Lower-order mechanism-based strain gradient plastic model considering stress gradient effect
Numerous experimental studies have demonstrated that when the characteristic length of nonuniform plastic deformation of metal materials reaches the micrometer level,the mechanical behavior of the material exhibits a significant size effect.Unlike traditional plasticity theory,strain gradient plasticity theory can effectively describe size effects induced by nonuniform deformation by introducing intrinsic length dimensions.The high-order strain gradient plasticity theory can effectively account for the size effects of materials during the initial yield and subsequent hardening stages.However,the finite element implementation of the theory is relatively complex.Moreover,the low-order strain gradient plasticity theory struggles to explain the size effect of microscale metal materials at the initial yield stage because it overlooks microstructure effects.Considerably,this article considers the stress gradient effect and proposes a low-order strain gradient plastic model capable of describing the size effect throughout the plastic deformation stage.The applicability and effectiveness of the model are verified through comparison with experimental data.Using the torsion of fine copper wire as an example,the contributions of strain gradient and stress gradient effects to the plastic hardening of fine copper wire torsion were quantified,and the evolution of geometrically necessary dislocation density and its spatial distribution characteristics were elucidated.Results indicate that the normalized yield torque of fine copper wire increases with the stress gradient during torsion.However,the strain gradient effect is not significant at＜0.05 shear strain.As the torsion angle increases,the plastic strain gradient grows,leading to an increase in the density of geometrically necessary dislocations,and the hardening gradually becomes dominated by the strain gradient effect.
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