Modeling damage and fracture within strain-gradient plasticity

In this work, the influence of the plastic size effect on the fracture process of metallic materials is numerically analyzed using the strain-gradient plasticity (SGP) theory established from the Taylor dislocation model. Since large deformations generally occur in the vicinity of a crack, the numerical framework of the chosen SGP theory is developed for allowing large strains and rotations. The material model is implemented in a commercial finite element (FE) code by a user subroutine, and crack-tip fields are evaluated thoroughly for both infinitesimal and finite deformation theories by a boundary-layer formulation. An extensive parametric study is conducted and differences in the stress distributions ahead of the crack tip, as compared with conventional plasticity, are quantified. As a consequence of the strain-gradient contribution to the work hardening of the material, FE results show a significant increase in the magnitude and the extent of the differences between the stress fields of SGP and conventional plasticity theories when finite strains are considered. Since the distance from the crack tip at which the strain gradient significantly alters the stress field could be one order of magnitude higher when large strains are considered, results reveal that the plastic size effect could have important implications in the modelization of several damage mechanisms where its influence has not yet been considered in the literature

An electro-chemo-mechanical framework for predicting hydrogen uptake in metals due to aqueous electrolytes

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

Phase field predictions of microscopic fracture and R-curve behaviour of fibre-reinforced composites

We present a computational framework to explore the effect of microstructure and constituent properties upon the fracture toughness of fibre-reinforced polymer composites. To capture microscopic matrix cracking and fibre-matrix debonding, the framework couples the phase field fracture method and a cohesive zone model in the context of the finite element method. Virtual single-notched three point bending tests are conducted. The actual microstructure of the composite is simulated by an embedded cell in the fracture process zone, while the remaining area is homogenised to be an anisotropic elastic solid. A detailed comparison of the predicted results with experimental observations reveals that it is possible to accurately capture the crack path, interface debonding and load versus displacement response. The sensitivity of the crack growth resistance curve (R-curve) to the matrix fracture toughness and the fibre-matrix interface properties is determined. The influence of porosity upon the R-curve of fibre-reinforced composites is also explored, revealing a stabler response with increasing void volume fraction. These results shed light into microscopic fracture mechanisms and set the basis for efficient design of high fracture toughness composites

An electro-chemo-mechanical framework for predicting hydrogen uptake in metals due to aqueous electrolytes

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

Phase field modelling of fracture and fatigue in Shape Memory Alloys

We present a new phase field framework for modelling fracture and fatigue in Shape Memory Alloys (SMAs). The constitutive model captures the superelastic behaviour of SMAs and damage is driven by the elastic and transformation strain energy densities. We consider both the assumption of a constant fracture energy and the case of a fracture energy dependent on the martensitic volume fraction. The framework is implemented in an implicit time integration scheme, with both monolithic and staggered solution strategies. The potential of this formulation is showcased by modelling a number of paradigmatic problems. First, a boundary layer model is used to examine crack tip fields and compute crack growth resistance curves (R-curves). We show that the model is able to capture the main fracture features associated with SMAs, including the toughening effect associated with stress-induced phase transformation. Insight is gained into the role of temperature, material strength, crack density function and fracture energy homogenisation. Secondly, several 2D and 3D boundary value problems are addressed, demonstrating the capabilities of the model in capturing complex cracking phenomena in SMAs, such as unstable crack growth, mixed-mode fracture or the interaction between several cracks. Finally, the model is extended to fatigue and used to capture crack nucleation and propagation in biomedical stents, a paradigmatic application of nitinol SMAs

Crack growth resistance in metallic alloys: The role of isotropic versus kinematic hardening

The sensitivity of crack growth resistance to the choice of isotropic or kinematic hardening is investigated. Monotonic mode I crack advance under small scale yielding conditions is modelled via a cohesive zone formulation endowed with a traction-separation law. R-curves are computed for materials that exhibit linear or power law hardening. Kinematic hardening leads to an enhanced crack growth resistance relative to isotropic hardening. Moreover, kinematic hardening requires greater crack extension to achieve the steady state. These differences are traced to the non-proportional loading of material elements near the crack tip as the crack advances. The sensitivity of the R-curve to the cohesive zone properties and to the level of material strain hardening is explored for both isotropic and kinematic hardening

Mode I crack tip fields: Strain gradient plasticity theory versus J2 flow theory

The mode I crack tip asymptotic response of a solid characterised by strain gradient plasticity is investigated. It is found that elastic strains dominate plastic strains near the crack tip, and thus the Cauchy stress and the strain state are given asymptotically by the elastic K-field. This crack tip elastic zone is embedded within an annular elasto-plastic zone. This feature is predicted by both a crack tip asymptotic analysis and a finite element computation. When small scale yielding applies, three distinct regimes exist: an outer elastic K field, an intermediate elasto-plastic field, and an inner elastic K field. The inner elastic core significantly influences the crack opening profile. Crack tip plasticity is suppressed when the material length scale $\ell$ of the gradient theory is on the order of the plastic zone size estimation, as dictated by the remote stress intensity factor. A generalized J-integral for strain gradient plasticity is stated and used to characterise the asymptotic response ahead of a short crack. Finite element analysis of a cracked three point bend specimen reveals that the crack tip elastic zone persists in the presence of bulk plasticity and an outer J-field

Fracture in distortion gradient plasticity

In this work, distortion gradient plasticity is used to gain insight into material deformation ahead of a crack tip. This also constitutes the first fracture mechanics analysis of gradient plasticity theories adopting Nye's tensor as primal kinematic variable. First, the asymptotic nature of crack tip fields is analytically investigated. We show that an inner elastic region exists, adjacent to the crack tip, where elastic strains dominate plastic strains and Cauchy stresses follow the linear elastic stress singularity. This finding is verified by detailed finite element analyses using a new numerical framework, which builds upon a viscoplastic constitutive law that enables capturing both rate-dependent and rate-independent behaviour in a computationally efficient manner. Numerical analysis is used to gain further insight into the stress elevation predicted by distortion gradient plasticity, relative to conventional J2 plasticity, and the influence of the plastic spin under both mode I and mixed-mode fracture conditions. It is found that Nye's tensor contributions have a weaker effect in elevating the stresses in the plastic region, while predicting the same asymptotic behaviour as constitutive choices based on the plastic strain gradient tensor. A minor sensitivity to X, the parameter governing the dissipation due to the plastic spin, is observed. Finally, distortion gradient plasticity and suitable higher order boundary conditions are used to appropriately model the phenomenon of brittle failure along elastic-plastic material interfaces. We reproduce paradigmatic experiments on niobium-sapphire interfaces and show that the combination of strain gradient hardening and dislocation blockage leads to interface crack tip stresses that are larger than the theoretical lattice strength, rationalising cleavage in the presence of plasticity at bi-material interfaces