Christophe Déprés

Low-strain fatigue in AISI 316L steel surface grains: a three-dimensional discrete dislocation dynamics modelling of the early cycles I. Dislocation microstructures and mechanical behaviour

The early stages of the formation of dislocation microstructures in low-strain fatigue are analysed, using three-dimensional discrete dislocation dynamics modelling. Simulations under various conditions of loading amplitude and grain size have been performed. Both the dislocation microstructures and the associated mechanical behaviour are accurately reproduced in single-slip as well as in double-slip loading conditions. The microstructures thus obtained are analysed quantitatively, in terms of number of slip bands per grain, band thickness and band spacing. The simulations show the crucial role of cross-slip both for the initial spreading of strain inside the grain and for the subsequent strain localization in the form of slip bands. A complete and detailed scheme for the persistent slip band formation is proposed, from the observation of the numerical dislocation arrangements.

Low-strain fatigue in 316L steel surface grains: a three dimension discrete dislocation dynamics modelling of the early cycles. Part 2: Persistent slip markings and micro-crack nucleation

The early stages of the formation of persistent slip markings in fatigue are analysed using three-dimensional discrete dislocation dynamics modelling. Surface displacements due to slip are computed using a specific post-processing method. Fatigue simulations under various strain ranges and grain sizes have been performed. The resulting surface slip markings and their evolutions are analyzed quantitatively in terms of marking height and thickness. A detailed scheme for persistent slip marking formation and morphology is proposed in relation to the persistent slip-band dislocation arrangements present within the grain. The simulations show the crucial role of these arrangements for the extrusion–intrusion growth and localisation of slip at the band edges. Local stress concentrations inside the crystal and their relationship to damage initiation are also analysed. The results provide insights for an original micro-crack initiation scheme, combining different initiation mechanisms as described in the literature.

An easy implementation of displacement calculations in 3D discrete dislocation dynamics codes

Barnett’s coordinate-free expression of the displacement field of a triangular loop in an isotropic media is revisited in a view to be implemented in 3D discrete dislocation dynamics codes. A general meshing procedure solving the problems of non-planar loops is presented. The method is user-friendly and can be used in numerical simulations since it gives the contribution of each dislocation segment to the global displacement field without defining the connectivity of closed loops. Easy to implement in parallel calculations, this method is successfully applied to large-scale simulations.

Compartmentalized Model for the Mechanical Behavior of Titanium

As close as you watch them, the materials (especially metals) present discontinuities that can easily be qualified as strong. Dislocations, structures formed by these dislocations, phases and grains are all discontinuities, also sources of heterogeneity, with effects on material behavior that are not really well reproduced by a model based on a continuity assessment. Consequently, the materials should be considered as a set of compartments with different behaviors. This promotes an alternative way to define models. A coherent modeling process is probably the integration of the different behaviors of the material compartments within the global model. The objective is here to build an efficient elasto(visco)plastic model of the mechanical behavior of titanium combining compartmentalized behaviors. After setting the frame of the study, which is of primary importance, the proposed modeling process is running as follows (i) choose a local behavior, (ii) identify the parameters of crystalline texture that must be integrated into the simulation and (iii) finally formulate a way of combining local compartments behaviors. The intrinsic properties of Finite Element codes are used to achieve the integration of the whole system.

A Fundamental Model of Aluminum Single Crystal Behavior with Physical Description of Kinematic Work Hardening

In this paper, we present a fundamental model of FCC single crystal behaviour at room temperature: this model includes kinematic work hardening derived from the elementary description of the collective dislocations density evolution during cyclic loading. This kinematic work hardening is then coupled with the isotropic work hardening mechanism. Using this original model, a simulation of a tensile test on a single crystal sample is carried out in the case of an initial crystal orientation that promotes single glide even at rather large strains. The evolution of resolved shear stresses on the primary and secondary slip systems are interpreted by means of the interaction between the evolution of isotropic and kinematic work hardening variables. The evolution of the model state-variables including applied resolved shear strain, dislocation densities, and critical shear stresses are represented as functions of the evolution of crystalline orientation during plastic deformation.

3D Discrete Dislocation Dynamics Investigations of Fatigue Crack Initiation and Propagation

Both nucleation and propagation of fatigue cracks in fcc metals are investigated, using 3D discrete dislocation dynamics (DDD) simulations. Firstly, DDD simulations explain the mechanisms leading to the formation of persistent slip bands in surface grains loaded in fatigue. Extrusions are evidenced where the bands intercept the free surface. The extrusion growth rate is estimated for different material parameters and loading conditions. 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. Secondly, a crack is 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.

A Three Dimensional Discrete Dislocation Dynamics Analysis of Cyclic Straining in 316L Stainless Steel

The early stages of the formation of dislocation microstructures in low strain fatigue are analysed,using three-dimensional discrete dislocation dynamics modelling (DDD). A detailed analysis of the simulated microstructures provide a detailed scheme for the persistent slip band formation, emphasizing the crucial role of cross-slip for both the initial strain spreading inside of the grain and for the subsequent strain localization in the form of slip bands. A new ad-hoc posttreatment tool evaluates the surface roughness as the cycles proceed. Slip markings and their evolutions are analysed, in relation to the dislocation microstructure. This dislocation-based study emphasizes the separate contribution of plastic slip in damage nucleation. A simple 1D dislocation based model for work-hardening in crystal plasticity is proposed. In this model, the forest dislocations are responsible for friction stress (isotropic work-hardening), while dislocation pile-ups and dislocation trapped in Persistent Slip Bands (PSB) produce the back stress (kinematic workhardening). The model is consistent with the stress-strain curves obtained in DDD. It is also consistent with the stress-strain curves experimentally obtained for larger imposed strain amplitudes.