Plenary Lectures

• Pierre-Olivier BOUCHARD (Centre de Mise en Forme des Matériaux - CEMEF, Mines ParisTech)

Title: A new finite element framework for the modeling of ductile fracture mechanisms in heterogeneous microstructures

P.-O. Bouchard¹, M. Shakoor¹, V. Trejo Navas¹ and M. Bernacki¹

¹ MINES ParisTech, PSL-Research University, CEMEF - Centre de mise en forme des matériaux, CNRS UMR 7635, CS10207 rue Claude Daunesse 06904 Sophia Antipolis Cedex, France – pierre-olivier.bouchard@mines-paristech.fr

Abstract: Ductile fracture has been studied for many years and has given rise to number of damage theories and failure criteria. However, predicting ductile fracture under complex loading path remains challenging, in particular for advanced heterogeneous materials for which failure mechanisms depend on microstructural properties such as particle characteristics (nature, shape and distribution), grains, and texture. Modeling failure at a mesoscale would help in the understanding of the role of these microstructural properties on ductile fracture mechanisms. Such a modeling requires an accurate numerical framework accounting for heterogeneous microstructure definition and meshing capabilities under large plastic strain as well as numerical methods for the modeling of failure events such as void nucleation –by interface debonding or particles failure –and coalescence.
In this work, a micromechanical approach is developed in order to conduct realistic full field finite element (FE) simulations of ductile fracture at the microscale. Meshing and remeshing methods relying on the use of Level-Set functions are proposed to discretize the microstructure and its behavior under large plastic strain [1, 2]. These numerical methods are extended to account for cracks and model the microstructure failure mechanisms: void nucleation, growth and coalescence. This new FE approach is used to study the influence of multiaxial and non-monotonic loading on ductile failure mechanisms. It is shown that different loading paths leading to the same final macroscopic strain activate different nucleation mechanisms and consequently different final void volume fraction.
These full field FE simulations can also be used to calibrate nucleation or coalescence failure criteria. This is done here thanks to the combination of Synchrotron Radiation Computed Laminography (SRCL) experiments and observations [3], Digital Volume Correlation (DVC) [4] and FE simulations[1, 2]. Thanks to SRCL images at the initial state, are presentative volume element (RVE) representing the exact microstructure is meshed using the body-fitted immersed method presented in [2]. The DVC also uses SRCL images at different stages of the mechanical test in order to extract the exact boundary conditions that need to be applied on the RVE. These boundary conditions play an important role on void growth as detailed in [5]. The FE framework enables the modeling of void nucleation growth and coalescence with criteria parameters that can be identified by comparison with SRCL images. The whole methodology ([6]) is carried out on nodular cast iron and comparisons with experimental observations are discussed.

References:[1]E. Roux, M. Shakoor, M. Bernacki and P.-O. Bouchard, A new finite element approach for modelling ductile damage void nucleation and growth –analysis of loading path effect on damage mechanisms, Modelling and Simulation in Materials Science and Engineering, 22 (2014) 1-23.
[2]M. Shakoor, M. Bernacki and P.-O. Bouchard, A new body-fitted immersed volume method for the modeling of ductile fracture: analysis of void clusters and stress state effects on coalescence, Engineering Fracture Mechanics, 147 (2015)398–417.
[3]T.F. Morgeneyer, T. Taillandier-Thomas, L. Helfen, T. Baumbach, I. Sinclair, S. Roux, F. Hild, In situ 3-D observation of early strain localization during failure of thin Al alloy (2198) sheet, Acta Materialia, 69(2014) 78-91.
[4] A. Buljac, T. Taillandier-Thomas, T.F. Morgeneyer, L. Helfen, S. Roux, F. Hild, Slant strained band development during flat to slant crack transition in AA 2198 T8 sheet: in situ 3D measurements, International Journal of Fracture 200 (2016) 49-62.
[5] M. Shakoor, A. Buljac, J. Neggers, F. Hild, T.F. Morgeneyer, L. Helfen, M. Bernacki and P.-O. Bouchard, submitted to International Journal of Solids and Structures.
[6] A. Buljac, M. Shakoor, J. Neggers, M.Bernacki, P.-O. Bouchard, L. Helfen, T.F. Morgeneyer and F. Hild, Computational Mechanics, in Press.

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• Blaise A. BOURDIN (Department of Mathematics and Center for Computation & Technology, Louisiana State University)

Title: Phase-field and variational models of fracture: twenty years and counting

Abstract: Since their inception in the mid-90's as regularization of Francfort and Marigo's variational model of brittle fracture, phase-field models of fracture have steadily gained popularity.

Part of this success is undoubtedly due to the relative ease of their three dimensional implementation, as well as to their postulated then demonstrated ability to capture complex fracture behavior.

In this talk, I will start by recalling the link between phase-field and variational models of fracture. Then, I will describe more recent effort to derive variational phase field models as specific examples of gradient damage models. I will illustrate both approaches using various quantitative validation and verification numerical simulations and highlight their differences and similarities. I will then present recent extensions, and will conclude with open problems and proposed extensions for the years to come.

