微薄梁三点弯曲的尺度效应研究  

THREE-POINT MICROBEND SIZE EFFECTS FOR PURE NI FOILS

作　　者：冯秀艳[1] 郭香华[2] 方岱宁[2] 王自强[1] 

机构地区：[1]中国科学院力学研究所非线性力学国家重点实验室,北京100080 [2]清华大学工程力学系,北京100084

出　　处：《力学学报》2007年第4期479-485,共7页Chinese Journal of Theoretical and Applied Mechanics

基　　金：国家自然科学基金(10272103).~~

摘　　要：应用高灵敏度的力传感器以及时间序列电子散斑干涉法,同时测出了不同厚度纯镍薄片三点弯曲试件的抗力与变形,得到薄梁中心点处的载荷与挠度曲线．应用Fleck和Hutchinson的偶应力理论,结合平面应变弯曲模型,建立了薄梁处于弹性状态和弹塑性状态的控制方程,应用Runge-Kutta法进行数值求解,并将计算得到的载荷-挠度曲线以及无量纲化弯矩-表面应变曲线和实验结果进行了比较．在理论计算过程中,没有拟合任何材料参数,所有的材料参数均来自实验测量的结果,材料特征尺度也是根据Stolken和Evans的工作给出的．结果表明:应用偶应力理论预测的结果和实验结果符合良好,而经典理论的预测结果与实验不相符合．The three-point microbend tests are performed for the pure Ni foils with different thicknesses. The deflection and load are measured by employing the sequence pulse counting method and a high sensitive micro load-sensor, respectively. All experimental results are analyzed using couple stress theory by Fleck and Hutchinson in which only rotation gradient is considered. Based on the plane-strain model we have derived the differential equations and boundary conditions, which include the effect of couple stress. The differential equations are solved by the Runge-Kutta method. The numerical results are compared with the experimental data. There is no any fitting parameter in the present theoretical calculation. All material parameters are taken from the experimental measurements. The length scale is taken from the work of Stolken and Evans. The present theoretical predictions are in good agreement with the experimental data.

关 键 词：偶应力 微薄梁三点弯曲 应变梯度 RUNGE-KUTTA法 

分 类 号：O344.4[理学—固体力学]