A New Deformation Theory with Strain Gradient Effects

A new phenomenological deformation theory with strain gradient effects is proposed. This theory, which belongs to nonlinear elasticity, fits within the framework of general couple stress theory and involves a single material length scale l. In the present theory three rotational degrees of freedom omega(i) are introduced in addition to the conventional three translational degrees of freedom u(i). omega(i) has no direct dependence upon ui and is called the micro-rotation, i.e. the material rotation theta(i) plus the particle relative rotation. The strain energy density is assumed to only be a function of the strain tensor and the overall curvature tensor, which results in symmetric Cauchy stresses. Minimum potential principle is developed for the strain gradient deformation theory version. In the limit of vanishing 1, it reduces to the conventional counterparts: J(2) deformation theory. Equilibrium equations, constitutive relations and boundary conditions are given in details. Comparisons between the present theory and the theory proposed by Shizawa and Zbib (Shizawa, K., Zbib, H.M., 1999. A thermodynamical theory gradient elastoplasticity with dislocation density Censor: fundamentals. Int. J. Plast. 15, 899) are given. With the same hardening law as Fleck et al. (Fleck, N.A., Muller, G.H., Ashby, M.F., Hutchinson, JW., 1994 Strain gradient plasticity: theory and experiment. Acta Metall. Mater 42, 475), the new strain gradient deformation theory is used to investigate two typical examples, i.e. thin metallic wire torsion and ultra-thin metallic beam bend. The results are compared with those given by Fleck et al, 1994 and Stolken and Evans (Stolken, J.S., Evans, A.G., 1998. A microbend test method for measuring the plasticity length scale. Acta Mater. 46, 5109). In addition, it is explained for a unit cell that the overall curvature tensor produced by the overall rotation vector is the work conjugate of the overall couple stress tensor. (C) 2002 Elsevier Science Ltd. All rights reserved.

微薄梁三点弯曲的尺度效应研究

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.

A microbent fiber optic pH sensor

Optical fiber sensors developed for measuring pH values usually employ an unclad and unstrained section of the fiber. In this paper, we describe the design and fabrication of a microbent fiber optic sensor that can be used for pH sensing. In order to obtain the desired performance, a permanently microbent portion of a plastic optic fiber is coated with a thin film of dye impregnated sol–gel material. The measurements are simultaneously carried out in two independent detection schemes viz., the bright field detection configuration for detecting the core modes and dark field detection configuration, for detecting the cladding modes. The results of measurements of core mode-power and cladding mode-power variation with change in pH of a solution surrounding the coated portion of the fiber is presented. This paper thus demonstrates how a bare plastic fiber can be modified for pH sensing in a simple and cost effective manner.

Microbent optical fibers as evanescent wave sensors

Microbent optical fibers are potential candidates for evanescent wave sensing. We investigate the behavior of a permanently microbent fiber optic sensor when it is immersed in an absorbing medium. Two distinct detection schemes, namely, bright-field and dark-field detection configuration, are employed for the measurements. The optical power propagating through the sensor is found to vary in a logarithmic fashion with the concentration of the absorbing species in the surrounding medium. We observe that the sensitivity of the setup is dependent on the bending amplitude and length of the microbend region for the bright-field detection scheme, while it is relatively independent of both for the dark-field detection configuration. This feature can be exploited in compact sensor designs where reduction of the sensing region length is possible without sacrificing sensitivity.