Publications
97 results found
Hageman T, Andrade C, Martínez-Pañeda E, 2023, Corrosion rates under charge-conservation conditions, Electrochimica Acta, Vol: 461, Pages: 1-13, ISSN: 0013-4686
Laboratory and numerical corrosion experiments impose an electric potential on the metal surface, differing from natural corrosion conditions, where corrosion typically occurs in the absence of external current sources. In this work, we present a new computational model that enables predicting corrosion under charge-conservation conditions. The metal potential, an output of the model, is allowed to change, capturing how the corrosion and cathodic reactions must produce/consume electrons at the same rates, as in natural conditions. Finite element simulations are performed over a large range of concentrations and geometric parameters. The results highlight the notable influence of the charge-conservation assumption and pioneeringly quantify corrosion rates under realistic conditions. They further show: (i) the strong coupling between the corrosion rate and the hydrogen and oxygen evolution reactions, (ii) under which circumstances corrosion pits acidify, and (iii) when corrosion is able to become self-sustained lacking oxygen.
Lucarini S, Dunne FPE, Martínez-Pañeda E, 2023, An FFT-based crystal plasticity phase-field model for micromechanical fatigue cracking based on the stored energy density, International Journal of Fatigue, Vol: 172, Pages: 1-11, ISSN: 0142-1123
A novel FFT-based phase-field fracture framework for modelling fatigue crack initiation and propagation at the microscale is presented. A damage driving force is defined based on the stored energy and dislocation density, relating phase-field fracture with microstructural fatigue damage. The formulation is numerically implemented using FFT methods to enable modelling of sufficiently large, representative 3D microstructural regions. The early stages of fatigue cracking are simulated, predicting crack paths, growth rates and sensitivity to relevant microstructural features. Crack propagation through crystallographic planes is shown in single crystals, while the analysis of polycrystalline solids reveals transgranular crack initiation and crystallographic crack growth.
Kristensen PK, Golahmar A, Martínez-Pañeda E, et al., 2023, Accelerated high-cycle phase field fatigue predictions, European Journal of Mechanics - A/Solids, Vol: 100, Pages: 1-11, ISSN: 0997-7538
Phase field fracture models have seen widespread application in the last decade. Among these applications, its use to model the evolution of fatigue cracks has attracted particular interest, as fatigue damage behaviour can be predicted for arbitrary loading histories, dimensions and complexity of the cracking phenomena at play. However, while cycle-by-cycle calculations are remarkably flexible, they are also computationally expensive, hindering the applicability of phase field fatigue models for technologically-relevant problems. In this work, a computational framework for accelerating phase field fatigue calculations is presented. Two novel acceleration strategies are proposed, which can be used in tandem and together with other existing acceleration schemes from the literature. The computational performance of the proposed methods is documented through a series of 2D and 3D boundary value problems, highlighting the robustness and efficiency of the framework even in complex fatigue problems. The observed reduction in computation time using both of the proposed methods in tandem is shown to reach a speed-up factor of 32, with a scaling trend enabling even greater reductions in problems with more load cycles.
Golahmar A, Niordson CF, Martínez-Pañeda E, 2023, A phase field model for high-cycle fatigue: Total-life analysis, International Journal of Fatigue, Vol: 170, Pages: 1-13, ISSN: 0142-1123
We present a generalised phase field formulation for predicting high-cycle fatigue in metals. Different fatigue degradation functions are presented, together with new damage accumulation strategies, to account for (i) a typical S–N curve slope, (ii) the fatigue endurance limit, and (iii) the mean stress effect. The numerical implementation exploits an efficient quasi Newton monolithic solution strategy and Virtual S–N curves are computed for both smooth and notched samples. The comparison with experiments reveals that the model can accurately predict fatigue lives and endurance limits, as well as naturally capture the influence of the stress concentration factor and the load ratio.
García-Merino JC, Calvo-Jurado C, Martínez-Pañeda E, et al., 2023, Multielement polynomial chaos Kriging-based metamodelling for Bayesian inference of non-smooth systems, Applied Mathematical Modelling: simulation and computation for engineering and environmental systems, Vol: 116, Pages: 510-531, ISSN: 0307-904X
This paper presents a surrogate modelling technique based on domain partitioning for Bayesian parameter inference of highly nonlinear engineering models. In order to alleviate the computational burden typically involved in Bayesian inference applications, a multielement Polynomial Chaos Expansion based Kriging metamodel is proposed. The developed surrogate model combines in a piecewise function an array of local Polynomial Chaos based Kriging metamodels constructed on a finite set of non-overlapping subdomains of the stochastic input space. Therewith, the presence of non-smoothness in the response of the forward model (e.g.~ nonlinearities and sparseness) can be reproduced by the proposed metamodel with minimum computational costs owing toits local adaptation capabilities. The model parameter inference is conductedthrough a Markov chain Monte Carlo approach comprising adaptive exploration and delayed rejection. The efficiency and accuracy of the proposed approach are validated through two case studies, including an analytical benchmark and a numerical case study. The latter relates the partial differential equation governing the hydrogen diffusion phenomenon of metallic materials in Thermal Desorption Spectroscopy tests.
