Subsurface microstructure alteration has been a major concern to implement micromachining of titanium alloy in the high-tech industry. To quantitatively promulgate the underlying mechanisms of this alteration, a discrete dislocation dynamics-based model is proposed and used to simulate the subsurface defects and their evolution under different cutting conditions. The model considers the subsurface dislocation configuration and inner stress distribution during the orthogonal cutting of titanium alloy. The results show that subsurface defect structure consists of plenty of dislocation dipoles, twining dislocation bands, and refined grains after cutting. In the primary shear zone, two different characteristics of subsurface damage layers can be found, the near-surface damage layer and deep-surface damage layer, which have different structural natures and distribution features. Moreover, it is found that high cutting speed and small depth of the cut can suppress the formation and propagation of subsurface defects. A powerful inner stress state would promote the distortion of the lattice and result in a microcrack within the subsurface matrix. The simulation results have been compared with experimental findings on the machined surface and subsurface of similar materials, and strong similarities were revealed and discussed.

In this study, a mesoscale dislocation simulation method was developed to study the orthogonal cutting of titanium alloy. The evolution of surface grain structure and its effects on the surface mechanical properties were studied by using two-dimensional climb assisted dislocation dynamics technology. The motions of edge dislocations such as dislocation nucleation, junction, interaction with obstacles, and grain boundaries, and annihilation were tracked. The results indicated that the machined surface has a microstructure composed of refined grains. The fine-grains bring appreciable scale effect and a mass of dislocations are piled up in the grain boundaries and persistent slip bands. In particular, dislocation climb can induce a perfect softening effect, but this effect is significantly weakened when grain size is less than 1.65 μm. In addition, a Hall–Petch type relation was predicted according to the arrangement of grain, the range of grain sizes and the distribution of dislocations.

In this paper, we consider a scalar Peierls--Nabarro model describing the motion of dislocations in the plane (x1,x2) along the line x2=0. Each dislocation can be seen as a phase transition and creates a scalar displacement field in the plane. This displacement field solves a simplified elasto-dynamics equation, which is simply a linear wave equation. The total displacement field creates a stress which makes move the dislocation itself. By symmetry, we can reduce the system to a wave equation in the half plane x2>0 coupled with an equation for the dynamics of dislocations on the boundary of the half plane, i.e. on x2=0. Our goal is to understand the dynamics of well-separated dislocations in the limit when the distance between dislocations is very large, of order 1/ɛ. After rescaling, this corresponds to introduce a small parameter ɛ in the system. For the limit ɛ → 0, we are formally able to identify a reduced ordinary differential equation model describing the dynamics of relativistic dislocations if a certain conjecture is assumed to be true.

In this paper, we develop an efficient numerical method based on the boundary integral equation formulation and new version of fast multipole method to solve the boundary value problem for the stress field associated with dislocations in a finite medium. Numerical examples are presented to examine the influence from material boundaries on dislocations.

We prove existence of minimizing movements for thedislocation dynamics evolution law of a propagating front, in which the normal velocity of the front is the sum of a non-local term and a mean curvature term. We prove that any such minimizing movement is a weak solution of this evolution law, in a sense related to viscositysolutions of the corresponding level-set equation. We also prove theconsistency of this approach, by showing that any minimizing movementcoincides with the smooth evolution as long as the latter exists. Inrelation with this, we finally prove short time existence and uniqueness of a smoothfront evolving according to our law, provided the initial shape issmooth enough.