PI & Resources
Ph.D. Advisor: Dr. Laurent Capolungo
Supervisor: Dr. Vincent Taupin (PI for ANR Nanomec)
Affiliations
Department of Mechanical Engineering, Georgia Institute of Technology, GA 30332, USA
Georgia Tech Lorraine, C.N.R.S. (UMI 2958) 57070 Metz, France
LEM3, C.N.R.S., 57070 Metz, France
Motivation
Experiments and atomistic simulations have revealed that the role of grain boundary (GB) interfaces on governing the plastic deformation becomes increasingly important with decreasing average grain size in the nanocrystalline (nc) regime. This role of GB interfaces manifests itself through microstructural geometric and energetic features at the inter-atomic, nano, and meso-scales. At the inter-atomic and nano-scales these include GB structure and misorientation, their energy and free volume, triple junction (TJ) geometry and stresses, defect content, net defect polarity of the domain, etc. At the meso-scale these are grain orientation distribution, grain morphology, GB misorientation, interface-to-volume ratio, defect distribution and associated internal stresses, among others. Furthermore, the inter-atomic/nano-scale features define the meso-scale microstructural properties and in turn the collective meso-scale behavior influences the local response at the inter-atomic scale.
Recent experimental observations using high resolution transmission electron microscopy on nc metals generated using severe plastic deformation techniques suggested that incompatible lattice curvature inducing line defects i.e. disclinations, can be generated during nano-structuring of conventional coarse grained materials. These defects manifest themselves in the form of dipoles or quadrupoles in the vicinity of GBs and TJs; for example, Roesner et al. (2011) found a rotational jump along a Σ9 GB bounded by a TJ and a quadruple junction in nc Pd (see figure below). Disclinations could have a crucial impact on the stability of nc/ufg metals and alloys, as well as GB mediated plasticity mechanisms. These could help identify deformation related phenomena such as possible sites for nucleation of grains, shear bands, cracks or twins. Furthermore, in ufg materials, in which plasticity is at a transition between dislocation slip and interface driven, disclinations may play a critical role in the formation of different structures; for example, micro shear bands.
the form of a line profile along the Σ9 boundary and averaged over the width of the
box. Two gradients of opposite sign emerge from the TJ and the quadruple point,
respectively. The dotted line indicates the average grain misorientation. Due to the
wavy character of the Σ9 boundary the rigid body rotation occurs as a periodically
modulated signal along its length. Note the jump in rigid body rotation at ≈ 0.6 nm
(adapted from R¨osner et al. Acta Mat. 59 (2011) 7380 – 7387).
Analysing the information obtained from experimental studies in a thermo-mechanically rigorous manner interprets deformation behavior, requires models based at the inter-atomic scale, nano-scale and meso-scale.
At the nano-scale, there had been very limited contributions to understand the role of GB disclinations on the energy and geometry of the local microstructure in nc materials. For static applications, disclinations have been successfully used to represent GBs and TJs. However, the energetic or geometric contributions of lattice curvatures were never taken into account. Furthermore, a rigorous treatment of the dynamics of dislocations and disclinations is lacking in these models. At the meso-scale, there had been no models that accounted for the role of disclinations or that of the incompatibilities in elastic curvatures induced by them, on the local and macroscopic response.
My approach
The main objective of this thesis is to obtain critical insight on the role of crystalline incompatibilities in strain and curvature, induced in presence of line defects i.e. dislocations and disclinations, on the energy and geometry of specific features of the local microstructure, and on the bulk mechanical response of nc/ultra-fine grained materials. To that end, studies were performed at the (1) inter-atomic and nano-scales, and (2) at the mesoscopic or polycrystalline scale. The modelling approach is based on the field dislocation and disclination mechanics theory of continuously representated dislocations and disclinations. New, thermodynamically rigorous, multi-scale elastic constitutive laws based on the couple stress theory are developed to capture the effect of strain and curvature incompatibilities on the Cauchy and couple stresses. A new mesoscale elasto-viscoplastic constitutive model of defect incompatibilities based on a fast Fourier transform technique is developed. The desired scale transitioning is achieved via novel phenomenological defect density transport equations and the newly developed elastic constitutive laws.
At the nano-scale, the model is applied to study energetic interactions between strain and curvature incompatibilities associated with GBs and their influence on TJ energies (see figure below). Results reveal that incompatible lattice strains have the most significant contribution to the energy. Incompatible lattice curvatures have negligible energetic contributions but are necessary to characterize the geometry of GBs. Finally, both incompatible lattice strains and curvatures are necessary to capture the structure sensitive mechanical behavior of GBs.
At the meso-scale, deformation of nc aggregates characterized by residual curvatures is studied to identify the impact of the latter’s presence on the local and bulk mechanical response. Relaxation of local stresses generated from residual curvatures reproduces the effect of GB dislocation emission. Uniaxial tensile loading of nc microstructures containing residual curvatures reveals a softening in the yield stress (see figure below) which could explain the breakdown in the Hall-Petch law in the nc regime.
Next, the possibility of characterizing incompatibilities using X-ray or neutron diffraction techniques is tested. Results reveal that only strains and their gradients contribute to the broadening of diffraction peaks; curvatures and their gradients have no contribution. This study leads to the development of a new multi-scale averaged strain based Fourier technique for generating virtual diffraction peaks.
Publications
- Upadhyay et al., “A higher order elasto-viscoplastic model using fast Fourier transforms: effects of lattice curvatures on mechanical response of nanocrystalline metals”, IJP, 83 (2016) 126 – 152. LINK
- Taupin et al., “A mesoscopic theory of dislocation and disclination fields for grain boundary-mediated crystal plasticity”, IJSS, 71 (2015) 277-290. LINK
- Bertin et al., “A FFT-based formulation for efficient mechanical fields computation in isotropic and anisotropic periodic discrete dislocation dynamics”, MSMSE, 26 (2015) 065009. LINK
- Upadhyay et al., Dissertation: “On the role of defect incompatibilities on mechanical properties of polycrystalline aggregates: a multi-scale study”, Georgia Institute of Technology, (2014). PDF
- Upadhyay et al., “On the computation of diffraction peaks from discrete defects in continuous media: comparison of displacement and strain-based methods”, JACr, 47 (2014) 861 – 878. LINK
- Upadhyay et al., “Elastic constitutive laws for incompatible crystalline media: the contributions of dislocations, disclinations and G-disclinations, Phil. Mag., 93 (2013) 794 – 832. LINK
- Taupin et al., “Grain boundary modeling using an elasto-plastic theory of dislocation and disclination fields”, JMPS, 61 (2013) 370 – 384. LINK
- Taupin et al., “A Theory of Disclination and Dislocation Fields for Grain Boundary Plasticity”, In: Generalized Continua as Models for Materials, Advanced Structured Materials, Springer, Berlin, Heidelberg, 22 (2013) 303 – 320. LINK
- Fressengeas et al., “Tangential continuity of elastic/plastic curvature and strain at interfaces”, IJSS, 49 (2012) 2660 – 2667. LINK
- Upadhyay et al., “Grain boundary and triple junction energies in crystalline media: A disclination based approach”, IJSS, 48 (2011) 3176 – 3193. LINK
Presentations
Main collaborators
Dr. Laurent Capolungo (now at LANL, USA)
Dr. Vincent Taupin (LEM3 CNRS, France)
Dr. Claude Fressengeas (LEM3 CNRS, France)
Dr. Ricardo A. Lebensohn (LANL, USA)