Deformation Mechanism Based Constitutive Modeling Of Gradient Structured Materials

Combining high strength and high ductility in material has been an important goal of materials research over many decades.Unfortunately,the two properties tend to be mutually exclusive.For example,coarse-grained metals usually exhibit satisfactory ductility,but low yield strength.When the grains in metals are refined to the submicron-or nano-scale,fewer dislocations pile up in front of grain boundaries due to the diminishing space.As a consequence,larger stress is required to assist the leading dislocation of a pileup in overcoming the grain boundary barrier,and the yield strength may increase significantly.On the other hand,the diminishing importance of dislocation multiplication and storage in the grain interiors reduces the strain hardening capability of the material.As a result,metals with finer grains often suffer from reduced ductility.Gradient structured(GS)materials exhibit spatially heterogeneous grain size distributions,with grain sizes changing from the submicron or nano-scale in the near-surface region to the micrometer scale in the core of a sample.The gradual change of grain sizes in GS materials avoids sharp discontinuities in mechanical properties that may lead to stress concentration and failure,and strain localization can be effectively suppressed during plastic deformation.Therefore,the advantages of high strength of the nano-grains and high ductility of the coarse-grains can be reconciled.Furthermore,the unique microstructure of GS materials enables scientists to optimize them by controlling the grain size distribution or the volume fraction of the graded region.Complementary to experimental investigation,constitutive modeling is an efficient way to guide the microstructural design of advanced materials for achieving better performances in engineering service.However,comparing with abundant experimental works on the preparation,characterization and mechanical testing of GS materials,the relevant strengthening and strain hardening mechanisms remain unclear,and the deformation mechanisms based constitutive model is lacking,which restricts the design of the GS materials to only experimental trial.Furthermore,since the back stress strengthening/strain hardening mechanisms are also not well clarified yet,constitutive models for the cyclic deformation of GS materials have not been reported yet,which further retards their engineering service.Therefore,in this dissertation,in view of the strengthening and strain hardening mechanisms of GS materials,and the construction of deformation mechanisms based constitutive model,the following works are conducted:(1)Based on the interaction mechanisms of blocking and transmission between dislocation and grain boundary,a new nonlocal crystal plasticity model is developed and implemented into the Düsseldorf Advanced Material Simulation Kit(DAMASK).Then the developed model is employed to study the tensile mechanical response of the GS materials,and to investigate the influences of geometrically necessary dislocations(GNDs)and back stress on the tensile deformation of GS materials.In this model,the dislocations are distinguished into positive edge type,negative edge type,positive screw type,negative screw type and dislocation dipole.Apart from the contributions of dislocation multiplication,annihilation and the change of dislocation state to the total dislocation density,a dislocation flux term basing on the spatial gradients of dislocation slip is also derived.Furthermore,the interfaces can be identified by judging the orientation difference in adjacent grains.The simulation results of homogeneously-grained and GS materials demonstrate that the smaller the grain size is,the higher the GNDs density is,and the higher the back stress is,indicating that the high back stress in GS materials mainly comes from fine grains.(2)Based on the deformation mechanisms revealed in(1),a multiple-mechanism-based constitutive model,in which constitutive laws for GNDs and back stress at both grain level and sample level are established.According to a conventional theory of mechanism-based strain gradient(CMSG)plasticity model,the GNDs are further distinguished into grain level GNDs and sample level GNDs.The former one is derived by the dislocation pileup model,form which the relationship between back stress and grain size is also constructed.Then,the established model is implemented into a finite element software ABAQUS by the user subroutine.Finally,the model is used to simulate the tensile deformation of homogeneouslygrained materials with grain size changing from nanoscale to microscale to validate the model and obtain parameters.(3)Based on the constitutive model established in(2)and the obtained parameters,the model and parameters are further applied to predict the tensile deformation responses of a GS copper,the prediction results are in good agreement with experimental ones.Then,the strength-ductility mapping of GS copper is also constructed by controlling the grain size distribution and the volume fraction of the graded region.The constitutive model predicts an inverse linear relationship between strength and ductility of GS copper with various microstructure characteristics,which is in a qualitative agreement with experimental observations.Furthermore,the tensile-compressive responses of a GS copper bar are also well predicted using the same model and parameters stated above.The back stress hardening mechanism shown here is in accordance with that revealed by the crystal plasticity finite element simulations in(1).