Stress influence on high temperature oxide scale growth: modeling and investigation on a thermal barrier coating system.

International audienceIn thermal barrier coating (TBC) systems, an oxide layer develops at high temperature below the ceramic coating, leading at long term to the mechanical failure of the structure upon cooling. This study investigates a mechanism of stress-affected oxidation likely to induce the growth of a non-uniform oxide scale detrimental to the TBC lifetime. A continuum thermodynamics formulation is derived accounting for the influence of the stress and strain situation at the sharp metal/oxide phase boundary on the local oxidation kinetics. It specially includes the contributions of the large volumetric strain and the mass consumption associated with metal oxidation. A continuum mechanics/mass diffusion framework is used along with the developed formulation for the interface evolution to study the growth of an oxide layer coupled with local stress development. The implementation of the model has required the development of a specific simulation tool, based on a finite element method completed with an external routine for the phase boundary propagation. Results on an electron-beam physical vapor deposited (EB-PVD) TBC case are presented. The processes resulting in a non-uniform oxide scale growth are analyzed and the main influences are discussed

Modelling stress-diffusion controlled phase transformations : application to stress corrosion cracking

National audienceStress Corrosion Cracking (SCC) represents a significant cause of failure in pressurised water reactors and many efforts have been made to address this problem [1]. It involves the combined action of the environment, mechanical stresses and material properties on the damage of engineering components. Current SCC models developed to predict crack growth behaviour or SCC susceptibility criteria do not fully incorporate the complex multiphysical processes that occur during oxidation at the scale of the microstructure. The aim of the work is to formulate a multi-physics modelling framework based on continuum thermodynamics able to describe the growth of an oxide film on a polycrystalline material using the phase field method

Multi-scale links in constitutive formulations for materials with heterogeneous microstructures, a micro-mechanics perspective

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Multiscale approaches : from the nanomechanics to the micromechanics

Computational modelling of materials behaviour is becoming a reliable tool to underpin scientific investigations and complement traditional theoretical and experimental approaches. In cases where an understanding of the dual nature of the structure of matter — continuous when viewed at large length scales and discrete when viewed at an atomic scale — and its interdependencies are crucial, multiscale materials modelling (MMM) approaches are required to complement continuum and atomistic analyses methods. At transitional (or microstructure) scales — in between continuum and atomistic — continuum approaches begin to break down, and atomistic methods reach inherent time and length-scale limitations (Ghoniem et al., 2003). Transitional theoretical frameworks and modelling techniques are being developed to bridge the gap between length scale extremes. The power of analytical theories lies in their ability to reduce the complex collective behaviour of the basic ingredients of a solid (e.g. electrons, atoms, lattice defects, single crystal grains) into insightful relationships between cause and effect. For example, the description of deformation beyond the elastic regime is usually described by appropriate constitutive equations, and the implementation of such relationships within continuum mechanics generally relies on the inherent assumption that material properties vary continuously throughout the solid

On the selection of active slip systems in crystal plasticity

The capabilities of existing rate-independent and rate-dependent constitutive models to select the active slip systems at the corners of non-smooth theories play a crucial role in predicting localisation phenomena. Even though the description of crystal plasticity within the context of modern continuum mechanics goes back to the early 1960s, there is no universally accepted solution as to how to identify a unique set of active slip systems. Furthermore, some recently proposed integration schemes have neither been compared with other methods nor tested under complex multiaxial stress conditions thus rendering a direct assessment difficult. In this work, the predictive capabilities of existing crystal plasticity and visco-plasticity formulations and algorithms when subjected to complex multiaxial loading paths are investigated, and their relative accuracies established. In order to compare consistently the performance of different models, a generic thermodynamics-based crystallographic framework, which incorporates current formulations as special cases, is proposed. Several two-dimensional boundary value problems for elasto-plastic and elasto-viscoplastic FCC crystals are selected as benchmark cases. The effects of multiaxial loading paths, latent hardening, and dissipated energy on the selection of active slip systems at sharp yield surface corners are investigated. The differences in the predicted behaviour were found to be associated with both the particular form of the single crystal formulations and the algorithms used in their numerical implementations. Experimental data obtained under multiaxial loading conditions will be required to judge the relative accuracy of each single crystal formulation

A mechanistic approach to extract the mechanical properties of individual constituents in plasma-sprayed metal matrix composite coatings

International audienceA mechanistic approach to determine the in-situ properties of individual constituents in a plasma sprayed metal matrix composite (MMC) coating was proposed. The approach was based on micro-indentation and inverse analysis techniques. Utilising the indentation data obtained from the micro-indentation experiments, elastic moduli of each constituent were calculated using a well-established method whereas yield strength and hardening exponent were extracted using the inverse procedure based on finite element analysis. Finite element results gave a satisfactory agreement between the numerically simulated and the measured indentation load–depth curves. Further studies using three dimensional finite element analyses of Vickers indentation on the MMC coating based on its actual microstructure also showed that the indentation behaviour of the MMC coatings is strongly dependent on its morphology, volume fraction, size and distribution of the reinforcing phase

Characterization of elastoplastic properties based on inverse analysis and finite element modelling of two separate indenters

International audienceA method that can determine uniquely the elastoplastic properties from indentation loading and unloading curves has been developed. It is based on finite element modeling and inverse analysis of two separate indenters. The approach was validated by numerical experiments using a fictitious material. It was demonstrated that the proposed method can uniquely recover the elastoplastic properties using only indentation load-displacement curves of two indenters. Although the proposed procedure has been used to predict elastoplastic strain hardening behavior, it is also applicable to estimate other mechanical properties where there are more than two unknown parameters, such as rate-dependent behavior

First vs. second gradient of strain theory for capillarity effects in an elastic fluid at small length scales

International audienceMindlin [22] wrote a milestone paper claiming that a second strain gradient theory is required for a continuum description of volume cohesion and surface tension in isotropic elastic media. The objective of the present work is to compare Mindlin's approach to more standard capillarity models based on a first strain gradient theory and Korteweg's equation. A general micromorphic model is then proposed as a numerical method to implement Mindlin's theory in a finite element code