磨矿介质形状对石英砂粉碎参数的影响

以粒径为 2～2. 36、0. 83～2 mm的石英砂为原料,钢球、短圆柱形钢锻为磨矿介质,磨矿质量为500 g,矿浆质量分数为65%,磨矿时间为0. 5、1、2、4、8 min,钢球的个数配比:D_(30)∶D_(25)∶D_(20)=43∶62∶96,短圆柱钢锻个数配比:D_(30×30):D_(25×25):D_(20×20)=28∶41∶64,介质充填率为0. 4,球磨机转速为96 r/min,进行分批次磨矿。结果表明:不同介质形状下,石英砂的粉碎速率遵循一阶动力学模型,且在短时间内短圆柱钢锻的粉碎速率明显大于钢球的,表征物料粉碎难易程度的γ值越小粉碎越容易,φ、β表征粗颗粒粒级破碎至相应细粒级的速率,短时间(1 min)粉碎过程中介质形状对初始粉碎分布参数有影响,钢锻和钢球介质相比:γ值偏小,而φ和β值偏大。建议在石英砂的粉碎过程中,可以选择钢锻介质对其进行快速破碎。     

TiNi基形状记忆合金的辐照效应

材料辐照效应是入射粒子与物质交互作用造成的物质微观组织结构与宏观性能的变化。辐照效应不仅是改善材料表面性能的重要手段,而且也是特殊环境应用材料可靠性评价的重要组成部分。TiNi基形状记忆合金是一种重要的金属智能材料,具有独特的形状记忆效应和超弹性,已在卫星、空间站等航天器以及生物医学中广泛应用。本文阐述了Ti-Ni基形状记忆合金在空间粒子(质子、电子)以及离子辐照改性的研究进展,辐照效应会对TiNi合金的微观组织结构产生影响,进而改变合金的相变行为和力学行为。然而目前关于TiNi基合金的辐照效应的研究仍处于起步阶段,组织结构和相变行为的变化规律和机理还未研究清楚,有关形状记忆效应的研究较少,仍需深入研究辐照参数、组织结构、相变行为和功能特性之间的内在联系。     

A medial axis based method for irregular grain shape representation in DEM simulations

This paper describes a novel method for representing arbitrary grain shapes in discrete element method (DEM) simulations. The method takes advantage of the efficient sphere contact treatment in DEM and approximates the overall grain shape by combining a number of overlapping spheres. The method is based on the medial axis transformation, which defines the set of spheres needed for total grain reconstruction. This number of spheres is then further diminished by selecting only a subset of reconstructing spheres and opting for a grain approximation rather than a full grain reconstruction. The effects of the grain approximating parameters on the key geometrical features of the grains and the overall mechanical response of the granular medium are monitored by an extensive sensitivity analysis. The results of DEM quasi-static oedometric compression on a granular sample of approximated grains exhibit a high level of accuracy even for a small number of spheres.     

A micromechanics based multiscale model for nonlinear composites

A micromechanics model for fiber-reinforced composites that can be used at the subscale in a multiscale computational framework is established to predict the effective nonlinear composite response. Using a fiber–matrix concentric cylinder model as the basic repeat unit to represent the composite, micromechanics is used to relate the applied composite strains to the fiber and matrix strains by a six by six transformation matrix. The resolved spatial variations of the matrix fields are found to be in good agreement with corresponding finite element analysis results. The evolution of the composite nonlinear response is assumed to be governed by two scalar, strain-based variables that are related to the extreme value of an appropriately defined matrix equivalent strain, and the matrix secant moduli are used to compute the composite secant moduli for nonlinear analysis. The results from the micromechanics model are compared well with a full finite element analysis. The predictive capability of the proposed model is illustrated by two distinct fiber-reinforced material systems, carbon and glass, for the fiber volume fraction varying from 50 to 70 %. Since fully analytical solutions are utilized for the micromechanical analysis, the proposed method offers a distinct computational advantage in a multiscale analysis and is therefore suitable for large-scale progressive damage and failure analyses of composite material structures.     

Fracture toughness of foams with tetrakaidecahedral unit cells using finite element based micromechanics

Fracture toughness of open-cell foams consisting of tetrakaidecahedral unit cells is predicted by simulating crack propagation using a finite element (FE) based micromechanical model. The inputs to the model are the geometric parameters required to model the repeating unit cell and tensile strength of the foam ligament or strut. Cracks are created by removing certain number of cells pertaining to a crack length. The FE model consists of a local micro-scale region surrounding the crack tip. For an assumed stress intensity factor, the displacements along the boundary of the local model are calculated based on linear elastic fracture mechanics for orthotropic materials. The stresses in the ligaments ahead of the crack tip calculated from this micro-model in conjunction with the tensile strength of the strut material are used to predict fracture toughness. A parametric study with different micro-model sizes and different crack lengths is performed to check for convergence of predicted Mode-I, Mode-II and mixed mode fracture toughness values. The effect of applying rotations as additional boundary conditions along with translational displacement boundary conditions on the predicted fracture toughness values is also studied.     

