Plasticity Simulation based on the Dynamics of Full Dislocation-density Functions
Event details
| Date | 14.12.2015 |
| Hour | 13:15 › 14:15 |
| Speaker | Prof. Alfonso H.W. Ngan, The University of Hong Kong, P.R. China |
| Location | |
| Category | Conferences - Seminars |
Current strategies of computational crystal plasticity that focus on individual atoms or dislocations are impractical for real-scale, large-strain problems even with today’s computing power. Dislocation-density based approaches are a way forward but most schemes published to-date give a heavier weight on the consideration of geometrically necessary dislocations (GNDs), while statistically stored dislocations (SSDs) are either ignored or treated in ad hoc manners. In reality, however, the motions of GNDs and SSDs are intricately linked through their mutual (e.g. Taylor) interactions, and in fact, GNDs and SSDs are indistinguishable on a microstructural level, notwithstanding the fact that the GNDs are simply the portion of dislocations associated with the overall shape change of the crystal. A correct scheme for dislocation dynamics should therefore be the one commonly used in discrete dislocation dynamics (DDD) simulations, namely, an “all-dislocation” treatment that is equally applicable for all dislocations comprising both the GNDs and SSDs, with a rigorous description of the interactions between them.
In this seminar, a new scheme for computational dynamics of dislocation-density functions, based on the above “all-dislocation” principle, is discussed. The dynamic evolution laws for the dislocation densities are derived by coarse-graining the individual density vector fields of all the discrete dislocation lines in the system, without distinguishing between GNDs and SSDs. The mutual elastic interactions between dislocations are treated in full by generalizing the elastic interactions between dislocation segments for dislocation densities, and reducing the Hirth-Lothe line-integral formulation into an algebraic form comprising only elementary functions which are straightforward enough for efficient numerical implementation. Other features in the model include forest (Taylor) hardening, stress due to dislocation curvature, generation due to the connectivity nature of dislocations, and dipole annihilation. Numerical implementation is by means of the finite volume method (FVM), which is well suited for high gradients often encountered in dislocation plasticity.
As a first case study, the model is utilized to predict vibration-induced softening and dislocation pattern formation experimentally observed in crystalline metals. The simulations reveal the main mechanism for subcell formation under oscillatory loadings to be the enhanced elimination of SSDs by the oscillatory stress, leaving behind GNDs with low Schmid factors which then form the subgrain walls. The depletion of the SSDs also accounts for the softening, and this occurs because the oscillatory loading brings reversals into the motions of SSDs which then increase their chance of meeting up and annihilation. This is the first simulation effort to successfully predict the cell formation phenomenon under vibratory loadings, and this example highlights the importance of a rigorous “all-dislocation” treatment since both the SSDs and GNDs have significant roles to play.
A second case study concerns size effects in crystal plasticity. The new model is found capable of capturing a number of key experimental features including the Hall-Petch relation in polycrystalline states, and power-law relation between strength and size in micro-crystals. In the former, dislocation pile-ups at grain boundaries, and in the latter case, low dislocation storage and jerky deformation, are predicted.
Keywords: Crystal plasticity; dislocations; dislocation-density functions; stress-strain behavior.
References:
[1] H.S. Leung, P.S.S. Leung, B. Cheng and A.H.W. Ngan, (2015), “A New Dislocation-density-function Dynamics Scheme for Computational Crystal Plasticity by Explicit Consideration of Dislocation Elastic Interactions”, Int. J. Plasticity, 67, 1-25.
[2] P.S.S. Leung, H.S. Leung, B. Cheng and A.H.W. Ngan, (2015), “Size dependence of yield strength simulated by a dislocation-density function dynamics approach”, Modelling and Simulation in Materials Science and Engineering, 23, 035001-1-27.
[3] B. Cheng, H.S. Leung and A.H.W. Ngan, (2015), “Strength of metals under vibrations – dislocation-density-function dynamics simulations”, Phil. Mag. 95 (Special Issue on Nanomechanical Testing), 1845-1865.
Bio: Professor Alfonso H.W. Ngan is currently Kingboard Professor in Materials Engineering, Chair Professor of Materials Science and Engineering, as well as Associate Dean of Engineering, at the University of Hong Kong. He obtained his BSc(Eng) degree from the University of Hong Kong in 1989, and PhD from the University of Birmingham in the U.K. in 1992. After a year of postdoctoral training at Oxford University, he joined HKU as a Lecturer in 1993, and was promoted through the ranks to Chair Professorship in 2011.
