考虑应力梯度效应的低阶应变梯度塑性模型

Lower-order mechanism-based strain gradient plastic model considering stress gradient effect

大量实验研究表明,当金属材料非均匀塑性变形的特征长度在微米量级时,材料力学行为呈现出很强的尺寸效应.不同于传统塑性理论,应变梯度塑性理论通过引入内禀长度尺寸可有效地描述因非均匀变形引起的尺寸效应.高阶应变梯度塑性理论可同时捕捉材料在初始屈服和后续硬化阶段的尺寸效应,但其有限元实现较为复杂;低阶应变梯度塑性理论则难以解释消除微结构效应的微尺度金属材料在初始屈服时的尺寸效应.鉴于此,本文考虑应力梯度效应,发展了能够描述整个塑性变形阶段尺寸效应的低阶应变梯度塑性模型,并通过与实验数据进行对比,验证了其适用性与有效性.以细丝扭转为例,量化了应变梯度和应力梯度效应对细铜丝扭转塑性硬化的贡献,阐明了细铜丝扭转的几何必需位错密度演化及其空间分布特征.结果表明,细铜丝扭转时归一化屈服扭矩会随应力梯度的增大而增大,而应变梯度效应在剪应变小于0.05时并不明显;随扭转角度的增大,塑性应变梯度增加,几何必需位错密度增加,硬化逐渐由应变梯度效应主导.

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.