【作者】 张帆；

【导师】 黄克智； 黄永刚；

【作者基本信息】 清华大学 ， 力学， 2005， 博士

【摘要】 为了解释微米和亚微米量级实验中发现的尺度效应,以及解决工业领域在该尺度下遇到的日益增多的问题,人们建立了应变梯度理论。其中Huang等在MSG理论的基础上,发展了一套CMSG低阶应变梯度塑性理论。本文的主要工作就是利用CMSG理论研究一系列的具体问题。 我们首先对CMSG理论进行了改进,并在此基础上发展了考虑有限变形的次弹塑性CMSG本构模型。然后,我们研究了如下四个具体问题: (1) 颗粒增强复合材料问题。前人的研究采用轴对称模型,在模型侧面施加自由边界条件以模拟单向拉伸载荷。他们的结果与实验相比偏低。我们发展了一个三维单位胞元,在胞元侧面采用周期性协调边界条件,使胞元在变形前后与邻近胞元保持一致。结果表明,与自由边界条件相比,周期性协调边界条件的三维单位胞元模型大大改善了与实验的比较结果。 (2) 材料表面纹理加工中的应变梯度问题。问题被简化为一个圆柱压头压入刚性基体上铝膜的问题。我们研究了薄膜厚度、压头尺寸及压入深度对压头压力的影响。结果表明压力随膜厚的增加而趋于一个常数值,它可以表示成一个膜厚和压头半径的函数。 (3) 硬膜软基体(钨膜铝基体)系统压痕问题。我们扩展了CMSG理论以考虑体心立方金属钨的摩擦应力。计算结果与实验吻合较好。研究表明,铝基体中的应变梯度效应可以忽略,但钨膜中应变梯度效应在浅压痕时起重要作用。由于钨的内禀材料尺度很小,所以这种效应会迅速衰减。 (4) 纳米压痕硬度偏离Nix-Gao模型的问题。我们建立了一个基于最大允许几何必需位错(GND)密度的解析模型。模型给出了纳米压痕硬度和压入深度之间简单的函数关系,在压入深度较大时它可以退化到Nix-Gao模型。模型与MgO和铱的微压痕、纳米压痕实验都符合较好。我们也发展了考虑最大允许GND密度的CMSG理论,结果与实验符合很好。此外,我们还证明在不考虑最大允许GND密度情况下,压头尖端半径影响不能单独解释纳米压痕中的这种尺度效应。更多还原

【Abstract】 Strain gradient theories have been established to explain the size dependent effect and to solve the industrial problems at the micron and submicron scales. Huang et al. developed a conventional theory of mechanism-based strain gradient plasticity (CMSG), which is a low-order theory version of MSG. The major work of this dissertation is to investigate a series of problems with CMSG.At First, we improve the original CMSG and extend it to a hypoelastic-plastic constitutive model for finite deformation. And then, four problems are investigated, respectively, as follows.1. In particle-reinforced metal-matrix composite materials, particle size effect is studied with CMSG theory. Prior studies used axisymmetric models with vanishing lateral stress tractions in order to represent the uniaxial tension condition and their results fell short to agree with the experimental data. A three-dimensional (3D) unit-cell model is adopted in the present study. The periodic boundary conditions are imposed to ensure the consistency of the unit cell with its neighboring cells before and after the deformation. It is shown that the unit-cell model with the periodic boundary conditions gives much better agreements with the experimental data than the one with the traction-free boundary conditions on the lateral surfaces.2. The effect of strain gradient in surface texturing is studied by a simple indentation model, which describes the indenting of a cylinder indenter into an aluminum film on rigid substrate. We investigate the dependence of indenter force on film thickness, cylinder radius and indentation depth. With the increase of indentation depth, indenter force approaches a constant. An analytic formula is established to obtain the constants with different film thicknesses and indenter radii.3. The indentation of a hard tungsten film on soft aluminum substrate is studied with CMSG theory. We extend CxMSG to account for the effect offriction stress (intrinsic lattice resistance), which is important in body-center-cubic tungsten. The results agree well with experiments. It is also shown that the strain gradient effect is insignificant in the soft aluminum substrate, but is important in the hard tungsten thin film in shallow indentation. The strain gradient effect in tungsten, however, disappears rapidly as the indentation depth increases because the intrinsic material length in tungsten is rather small.4. At last, problems in nanoindentation are studied. The indentationhardness-depth relation established by Nix and Gao in 1998 agrees well withthe microindentation but not nanoidentation hardness data. We establish ananalytic model for nanoindentatin hardness based on the maximum allowabledensity of geometrically necessary dislocations (GND). The model gives asimple relation between indentation hardness and depth, which degenerates toNix-Gao model for microindentation. The model agrees well with bothmicron- and nanoindentation hardness data for MgO and iridium. We alsoextend CMSG to consider the maximum allowable GND density and find goodagreement with experiments. The indenter tip radius effect is also studied andthe results show that it cannot fully explain the nanoindentation size effectwithout accounting for the maximum allowable GND density.更多还原