*Multiscale simulations in crystalline materials are based on 3D Discrete Dislocation Dynamics (DDD) investigations.When needed, atomistic information provided by Molecular Dynamics (MD) are introduced as local rules in the DDD modeling.At the upper scale, DDD simulations can estimate parameters of constitutive equations in crystal plasticity Finite Element (FE) models.At the continuum scale, cavitation erosion is investigated using classical FE models and Smoothed Particles Hydrodynamics (SPH) simulations. Both models account for the fluid/structure interaction.*

**PhD and post-docs: **Julian SOULACROIX, Oraib AL-KHITAN, Camila MALLMANN, Hareesh TUMMALA, Siwen GAO (Bochum Univ., Germany), Guru PRASAD REDDY (IGCAR, India), Gururaj KADIRI (IGCAR, India), Samir Chandra ROY, Ph.D. Univ. Grenoble Alpes, December 11th 2015, Tiana DEPLANCKE (Post Doc 2015), Yves PAQUETTE, Shrey JOSHI, Prasantha SARKAR, Markku YLONEN, Fabien MENG, Elena JOVER-CARRASCO, Jessica MUZI, Corentin VELARD.**Collaborations : **Christophe DEPRES (SYMME, Annecy) ; Christian ROBERTSON and Laurent DUPUY (SRMA, CEA Saclay) ; Hyung-Jun CHANG (SafranTech) ; Marc BLETRY (ICMPE, Paris XII) ; Laurent DELANNAY and Thomas PARDOEN (UCL, Louvain-La-Neuve), Anxin MA and Alexander HARTMAIER (ICAMS, Univ. Bochum, Germany) ; Jean-Pierre FRANC, Giovanni GHIGLIOTTI (LEGI, Grenoble) and Christian PELLONE (LEGI, Grenoble) ; Nicolas RANC (PIMM, ENSAM Paristech) ; Khi Han KIM (ONR, USA), Erik JOHNSEN (Michigan Univ, USA).

Our simulations of nanoindentation in copper are emblematic of our multiscale approach. In this study, Molecular Dynamics simulations provide the details of the nucleation mechanism beneath a spherical indenter. The mechanism is then introduced as local rules in DD simulations which can simulate the dynamic expansion of the dislocation microstructure as well as the surface relief (including pile-up and sink-in zones). At the continuum scale, DD simulations are used to define physical constitutive equations for FE crystal plasticity simulations which are performed and directly compared to AFM observations.

DDD simulations were able to successfully simulate the formation of persistent slip bands in surface grains loaded in fatigue. Extrusions are evidenced where the bands intercept the free surface. Energy and stress calculations performed inside the simulated grain lead to a possible scenario for the crack initiation at the interface between the band and the matrix, as reported in the literature. More recently, a crack was inserted at the persistent slip band interface and the crack tip slip displacement evolutions are evaluated. It is shown that the crack growth rate is strongly related to the grain size and to the distance to the grain boundary; the smaller the grain, the faster the crack growth. Finally, the crack propagation to the next grain is investigated by conducting DDD fatigue simulations in a surface grain next to a cracked grain. It is shown that the development of the persistent slip band is modified by the presence of the crack. The crack orientation affects the orientation of the persistent slip band, as well as the extrusion rate, and consequently the crack propagation in the next grain.

In collaboration with Université Catholique de Louvain-La-Neuve, we are working on the role of interfaces in plasticity. The effect of the grain shape on the back stress induced in a single closed grain has been investigated in order to implement the microscopic features in a continuum description of the plasticity. Slip transmission and dislocation interactions between different grains of polycrystalline aggregates are also investigated for different orientations of the grains.

Cavitation erosion occurs when multiple bubbles collapse near a solid surface. During the bubble collapse, a fast reintrant jet impacts the surface and creates a deformation pit.

An inverse method has been conducted in order to estimate the aggressiveness of the flow from the observation of the pits printed on the surface in the first moments of the cavitation erosion. Assuming that each pit was generated by a single bubble collapse whose pressure field is treated as a Gaussian shape, finite element calculations are used for estimating the load that created each residual imprint. It is shown that the load distribution falls on a master curve independent of the tested material; the softer material (aluminum alloy) measuring the lowest impacts while the most resistant material (duplex stainless steel) provides access to the largest impact pressures.

Mass loss prediction in cavitation erosion could be predicted by numerical simulations provided the coupling between the cavitating fluid and the elasto-visco-plastic solid is accurately taken into account. We selected two approaches to tackle this problem. In the first approach, the Finite Element code CAST3M is coupled to a CFD code developed at Michigan University. In the second approach Smoothed Particules Hydrodynamics (SPH) simulations are developed in order to account both for the fluid part and the solid part in the same code.

- C. Déprés, C. Robertson and M. Fivel,
*3D Discrete dislocation dynamics investigations of fatigue crack initiation and propagation*,*Aerospace Lab Journal*,**AL09-01**, (2015). - M. Fivel and C. Déprés,
*An easy implementation of displacement calculations in 3D discrete dislocation dynamics codes*,*Philosophical Magazine*,**94**(28), pp. 3206-3214, (2014). - G.V. Prasad Reddy, C. Robertson, C. Déprés and M. Fivel,
*An extensive 3D Dislocation Dynamics investigation of Stage-I fatigue crack propagation, Philosophical Magazine*,**94**(36), pp. 4115-4137 (2014). - G.V. Prasad Reddy, C. Robertson, C. Déprés and M. Fivel,
*Effect of grain disorientation on early fatigue crack propagation in face-centred polycrystals: A three-dimensional dislocation dynamics investigation*,*Acta Materialia*,**61**, pp. 5300-5310, (2013). - H.-J. Chang, M. Fivel, D. Rodney et M. Verdier,
*Multiscale modelling of indentation in fcc metals : from atomic to continuum*,*Comptes Rendus – Physiques*,**11**, pp. 285-292, (2010). - S. Gao, M.K. Rajendran, M. Fivel, A. Ma, O. Shchyglo, A. Hartmaier et I. Steinbach,
*Primary combination of phase-field and discrete dislocation dynamics methods for investigating athermal plastic deformation in various realistic Ni-base single crystal superalloy structures*,*Modelling and Simulations in Materials Science and Engineering*,**23**(7), 075003, (2015). - S. Gao, M. Fivel, A. Ma et A. Hartmaier,
*Influence of misfit stresses on dislocation glide in single crystal superalloys: a 3D discrete dislocation dynamics study*,*Journal of Physics and Mechanics of Solids*,**76**, pp. 276-290, (2015).

Written by Charles Josserond

Date of update March 15, 2018

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