Analysis Of Crack Propagation Based On Improved Beam-type Bond-based Peridynamic Model

The mechanical parts may be deformed,damaged and broken during the mechanical load of automobile collision and impact,which may lead to safety accidents.Therefore,it is necessary to fundamentally figure out the mechanical response characteristics and deformation failure laws of materials under external load,which is of great significance for the safety protection of automobile parts.Peridynamics is suitable for describing the damage of micromedia and the formation of macro-cracks,which include two versions of "bond-based" and "state-based" peridynamic theory.Since the calculation process of the state-based model is more complicated than the bond-based model,the latter is more widely used in practical applications.However,it is difficult for the existing bond-based model to take into account the accuracy and effectiveness of numerical calculation,and mesh discretization strategy when performing crack propagation analysis.Therefore,the research work in this paper focuses on solving the problems of the bond-based model,such as the accuracy and efficiency of numerical implement,and the applicability of the grid and so on.Firstly,in order to solve the problem that the traditional model cannot truly describe the material parameters and characteristics in the simulation of deformation and crack propagation,the mathematical constitutive of the bond-based peridynamic model based on Timoshenko beam theory is introduced.Then,in order to improve the accuracy and convergence stability of numerical quantitative calculation of the mentioned model,a virtual node integration algorithm is proposed,and at the same time,the efficacy of an influence function that reflects the change of the stiffness of the bond with the distance between the particles weakens the effect of the surface effect.The improved beam-type bond-based peridynamic model is established by comparing and analyzing the results of convergence and calculation accuracy of strain energy density with different types of discrete grids.Secondly,to verify the effectiveness of the improved beam-type bond-based peridynamic model,the uniaxial stretching and transverse shear of the grid properties of square,triangle,and quadrilateral and triangle mixed grids are investigated respectively.By comparing the average relative error value and convergence of node displacement of different mesh sizes,the improved beam-type bond-based peridynamic model has good applicability of the grid and accuracy and efficiency of the numerical examples when dealing with different types of discrete grids.Finally,the bond damage criterion considering the rotation of the material point is used to simulate the crack growth of different material models with a preset crack based on the improved beam-type bond-based peridynamic model.Several representative crack problems are simulated respectively: the uniaxial stretching of a pre-cracked rectangular plate with different types of discrete grids are simulated.The crack propagation path and the propagation speed of the crack tip with different grid types are analyzed,it is mentioned that the simulation results are in good agreement with the test results.The uniaxial tension of the pre-cracked rectangular plate with off-set circular hole in the hybrid grid is simulated,as the distance between the pre-crack and the hole decreases,the closer the crack propagation path is to the hole.And the brittle fracture of the cracked plate under impact load is simulated based on the Kalthoff-Winkler test model.The obtained crack propagation path is in good agreement with the test result.