Zafra A, Álvarez G, Benoit G, et al., 2023, Hydrogen-assisted fatigue crack growth: Pre-charging vs in-situ testing in gaseous environments, Materials Science and Engineering: A, Vol: 871, Pages: 1-14, ISSN: 0921-5093
We investigate the implications of conducting hydrogen-assisted fatigue crack growth experiments in a hydrogen gas environment (in-situ hydrogen charging) or in air (following exposure to hydrogen gas). The study is conducted on welded 42CrMo4 steel, a primary candidate for the future hydrogen transport infrastructure, allowing us to additionally gain insight into the differences in behavior between the base steel and the coarse grain heat affected zone. The results reveal significant differences between the two testing approaches and the two weld regions. The differences are particularly remarkable for the comparison of testing methodologies, with fatigue crack growth rates being more than one order of magnitude higher over relevant loading regimes when the samples are tested in a hydrogen-containing environment, relative to the pre-charged samples. Aided by finite element modelling and microscopy analysis, these differences are discussed and rationalized. Independent of the testing approach, the heat affected zone showed a higher susceptibility to hydrogen embrittlement. Similar microstructural behavior is observed for both testing approaches, with the base metal exhibiting martensite lath decohesion while the heat affected zone experienced both martensite lath decohesion and intergranular fracture.
Lewis JA, Sandoval SE, Liu Y, et al., 2023, Accelerated short circuiting in anode‐free solid‐state batteries driven by local lithium depletion, Advanced Energy Materials, Vol: 13, Pages: 1-12, ISSN: 1614-6832
“Anode-free” solid-state batteries (SSBs), which have no anode active material, can exhibit extremely high energy density (≈1500 Wh L−1). However, there is a lack of understanding of the lithium plating/stripping mechanisms at initially lithium-free solid-state electrolyte (SSE) interfaces because excess lithium metal is often used. Here, it is demonstrated that commercially relevant quantities of lithium (>5 mAh cm−2) can be reliably plated at moderate current densities (1 mA cm−2) using the sulfide SSE Li6PS5Cl. Investigations of lithium plating/stripping mechanisms, in conjunction with cryo-focused ion beam (FIB) imaging, synchrotron tomography, and phase-field modeling, reveal that the cycling stability of these cells is fundamentally limited by the nonuniform presence of lithium during stripping. Local lithium depletion causes isolated lithium regions toward the end of stripping, decreasing electrochemically active area and resulting in high local current densities and void formation. This accelerates subsequent filament growth and short circuiting compared to lithium-excess cells. Despite this degradation mode, it is shown that anode-free cells exhibit comparable Coulombic efficiency to lithium-excess cells, and improved resistance to short circuiting is achieved by avoiding local lithium depletion through retention of thicker lithium at the interface. These new insights provide a foundation for engineering future high-energy anode-free SSBs.
Quinteros L, García-Macías E, Martínez-Pañeda E, 2023, Electromechanical phase-field fracture modelling of piezoresistive CNT-based composites, Computer Methods in Applied Mechanics and Engineering, Vol: 407, Pages: 1-24, ISSN: 0045-7825
We present a novel computational framework to simulate the electromechanical response of self-sensing carbon nanotube (CNT)-based composites experiencing fracture. The computational framework combines electrical-deformation-fracture finite element modelling with a mixed micromechanics formulation. The latter is used to estimate the constitutive properties of CNT-based composites, including the elastic tensor, fracture energy, electrical conductivity, and linear piezoresistive coefficients. These properties are inputted into a coupled electro-structural finite element model, which simulates the evolution of cracks based upon phase-field fracture. The coupled physical problem is solved in a monolithic manner, exploiting the robustness and efficiency of a quasi-Newton algorithm. 2D and 3D boundary value problems are simulated to illustrate the potential of the modelling framework in assessing the influence of defects on the electromechanical response of meso- and macro-scale smart structures. Case studies aim at shedding light into the interplay between fracture and the electromechanical material response and include parametric analyses, validation against experiments and the simulation of complex cracking conditions (multiple defects, crack merging). The presented numerical results showcase the efficiency and robustness of the computational framework, as well as its ability to model a large variety of structural configurations and damage patterns. The deformation-electrical-fracture finite element code developed is made freely available to download.
