CuZn37黄铜板料微塑性成形中的尺寸效应研究

为研究金属微塑性成形特点,对厚度不同及粗细两种晶粒尺寸的黄铜箔试样进行了单向拉伸和微弯曲实验,并采用经典塑性理论和应变梯度理论对弯曲回弹角进行了预测.粗晶粒板料试样单向拉伸实验表明,CuZn37黄铜的硬化曲线存在一种明显的尺寸效应,即板料厚度越小,屈服强度越高.弯曲回弹实验结果也存在另一种明显的尺寸效应现象,即板料厚度...     

基于一种新修正偶应力理论的平面正交各向异性功能梯度梁静弯曲模型及尺度效应

基于一种新修正偶应力理论建立了微尺度平面正交各向异性功能梯度梁模型。模型中包含两个材料尺度参数,因此能够分别描述在两个正交方向上由尺度效应带来的不同大小弯曲刚度增强。基于最小势能原理推导了平衡方程和边界条件,并以自由端受集中载荷作用的悬臂梁为例给出了弯曲问题的解析解。该梁模型的控制方程以及解的形式和经典梁模型是一致的,只是在刚度项中增加了一项和尺度效应有关的项。算例结果表明:采用本文模型所预测的梁挠度总是小于经典理论的结果,即捕捉到了尺度效应。尺度效应会随着梁几何尺寸的减小而增大,并在梁的几何尺寸远大于尺度参数时逐渐消失。     

微尺度悬臂管的空间弯曲振动-非线性运动方程及尺度效应EI北大核心CSCD

具有圆环形横截面的微尺度悬臂输液管可以同等地向空间各方向产生弯曲振动。按照欧拉-伯努利梁理论,在分析管道上点的位移及相关几何关系的基础上,考虑Lagrange应变张量所给出的几何非线性,基于修正的偶应力理论计算了管的应变能,运用Hamilton原理建立了微尺度悬臂输液管的空间弯曲振动的非线性动力学方程。研究了无量纲材料长度尺寸参数对系统动力学性质的影响,结果表明,尺度效应增大管道的临界流速,并使得稳定的平面周期运动(空间周期运动)在整个质量比区间上占的比例越大(小)。     

一种用微弯曲实验测定内禀材料长度的新方法

提出了一种用微弯曲实验测定材料的与应变梯度塑性相联系的内禀长度的新方法.由一组不同的加载时曲率半径Ri和对应的卸载后曲率半径RFi的比值与Ri的关系,求出屈服强度与杨氏模量的比和硬化系数与杨氏模量的比;再应用这两个比值求出不同样品厚度的无量纲弯曲力矩与表面应变的实验关系曲线,对曲线拟合求出材料的内禀长度.将这种方法用于测定铝的内禀材料长度,研究其弯曲强度的尺寸效应,所得结果与前人用微弯曲和微拉伸两种实验方法得到的结果符合得很好.     

微细铣削加工过程中微毛刺形成机理的模拟与实验分析

研究了采用硬质合金微铣刀铣削加工硬铝合金微槽结构时微毛刺的形成机理．建立了三维微细铣削加工硬铝合金A12024-T6的有限元模型,利用该模型动态模拟微毛刺的形成过程．分析了不同进给量与切削刃钝圆半径比值下微毛刺的形成机理,动态模拟了微槽加工过程中切削参数及切削刃钝圆半径变化对微毛刺影响的变化规律．仿真结果表明,随着每齿进给量、背吃刀量及切削刃钝圆半径的增加,微毛刺的尺寸随之增大;切削刃钝圆半径与最大有效应力是影响微毛刺尺寸的主要因素．微细铣削加工过程中,毛刺顶端所受最大有效应变明显比常规铣削加工过程中的最大有效应变高,呈现出显著的尺寸效应．通过微细铣削加工微槽实验,获得了切削参数及切削刃钝圆半径变化对微毛刺形成的影响变化规律,验证了相应有限元模型的正确性．通过数值模拟与实验方法获得了切削刃钝圆半径与毛刺尺寸（毛刺高度和毛刺厚度）的关系曲线,实验与仿真结果最大误差不超过9．8％．进一步验证了所建立的三维有限元模型适于研究并预测毛刺形成机理及毛刺尺寸的变化规律．     