Pedro P. CAMANHO (Department of Mechanical Engineering, University of Porto)

Title: The role of numerical tools on the development of a new generation of polymer composite materials

P.P. Camanho¹

¹ DEMec/INEGI, University of Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal – pcamanho@fe-up.pt

Abstract: The stringent guidelines on emissions combined with the strong competition between aerospace companies motivate the development of a new generation of polymer composite materials. New requirements, ranging from lightness, multi-functionality, recyclability, structural health monitoring, and faster manufacturing processes are imposed by the market. However, the time frame from material development to implementation is currently too high (up to 20 years) [1], and product innovation based on new materials is particularly fraught with risk and uncertainty. The use of computational mechanics mitigates these risks and uncertainties: not only the development of new materials is faster due to the reduced number of physical tests, but also increased knowledge on the material performance is obtained at early stages of material development.
This work addresses the role of Computational Fracture Mechanics on the development of a new generation of non-conventional polymer composite materials based on ultra-thin plies [2], fibre hybridisation [3], and carbon-nanotubes [4]. The analysis models that support the development of the non-conventional polymer composite materials are based on computational micro-mechanics, cohesive zone models, and continuum damage mechanics. The models developed represent the mechanics of non-linear deformation and fracture of the new material systems proposed. Furthermore, the models are able to explain the reasons why the new materials have an improved performance over conventional materials with respect to the main failure mechanisms of polymer composite laminates, such as delamination, matrix cracking, and fibre fracture.
The work presented corresponds to one of the building-blocks required for the effective optimisation of the micro-structure of composite materials with respect to a set of design drivers.

References:[1] Materials Genome Initiative for Global Competitiveness, Executive Office of the President, National Science and Technology Council, U.S.A., 2011.
[2] A. Arteiro, G. Catalanotti, A.R. Melro, P. Linde, P.P. Camanho, Micro-mechanical analysis of the in situ effect in polymer composite laminates, Composite Structures, 116, 827-840, 2014.
[3] R.P. Tavares, A.R. Melro, M. Bessa, A. Turon, W.K. Liu, P.P. Camanho, Mechanics of hybrid polymer composites: analytical and computational study, Computational Mechanics, 57, 405-421, 2016.
[4] X. Ni, E. Kalfon-Cohen, C. Furtado, A. Arteiro, G. Valdes, T. Hank, N. Fritz, R. Kopp, G. Borstnar, M.N. Mavrogordato, S.M. Spearing, P.P. Camanho, B.L. Wardle, Interlaminar Reinforcement of Carbon Fiber Composites Using Aligned Carbon Nanotubes, submitted to the 21st International Conference on Composite Materials (ICCM), Xi’an, China, Aug. 20-25, 2017.

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• Laura DE LORENZIS (Institut für Angewandte Mechanik, Technische Universität Braunschweig)

Title: Recent research results on phase-field modeling and computation of brittle fracture

Abstract: The talk discusses recent research results obtained in the group of the speaker in the framework of the phase-field approach to fracture, based on the regularization of Francfort and Marigo's variational formulation of brittle fracture. After a general overview on recently completed and ongoing work, the focus is placed on two main topics: i. a phase-field modeling framework for fracture in partially saturated porous media, applied to the study of desiccation phenomena in soils and shrinkage in cementitious materials; ii. a computational approach to combine the phase-field approach to brittle fracture with the Kirchhoff-Love shell kinematics, while accounting for the different material behavior in tension and compression.

• Lambertus J. SLUYS (Delft University of Technology, Faculty of Civil Engineering and Geosciences)

Title: Multi-scale modelling of quasi-brittle fracture processes

Abstract: In this presentation different multi-scale modelling techniques for the description of quasi-brittle fracture processes will be discussed.

A number of relevant issues will be treated in more detail, such as the non-standard computational homogenization for localization phenomena, the extension of multi-scale modelling techniques to dynamic fracture problems and the introduction of multi-physics aspects.

Enhanced computational homogenization schemes have been developed for modelling heterogeneous quasi-brittle materials. They are characterized by the introduction of cohesive cracks at the coarse scale which are derived from propagating localisation bands at the fine scale. The schemes are objective with respect to the coarse scale discretisation and the fine scale modelling size and discretisation.

There are limitations to the well-known multi-scale schemes in cases where the separation of scales is relatively small. Direct coupling can be used then through coupled-volume or domain decomposition techniques. Furthermore, small-scale effects that are normally averaged out through computational homogenization can not always be ignored. For instance, dispersive effects may become relevant in dynamic multi-scale analyses when dominant wave lengths in the macroscopic response are of the same order as the size of a representative volume element. A dispersion tensor can then be derived in order to enhance the multi-scale scheme. The issue of multiple interacting and non-interacting length and time scales (e.g. for fatigue fracture problems) will be discussed. The use of failure models which are regularized by the introduction of a length scale parameter further complicates this issue.

Examples of multi-scale analyses of quasi-brittle fracture processes in various engineering materials will be demonstrated. Furthermore, efficiency of the computational multi-scale modelling schemes will be discussed.