Instantiation of crystal plasticity simulations for micromechanical modelling with direct input from microstructural data collected at light sources

doi:10.1016/j.scriptamat.2017.01.025

Scripta Materialia

Volume 132, 15 April 2017, Pages 73-77

https://doi.org/10.1016/j.scriptamat.2017.01.025 Get rights and content

Abstract

Novel non-destructive characterization techniques performed at light sources provide previously inaccessible 3-D mesoscopic information on the deformation of polycrystalline materials. One major difficulty for interpretation of these experiments through micromechanical modelling is the likelihood that processing and/or mounting the sample introduce residual stresses in the specimen. These stresses need to be incorporated into crystal plasticity formulations, for these models to operate directly from microstructural images and be predictive. To achieve this, the initial micromechanical state of each voxel needs to be specified. In this letter we present a method for incorporating grain-averaged residual stresses for instantiation of crystal plasticity simulations.

Graphical abstract

Introduction

Novel non-destructive techniques for microstructure characterization performed at light sources, such as high-energy X-ray diffraction microscopy (HEDM) [1], provide previously inaccessible 3-D in-situ information on the deformation of polycrystalline materials at the scale of the material's heterogeneity, i.e. the mesoscale. 3-D imaging is enabled by the collection of multiple diffraction patterns obtained by rotating the sample as it is quasi-statically deformed. Near-field (nf) HEDM allows characterization of crystal orientation fields in the form of voxelized microstructural images, while far-field (ff) HEDM provides local micromechanical information in the form of average stresses/elastic strains in the single crystal grains and the location of the centers of mass of the grains. One major difficulty of such techniques for interpretation of the deformation process through micromechanical modelling with direct input from the collected data is the likelihood that machining, or other type of processing (e.g. additive manufacturing), as well as handling, and/or mounting the sample introduce initial inter- and intragranular stresses in the specimen. These residual stresses (RS) need to be incorporated into full-field crystal plasticity (CP) formulations, for these models to be able to operate directly from microstructural images and be predictive. To achieve this, the initial micromechanical state of each voxel in the image needs to be specified. However, if the initial grain average stresses measured by ff-HEDM were to be simplistically assigned to each voxel, this would lead to a non-equilibrated stress field in the specimen. In this letter we present a method for incorporating initial grain-averaged RS for instantiation of image-based CP simulations.

Concurrent and synergetic advances in material characterization and modelling techniques have opened vast opportunities to integrate increasingly sophisticated microstructural and micromechanical experiments and complex multiscale formulations, for simulating mechanical performance of polycrystalline materials (e.g. [2], [3].). However, until very recently, the nature of the available experimental data was either statistical (e.g. X-ray or neutron diffraction), i.e. lacking space-resolved information on local fields, or destructive (e.g. Electron Back-Scattering Diffraction, EBSD), lacking information on microstructural and micromechanical evolution in the bulk of the material. These limitations are rapidly disappearing. Nowadays, powerful characterization techniques enabled by the availability of high energy radiation at light sources, are emerging to perform non-destructive space-resolved 3-D measurements. HEDM is one of such novel techniques [1], [4], [5], [6], providing spatially-resolved 3-D orientation fields [7], [8] as well as grain-averaged elastic strain measurements for multiple states of a single sample subjected to external mechanical solicitation [9], [10]. Such data has great potential for testing and calibrating full-field CP models [7], [11], [12] and in turn these models can be instrumental to improve experimental data reduction. However, the likely introduction of RS due to fabrication and manipulation of HEDM samples determines the need for image-based CP formulations to be properly initialized, voxel by voxel, to assure predictive capability of these models when operating directly on HEDM images. The assignation of grain-averaged stresses measured by ff-HEDM to each voxel is not a viable option, since this simplistic assumption would violate stress equilibrium in the specimen.

Section snippets

Methods

Our image-based CP formulation of choice is the well-established fast Fourier transform (FFT)-based elasto-viscoplastic (EVPFFT) model [13] with the addition of an initial eigenstrain term [14] to reproduce the measured RS in the material and efficiently use HEDM input to predict micromechanical response of polycrystalline samples. However, despite the specific use here of FFT-based models, the proposed methodology is general, i.e. easily extendable and applicable to instantiate other popular

Results

Fig. 1 schematically illustrates the workflow implemented to assess Eshelby's approximation (Eq. (2)) and its refinement using the correction factors β_ij (Eq. (3)). A synthetic orientation field generated by Voronoi tessellation, representing a cylindrical polycrystalline sample with 14,592 grains (#1 in the figure), is used as input. Note that specific sample geometries (smooth cylindrical specimen in this case) can be handled using FFT-based methods (which operate on periodic unit cells)

Conclusions

In this letter we have demonstrated a methodology to incorporate 3-D measurements of grain-averaged RS for instantiation of image-based full-field CP simulations. The workflow, illustrated in Fig. 1, requires performing several operations on orientation fields and grain-averaged data, which, in the context of a 3-D experiment, can be obtained by ff-HEDM or concurrent nf- and ff-HEDM. This sequence of operations can be automated for rapid and convenient instantiation of CP simulations.

The key

Acknowledgements

This work was supported by Los Alamos National Laboratory's Laboratory-Directed Research and Development (LDRD) (Project # 20140114DR) program. Fruitful discussions with Cristina Garcia-Cardona, Marian Anghel (LANL), Jette Oddershede, Grethe Winther (DTU) and Tony Rollett (CMU) are acknowledged.

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Regular ArticleInstantiation of crystal plasticity simulations for micromechanical modelling with direct input from microstructural data collected at light sources

Abstract

Graphical abstract

Introduction

Section snippets

Methods

Results

Conclusions

Acknowledgements

Int. J. Plast.

Int. J. Plast.

Mater. Charact.

Acta Mater.

Int. J. Plast.

Comput. Mater. Sci.

JOM

J. Mater. Sci.

Three-dimensional X-ray Diffraction Microscopy: Mapping Polycrystals and their Dynamics

Rev. Sci. Instrum.

J. Appl. Crystallogr.

Regular Article
Instantiation of crystal plasticity simulations for micromechanical modelling with direct input from microstructural data collected at light sources