| In real life,elastic-plastic finite deformation is a common phenomenon,such as metal extrusion and car collisions,etc.Material or structural failure often occurs with elastic-plastic finite deformation,even with fracture failure.In addition to this,fatigue damage fracture is one of the main failure modes of material or structure.In modern industry,aerospace equipment,ships,vehicles,etc.,undergo alternating loads due to the complexity of service conditions.Fatigue failure is the main failure mode of their parts or components,and studies show that 80%of component failures are allied with fatigue.Therefore,fatigue life is a crucial index in structural design.Both the analysis of elastic-plastic finite deformation and the prediction of fatigue life are related to the damage fracture of material or structures,which is always a nuisance in the study of solid mechanics.Peridynamics employs motion equations in the form of spatial integrals to determine pairwise interactions of material points within the horizon.Damage fracture is a part of the force state vector.Initiation and propagation of cracks occur naturally without additional criteria and have benefits in the simulation of discontinuity problems.In particular,non-ordinary state-based peridynamics has been developed rapidly as it can help directly introduce the constitutive model and failure criterion of traditional mechanics,which simulates complex mechanical problems.Therefore,investigating the calculation method of the elastic-plastic finite deformation and fatigue for non-ordinary statebased peridynamics is very critical.In the present study,some research about elastic-plastic finite deformation and fatigue calculation in the formwork of non-ordinary state-based peridynamics can be carried out.The main findings of the present study are as follows:1.The theory of non-ordinary state-based peridynamics and solution algorithms were studied.Furthermore,the non-uniform discretization calculation model was established.First,an adaptive dynamic relaxation scheme of non-ordinary state-based peridynamics was specified,and some benchmark problems,such as the tensile of the plate,the plate white center hole,and the bending of the cantilever beam,etc.,were simulated.Also,the correction coefficient of the force state vector was estimated using the volume-modified strain energy density function as a reference.The non-uniform discretization calculation model of non-ordinary state-based peridynamics was determined.The simulation of a plate with a center hole was performed to verify the calculation model,which is in good agreement with the analytical solution.It can effectively increase the calculation efficiency.2.An elastic-plastic theory of finite deformation for non-ordinary state-based peridynamics was established.In the framework of non-ordinary state-based peridynamics,the strain and stress and their corresponding objective rates were determined based on the reference configuration and present configuration,such as green strain,second Piol-Kirchhoff stress,true strain(Almansi strain),true stress(Cauchy stress),and their corresponding objective strain rate and objective stress rate.The objective rate forms of the force state vector consisting of the second Piol-Kirchoff stress and Cauchy stress separately were ascertained.Two kings of rate forms for non-ordinary stress and Cauchy stress separately were achieved.Two kings of rate forms for non-ordinary state-based peridynamics were established.The elastoplastic consecutive relations of finite deformation were elucidated using the Jaumann stress rate,Almansi strain rate,von Miss yield criteria,associated flow,and isotropic hardening rule under the framework of non-ordinary state-based peridynamics.Further,the updated Lagrange solution method to constitutive relations has also been proposed.The solution was employed to simulate the large elastoplastic tensile deformation of a rod and the large displacement analysis of a cantilever beam,and the results were consistent with the analytical solution.The solution was also applied to simulate the problem of a neck for cylindrical has been simulated,which was consistent with the experiment.3.In the finite deformation theory framework,the cycle fatigue calculating theories of non-ordinary state-based peridynamics for small strain and finite strain were established.First,the finite deformation small strain low cycle fatigue calculation theory in the rate form framework of non-ordinary state-based peridynamics was accomplished using mixed hardening models composed of Ohno-wang model II,the nonlinear isotropic hardening model,associated flow,and von Mises yield criteria.Further,the numerical solution method of the elastoplastic constitutive was specified.The simulations of the 316 L steel strain control symmetric cyclic test and the hardening and softening of peak stress with cycle number during low cycle fatigue can be captured in the simulation process.When the cumulative plastic strain was utilized as the failure criterion,the fatigue cracking process of Q235 steel can well capture the propagation process of fatigue cracks and predict the fatigue life of specimens.Second,the finite strain low cycle fatigue calculation theory in the rate form framework of non-ordinary state-based peridynamics was attained using the Almansi strain rate,Jaumann stress rate,and the cyclic elastoplastic constitutive equation.The simulations of fatigue life prediction of the T-type component were in good agreement with the experiment.4.By introducing Silling’s fatigue model,a high-cycle fatigue calculation method within the framework of non-ordinary state-based peridynamics was established,which can characterize fatigue nucleation and fatigue crack propagation.Based on the above results,the wheeler model was introduced to expand its ability to describe overload.The wheeler model was applied to simulate the fatigue crack nucleation and crack propagation of aluminum alloy dog bone specimens under constant and variable loads,which is consistent with the experimental results. |
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