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...     

纳米材料微阵列超塑微成形机理与尺度效应

微成形技术是未来批量制造高精密微小零件的关键技术,但是,微小尺度下材料的塑性变形行为不仅表现出明显的尺度效应,而且零件尺度已经接近常规材料的晶粒尺寸,每个晶粒的形状、取向、变形特征对整体变形产生复杂的影响,难以保证微成形的工艺稳定性。本项目采用纳米材料进行微成形,制造微阵列,零件内部包含大量的晶粒,可以排除晶粒复杂性的影响,而且纳米材料具有超塑性,在超塑状态下,变形抗力和摩擦力都明显降低,从而显著降低微成形工艺对模具性能的苛刻要求,提高工艺稳定性和成形精度。目前,纳米材料超塑性微成形技术方面的研究极少,变形时纳米材料的力学行为、变形机理、尺度效应、位错演化、力学模型等关键问题还有待研究。采用电沉积技术制备晶粒尺寸可控的纳米材料,将工艺实验研究、性能测试、组织分析、力学性能表征、数值模拟相结合,深入探究了纳米材料微阵列超塑性微成形机理和成形规律,以促进该技术的广泛应用。     

多孔材料剪切局部化中的尺寸效应

微孔洞的尺寸对于孔洞长大率的影响显著,研究了这种尺寸效应在延性材料的塑性流动局部化中的作用.在拓展的Gurson模型基础上,采用Rice提出的一个简单的模型,剪切带内外的材料在发生塑性流动局部化时分别为不同的响应,讨论了孔洞尺寸a和初始孔洞体积百分比f0的影响.结果表明:考虑孔洞尺寸后单轴拉伸曲线变化比较大,但剪切带角度几乎没有变化.     

非均质材料微成形过程的晶体塑性模拟

微塑性成形中,由于参与变形的晶粒数量有限,材料非均质现象显著,基于均匀化假设的宏观弹塑性模型不再适用,为了研究有限数量晶粒组成的材料塑性变形过程,需结合其微结构与微观塑性变形机制.参照金属材料的微结构,构建了非均质多晶模型,采用晶体塑性本构关系和Cauchy应力更新算法,设计了材料子程序(VUMAT),对含不同晶粒数目的圆形板料拉深过程进行模拟分析.研究表明,非均质多晶板料成形的筒形件具有明显制耳,但制耳轮廓无规律.晶粒数目增加会弱化材料非均质现象,使制耳高度降低,但又引起晶粒间约束增强,使拉深力小幅增长.     

有限元法在粉末成形中的应用

对粉末成形的本构方程和有限元列式进行了系统全面的推导，并详细分析和讨论了有限元法分析粉体成形时的关键技术及目前粉末成形数值模拟存在的问题。     

金属塑性成形过程中的多尺度建模方法

金属塑性成形涉及到多尺度问题,进行多尺度建模仿真是研究金属塑性成形成性一体化理论与技术的重要途径。综述了目前国内外重要的多尺度建模方法,着重分析了多尺度层阶建模思路和结合多个多尺度模型实现多尺度同步耦合响应的建模方法。对进行多尺度建模仿真以研究金属塑性成形成性机理有重要的参考价值。     

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。     

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。     

润滑剂在材料成形中的应用

阐述了润滑剂在材料加工过程中的分类和用途,对各类润滑剂的使用情况和优缺点进行了比较,并针对各类问题提出了产品改良的必要性。介绍了目前对一些矿物的改进方法,分析新型润滑剂在材料成形中的应用情况,并对润滑剂的发展趋势进行了初步探讨。     

泡沫金属弹性变形尺度效应的理论与数值研究

泡沫金属的力学性能强烈依赖于内部结构。当构件特征尺寸与胞孔特征尺寸d处于相同数量级时,表现出明显的尺度效应。为了揭示这种尺度效应的力学机理,研究了泡沫金属试件的剪切和纯弯曲试验。一方面,利用应变梯度弹性理论给出解析解,其中包含了材料内禀尺寸l_c这一关键模型参数。另一方面,把每段胞壁视为铁木辛柯梁,从而建立梁链网作为泡沫金属的微观力学模型。通过应变能等效原理建立应变梯度连续体和基体金属材料弹性参数之间的关系。发现,边界层的约束条件对泡沫金属的力学响应有重要影响。弯曲问题中,只有对离散模型上下表面施加恰当的附加转角约束后,应变梯度理论解与链网模型数值解才能够吻合。这为理解应变梯度理论中的非传统边界条件提供了一个直观的实例。通过数据拟合,得到了内禀尺寸l_c与胞孔特征尺寸d之间的关系,与文献结论相符。     

Non‐uniform plastic deformation of micron scale objects

Significant increases in apparent flow strength are observed when non‐uniform plastic deformation of metals occurs at the scale ranging from roughly one to ten microns. Several basic plane strain problems are analysed numerically in this paper based on a new formulation of strain gradient plasticity. The problems are the tangential and normal loading of a finite rectangular block of material bonded to rigid platens and having traction‐free ends, and the normal loading of a half‐space by a flat, rigid punch. The solutions illustrate fundamental features of plasticity at the micron scale that are not captured by conventional plasticity theory. These include the role of material length parameters in establishing the size dependence of strength and the elevation of resistance to plastic flow resulting from constraint on plastic flow at boundaries. Details of the finite element method employed in the numerical analysis of the higher order gradient theory will be discussed and related to prior formulations having some of the same features. Copyright © 2003 John Wiley & Sons, Ltd.     