双层微梁固有特性的尺寸效应

微尺寸梁存在明显尺寸效应,应变梯度理论可以描述这种尺寸效应。该文基于修正偶应力理论,应用双层梁与单层梁的等效关系,给出了双层微梁的动力学模型,具体求解了简支双层微梁的固有频率,并分析了微梁特征尺寸及双材料参数对双层微梁固有特性的影响规律。结果表明,当双层微梁的厚度接近材料内秉特征尺寸参数时,其固有频率值明显大于传统理论下的值;当双层微梁的厚度远大于材料内秉特征尺寸时,其固有频率值与传统理论下的值基本一致。双层微梁无量纲固有频率表现出明显尺寸效应,并随双材料参数的改变表现出一定的差异。当一层梁厚度远大于另一层厚度时,双层微梁可简化为单层微梁。     

微尺度悬臂管的空间弯曲振动-非线性运动方程及尺度效应

具有圆环形横截面的微尺度悬臂输液管可以同等地向空间各方向产生弯曲振动。按照欧拉-伯努利梁理论,在分析管道上点的位移及相关几何关系的基础上,考虑Lagrange应变张量所给出的几何非线性,基于修正的偶应力理论计算了管的应变能,运用Hamilton原理建立了微尺度悬臂输液管的空间弯曲振动的非线性动力学方程。研究了无量纲材料长度尺寸参数对系统动力学性质的影响,结果表明,尺度效应增大管道的临界流速,并使得稳定的平面周期运动(空间周期运动)在整个质量比区间上占的比例越大(小)。     

一种新型非调质钢弯曲疲劳性能的试样尺寸效应

使用液压伺服疲劳试验机考察一种新型(汽车前轴用)Nb+V复合微合金非调质钢的疲劳行为,绘制出S-N曲线并分析了疲劳断日特征,研究了其三点弯曲疲劳性能的试样尺寸效应及其原因.结果表明,试样的尺寸对非调质钢的三点弯曲疲劳性能有显著的影响,其三点弯曲疲劳极限随着试样尺寸的减小而增加,但是试样尺寸对疲劳试样的断口形貌几乎没有影响;在三点弯曲疲劳试验中,试样尺寸效应源于试样内部的应力梯度,小尺寸试样的应力梯度比大尺寸试样的高.     

金属圆棒试样室温下高应变速率拉伸试验浅析

在不同应变速率下对铸铁和铸铝圆棒试样进行了单轴高速拉伸试验,研究了它们的动态力学性能及断裂情况,分析了相关因素对试验的影响。结果表明:测试应变、应力的方法,试样标距长度及夹持端长度等对试验准确性和曲线振荡程度有较大影响;使用比刚度和比强度高的夹具、短标距试样、应变片测试应力、两台相机测试应变、适当增加夹持端长度可以提高试验结果的准确性。     

含约束薄膜的单轴拉伸的理论与数值研究

基于微态理论与应变梯度弹性理论框架,对含约束薄膜的单轴拉伸问题进行了研究。推导出在不同微观约束边界条件下薄膜单轴拉伸的解析解,较好的预测了薄膜内的边界层效应。通过分析两种理论之间的内在联系,发现可选取微态理论中的耦合因子作为罚参数,使得微态理论可以退化至应变梯度弹性理论。计算结果表明施加罚参数后的有限元解在边界层区域外...     