Professor Ngan’s research work is focused on the microstructural basis of properties of engineering materials, and, in particular, crystalline defects and their modeling, and more recently, nanomechanics including applications to biological systems. He has published over 180 ISI papers, and co-authored two books. His research-related honours include the prestigious Rosenhain Medal and Prize from the Institute of Materials, Minerals and Mining, U.K., in 2007 – he is the only non-British national so far to receive this award since its establishment in 1951. He was also awarded a higher doctorate (DSc) from his alma mater the University of Birmingham in 2008, and the Croucher Senior Research Fellowship in 2009 which is perhaps the highest honour awarded to academics in Hong Kong. In 2014, he was elected to the Hong Kong Academy of Engineering Sciences. He is a well sought-after journal reviewer and he won the Outstanding Reviewer Award of Scripta Materialia three times, in 2006, 2008 and 2011. He has organized a number of key conferences, including Dislocations 2008 and Gordon Research Conference on Nanomechanical Interfaces in 2013, both held in Hong Kong. He will serve as one of four Meeting Chairs in the Materials Research Society 2017 Spring Meeting to be held in the USA.
In this seminar, a new scheme for computational dynamics of dislocation-density functions, based on the above “all-dislocation” principle, is discussed. The dynamic evolution laws for the dislocation densities are derived by coarse-graining the individual density vector fields of all the discrete dislocation lines in the system, without distinguishing between GNDs and SSDs. The mutual elastic interactions between dislocations are treated in full by generalizing the elastic interactions between dislocation segments for dislocation densities, and reducing the Hirth-Lothe line-integral formulation into an algebraic form comprising only elementary functions which are straightforward enough for efficient numerical implementation. Other features in the model include forest (Taylor) hardening, stress due to dislocation curvature, generation due to the connectivity nature of dislocations, and dipole annihilation. Numerical implementation is by means of the finite volume method (FVM), which is well suited for high gradients often encountered in dislocation plasticity.
As a first case study, the model is utilized to predict vibration-induced softening and dislocation pattern formation experimentally observed in crystalline metals. The simulations reveal the main mechanism for subcell formation under oscillatory loadings to be the enhanced elimination of SSDs by the oscillatory stress, leaving behind GNDs with low Schmid factors which then form the subgrain walls. The depletion of the SSDs also accounts for the softening, and this occurs because the oscillatory loading brings reversals into the motions of SSDs which then increase their chance of meeting up and annihilation. This is the first simulation effort to successfully predict the cell formation phenomenon under vibratory loadings, and this example highlights the importance of a rigorous “all-dislocation” treatment since both the SSDs and GNDs have significant roles to play.
A second case study concerns size effects in crystal plasticity. The new model is found capable of capturing a number of key experimental features including the Hall-Petch relation in polycrystalline states, and power-law relation between strength and size in micro-crystals. In the former, dislocation pile-ups at grain boundaries, and in the latter case, low dislocation storage and jerky deformation, are predicted.
Keywords: Crystal plasticity; dislocations; dislocation-density functions; stress-strain behavior.
References:
[1] H.S. Leung, P.S.S. Leung, B. Cheng and A.H.W. Ngan, (2015), “A New Dislocation-density-function Dynamics Scheme for Computational Crystal Plasticity by Explicit Consideration of Dislocation Elastic Interactions”, Int. J. Plasticity, 67, 1-25.
[2] P.S.S. Leung, H.S. Leung, B. Cheng and A.H.W. Ngan, (2015), “Size dependence of yield strength simulated by a dislocation-density function dynamics approach”, Modelling and Simulation in Materials Science and Engineering, 23, 035001-1-27.
[3] B. Cheng, H.S. Leung and A.H.W. Ngan, (2015), “Strength of metals under vibrations – dislocation-density-function dynamics simulations”, Phil. Mag. 95 (Special Issue on Nanomechanical Testing), 1845-1865.
Bio: Professor Alfonso H.W. Ngan is currently Kingboard Professor in Materials Engineering, Chair Professor of Materials Science and Engineering, as well as Associate Dean of Engineering, at the University of Hong Kong. He obtained his BSc(Eng) degree from the University of Hong Kong in 1989, and PhD from the University of Birmingham in the U.K. in 1992. After a year of postdoctoral training at Oxford University, he joined HKU as a Lecturer in 1993, and was promoted through the ranks to Chair Professorship in 2011.
Professor Ngan’s research work is focused on the microstructural basis of properties of engineering materials, and, in particular, crystalline defects and their modeling, and more recently, nanomechanics including applications to biological systems. He has published over 180 ISI papers, and co-authored two books. His research-related honours include the prestigious Rosenhain Medal and Prize from the Institute of Materials, Minerals and Mining, U.K., in 2007 – he is the only non-British national so far to receive this award since its establishment in 1951. He was also awarded a higher doctorate (DSc) from his alma mater the University of Birmingham in 2008, and the Croucher Senior Research Fellowship in 2009 which is perhaps the highest honour awarded to academics in Hong Kong. In 2014, he was elected to the Hong Kong Academy of Engineering Sciences. He is a well sought-after journal reviewer and he won the Outstanding Reviewer Award of Scripta Materialia three times, in 2006, 2008 and 2011. He has organized a number of key conferences, including Dislocations 2008 and Gordon Research Conference on Nanomechanical Interfaces in 2013, both held in Hong Kong. He will serve as one of four Meeting Chairs in the Materials Research Society 2017 Spring Meeting to be held in the USA.
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- General public
- Free
Organizer
- Michele Ceriotti
Contact
- Michele Ceriotti