dislocation density near the GB, which was associated with an increase in the Von Mises stress. In contrast, the dislocation pile-ups and the stress concentration were less pronounced in the case of partially-transparent boundaries as the slip in one grain can progress into the next grain with some degree of continuity. No stress concentrations were found at these boundaries for fully-transparent boundaries, and there was continuity of strain across the boundary, which is not typical of most experimentally observed GBs. Simulations of ideal bicrystals oriented for favorable slip transfer on the most highly favored slip system in grains with high Schmid factors for slip transfer depends on the number of active SS in operation in the neighborhood and that most boundaries will lead to nearly opaque conditions while some boundaries will be transparent. Finally, the model was applied to a particular experimentally observed GB in which slip transfer was clearly operating indicating that the model predicted a nearly transparent GB.

cond-mat.mtrl-sci↗

arXiv2019

An algorithm for stress and mixed control in Galerkin based FFT homogenization

A new algorithm is proposed to impose a macroscopic stress or mixed stress/deformation gradient history in the context of non-linear Galerkin based FFT homogenization. The method proposed is based in the definition of a modified projection operator in which the null frequencies enforce the type of control (stress or strain) for each component of either the macroscopic first Piola stress or the deformation gradient. The resulting problem is solved exactly as the original variational method and it does not require additional iterations compared to the strain control version, neither in the linear iterative solver, nor in the Newton scheme. The efficiency of the method proposed is demonstrated with a series of numerical examples, including a polycrystal and a particle reinforced hyperelastic material.

cond-mat.mtrl-sci↗

arXiv2018

An atomistic investigation of the interaction of dislocations with Guinier-Preston zones in Al-Cu alloys

The interaction between edge dislocations and Guinier-Preston zones in an Al-Cu alloy was analyzed by means of atomistic simulations. The different thermodynamic functions that determine the features of these obstacles for the dislocation glide were computed using molecular statics, molecular dynamics and the nudged elastic band method. It was found that Guinier-Preston zones are sheared by dislocations and the rate at which dislocations overcome the precipitate is controlled by the activation energy, $ΔU$, in agreement with the postulates of the harmonic transition state theory. Moreover, the entropic contribution to the Helmholtz activation free energy was in the range 1.3-1.8$k_b$, which can be associated with the typical vibrational entropy of solids. Finally, an estimation of the initial shear flow stress as a function of temperature was carried out from the thermodynamic data provided by the atomistic simulations. Comparison with experimental results showed that the effect of the random precipitate distribution and of the dislocation character and dislocation/precipitation orientation has to be taken into account in the simulations to better reproduce experiments.

cond-mat.mtrl-sci↗

arXiv2018

Computational Homogenization of Polycrystals

This paper reviews the current state-of-the-art in the simulation of the mechanical behavior of polycrystalline materials by means of computational homogenization. The key ingredients of this modelling strategy are presented in detail starting with the parameters needed to describe polycrystalline microstructures and the digital representation of such microstructures in a suitable format to perform computational homogenization. The different crystal plasticity frameworks that can describe the physical mechanisms of deformation in single crystals (dislocation slip and twinning) at the microscopic level are presented next. This is followed by the description of computational homogenization methods based on mean-field approximations by means of the viscoplastic self-consistent approach, or on the full-field simulation of the mechanical response of a representative polycrystalline volume element by means of the finite element method or the fast Fourier transform-based method. Multiscale frameworks based on the combination of mean-field homogenization and the finite element method are presented next to model the plastic deformation of polycrystalline specimens of arbitrary geometry under complex mechanical loading. Examples of application to predict the strength, fatigue life, damage, and texture evolution under different conditions are presented to illustrate the capabilities of the different models. Finally, current challenges and future research directions in this field are summarized.

cond-mat.mtrl-sci↗

arXiv2018

Discrete dislocation dynamics simulations of dislocation-$θ'$ precipitate interaction in Al-Cu alloys

The mechanisms of dislocation/precipitate interaction were studied by means of discrete dislocation dynamics within a multiscale approach. Simulations were carried out using the discrete continuous method in combination with a fast Fourier transform solver to compute the mechanical fields. The original simulation strategy was modified to include straight dislocation segments by means of the field dislocation mechanics method and was applied to simulate the interaction of an edge dislocation with a $θ'$ precipitate in an Al-Cu alloy. It was found that the elastic mismatch has a negligible influence on the dislocation/precipitate interaction in the Al-Cu system. Moreover, the influence of the precipitate aspect ratio and orientation was reasonably well captured by the simple Orowan model in the absence of the stress-free transformation strain. Nevertheless, the introduction of the stress-free transformation strain led to dramatic changes in the dislocation/precipitate interaction and in the critical resolved shear stress to overcome the precipitate, particularly in the case of precipitates with small aspect ratio. The new multiscale approach to study the dislocation/precipitate interactions opens the possibility to obtain quantitative estimations of the strengthening provided by precipitates in metallic alloys taking into account the microstructural details.

cond-mat.mtrl-sci↗