On the fracture of small samples under higher order strain gradient plasticity

In this work we perform Finite Element simulations within the framework of large deformation elasto-viscoplasticity on a material that is sensitive to the gradients of plastic strain and incorporates a single intrinsic length scale parameter. Both small scale yielding simulations and those on a finite sized sample show that large stress enhancements can occur at the tip of a notch due to gradient effects. The amount of plastic strain and opening stress that can be expected at the notch tip depends on an interplay between the notch radius, specimen dimensions and boundary conditions. It is shown that cleavage can be the favored criterion for failure in even a ductile material when the notch radius is small compared to the intrinsic length scale. Moreover, for large intrinsic length scales, failure may not always initiate at a notch but may be triggered away from it due to the presence of a boundary impermeable to dislocations.     

On the role of strain gradients in adiabatic shear banding

Summary The effect of higher order strain gradients on adiabatic shear banding is investigated by considering the simple shearing of a heat conducting thermoviscoplastic material with a gradient-dependent flow stress. The competition between the gradient-dependent plastic flow and heat conduction and their influence on the shear band width and structure are examined. Two internal length scales, i.e., the deformation internal length and the thermal internal length, are incorporated into the linear stability analysis, which shows that the band width size scales either with the square root of the strain gradient coefficient (in the absence of heat conduction) or the thermal conductivity (in the absence of strain gradients), respectively. The numerical computation for the nonlinear problem reveals that the diffusive effect of the strain gradient is much stronger than that of the heat conduction and dictates the constitutive response of the material in the postlocalization regime, and shows that the deformation length scale is much larger than the termal length scale. The band width predicted by the gradient theory agrees reasonably well with the experimental observations found in the literature.     

Numerical modeling of size effects with gradient elasticity - Formulation, meshless discretization and examples

A theory of gradient elasticity is used and numerically implemented by a meshless method to model size effects. Two different formulations of this model are considered, whereby the higher-order gradients are incorporated explicitly and implicitly, respectively. It turns out that the explicit gradient dependence leads to a straightforward spatial discretization, while use of the implicit gradient dependence can result in an awkward form of the stiffness matrix. For the numerical analyses the Element-Free Galerkin method has been used, due to its ability to incorporate higher-order gradients in a straightforward manner. Two boundary value problems have been considered, which show the capability of the gradient elasticity theory to capture size effects. In a follow-up paper, the formulation developed herein will be used to analyze additional configurations with attention to comparison with available experimental data on size effects and verification of available scaling laws for structural components.     

Microstructure-dependent fatigue damage process zone and notch sensitivity index

The development of simulation methods for calculating notch root parameters for purposes of estimating the fatigue life of notched components is a critical aspect of designing against fatigue failures. At present, however, treatment of the notch root stress and plastic strain field gradients, coupled with intrinsic length scales of grains or other material attributes, has yet to be developed. Ultimately, this approach will be necessary to form a predictive basis for notch size effects in forming and propagating microstructurally small cracks in real structural materials and components. In this study, computational micromechanics is used to clarify and distinguish process zone for crack formation and microstructurally small crack growth, relative to scale of notch root radius and spatial extent of stress concentration at the notch. A new nonlocal criterion for the fatigue damage process zone based on the distribution of a shear-based fatigue indicator parameter is proposed and used along with a statistical method to obtain a new microstructure-sensitive fatigue notch factor and associated notch sensitivity index, thereby extending notch sensitivity to explicitly incorporate microstructure sensitivity and attendant size effects via probabilistic arguments. The notch sensitivity values obtained for a range of notch root radii using the new statistical approach presented in this study predict the general trends obtained from experimental results available in literature.     

