A Peridynamics-based Approach For Discrete Dislocation Dynamics Simulation: Model And Applications

The evolution of dislocations is the main reason for the plastic deformation of crystal materials.Discrete dislocation dynamics(DDD),a numerical method based on the elastic theory of dislocations,can be applied to reproduce the plastic properties of crystalline materials,by tracking the dynamic evolution of discrete dislocations and the interaction between dislocations and other defects or obstacles.However,the current DDD models are based on the classical continuum theory.When dealing with displacement discontinuities like damage and cracks,special treatments(e.g.,presetting crack paths)need to be introduced,which adversely affects the simulation accuracy of plastic cracking in crystalline materials.Peridynamics(PD)is a nonlocal alternative to classical continuum mechanics.The governing equations in a PD model use spatial integration,making it well-suited for problems in which discontinuities,such as cracks,may occur and evolve.In this dissertation,a new DDD method in the framework of peridynamics(DDD-PD)is developed and employed to simulate and analyze elastoplastic deformation,damage and fracture behavior in crystalline materials.The main contents and conclusions of this dissertation are as follows:(1)A new DDD algorithm based on the nonlocal PD theory is proposed,and the DDDPD model is established.By avoiding singularity,the new DDD-PD model allows cracks to initiate and propagate autonomously,and can automatically track the evolution of interfaces,cracks,and boundaries without additional treatment.Compared with the classical DDD methods,the DDD-PD model has a more straightforward calculation process and more realistic crack growth results.(2)The new DDD-PD model is verified by solving several typical boundary value problems.The simulation results from the new method are compared with theoretical solutions and those calculated by the other DDD models.The comparisons indicate: the DDD-PD model can accurately calculate the dislocation-dislocation,dislocation-crack and dislocation-void interactions;the superposition algorithm for the DDD-PD model is more accurate than the discrete-continuous algorithm;bond-based DDD-PD is limited by Poisson’s ratio,but its computational efficiency is higher than that of state-based DDD-PD.(3)Based on the new DDD-PD model,the elastoplastic deformation behavior of crystalline and polycrystalline materials under uniform or non-uniform loading is numerically studied,and the dislocation evolution mechanism of the elastoplastic response in crystalline materials is discussed.The numerical results indicate: the yield stress of a single crystal under uniaxial tension follows the Schmid law;the valley stresses decrease with increasing strain rates due to the simultaneous nucleation of more dislocations at the higher strain rates,but the peak stresses are independent of the strain rates;the dependence between the grain size of polycrystals and the nominal yield stress follows the Hall-Petch law,i.e.,decreasing grain size increases the plastic hardening rate and the nominal yield stress.(4)The orientation and size effects of a single crystal’s Mode I elastoplastic fracture are investigated,and the intrinsic mechanisms of elastoplastic deformation and fracture are studied.The simulation results indicate: dislocations tend to nucleate and glide on the slip planes with a larger Schmid factor;the nucleation and evolution of dislocations and the interaction between dislocations and cracks affect the fracture behavior in crystals;different orientations or sizes lead to differences in the crystal’s fracture pattern and toughness;and the toughness increase with decreasing the crystal size.(5)The elastoplastic deformation and fracture in gradient-structured(GS)and homogeneous-structured(HS)polycrystals are modeled,and the effects of polycrystalline structure and gradient orientation on crack propagation and dislocation evolution are analyzed,respectively.The modeling results indicate: the crack path is more tortuous in the zone with smaller grain sizes;the deflection of the crack path is consistent with the deflection of the main slip direction.The GS polycrystals are better than the HS polycrystals in the balance of mechanical properties(e.g.,strength,ductility,and fracture resistance),and the gradient orientation has a significant effect on these properties and the fracture propagation.