PhD at Arts et Métiers ParisTech. Phase field modeling of damage and fracture in polycrystalline materials

A PhD research subject is proposed for students to apply at Arts et Métiers ParisTech.

The ability of scientists and engineers to exploit, design and process new materials with improved properties has often been fundamental for the technological advances of societies. In fact, advances in many key domains like aerospace, automotive industry, energy, nanotechnology, rely on our ability to engineer new materials and exploit their properties. For metallic materials, such technological advances usually requires a deep understanding of how mechanical and physical properties are influenced by microstructural features (e.g. grain size, crystallographic orientation). The investigation of the relation between macroscopic properties and microstructure is however a complex task. Indeed, under service conditions or during processing, microstructural transformations are observed and the associated properties may significantly change depending on the loading conditions. An optimal exploitation of engineering alloys therefore requires the development of microstructure sensitive constitutive models, which explicitly account for the influence of microstructural heterogeneities on the mechanical behavior.In the present work, we are interested in the development of a model which is dedicated to the description of damage in polycrystalline metallic materials. Indeed, the progressive degradation of mechanical properties for such materials is an important issue in many engineering situations (e.g. fatigue design, creep design). This study thus aims at building a model that would describe how cracks initiate, propagate and interact with each other at the micro-scale.To reach this objective, it is proposed to use the phase field method (PFM) within the context of polycrystalline plasticity. Indeed, within the framework of irreversible thermodynamics, the phase-field method has proved to be extremely powerful in the description of microstructural transformations without having to track the evolution of individual interfaces, as in the case of sharp interface models. In the present case, it is expected that the introduction of an order parameter associated with damage will allow capturing some complex phenomena like crack kinking or crack branching. The proposed study would therefore consists of:
(1) Defining an appropriate set of internal variables (and the associated energy potential) to deal with both elasticity, plasticity and damage in crystalline materials at the microscale
(2) Deriving the evolution equations associated with the different internal variables within the context of the phase field method
(3) Implementing the constitutive equations within an appropriate numerical solver (finite element solver for instance)
(4) Validating the proposed formulation by testing its ability to reproduce some known experimental results.At the end of this PhD research program, the numerical model will allow for investigating the interactions between various physical mechanisms governing the macroscopic behavior (e.g. plasticity, damage) at different length scales. Also, since the proposed model will offer a more accurate description of the mechanical behavior of metallic materials, it will help in optimizing the design structural components.

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