The mode III full-field solution in elastic materials with strain gradient effects

The near-tip asymptotic field and full-field solution are obtained for a mode III crack in an elastic material with strain gradient effects. The asymptotic analysis shows that, even though the near-tip field is governed by a single parameter B (similar to the mode III stress intensity factor), the near-tip field is very different from the classical K_III field; stresses have r ^-3/2 singularity near the crack tip, and are significantly larger than the classical K _III field within a zone of size l to the crack tip, where l is an intrinsic material length, depending on microstructures in the material. This high-order stress singularity, however, does not violate the boundness of strain energy around a crack tip. The parameter B of the near-tip asymptotic field has been determined for two anti-plane shear loadings: the remotely imposed classical K _III field, and the arbitrary shear stress tractions on crack faces. The mode III full-field solution is obtained analytically for an elastic material with strain gradient effects subjected to remotely imposed classical K _III field. It shows that the near-tip asymptotic field dominates within a zone of size 0.5 l to the crack tip, while strain gradient effects are clearly observed within 5l. It is also shown that the conventional way to evaluate the crack tip energy release rate would lead to an incorrect, infinite value. A new evaluation gives a finite crack tip energy release rate, and is identical to the J-integral. This revised version was published online in August 2006 with corrections to the Cover Date.     

Ductile fracture and deformation behavior in progressive microforming

With the increasing demand for the quality and quantity of miniaturized parts, fabrication of microparts directly using sheet metals is proven to be promising and efficient for mass production. In this process, however, there are many unknowns in terms of size effect and its affected fracture and deformation behavior. This study is thus aimed at investigating the micromechanical damage and deformation behavior in progressive microforming and establishing a systematic knowledge to support the microformed part design, process configuration and tooling design. In detail, a micro cylindrical part is fabricated via shearing process and a multi-level flanged part is produced via progressive micro extrusion and blanking. To explore the effect of material microstructure on the deformation behavior, ductile fracture and the product quality of microformed part, the original sheet metals are annealed under different temperatures. To realize the microforming process, a progressive microforming system is developed and its characteristics are investigated. The effect of grain size on dimensional accuracy, microstructure evolution and fracture behavior in microforming is also studied. The ductile fracture and its induced defects are identified and the damage accumulation is predicted. In the end, the validity and applicability of different fracture criteria in microforming is discussed.     

Size effects in phenomenological strain gradient plasticity constitutively involving the plastic spin

In the small deformation range, we consider and discuss the phenomenological (or isotropic) “higher-order” theory of strain gradient plasticity put forward in Section 12 of Gurtin [1], which includes the dissipation due to the plastic spin through a material parameter called χ. In fact, χ weighs the square of the plastic spin rate into the definition of an effective measure of plastic flow peculiar of the isotropic hardening function. Such a model has been identified by Bardella [2] as a good isotropic approximation of a crystal model to describe the multislip behaviour of a single grain, provided that χ be set as a specific function of other material parameters involved in the modelling, including the length scales. The main feature of the underlying gradient approach is the accounting for both dissipative and energetic strain gradient dependences, with related size effects. The dissipative strain gradients enter the model through the definition of the above mentioned effective measure of plastic flow, whereas the energetic strain gradients are involved in the modelling by defining the defect energy, a function of Nye’s dislocation density tensor added to the free energy to account for geometrically necessary dislocations (see, e.g., Gurtin [1]). By exploiting the deformation theory approximation, we apply the model to a simple boundary value problem so that we can discuss the effects of (a) the criterium derived by Bardella [2] for choosing χ and (b) non-quadratic forms of the defect energy. We show that both χ and the nonlinearity chosen for the defect energy strongly affect quality and magnitude of the energetic size effect which is possible to predict.     