Hageman T, Martinez-Paneda E, 2023, Stabilising effects of lumped integration schemes for thesimulation of metal-electrolyte reactions, Journal of The Electrochemical Society, Vol: 170, Pages: 1-17, ISSN: 0013-4651
Computational modelling of metal-electrolyte reactions is central to the understanding and prediction of a wide range of physical phenomena, yet this is often challenging owing to the presence of numerical oscillations that arise due to dissimilar reaction rates. The ingress of hydrogen into metals is a paradigmatic example of a technologically-relevant phenomenon whose simulation is compromised by the stiffness of the reaction terms, as reaction rates vary over orders of magnitude and this significantly limits the time increment size. In this work, we present a lumped integration scheme for electro-chemical interface reactions that does not suffer from numerical oscillations. The scheme integrates the reactions in a consistent manner, while it also decouples neighbouring nodes and allows for larger time increments to be used without oscillations or convergence issues. The stability and potential of our scheme is demonstrated by simulating hydrogen ingress over a wide range of reaction rate constants and environmental conditions. While previous hydrogen uptake predictions were limited to time scales of minutes, the present lumped integration scheme enables conducting simulations over tens of years, allowing us to reach steady state conditions and quantify hydrogen ingress for time scales relevant to practical applications.
Zafra A, Harris Z, Korec E, et al., 2023, On the relative efficacy of electropermeation and isothermal desorption approaches for measuring hydrogen diffusivity, International Journal of Hydrogen Energy, Vol: 48, Pages: 1218-1233, ISSN: 0360-3199
The relative efficacy of electrochemical permeation (EP) and isothermal desorption spectroscopy (ITDS) methods for determining the hydrogen diffusivity is investigated using cold-rolled pure iron. The diffusivities determined from 13 first transient and 8 second transient EP experiments, evaluated using the conventional lag and breakthrough time methods, are compared to the results of 10 ITDS experiments. Results demonstrate that the average diffusivity is similar between the second EP transient and ITDS, which are distinctly increased relative to the first EP transient. However, the coefficient of variation for the ITDS experiments is reduced by 2 and 3-fold relative to the first and second EP transients, confirming the improved repeatability of ITDS diffusivity measurements. The source of the increased error in EP measurements is systematically evaluated, revealing an important influence of assumed electrochemical boundary conditions on the analysis and interpretation of EP experiments.
Navidtehrani Y, Betegón C, Zimmerman RW, et al., 2022, Griffith-based analysis of crack initiation location in a Brazilian test, International Journal of Rock Mechanics and Mining Sciences, Vol: 159, Pages: 1-16, ISSN: 0020-7624
The Brazilian test has been extremely popular while prompting significant debate. The main source of controversy is rooted in its indirect nature; the material tensile strength is inferred upon assuming that cracking initiates at the centre of the sample. Here, we use the Griffith criterion and finite element analysis to map the conditions (jaws geometry and material properties) that result in the nucleation of a centre crack. Unlike previous studies, we do not restrict ourselves to evaluating the stress state at the disk centre; the failure envelope of the generalised Griffith criterion is used to establish the crack nucleation location. We find that the range of conditions where the Brazilian test is valid is much narrower than previously assumed, with current practices and standards being inappropriate for a wide range of rock-like materials. The results obtained are used to develop a protocol that experimentalists can follow to obtain a valid estimate of the material tensile strength. This is showcased with specific case studies and examples of valid and invalid tests from the literature. Furthermore, the uptake of this protocol is facilitated by providing a MATLAB App that determines the validity of the experiment for arbitrary test conditions.
Zhao Y, Wang R, Martínez-Pañeda E, 2022, A phase field electro-chemo-mechanical formulation for predicting void evolution at the Li-electrolyte interface in all-solid-state batteries, Journal of the Mechanics and Physics of Solids, Vol: 167, Pages: 1-25, ISSN: 0022-5096
We present a mechanistic theory for predicting void evolution in the Li metal electrode during the charge and discharge of all-solid-state battery cells. A phase field formulation is developed to model vacancy annihilation and nucleation, and to enable the tracking of the void-Li metal interface. This is coupled with a viscoplastic description of Li deformation, to capture creep effects, and a mass transfer formulation accounting for substitutional (bulk and surface) Li diffusion and current-driven flux. Moreover, we incorporate the interaction between the electrode and the solid electrolyte, resolving the coupled electro-chemical-mechanical problem in both domains. This enables predicting the electrolyte current distribution and thus the emergence of local current 'hot spots', which act as precursors for dendrite formation and cell death. The theoretical framework is numerically implemented, and single and multiple void case studies are carried out to predict the evolution of voids and current hot spots as a function of the applied pressure, material properties and charge (magnitude and cycle history). For both plating and stripping, insight is gained into the interplay between bulk diffusion, Li dissolution and deposition, creep, and the nucleation and annihilation of vacancies. The model is shown to capture the main experimental observations, including not only key features of electrolyte current and void morphology but also the sensitivity to the applied current, the role of pressure in increasing the electrode-electrolyte contact area, and the dominance of creep over vacancy diffusion.
