We present a gradient-based theoretical framework for predicting hydrogen assisted fracture in elastic-plastic solids. The novelty of the model lies in the combination of: (i) stress-assisted diffusion of solute species, (ii) strain gradient plasticity, and (iii) a hydrogen-sensitive phase field fracture formulation, inspired by first principles calculations. The theoretical model is numerically implemented using a mixed finite element formulation and several boundary value problems are addressed to gain physical insight and showcase model predictions. The results reveal the critical role of plastic strain gradients in rationalising decohesion-based arguments and capturing the transition to brittle fracture observed in hydrogen-rich environments. Large crack tip stresses are predicted, which in turn raise the hydrogen concentration and reduce the fracture energy. The computation of the steady state fracture toughness as a function of the cohesive strength shows that cleavage fracture can be predicted in otherwise ductile metals using sensible values for the material parameters and the hydrogen concentration. In addition, we compute crack growth resistance curves in a wide variety of scenarios and demonstrate that the model can appropriately capture the sensitivity to: the plastic length scales, the fracture length scale, the loading rate and the hydrogen concentration. Model predictions are also compared with fracture experiments on a modern ultra-high strength steel, AerMet100. A promising agreement is observed with experimental measurements of threshold stress intensity factor $K_{th}$ over a wide range of applied potentials.
Metallic materials, especially steel, underpin transportation technologies. High-manganese twinning induced plasticity (TWIP) austenitic steels exhibit exceptional strength and ductility from twins, low-energy microstructural defects that form during plastic loading. Their high-strength could help light-weighting vehicles, and hence cut carbon emissions. TWIP steels are however very sensitive to hydrogen embrittlement that causes dramatic losses of ductility and toughness leading to catastrophic failure of engineering parts. Here, we examine the atomic-scale chemistry and interaction of hydrog…
Atomic scale understanding of the role of hydrogen and oxygen segregation in the embrittlement of grain boundaries in a twinning induced plasticity steel
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 kinematic variables the displacement components, the phase field corrosion order parameter, the metal ion concentration, the phase field fract…
The present paper studies non-uniform plastic deformations of crystals undergoing anti-plane constrained shear. The asymptotically exact energy density of crystals containing a moderately large density of excess dislocations is found by the averaging procedure. This energy density is extrapolated to the cases of extremely small or large dislocation densities. By incorporating the configurational temperature and the density of redundant dislocations, we develop the thermodynamic dislocation theory for non-uniform plastic deformations and use it to predict the stress-strain curves and the disloc…
We present a new mechanistic, phase field-based formulation for predicting hydrogen embrittlement. The multi-physics model developed incorporates, for the first time, a Taylor-based dislocation model to resolve the mechanics of crack tip deformation. This enables capturing the role of dislocation hardening mechanisms in elevating the tensile stress, hydrogen concentration and dislocation trap density within tens of microns ahead of the crack tip. The constitutive strain gradient plasticity model employed is coupled to a phase field formulation, to simulate the fracture process, and to a multi-…
Crystal plasticity theory is often employed to predict the mesoscopic states of polycrystalline metals, and is well-known to be costly to simulate. Using a neural network with convolutional layers encoding correlations in time and space, we were able to predict the evolution of the stress field given only the initial microstructure and external loading. In comparison to our recent work we were able to predict not only the spatial average of the stress response but the field itself. We show that the stress fields and their rates are in high fidelity with the crystal plasticity data and have no …
In this work hydrogen diffusion towards the fracture process zone is examined accounting for local hardening due to geometrically necessary dislocations (GNDs) by means of strain gradient plasticity (SGP). Finite element computations are performed within the finite deformation theory to characterize the gradient-enhanced stress elevation and subsequent diffusion of hydrogen towards the crack tip. Results reveal that GNDs, absent in conventional plasticity predictions, play a fundamental role on hydrogen transport ahead of a crack. SGP estimations provide a good agreement with experimental meas…
Hydrogen embrittlement (HE) affects all major high-strength structural materials and as such is a major impediment to lightweighting e.g. vehicles and help reduce carbon-emissions and reach net-zero. The high-strength 7xxx series aluminium alloys can fulfil the need for light, high strength materials, and are already extensively used in aerospace for weight reduction purposes. However, depending on the thermomechanical and loading state, these alloys can be sensitive to stress-corrosion cracking (SCC) through anodic dissolution and hydrogen embrittlement. Here, we study at the near-atomic-scal…
A coupled fully kinetic hydrogen transport and ductile phase-field fracture framework for modeling hydrogen embrittlement
University of Oulu（奥卢大学）；Université Sorbonne Paris Nord, Laboratoire des Sciences des Procédés et des Matériaux, LSPM, CNRS, UPR 3407（索邦巴黎北大学，工艺与材料科学实验室，LSPM，CNRS，UPR 3407）
Zircaloy-4 is used extensively as nuclear fuel cladding materials and hydride embrittlement is a major failure mechanism. To explore the effect of δ-hydride on plastic deformation and performance of Zircaloy-4, in situ high angular resolution electron backscatter diffraction (HR-EBSD) was used to quantify stress and geometrically necessary dislocation (GND) density during bending tests of hydride-free and hydride-containing single crystal Zircaloy-4 microcantilevers. Results suggest that while the stress applied was accommodated by plastic slip in the hydride-free cantilever, the hydride-conta…
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 f…
Titanium alloys can suffer from halide-associated stress corrosion cracking at elevated temperatures e.g., in jet engines, where chlorides and Ti-oxide promote the cracking of water vapour in the gas stream, depositing embrittling species at the crack tip. Here we report, using isotopically-labelled experiments, that crack tips in an industrial Ti-6Al-2Sn-4Zr-6Mo alloy are strongly enriched (>5 at.%) in oxygen from the water vapour, far greater than the amounts (0.25 at.%) required to embrittle the material. Surprisingly, relatively little hydrogen (deuterium) is measured, despite careful prep…
We study the intermittency and noise of dislocation systems undergoing shear deformation. Simulations of a simple two-dimensional discrete dislocation dynamics model indicate that the deformation rate exhibits a power spectrum scaling of the type $1/f^α$. The noise exponent is far away from a Lorentzian, with $α\approx 1.5$. This result is directly related to the way the durations of avalanches of plastic deformation activity scale with their size.
