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Abstract:In this study, a mesoscale dislocation simulation method was developed to study the orthogonal cutting of Titanium alloy. The evolution of the surface grain structure and its effects on the mechanical properties was studied using two-dimensional climb assisted dislocation dynamic technology. The motions of edge dislocations in an elastic matrix such as dislocation nucleation, lock, interaction with obstacles and grain boundaries, and annihilation were tracked. The results showed that the machined surface has a graded microstructure composed of ultrafine grains. A grain refinement process was observed in micro-cutting of titanium alloy. The process can be described as follows: (i) the development of dislocation lines in original grains, (ii) the formation of dense dislocation bands, (iii) the transformation of dislocation bands into subgrain boundaries, and (iv) the continuous dynamic recrystallization in subgrain boundaries. The fine-grains formed in this process bring appreciable scale effect and a mass of dislocations pile up in the grain boundary and persistent slip band (PSB). In particular, the flow stress and hardening rate was reduced by dislocation climb. However, this effect is significantly weakened when grain size was less than 1.65 µm. In addition, a Hall-Petch type relation is predicted depending on the amount of slips, the dislocation density, the grain arrangement and the range of grain sizes to which a Hall-Petch expression is fit. The numerical results obtained were compared with experimental data gathered from literature and a satisfied agreement was found.

The impact resistance of fiber-reinforced polymer composites is a critical concern for structure design in aerospace applications. In this work, experiments were conducted to evaluate the impact performance of four types of composite panels, using a gas-gun test system. Computational efficient finite element models were developed to model the high-speed ballistic impact behavior of laminate and textile composites. The models were first validated by comparing the critical impact threshold and the failure patterns against experimental results. The damage progression and energy evolution behavior were combined to analyze the impact failure process of the composite panels. Numerical parametric studies were designed to investigate the sensitivity of impact resistance against impact attitude, including impact deflection angles and projectile deflection angles, which provide a comprehensive understanding of the damage tolerance of the composite panels. The numerical results elaborate the different impact resistances for laminate and textile composites and their different sensitivities to deflection angles.

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Garey and Johxon have proved that the problem to determine the crossing number of graphs is NP-complete. Because of its difficulty, presently we only know the crossing number of some classes of special graphs. The crossing number of cartesian products of paths and cycles with 5-vertex graphs mostly are known, but only few cartesian products of 5-vertex graphs with star n K , 1 are known. In this paper, we extent those results,and determine the crossing numbers of cartesian products of two 5-vertex graphs with star n K , 1 .

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