José Maria Andrade Barbosa

On the Modeling of Deformation-Diffusion-Damage Coupling in Elastic Solids

This paper deals with the formulation and numerical implementation of a fully coupled continuum model for deformation-diffusion-damage in elastic solids. The formulation is carried out within the framework of continuum mechanics, where, in addition to the standard fields, extra fields are introduced in order to describe diffusion and damage processes. The governing equations are then obtained after supplementing the basic balances with a thermodynamically consistent constitutive theory. The couplings are implemented via the free energy response and include both deformation and damage assisted diffusion. It is worth mentioning that a gradient damage theory is obtained, which allows the modeling of fracture problems. The numerical implementation is based on the finite element method and a Euler implicit scheme for spatial and temporal discretizations, respectively. A numerical algorithm is presented to solve the discrete system of equations. In order to illustrate the potentiality of the proposed model, applications in the context of hydrogen embrittlement are presented.

Application of elastic fracture and damage mechanics models for numerical simulation of hydrogen embrittlement in steels

Purpose – The purpose of this paper is to present a numerical simulation of the hydrogen atomic effect on the steels fracture toughness, as well as on crack propagation using fracture mechanics and continuous damage mechanics models.Design/methodology/approach – The simulation was performed in an idealized elastic specimen with an edge crack loaded in the tensile opening mode, in a plane strain state. In order to simulate the effect of hydrogen in the steel, the stress intensity factor ahead of the crack tip in the hydrogenated material was obtained. The damage model was applied to simulate the growth and crack propagation being considered only two damage components: a mechanical damage produced by a static load and a non‐mechanical damage produced by the hydrogen.Findings – The simulation results showed that the changes in the stress field at the crack tip and the reduction in the time of growth and crack propagation due to hydrogen effect occur. These results showed a good correlation and consistency wi...

Effect of Reversible Hydrogen Trapping on Crack Propagation in the API 5CT P110 Steel - A Numerical Simulation

This paper presents a numerical simulation of the reversible hydrogen trapping effect on crack propagation in the API 5CT P110 steel using a model based on a synthesis of fracture mechanics and continuum damage mechanics. The trapping term at the diffusion equation of this model was replaced by the equivalent term of McNab & Fosters model. Was simulated an C(T) specimen loaded in the mode I, in linear elastic regime, in plane strain state, and under the action of a static mechanical loading and hydrogen effect. The simulations showed that the material degradation ahead of crack tip increases with increasing in hydrogen concentration due the trapping with low interaction energies. Furthermore, the process of onset and crack growth in material with reversible traps is faster than the material free of traps. These results show a good correlation and consistency with macroscopic observations of the trapping effect, providing a better understanding of the hydrogen embrittlement in structural steels.

Simulación Numérica de la Propagación de una Fisura en un Material Degradado por efecto de la Fragilización por Hidrógeno

A numeric formulation is presented based on a combination of fracture mechanics and continuum damage mechanics to treat the problem of the crack propagation in elastic regime, under the effect of a mechanical action defined by a static load applied in the tensile mode and of an environmental action characterized by hydrogen diffusion into the lattice. The equations that describe the evolution of the variables at the crack tip form a non-linear system of ordinary differential equations that is solved using the 4 th order Runge-Kutta method. The results show the influence of hydrogen on the decrease of the time at which cracks starts and propagates, which is consistent with macroscopic observations of the hydrogen embrittlement phenomenon.

On Deformation, Degradation and Solute Diffusion in Solids

This paper deals with the formulation and numerical implementation of a fully coupled continuum model for deformation, solute diffusion and degradation in solids. The formulation is carried out within the framework of the multifield continuum mechanics whereas the numerical implementation is based on the finite element method, an Euler implicit scheme and a staggered strategy. In order to illustrate the potentiality of the proposed model, applications in the context of hydrogen transport through tubular membranes of Palladium coated Niobium are presented.