We analyze dissipative scale effects within a one-dimensional theory, developed in [L. Anand et al. (2005) J. Mech. Phys. Solids 53], which describes plastic flow in a thin strip undergoing simple shear. We give a variational characterization of the {\emph{ yield (shear) stress}} --- the threshold for the inset of plastic flow --- and we use this characterization, together with results from [M. Amar et al. (2011) J. Math. Anal. Appl. 397], to obtain an explicit relation between the yield stress and the height of the strip. The relation we obtain confirms that thinner specimens are stronger, in…
Hydrogen segregation around a straight screw dislocation in bcc iron
Laboratoire des Sciences de l’Ingénieur pour l’Environnement (LaSIE) - UMR CNRS 7356（环境工程科学实验室）；Laboratoire des Sciences des Procédés et des Matériaux (LSPM) - UPR 3407（工艺与材料科学实验室）
We formulate a phenomenological elasto-plastic theory to describe a solid undergoing a structural transition from a square (p4mm) to an oblique (p2) lattice in two dimensions. Within our theory, the components of the strain may be decomposed additively into separate elastic and plastic contributions. The plastic strain, produced when the local stress crosses a threshold, is governed by a phenomenological equation of motion. We investigate the dynamics of shape of an initially square solid as it is cycled through a transformation protocol consisting of (1) a quench across the transition (2) def…
We measure the stress state in and around a deformation nanotwin in a twinning-induced plasticity (TWIP) steel. Using four-dimensional scanning transmission electron microscopy (4D-STEM), we measure the elastic strain field in a 68.2-by-83.1 nm area of interest with a scan step of 0.36 nm and a diffraction limit resolution of 0.73 nm. The stress field in and surrounding the twin matches the form expected from analytical theory and is on the order of 15 GPa, close to the theoretical strength of the material. We infer that the measured back-stress limits twin thickening, providing a rationale fo…
It is shown here that fracture after a brief plastic strain, typically of a few percents, is a necessary consequence of the polycrystalline nature of the materials. The polycrystal undergoing plastic deformation is modeled as a flowing continuum of random deformable polyhedra, representing the grains, which fill the space without leaving voids. Adjacent grains slide with a relative velocity proportional to the local shear stress resolved on the plane of the shared grain boundary, when greater than a finite threshold. The polyhedral grains reshape continuously to preserve matter continuity, bei…
Despite numerous experimental and theoretical investigations of the mechanical behavior of high-capacity Si and Ge Li-ion battery anodes, our basic understanding of swelling-driven fracture in these materials remains limited. Existing theoretical studies have provided insights into elasto-plastic deformations caused by large volume change phase transformations, but have not modeled fracture explicitly beyond Griffith's criterion. Here we use a multi-physics phase-field approach to model self-consistently anisotropic phase transformation, elasto-plastic deformation, and crack initiation and pro…
The transition from elastic to plastic deformation in crystalline metals shares history dependence and scale-invariant avalanche signature with other non-equilibrium systems under external loading: dilute colloidal suspensions, plastically-deformed amorphous solids, granular materials, and dislocation-based simulations of crystals. These other systems exhibit transitions with clear analogies to work hardening and yield stress, with many typically undergoing purely elastic behavior only after 'training' through repeated cyclic loading; studies in these other systems show a power law scaling of …
We measure the local yield stress, at the scale of small atomic regions, in a deeply quenched two-dimensional glass model undergoing shear banding in response to athermal quasistatic (AQS) deformation. We find that the occurrence of essentially a single plastic event suffices to bring the local yield stress distribution to a well-defined value for all strain orientations, thus essentially erasing the memory of the initial structure. It follows that in a well-relaxed sample, plastic events cause the abrupt (nucleation-like) emergence of a local softness contrast and thus precipitate the formati…
In dislocation-free martensites the components of the elastic strain tensor are constrained by the Saint-Venant compatibility condition which guarantees continuity of the body during external loading. However, in dislocated materials the plastic part of the distortion tensor introduces a displacement mismatch that is removed by elastic relaxation. The elastic strains are then no longer compatible in the sense of the Saint-Venant law and the ensuing incompatibility tensor is shown to be proportional to the gradients of the Nye dislocation density tensor. We demonstrate that the presence of this…
