8th May Dislocations meeting

Prof Dr Markus Lazar, Head of the Heisenberg Research Group, Darmstadt University of Technology, will be visiting the department from 6th to 9th of May. 
 
On May 8th, we will hold a “mini-workshop” in the 21 Banbury Road Committee Room. Please email Steve Fitzgerald if you would like to attend.  
 
10.30 Prof Lazar: Non-singular Dislocations in the Theory of Gradient Elasticity
 
The fundamental problem of non-singular dislocations in the framework of the theory of gradient elasticity will be presented in this talk. A general theory of non-singular dislocations is developed for linearly elastic, infinitely extended, homogeneous, and isotropic media. Dislocation loops and straight dislocations are investigated. Using the theory of gradient elasticity, the non-singular fields which are produced by arbitrary dislocation loops are given. `Modified' Mura, Peach-Koehler, and Burgers formulae are presented in the framework of gradient elasticity theory. These formulae are given in terms of an elementary function, which regularizes the classical expressions, obtained from the Green tensor of the Helmholtz-Navier equation. Using the mathematical method of Green's functions and the Fourier transform, exact, analytical, and non-singular solutions were found. The obtained dislocation fields are non-singular due to the regularization of the classical singular fields.
 
2.00 Beñat Gurrutxaga Lerma (Imperial College, London): A study of the attenuation of the dynamic yield point using dynamic discrete dislocation plasticity
 
In crystalline materials subjected to dynamic shock loading, the yield point that marks the onset of plasticity is usually identified as the "Hugoniot Elastic Limit" (HEL). The HEL is a well-defined value of materials subjected to rapid compressive loads. However, upon being shocked, crystalline solids do not display the HEL straight away; rather, the yield point tends to decrease as the shock front advances, ranging from the shocked state value down to the HEL. This attenuation of the `dynamic' yield point, also known as the `decay of the elastic precursor', is one of the most striking features of dynamic plasticity, because the traditional understanding of plasticity based in the quasi-static theory of dislocations fails to predict it. In this talk, I will introduce a new method of 2D dislocation dynamics that includes the full elastodynamic solutions for the creation and non-uniform motion of straight edge dislocations. Using this new methodology, I will show that the most relevant features of the attenuation of the dynamic yield point can be successfully explained as the result of the interaction between dislocations created at the shock front with the shock front itself.
 
3.00 Tom Swinburne (Imperial College, London): Stochastic and Crystallographic Dislocation Dynamics
 
Whilst elasticity plays a crucial role in dislocation dynamics, other forces are at work in any real environment. It is well known that the discrete core structures can give rise to significant migration barriers, but the stochastic, dissipative effect of thermal forces remains poorly understood. This lack of quantitative knowledge is alarming, given the prominence of drift and diffusion in experiment and the purely dissipative mobility laws used in all DD simulations.
 
In my talk I will discuss methods to accurately simulate thermal forces in dislocation dynamics and analyse the resultant behaviour in various illustrative scenarios. I will also explain how these forces can be parametrised from atomistic calculations, and, if time allows, briefly introduce a new projection operator approach which can provide quantitative predictions of the thermal forces on defects and dislocations.
 
 
 
Registered attendees: Daniel Thompson, Tom Hudson, Alexander Korsunsky, Ricky Ying, Matthew Ryder, Pierluigi Cesana, Jianan Hu, Felix Hoffman, Francesco Ferroni, John Ockendon, Matthew Noble, Jon Chapman