Navidtehrani Y, Betegón C, Martínez-Pañeda E, 2022, A general framework for decomposing the phase field fracture driving force, particularised to a Drucker–Prager failure surface, Theoretical and Applied Fracture Mechanics, Vol: 121, Pages: 103555-103555, ISSN: 0167-8442
Due to its computational robustness and versatility, the phase field fracture model has become the preferred tool for predicting a wide range of cracking phenomena. However, in its conventional form, its intrinsic tension–compression symmetry in damage evolution prevents its application to the modelling of compressive failures in brittle and quasi-brittle solids, such as concrete or rock materials. In this work, we present a general methodology for decomposing the phase field fracture driving force, the strain energy density, so as to reproduce asymmetrical tension–compression fracture behaviour. The generalised approach presented is particularised to the case of linear elastic solids and the Drucker–Prager failure criterion. The ability of the presented model to capture the compressive failure of brittle materials is showcased by numerically implementing the resulting strain energy split formulation and addressing four case studies of particular interest. Firstly, insight is gained into the capabilities of the model in predicting friction and dilatancy effects under shear loading. Secondly, virtual direct shear tests are conducted to assess fracture predictions under different pressure levels. Thirdly, a concrete cylinder is subjected to uniaxial and triaxial compression to investigate the influence of confinement. Finally, the localised failure of a soil slope is predicted and the results are compared with other formulations for the strain energy decomposition proposed in the literature. The results provide a good qualitative agreement with experimental observations and demonstrate the capabilities of phase field fracture methods to predict crack nucleation and growth under multi-axial loading in materials exhibiting asymmetric tension–compression fracture behaviour.
Ai W, Wu B, Martínez-Pañeda E, 2022, A coupled phase field formulation for modelling fatigue cracking in lithium-ion battery electrode particles, Journal of Power Sources, Vol: 544, ISSN: 0378-7753
Electrode particle cracking is one of the main phenomena driving battery capacity degradation. Recent phase field fracture studies have investigated particle cracking behaviour. However, only the beginning of life has been considered and effects such as damage accumulation have been neglected. Here, a multi-physics phase field fatigue model has been developed to study crack propagation in battery electrode particles undergoing hundreds of cycles. In addition, we couple our electrochemo-mechanical formulation with X-ray CT imaging to simulate fatigue cracking of realistic particle microstructures. Using this modelling framework, non-linear crack propagation behaviour is predicted, leading to the observation of an exponential increase in cracked area with cycle number. Three stages of crack growth (slow, accelerating and unstable) are observed, with phenomena such as crack initialisation at concave regions and crack coalescence having a significant contribution to the resulting fatigue crack growth rates. The critical values of C-rate, particle size and initial crack length are determined, and found to be lower than those reported in the literature using static fracture models. Therefore, this work demonstrates the importance of considering fatigue damage in battery degradation models and provides insights on the control of fatigue crack propagation to alleviate battery capacity degradation.
Díaz A, Alegre JM, Cuesta II, et al., 2022, Notch fracture predictions using the Phase Field method for Ti-6Al-4V produced by Selective Laser Melting after different post-processing conditions, Theoretical and Applied Fracture Mechanics, Vol: 121, Pages: 1-10, ISSN: 0167-8442
Ti-6Al-4V is a titanium alloy with excellent properties for lightweight applications and its production through Additive Manufacturing processes is attractive for different industrial sectors. In this work, the influence of mechanical properties on the notch fracture resistance of Ti-6Al-4V produced by Selective Laser Melting is numerically investigated. Literature data is used to inform material behaviour. The as-built brittle behaviour is compared to the enhanced ductile response after heat treatment (HT) and hot isostatic pressing (HIP) post-processes. A Phase Field framework is adopted to capture damage nucleation and propagation from two different notch geometries and a discussion on the influence of fracture energy and the characteristic length is carried out. In addition, the influence of oxygen uptake is analysed by reproducing non-inert atmospheres during HT and HIP, showing that oxygen shifts fracture to brittle failures due to the formation of an alpha case layer, especially for the V-notch geometry. Results show that a pure elastic behaviour can be assumed for the as-built SLM condition, whereas elastic-plastic phenomena must be modelled for specimens subjected to heat treatment or hot isostatic pressing. The present brittle Phase Field framework coupled with an elastic-plastic constitutive analysis is demonstrated to be a robust prediction tool for notch fracture after different post-processing routes.
