SIZE EFFECTS IN METAL PLASTICITY
Experiments and dislocation dynamics simulations have shown that metallic materials display strong size effects at the micron and sub-micron scales, with smaller being stronger. Such size effects have been attributed to Geometrically Necessary Dislocations (GNDs) associated with inhomogeneous plastic flow and much research has been devoted to modeling observed size effects in the past two decades. Several continuum Strain Gradient Plasticity (SGP) theories have been developed in order to incorporate some length scale in the constitutive equations.
The influence of GNDs could be particularly relevant in fracture problems, as the plastic zone adjacent to the crack tip is physically small and contains strong spatial gradients of deformation. However, a very refined mesh near the crack-tip is needed to capture the effect of the strain gradients, increasing computation time and leading to several numerical problems. Consequently, the use of the eXtendend Finite Element Method (X-FEM) and other advanced numerical tools is expected to alleviate these issues and provide an appropriate numerical framework for modeling crack-tip fields accounting for size effects.
A numerical scheme within the framework of the X-FEM has been developed with the aim of tackling fracture problems by means of SGP theories. A mechanism-based gradient plasticity model is employed and the approximation of the displacement field is enriched with the stress singularity of the gradient-dominated solution. Results reveal that the proposed numerical methodology largely outperforms the standard finite element approach. The present work could have important implications for the use of microstructurally-motivated models in large-scale applications. The non-linear X-FEM code developed in MATLAB can be downloaded from www.empaneda.com/codes
E. Martínez-Pañeda, S. Natarajan, S. Bordas. Gradient plasticity crack tip characterization by means of the extended finite element method. Computational Mechanics, 59: 831-842 (2017)
Orbilu repository: http://orbilu.uni.lu/bitstream/10993/30226/1/CM2017.pdf
Other relevant references
E. Martínez-Pañeda and C. Betegón. 2015. Modeling damage and fracture within strain-gradient plasticity. International Journal of Solids and Structures, 59, pp. 208-215.
E. Martínez-Pañeda and C. F. Niordson. 2016. On fracture in finite strain gradient plasticity. International Journal of Plasticity 80: 154-167 (2016)