应变梯度塑性理论下超薄梁弯曲中尺度效应的数值研究

构造了一个在物理空间二次完备的应变梯度非协调单元,在验证了单元数值可靠性后,采用该单元详细研究了均布载荷作用下超薄梁弯曲中的尺度效应现象。计算结果与实验观测一致,即随着梁厚度的减小,其尺度效应增强。并发现在平面应力状态下,梁的梯度效应略强于平面应变状态。最后指出,尽管梁越薄,其梯度效应越强,但梁抗弯刚度仍随厚度的增加而增大。     

Size-dependent fracture and higher order J-integral for solids characterized by strain gradient elasticity

Elastic fracture is governed by the material's strain energy released rate and depends on the applied loads and the stiffness of the structure. The effect of stiffness on fracture as a function of structural size is typically modeled using strain-based elastic fracture mechanics, but recent experimental evidence indicated that when the size of the structure is on the order of the higher order material length scale parameters, elastic strain gradients would stiffen the structure. In this paper, the higher order J-integral and energy-released rate for the analysis of fracture of strain gradient stiffened structures are developed. The effects of beam size on the fracture behaviors of strain gradient stiffened cantilevers on a substrate were analyzed using the higher order J-integral and the energy-released rate. Analyses revealed that the fracture load is elevated to more than 1.4 times of the un-stiffened case when the bending stiffness is doubled by strain gradient stiffening. Elastic fracture is shown to have an added dependence on the size of the structure when strain gradient stiffening is non-negligible.     

Elastic mechanical behavior of nano-scaled FGM films incorporating surface energies

A general, global theory is developed for nano-scaled functionally graded films considering surface effects. In addition to the Kirchhoff hypothesis of the classical thin plate theory, the surface layers of the film are modeled by the continuum theory of surface elasticity. Bulk stresses on the surfaces are required to satisfy the surface balance conditions involving surface stresses. Unlike the classical plate theory, the bulk transverse normal stress is preserved here. By incorporating the surface energies into the principle of minimum potential energy, a series of non-classical governing differential equations which include intrinsic length scales are derived. To illustrate application of the theory, a simply supported nano-scaled film in cylindrical bending is investigated. Numerical examples are presented to clarify the effects of surface energies on the bending behavior of FGM films, whose effective elastic moduli are predicted using the Mori–Tanaka method. Finally, the nature of intrinsic length scales, and the effects of gradient index and aspect ratio on the displacements are discussed.     

Analysis of size effects based on a symmetric lower-order gradient plasticity model

Size effects become significant as soon as strain gradients are high. For instance the stress state around the crack tip cannot be described using conventional plasticity theory due to the extreme strain gradients and micro-structural metallurgical changes. To give an accurate prediction of the structure integrity and to quantify the material failure process, it is necessary to combine the strain gradients into constitutive equations. The present paper deals with developing a symmetric lower-order gradient-dependent constitutive model, which contains only the first-order gradient of equivalent plastic strain as regulator and introduces an intrinsic material length scale to take into account the micro-structure characteristics of materials. The flow stress is assumed linearly depending on the square root of first gradient of the equivalent plastic strain. Our analytical solutions for bending, torsion, void growth and interface stress fields show that the present model is computationally efficient to implement and may catch size effects in different geometries, in comparing with the known experiments. Furthermore, we are briefly discussing the micro-indentation based on the gradient plasticity. The quadratic dependence of the hardness on the inverse of the indentation depth is confirmed. The introduced intrinsic material length can be identified from the micro-indentation test.     

STRESS GRADIENTS AROUND NOTCHES

Abstract— Stress gradients at the root of a notch are significant for the notch effect and the size effect of fatigue properties. Usually the gradient of the stress distribution in the minimum section is considered. In the present paper the variation of the tensile stress along the edge of the notch is considered. Calculations are made for a variety of notches. The results indicate a remarkable conformity of stress distributions at the notch root if the same peak stress and notch root radius ( ρ ) apply. Consequently K ₁and ρare highly characteristic for the stress distribution around the notch. Along the edge of the notch the stress decreases at a much slower rate than in the minimum section going away from the material surface. For the stress along the edge of the notch a stress gradient coefficient is defined. The variation of this coefficient is fairly small for several notches and K ₁, values. A 5% lower stress as compared to the peak stress at the notch root is obtained at about 0.02 ρbelow the material surface and at a distance of about 0.18 ρalong the material surface.