Hageman T, Martínez-Pañeda E, 2022, An electro-chemo-mechanical framework for predicting hydrogen uptake in metals due to aqueous electrolytes, Corrosion Science, Vol: 208, ISSN: 0010-938X
We present a theoretical and numerical scheme that enables quantifying hydrogen ingress in metals for arbitrary environments and defect geometries. This is achieved by explicitly resolving the electrochemical behaviour of the electrolyte, the hydrogen and corrosion reactions, the kinetics of surface adsorption, and hydrogen uptake, diffusion and trapping in mechanically-deforming solids. This new framework is used to produce maps that relate the absorbed hydrogen with the applied potential, specimen geometry and fluid velocity. We also present simplified versions of our generalised model, and benchmark predictions of these and other existing models against the generalised electro-chemo-mechanical results, establishing regimes of validity.
Valverde-González A, Martínez-Pañeda E, Quintanas-Corominas A, et al., 2022, Computational modelling of hydrogen assisted fracture in polycrystalline materials, International Journal of Hydrogen Energy, Vol: 47, Pages: 1-17, ISSN: 0360-3199
We present a combined phase field and cohesive zone formulation for hydrogen embrittlement that resolves the polycrystalline microstructure of metals. Unlike previous studies, our deformation-diffusion-fracture modelling framework accounts for hydrogen-microstructure interactions and explicitly captures the interplay between bulk (transgranular) fracture and intergranular fracture, with the latter being facilitated by hydrogen through mechanisms such as grain boundary decohesion. We demonstrate the potential of the theoretical and computational formulation presented by simulating inter- and trans-granular cracking in relevant case studies. Firstly, verification calculations are conducted to show how the framework predicts the expected qualitative trends. Secondly, the model is used to simulate recent experiments on pure Ni and a Ni–Cu superalloy that have attracted particular interest. We show that the model is able to provide a good quantitative agreement with testing data and yields a mechanistic rationale for the experimental observations.
Cui C, Ma R, Martínez-Pañeda E, 2022, A generalised, multi-phase-field theory for dissolution-driven stress corrosion cracking and hydrogen embrittlement, Journal of the Mechanics and Physics of Solids, Vol: 166, Pages: 104951-104951, ISSN: 0022-5096
We present a phase field-based electro-chemo-mechanical formulation for modelling mechanics-enhanced corrosion and hydrogen-assisted cracking in elastic–plastic solids. A multi-phase-field approach is used to present, for the first time, a general framework for stress corrosion cracking, incorporating both anodic dissolution and hydrogen embrittlement mechanisms. We numerically implement our theory using the finite element method and defining as primary fields the displacement components, the phase field corrosion order parameter, the metal ion concentration, the phase field fracture order parameter and the hydrogen concentration. Representative case studies are addressed to showcase the predictive capabilities of the model in various materials and environments, attaining a promising agreement with benchmark tests and experimental observations. We show that the generalised formulation presented can capture, as a function of the environment, the interplay between anodic dissolution- and hydrogen-driven failure mechanisms; including the transition from one to the other, their synergistic action and their individual occurrence. Such a generalised framework can bring new insight into environment–material interactions and the understanding of stress corrosion cracking, as demonstrated here by providing the first simulation results for Gruhl’s seminal experiments.
Fernández-Sousa R, Betegón C, Martínez-Pañeda E, 2022, Cohesive zone modelling of hydrogen assisted fatigue crack growth: the role of trapping, International Journal of Fatigue, Vol: 162, ISSN: 0142-1123
We investigate the influence of microstructural traps in hydrogen-assisted fatigue crack growth. To this end, a new formulation combining multi-trap stress-assisted diffusion, mechanism-based strain gradient plasticity and a hydrogen- and fatigue-dependent cohesive zone model is presented and numerically implemented. The results show that the ratio of loading frequency to effective diffusivity governs fatigue crack growth behaviour. Increasing the density of \emph{beneficial} traps, not involved in the fracture process, results in lower fatigue crack growth rates. The combinations of loading frequency and carbide trap densities that minimise embrittlement susceptibility are identified, providing the foundation for a rational design of hydrogen-resistant alloys.
