Research Topic for the ParisTech/CSC PhD Program
Subfield: Mechanics of materials, Applied Physics, Applied Mathematics, Mech. Eng.
ParisTech School: Arts et Métiers ParisTech, Centre d'Angers.
Title: Phase field modeling of damage and fracture in polycrystalline materials
Advisor(s): Prof. Amine Ammar (amine.ammar@ensam.eu)
Dr. Charles Mareau (charles.mareau@ensam.eu),
Dr. Saber El Arem (saber.elarem@ensam.eu)
Short description of possible research topics for a PhD: 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 necessitates 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 phasefield 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 for 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.
Required background of the student: Material sciences, Solid mechanics, Physics, Applied
mathematics.
Publications of the group:
1. Mareau, C., Berbenni, S., (2015), An affine formulation for the self-consistent modeling of
elasto-viscoplastic heterogeneous materials based on the translated field method,
International Journal of Plasticity, (64), pages 134-150.
2. Mareau, C., Cuillerier, D., Morel, F., (2013), Experimental and numerical study of the
evolution of stored and dissipated energies in a medium carbon steel under cyclic loading,
Mechanics of Materials, (60), pages 93-106.
3. F. Chinesta, A. Ammar, H. Lamari, N. Ranc. Atoms, Molecules and Flows: Recent Advances
and New Challenges in their Multi-Scale Numerical Modeling at the Beginning of the Third
Millenium. Trends in Engineering Computational Technology, B.H.V. Topping Edt., SaxeCoburg Publications, Chapter 13 : 247-269, 2008.
4. I. Gueye, S. El Arem, F. Feyel, F.-X. Roux, G. Cailletaud : A new parallel sparse direct solver :
presentation and numerical experiments in large-scale structural mechanics parallel computing,
International Journal for Numerical Methods in Engineering, Vol. 88(4), P. 370-384, 2011.