| Developing a thorough understanding with an efficient and accurate prediction on shear bands is of great value and importance in improving the mechanical properties and optimizing the design of materials.Multi-scale crystal plasticity finite element method(CPFEM)simulations are applied to propose an approach that can quickly and accrurately predicting shear band formation and to study the mechanism and influence factors of shear banding systematically.By investigating the shear band development with three scales CPFEM simulations in quasi-static loading,the computational accuracy and cost among three scales on predicting the shear band formation with different degrees of strain localization are compared,and a highly economical approach is proposed to optimize the prediction on the extent and properties of shear banding.By comparing the shear band development among various strain rates,and also compared with simulations only considering texture evolution or thermal softening,a systematical study is applied to investigate the effect of crystallographic texture and strain rate on adabatic shear banding.The major conclusions are as follows.(1)A “two-step” approach that can quickly and accurately predict the probability and features of shear band formation is proposed: In the first step,the User-Defined Material Subroutine(UMAT)of Taylor-type polycrystal plasticity constitutive model is developed and combined with the finite element model consisting of one element in ABAQUS/Standard,i.e,one-element method,to compute the stress-strain curve of the deformation.The probability of shear band formation can therefore be estimated based on the hardening/softening feature of stress-strain curves.In the second step,a full scale simulation is applied for a further study on the details of the shear band development for cases with strong possibility of shear band formation as judged from the results in step 1.When it is needed to investigate probabilities and features of shear band formation in many samples or various loading modes,e.g.loading along different directions,the computation efficiency can be substantially improved by the “two-step” approach.The feasibility of “two-step” approach is verified by comparing the predictions on shear band formation through the two methods applied in two steps,respectively,during plane strain tension,compression and simple shear tests in the cold-rolled aluminum alloy sheet.It is demonstrated that the hardening/softening features of stress-strain curves obtained by oneelement method used in the first step are well agreed with the extent of macroscale shear band developments in grain-scopic scale simulations: softening or flat stress-strain curves correspond to the formation of severe shear bands in grain-scale simulation,and the stronger the softening is,the more severe the shear band is;no shear band is developed when the curves exhibit continuous and obvious hardening;.shear bands formed then localized when the curves exhibit rehardening following softening.(2)The accuracy and the computational cost in predicting the shear band development with different degrees of localization are compared among the macro-,grain-and subgrainscale CPFEM simulations.In macro-,grain-or subgrain-scale,each element represents an aggregate of polycrystal,a single crystal or part of a grain,respectively.The constitutive response of an integration point is thus described by the Taylor-type polycrystalline model in the macroscale,or by the single crystal constitutive model in the two finer scales.The three scale CPFEM simulations are applied to study the shear band development in coldrolled AA5182-H28 aluminum alloy sheets under simple shear along various directions with respect to the rolling direction.It is demonstrated that the capability to capture the development of shear bands with different degrees of localization is not the same for the three simulation scales: for cases with severe/no shear band forming,simulations in all the three scales can capture the features,however,for cases with weak shear banding,only the subgrain-scale simulations can give right predictions.The cost of the three scales is also quite different: the computation time increases nearly an order of magnitude when the simulation runs at a lower scale.Therefore,in view of both the accuracy and the cost,the “two-step” approach can be further optimized.In the first step,the one-element method is still applied to give a quick estimation for the extent of shear band development for all cases of concern.In the second step,appropriate simulation scale can be chosen according to the degree of localization: For cases with severe/no shear band forming,a macroscale simulation with Taylor-type model is sufficient to give good predictions;but for cases with weak shear bands formation,a subgrain-scale simulation is needed.(3)It is found that both the geometrical softening/hardening effect accompanying texture evolution and thermal softening effect under high strain rate loading determine the adiabatic shear band formation synergeticly.In view of the fact that the effects of strain rate on deformation relate to the rate sensitivity of materials,the adabitic shear band formation in both cold-rolled IF steels with high rate sensitivity and aluminum alloys with quite low rate sensitivity are investigated by building the crystal plasticity constitutive model and developing the Vectorized User Defined Material Subroutine(VUMAT)in ABAQUS/Explicit.The simulation results indicate that with thetexture without shear banding under quasi-static loading,thermal softening effect results in the adiabatic shear band formation under high strain rate loading,while the geometrical hardening only delays the occurrence of shear banding and enlarges the minimum strain for shear band formation.With the texture exhibiting shear banding under quasi-static loading,the geometrical and thermal softening promote shear band formation synergistically.Shear bands form at much lower strain rate and strain as well as with higher degree of localization,as compared to the cases that only one type of softening was switched on,in which geometrical softening induces shear band formation at any strain rates while thermal softening only induces shear band formation at high strain rates.With the texture exhibiting shear band formation then delocalization under quasi-static loading,the thermal softening effect intensifies the degree of strain localization of initial shear banding,retards the delocalization of the initial shear banding and “re-uniforming” of the strain,and then leads to the adiabatic shear band formation at large strains in high-strain-rate dynamic loading;while the retard from geometrical hardening on adiabatic shear band formation is more severe than in the situation where texture evolution induces only geometrical hardening without geometrical softening. |
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