Islas A, Fernandez AR, Betegon C, et al., 2022, Computational assessment of biomass dust explosions in the 20L sphere, Process Safety and Environmental Protection, Vol: 165, Pages: 791-814, ISSN: 0263-8762
Determination of the explosion severity parameters of biomass is crucial for the safety management and dust explosion risk assessment of biomass-processing industries. These are commonly determined following experimental tests in the 20L sphere according to the international standards. Recently, CFD simulations have emerged as a reliable alternative to predict the explosion behavior with good accuracy and reduced labor and capital. In this work, numerical simulations of biomass dust explosions are conducted with the open-source CFD code OpenFOAM. The multi-phase (gas-solid) flow is treated in an Eulerian-Lagrangian framework, using a two-way coupling regime and considering the reactions of biomass conversion (moisture evaporation, devolatilization, and char oxidation), the combustion of volatile gases, and convective and radiative heat transfer. The model is validated with pressure-time and concentration-dependent experimental measurements of two biomass samples. Results suggest that the characteristics of the cold-flow (ı.e., turbulence levels, actual dust concentration, spatial distribution of the dust cloud, and turbophoresis effect) govern the course of the explosion process, and depend strongly on particle size, dust concentration, and ignition delay time effects. These findings may be relevant in the design of better dust explosion testing devices and to the reexamination of the guidelines for the operation of the experiment. Finally, a thorough discussion on the explosion pressures, degree of biomass conversion, flame temperature, flame propagation patterns, and the dust agglomeration effect is presented.
Clayton T, Duddu R, Siegert M, et al., 2022, A stress-based poro-damage phase field model for hydrofracturing of creeping glaciers and ice shelves, Engineering Fracture Mechanics, Vol: 272, Pages: 1-24, ISSN: 0013-7944
There is a need for computational models capable of predicting meltwater-assisted crevasse growth in glacial ice. Mass loss from glaciers and ice sheets is the largest contributor to sea-level rise and iceberg calving due to hydrofracture is one of the most prominent yet less understood glacial mass loss processes. To overcome the limitations of empirical and analytical approaches, we here propose a new phase field-based computational framework to simulate crevasse growth in both grounded ice sheets and floating ice shelves. The model incorporates the three elements needed to mechanistically simulate hydrofracture of surface and basal crevasses: (i) a constitutive description incorporating the non-linear viscous rheology of ice, (ii) a phase field formulation capable of capturing cracking phenomena of arbitrary complexity, such as 3D crevasse interaction, and (iii) a poro-damage representation to account for the role of meltwater pressure on crevasse growth. A stress-based phase field model is adopted to reduce the length-scale sensitivity, as needed to tackle the large scales of iceberg calving, and to adequately predict crevasse growth in tensile stress regions of incompressible solids. The potential of the computational framework presented is demonstrated by addressing a number of 2D and 3D case studies, involving single and multiple crevasses, and considering both grounded and floating conditions. The model results show a good agreement with analytical approaches when particularised to the idealised scenarios where these are relevant. More importantly, we demonstrate how the model can be used to provide the first computational predictions of crevasse interactions in floating ice shelves and 3D ice sheets, shedding new light into these phenomena. Also, the creep-assisted nucleation and growth of crevasses is simulated in a realistic geometry, corresponding to the Helheim glacier. The computational framework presented opens new horizons in the modelling of iceberg
Quinteros L, García-Macías E, Martínez-Pañeda E, 2022, Micromechanics-based phase field fracture modelling of CNT composites, Composites Part B: Engineering, Vol: 236, ISSN: 0961-9526
We present a novel micromechanics-based phase field approach to model crack initiation and propagation in carbon nanotube (CNT) based composites. The constitutive mechanical and fracture properties of the nanocomposites are first estimated by a mean-field homogenisation approach. Inhomogeneous dispersion of CNTs is accounted for by means of equivalent inclusions representing agglomerated CNTs. Detailed parametric analyses are presented to assess the effect of the main micromechanical properties upon the fracture behaviour of CNT-based composites. The second step of the proposed approach incorporates the previously estimated constitutive properties into a phase field fracture model to simulate crack initiation and growth in CNT-based composites. The modelling capabilities of the framework presented is demonstrated through three paradigmatic case studies involving mode I and mixed mode fracture conditions.
