Discrete dislocation plasticity analysis of the wedge indentation of films

Abstract

Take-down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim.Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons the number of authors shown on this cover page is limited to 10 maximum. AbstractThe plane strain indentation of single crystal films on a rigid substrate by a rigid wedge indenter is analyzed using discrete dislocation plasticity. The crystals have three slip systems at AE35:3 and 90 with respect to the indentation direction. The analyses are carried out for three values of the film thickness, 2, 10 and 50 mm, and with the dislocations all of edge character modeled as line singularities in a linear elastic material. The lattice resistance to dislocation motion, dislocation nucleation, dislocation interaction with obstacles and dislocation annihilation are incorporated through a set of constitutive rules. Over the range of indentation depths considered, the indentation pressure for the 10 and 50 mm thick films decreases with increasing contact size and attains a contact size-independent value for contact lengths A44 mm. On the other hand, for the 2 mm films, the indentation pressure first decreases with increasing contact size and subsequently increases as the plastic zone reaches the rigid substrate. For the 10 and 50 mm thick films sink-in occurs around the indenter, while pile-up occurs in the 2 mm film when the plastic zone reaches the substrate. Comparisons are made with predictions obtained from other formulations: (i) the contact sizeindependent indentation pressure is compared with that given by continuum crystal plasticity; (ii) the scaling of the indentation pressure with indentation depth is compared with the relation proposed by Nix and Gao [1998

Multi-asperity contact: A comparison between discrete dislocation and crystal plasticity predictions

“…This condition is not required in the crystal plasticity calculations because they maintain symmetry about x 1 = 0. The connection between the stress state in the body and the evolution of the dislocation structure is given through a set of constitutive equations, similar to the ones proposed in [26] and used previously in [13] as well as in related investigations, [3,4,27]. These rules control the nucleation, glide, annihilation of dislocations as well as their pinning at obstacles.…”

“…Dislocations can exit the crystal through the top (x 2 = h) free surface, by the incompatibility of the disclocation displacement fields with the prescribed displacement boundary conditions in Eqs. (1)- (4). Dislocations do escape from the crystal along the free surface.…”

“…This is precisely the range in which plastic deformation of crystalline solids is known to be size dependent and thus not adequately described by conventional continuum plasticity theory. Discrete dislocation plasticity simulations have proven to be capable of capturing size-dependent plasticity in various situations, including (sub)micron-indentation with single indenters [1][2][3][4]. Recent models of contact between elastic-plastic rough surfaces have shown that interactions between neighboring asperity contacts play a critical role in determining the true area of contact between the surfaces [5][6][7].…”

“…However, there are circumstances involving plastic deformation in small volumes where long-range elastic dislocation interactions dominate which permits a wide range of complex phenomena involving plastic deformation to be represented qualitatively, e.g. [4,17,23], and, to a remarkable extent even quantitatively, e.g. [16,24].…”

Finite versus small strain discrete dislocation analysis of cantilever bending of single crystals

“…Following the pioneering work of Van der Giessen and Needleman [9], the DDP method has been shown to successfully predict numerous observations of plasticity size effects due to the above mentioned phenomena at the micron and sub-micron length scale. These include size effects in composites [10], bending [11], indentation [12], uniaxial compression [13], and under constrained shear [14]. The framework has also been used to investigate crack growth under monotonic [15] and fatigue loading [16].…”