Temperature dependant polycrystal model application to bainitic steel behavior under tri-axial loading in the ductile–brittle transition

Abstract

Keywords:Polycrystal plasticity Steel Mechanical behavior Bainite Cleavage fracture Fracture probability Pressure vessel steel Constraint effect a b s t r a c t A polycrystal finite element (FE) model describing the temperature evolution of low carbon steel is proposed in order to forecast the local mechanical fields as a function of temperature, for bainitic microstructure submitted to tri-axial loading. The model is designed for finite strains, large lattice rotations and temperatures ranging into the brittle-ductile transition domain. The dislocation densities are the internal variables. At low temperature in Body Centred Cubic (BCC) materials, plasticity is governed by double kink nucleation of screw dislocations, whereas at high temperature, plasticity depends on interactions between mobile dislocations and the forest dislocations. In this paper, the constitutive law and the evolution of the dislocation densities are written as a function of temperature and describe low and high temperature mechanisms. The studied aggregates are built from Electron Back Scattering Diffraction (EBSD) images of real bainitic steel. The aggregate is submitted to a tri-axial loading in order to describe the material at a crack tip. Mechanical parameters are deduced from mechanical tests. The local strain and stress fields, computed for different applied loadings, present local variations which depend on temperature and on tri-axial ratio. The distribution curves of the maximal principal stresses show that heterogeneities respectively increase with temperature and decrease with tri-axial ratio. A direct application of this model provides the evaluation of the rupture probability within the aggregate, which is treated as the elementary volume in the weak link theory. A comparison with the Beremin criterion calibrated on experimental data, shows that the computed fracture probability dispersion induced by the stress heterogeneities is of the same order than the measured dispersion. Temperature and stress tri-axiality ratio effects are also investigated. It is shown that these two parameters have a strong effect on fracture owing to their influence on the heterogeneous plastic strain. These inhomogeneities can initiate cleavage fracture.

Modelling Polycrystalline Materials: An Overview of Three-Dimensional Grain-Scale Mechanical Models

“…3D Voronoi polyhedra have been employed by Diard 60 for studying the plasticity of polycrystalline aggregates through crystal plasticity finite elements and by Zhang et al 61 , who simulated microplasticity-induced deformations in uniaxially strained ceramics. Threedimensional Voronoi tessellations have also been used by Kamaya et al 62 , who performed a statistical analysis of grain-boundary stresses in a microstructure comprised of 100 grains, by 63,64,65,32 , who modeled bainitic steel with crystal plasticity finite elements, by Luther and Könke 66 , who developed an algorithm to generate polycrystals with arbitrary grain size distribution functions for studying brittle intergranular damage in metallic polycrystals, by Musienko and Cailletaud 67 , to study intergranular stress corrosion cracking, transgranular cracking in a crystal plasticity framework, by Weinzapfel et al 68 , who presented a finite element model for analyzing subsurface stresses in an elastic half-space subjected to a general Hertzian contact load, with explicit consideration of the material microstructure topology, by Bomidi et al 21 , who developed a 3D finite element model to investigate intergranular fatigue damage of micro-electromechanical systems (MEMS) devices and to account for the effects of topological randomness of material microstructure on fatigue lives and by Benedetti and Aliabadi 69,70 , who studied the evolution of intergranular damage and cracking through cohesive-frictional boundary elements. It is worth noting that Voronoi tessellations are also frequently taken as initial microstructures in many thermodynamics-based models (phase field, level-set, .…”

“…In a typical dislocation-density based model (see e.g. 65 ),γ s is determined from a flow rule of the type of eq 11, as a function of τ s and temperature; the hardening rule for τ s accounts for the dislocation densities ρ s in all the slip systems and these dislocation densities are determined according to the slip rateγ s and the mean free path of a dislocation D path by means of an evolution law as illustrated in eq 12.…”

“…Among the conclusions, an interesting suggestion was given on the suitable number of grains/finite elements to be considered in microstructural failure initiation modelling, taking into account the possibility of extreme intergranular events that may enable damage initiation. Since then, the approach has been extended to large deformation computations with dislocation-density based constitutive laws presented in 65 . N'Guyen et al…”

“…For this application, all the characteristics of the approach presented in 63,64,65 have been gathered and complemented by the use of a large scale and statistically representative microstructure of bainite polycrystal enabling the prediction of rare cleavage micro-cracks events. Fig.3 presents some of the results of this study.…”

Introducing stress random fields of polycrystalline aggregates into the local approach to fracture

“…Within the weakest link theory the failure of a single critical carbide induces the failure of the RVE. Then the failure probability curve of the RVE is fitted using the Beremin model [3,4] to explain the dependence on temperature of material properties. However it is believed that numerous parameters such as grain geometry and orientation may influence the stress field and thus the final result.…”