Tan W, Martínez-Pañeda E, 2022, Phase field fracture predictions of microscopic bridging behaviour of composite materials, Composite Structures, Vol: 286, Pages: 1-13, ISSN: 0263-8223
We investigate the role of microstructural bridging on the fracture toughness of composite materials. To achieve this, a new computational framework is presented that integrates phase field fracture and cohesive zone models to simulate fibre breakage, matrix cracking and fibre-matrix debonding. The composite microstructure is represented by an embedded cell at the vicinity of the crack tip, whilst the rest of the sample is modelled as an anisotropic elastic solid. The model is first validated against experimental data of transverse matrix cracking from single-notched three-point bending tests. Then, the model is extended to predict the influence of grain bridging, brick-and-mortar microstructure and 3D fibre bridging on crack growth resistance. The results show that these microstructures are very efficient in enhancing the fracture toughness via fibre-matrix debonding, fibre breakage and crack deflection. In particular, the 3D fibre bridging effect can increase the energy dissipated at failure by more than three orders of magnitude, relative to that of the bulk matrix; well in excess of the predictions obtained from the rule of mixtures. These results shed light on microscopic bridging mechanisms and provide a virtual tool for developing high fracture toughness composites.
Simoes M, Braithwaite C, Makaya A, et al., 2022, Modelling fatigue crack growth in shape memory alloys, Fatigue and Fracture of Engineering Materials and Structures, Vol: 45, Pages: 1243-1257, ISSN: 1460-2695
We present a phase field-based framework for modelling fatigue damage in Shape Memory Alloys (SMAs). The model combines, for the first time: (i) a generalized phase field description of fracture, incorporating multiple phase field formulations, (ii) a constitutive model for SMAs, based on a Drucker–Prager form of the transformation surface, and (iii) a fatigue degradation function, with damage driven by both elastic and transformation strains. The theoretical framework is numerically implemented, and the resulting linearized system is solved using a robust monolithic scheme, based on quasi-Newton methods. Several paradigmatic boundary value problems are addressed to gain insight into the role of transformation stresses, stress-strain hysteresis, and temperature. Namely, we compute Δε − N curves, quantify Paris law parameters, and predict fatigue crack growth rates in several geometries. In addition, the potential of the model for solving large-scale problems is demonstrated by simulating the fatigue failure of a 3D lattice structure.
Boyce AM, Martínez-Pañeda E, Wade A, et al., 2022, Cracking predictions of lithium-ion battery electrodes by X-ray computed tomography and modelling, Journal of Power Sources, Vol: 526, Pages: 1-14, ISSN: 0378-7753
Fracture of lithium-ion battery electrodes is found to contribute to capacity fade and reduce the lifespan of a battery. Traditional fracture models for batteries are restricted to consideration of a single, idealised particle; here, advanced X-ray computed tomography (CT) imaging, an electro-chemo-mechanical model and a phase field fracture framework are combined to predict the void-driven fracture in the electrode particles of a realistic battery electrode microstructure. The electrode is shown to exhibit a highly heterogeneous electrochemical and fracture response that depends on the particle size and distance from the separator/current collector. The model enables prediction of increased cracking due to enlarged cycling voltage windows, cracking susceptibility as a function of electrode thickness, and damage sensitivity to discharge rate. This framework provides a platform that facilitates a deeper understanding of electrode fracture and enables the design of next-generation electrodes with higher capacities and improved degradation characteristics.
Zafra A, Harris Z, Sun C, et al., 2022, Comparison of hydrogen diffusivities measured by electrochemical permeation and temperature-programmed desorption in cold-rolled pure iron, Journal of Natural Gas Science and Engineering, Vol: 98, Pages: 1-10, ISSN: 1875-5100
The diffusivity of hydrogen in cold-rolled pure iron is investigated using permeation and desorption methods. Electrochemical charging, electro permeation and thermal desorption spectroscopy (TDS) experiments are conducted. Firstly, the relation between the charging current and the hydrogen concentration is established. Secondly, permeation experiments are conducted at 22, 40 and 67{\deg}C to quantify the diffusivity dependence on temperature. Finally, the diffusivity is estimated by using two types of desorption experiments and Fick's law: (i) a `rest time' method, by which we measure the hydrogen content of samples held at room temperature for different times, and (ii) isothermal desorption experiments at temperatures ranging from 22 to 80{\deg}C, fitting the resulting desorption rate versus time curves. Good agreement is obtained between the isothermal desorption and permeation approaches, with observed differences discussed and rationalised. Moreover, measured diffusivity values for cold-rolled pure iron are also found to be comparable to those reported in the literature. This work demonstrates that isothermal desorption experiments are a convenient approach to determine hydrogen diffusivity over a wide range of temperatures, as facilitated by new TDS systems with fast heating rates.