Analytic and numerical studies on mode I and mode II fracture in elastic-plastic materials with strain gradient effects

This paper presents a study on fracture of materials at microscale (∼1 μm) by the strain gradient theory (Fleck and Hutchinson, 1993; Fleck et al., 1994). For remotely imposed classical K fields, the full-field solutions are obtained analytically or numerically for elastic and elastic-plastic materials with strain gradient effects. The analytical elastic full-field solution shows that stresses ahead of a crack tip are significantly higher than their counterparts in the classical K fields. The sizes of dominance zones for mode I and mode II near-tip asymptotic fields are 0.3l and 0.5l,while strain gradient effects are observed within land 2l to the crack tip, respectively, where l is the intrinsic material length in strain gradient theory and is on the order of microns in strain gradient plasticity (Fleck et al., 1994; Nix and Gao, 1998; Stolken and Evans, 1997). The Dugdale–Barenblatt type plasticity model is obtained to provide an estimation of plastic zone size for mode II fracture in materials with strain grain effects. The finite element method is used to investigate the small-scale-yielding solution for an elastic-power law hardening solid. It is found that the size of the dominance zone for the near-tip asymptotic field is the intrinsic material lengthl. For mode II fracture under the small-scale-yielding condition, transition from the remote classical K _IIfield to the near-tip asymptotic field in strain gradient plasticity goes through the HRR field only when K _IIis relatively large such that the plastic zone size is much larger than the intrinsic material length l. For mode I fracture under small-scale-yielding condition, however, transition from the remote classical K _I field to the near-tip asymptotic field in strain gradient plasticity does not go through the HRR field, but via a plastic zone. This revised version was published online in July 2006 with corrections to the Cover Date.     

Mode III crack growth in linear hardening materials with strain gradient effects

The flow-theory version of couple stress strain gradient plasticity is adopted for investigating the asymptotic fields near a steadily propagating crack-tip, under Mode III loading conditions. By incorporating a material characteristic length, typically of the order of few microns for ductile metals, the adopted constitutive model accounts for the microstructure of the material and can capture the strong size effects arising at small scales. The effects of microstructure result in a substantial increase in the singularities of the skew-symmetric stress and couple stress fields, which occurs also for a small hardening coefficient. The symmetric stress field turns out to be non-singular according to the asymptotic solution for the stationary crack problem in linear elastic couple stress materials. The performed asymptotic analysis can provide useful predictions about the increase of the traction level ahead of the crack-tip due to the sole contribution of the rotation gradient, which has been found relevant and non-negligible at the micron scale.     

Constraint effects on the elastic–plastic fracture behaviour in strain gradient solids

ABSTRACT Crack‐tip constraint effects (or T‐stress effects) on the elastic–plastic fracture behaviour in strain gradient materials are analysed in the present study. The T‐stress effects on the stress distributions along the plane ahead of the stationary and growing crack tip, respectively, are analysed by using the Fleck and Hutchinson strain gradient plasticity formation. For a steadily growing crack, the T‐stress effects on the steady‐state fracture toughness are analysed by adopting the embedded fracture process zone model. In addition, the analysis for the growing crack is applied to an interfacial cracking experiment for a metal/ceramic system, and the material length‐scale parameter appearing in the strain gradient plasticity theory is predicted. In the present analyses, a new finite element method specially designed for strain gradient problems by Wei and Hutchinson is adopted.     

Finite element analysis of geometrically necessary dislocations in crystal plasticity

We present a finite element method for the analysis of ductile crystals whose energy depends on the density of geometrically necessary dislocations (GNDs). We specifically focus on models in which the energy of the GNDs is assumed to be proportional to the total variation of the slip strains. In particular, the GND energy is homogeneous of degree one in the slip strains. Such models indeed arise from rigorous multiscale analysis as the macroscopic limit of discrete dislocation models or from phenomenological considerations such as a line‐tension approximation for the dislocation self‐energy. The incorporation of internal variable gradients into the free energy of the system renders the constitutive model non‐local. We show that an equivalent free‐energy functional, which does not depend on internal variable gradients, can be obtained by exploiting the variational definition of the total variation. The reformulation of the free energy comes at the expense of auxiliary variational problems, which can be efficiently solved using finite element approximations. The addition of surface terms in the formulation of the free energy results in additional boundary conditions for the internal variables. The proposed framework is verified by way of numerical convergence tests, and simulations of three‐dimensional problems are presented to showcase its applicability. A performance analysis shows that the proposed framework solves strain‐gradient plasticity problems in computing times of the order of local plasticity simulations, making it a promising tool for non‐local crystal plasticity three‐dimensional large‐scale simulations. Copyright © 2012 John Wiley & Sons, Ltd.     

Evaluation of the Toupin-Mindlin Theory for Predicting the Size Effects in the Buckling of the Carbon Nanotubes

Conventional continuum theories are unable to capture the observed indentation size effects, due to the lack of intrinsic length scales that represent the measures of nanostructure in the constitutive relations. In order to overcome this deficiency, the Toupin-Mindlin strain gradient theory of nanoindentation is formulated in this paper and the size dependence of the hardness with respect to the depth and the radius of the indenter for multiple walled carbon nanotubes is investigated. Results show a peculiar size influence on the hardness, which is explained via the shear resistance between the neighboring walls during the buckling of the multiwalled nanotubes.