Khalil Z, Elghazouli AY, Martínez-Pañeda E, 2022, A generalised phase field model for fatigue crack growth in elastic-plastic solids with an efficient monolithic solver, Computer Methods in Applied Mechanics and Engineering, Vol: 388, Pages: 1-22, ISSN: 0045-7825
We present a generalised phase field-based formulation for predicting fatigue crack growth in metals. The theoretical framework aims at covering a wide range of material behaviour. Different fatigue degradation functions are considered and their influence is benchmarked against experiments. The phase field constitutive theory accommodates the so-called AT1, AT2 and phase field-cohesive zone (PF-CZM) models. In regards to material deformation, both non-linear kinematic and isotropic hardening are considered, as well as the combination of the two. Moreover, a monolithic solution scheme based on quasi-Newton algorithms is presented and shown to significantly outperform staggered approaches. The potential of the computational framework is demonstrated by investigating several 2D and 3D boundary value problems of particular interest. Constitutive and numerical choices are compared and insight is gained into their differences and similarities. The framework enables predicting fatigue crack growth in arbitrary geometries and for materials exhibiting complex (cyclic) deformation and damage responses. The finite element code developed is made freely available at www.empaneda.com/codes.
Golahmar A, Kristensen PK, Niordson CF, et al., 2022, A phase field model for hydrogen-assisted fatigue, International Journal of Fatigue, Vol: 154, ISSN: 0142-1123
We present a new theoretical and numerical phase field-based formulation for predicting hydrogen-assisted fatigue. The coupled deformation-diffusion-damage model presented enables predicting fatigue crack nucleation and growth for arbitrary loading patterns and specimen geometries. The role of hydrogen in increasing fatigue crack growth rates and decreasing the number of cycles to failure is investigated. Our numerical experiments enable mapping the three loading frequency regimes and naturally recover Paris law behaviour for various hydrogen concentrations. In addition, Virtual S–N curves are obtained for both notched and smooth samples, exhibiting a good agreement with experiments.
Islas A, Rodríguez-Fernández A, Betegón C, et al., 2022, CFD simulations of turbulent dust dispersion in the 20 L vessel using OpenFOAM, Powder Technology, Vol: 397, Pages: 117033-117033, ISSN: 0032-5910
Dust explosions are among the most hazardous accidents affecting industrial facilities processing particulate solids. Describing the severity parameters of dust clouds is critical to the safety management and risk assessment of dust explosions. These parameters are determined experimentally in a 20 L spherical vessel, following the ASTM E1226 or UNE 14034 standards. Since their reproducibility depends on the levels of turbulence associated with the dust cloud, a computational model of the multi-phase (gas-solid) flow is used to simulate the dispersion process with the open-source CFD code OpenFOAM. The model is successfully validated against experimental measurements from the literature and numerical results of a commercial CFD code. In addition, this study considers the impact of particle size on the turbulence of the carrier phase, suggesting that particles attenuate its turbulence intensity. Moreover, the model predicts well the formation of a two-vortex flow pattern, which has a negative impact on the distribution of the particle-laden flows with dp≤ 100 μm, as most of the particles concentrate at the near-wall region. Contrarily, an improved homogeneity of dust cloud is observed for a case fed with larger particles (dp= 200 μm), as the increased inertia of these particles allows them to enter into the re-circulation regions.
Shlyannikov V, Martínez-Pañeda E, Tumanov A, et al., 2021, Mode I and Mode II stress intensity factors and dislocation density behaviour in strain gradient plasticity, Theoretical and Applied Fracture Mechanics, Vol: 116, Pages: 1-15, ISSN: 0167-8442
In this study, we use the mechanism-based strain gradient plasticity theory to evaluate both crack tip dislocation density behaviour and the coupled effect of the material plastic properties and the intrinsic material length on non-linear amplitude factors. The two planar classical stress-strain states are examined, namely, plane strain and plane stress, both under pure mode I and pure mode II loading conditions. The constitutive relations are based on Taylor's dislocation model, which enables gaining insights into the role of the increased dislocation density associated with large gradients in plastic strain near cracks. The material model is implemented in a commercial finite element (FE) software package using a user subroutine, and the nonlinear stress intensity factors (SIF) are evaluated as a function of the intrinsic material length, characterising the scale at which gradient effects become significant. As a result of the FE calculations of dislocation density distributions, the effects of both the fracture mode and the stress-strain state are determined. In pure mode I, the geometrically necessary dislocation (GND) density is located symmetrically with respect to the blunted crack tip. On the contrary, under pure mode II, the GND density becomes concentrated in the blunted and sharp parts of the crack tip. In this case, fracture initiation is shown to be likely to occur near the blunted region of the crack tip, where both the stress triaxiality and the GND density are at their maximum. The relation between the equilibrium state of dislocation densities and the intrinsic material length as well as the plastic SIF as a function of the work hardening exponent is discussed.
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