形状记忆合金/聚合物有效时变和伪弹性响应的变分渐近细观力学

为有效模拟形状记忆合金增强聚合物基复合材料(SMA/PMCs)有效时变和伪弹性响应,基于变分渐近理论框架构建增量型细观力学模型。首先分别导出聚合物和形状记忆合金增量本构方程,建立统一的本构方程;以此为基础推导出能量泛函的变分表达式。考虑材料的时变和非线性特征,建立与求解切向瞬时有效矩阵有关的增量过程,并通过有限元数值实现。通过数值算例表明:构建的模型可用于模拟SMA/PMCs在不同加载率和温度下的有效时变、伪弹性响应,准确捕捉聚合物基体黏弹性诱发的复合材料率相关、滞回行为等。     

Computational micromechanics evaluation of the effect of fibre shape on the transverse strength of unidirectional composites: An approach to virtual materials design

Computational micromechanics of composites is an emerging tool required for virtual materials design (VMD) to address the effect of different variables involved before materials are manufactured. This strategy will avoid unnecessary costs, reducing trial-and-error campaigns leading to fast material developments for tailored properties. In this work, the effect of the fibre cross section on the transverse behaviour of unidirectional fibre composites has been evaluated by means of computational micromechanics. To this end, periodic representative volume elements containing uniform and random dispersions of 50% of parallel non-circular fibres with lobular, polygonal and elliptical shapes were generated. Fibre/matrix interface failure as well as matrix plasticity/damage were considered as the fundamental failure mechanisms operating at the microscale under transverse loading. Circular fibres showed the best averaged behaviour although lobular fibres exhibited superior performance in transverse compression mainly due to the higher tensile thermal residual stresses generated during cooling at the fibre/matrix interface.     

A generalized micromechanics model with shear-coupling

Summary A unified mathematical framework for a higher-order transverse shear-normal stress coupled micromechanical model is presented. The model is developed based on the analysis of a repeating unit cell in a doubly periodic array of fibers. The behavior in subregions within the unit cell is modeled using an expansion for the displacement field. The order and form of the displacement expansions in the subregions are arbitrary. The higher-order terms in the displacement expansion result in coupling between the transverse shearing and the normal deformation responses (shear coupling). The formulation is sufficiently general to allow generic elastic, plastic, viscoelastic, viscoplastic, or damage constitutive models (within the context of infinitesimal strain theory) for history-dependent behavior to be incorporated into the micromechanical framework. The proposed approach is analytical and provides closed-form expressions for the effective macroscopic behavior of a continuous fiber composite.The model is validated by comparison with existing micromechanics models. The agreement between the predicted effective moduli obtained from the current model and other existing models indicates that the current formulation accurately predicts the effective elastic behavior of a composite. Furthermore, comparison with existing data for the local elastic stress distributions around the inclusion indicates that the current model correctly captures the trends and magnitudes in these distributions. The predictions obtained from the current theory are shown to be more accurate than the corresponding MOC predictions. The ability to more accurately capture the spatial stress distributions can be directly attributed to the incorporation of the shear-coupling phenomena.Finally, the influence of the presence of shear coupling on the local field distributions is considered for the simple macroscopic loading cases of transverse tension and transverse shearing. It is shown that signficant coupling between the local transverse shearing and normal deformation responses exists even when the composite is subjected to a macroscopically simple loading field. The existence of this coupling has potentially significant implications in the implementation of history-dependent constitutive models.     

A micromechanics based analysis of hollow fiber composites using DQEM

In this study, a generalized plane strain micromechanical model is presented to obtain micro-stress/strain fields within the unidirectional (UD) hollow fiber reinforced composites. In addition, the thermally induced residual stresses during cooling down process, overall elastic properties and energy absorption capability of hollow reinforced composite are studied. The representative volume element (RVE) of the composite consists of a quarter of the fiber surrounded by matrix to represent the real composite with repeating square array of fibers. Fully bonded fiber–matrix interface condition is considered and the displacement continuity and traction reciprocity are properly imposed to the interface. The cubic serendipity shape functions are used to convert the solution domain to a proper rectangular domain. A Least-squares based differential quadrature element method (DQEM) is used to obtain solutions for the governing partial differential equations of the problem. Results of the presented method for various stress and displacement components and thermal residual stresses show excellent agreement with finite element analysis. Furthermore, predicted overall properties also show good agreement with other available analytical and finite element results. Moreover, results also revealed that the presented model can provide highly accurate predictions with a few number of elements and grid points within each element.     

The effect of rod nose shape on the internal flow fields during the ballistic penetration of sand

This paper discusses the technique of Digital Speckle Radiography (DSR) and its application to the measurement of the internal flow fields in penetration of sand by long-rod projectiles at velocities up to 200 m/s. Three different rod nose shapes were studied: flat-ended, ogive-2, and hemispherical. Impacts performed on gelatine and concrete gave significantly different displacement fields to sand. Sand, therefore, cannot either be modelled as a fluid or as a conventional solid. Simulations performed using a code written by two of the authors (Bobaru and Promratana) showed that the velocity distribution has a very different appearance to the force distribution. This suggests that processes such as reorganisation, sliding and void filling take place, allowing the grains to move in directions other than the applied force. The resulting velocity distribution bears a strong resemblance to the experimentally measured displacement fields.     

Influence of grain size on arrest of a dynamically propagating cleavage crack in ferritic steels—micromechanics

Cleavage fracture in ferritic steels is controlled by several critical steps. First a microcrack must nucleate, grow and overcome barriers, such as grain boundaries. The latter is examined here by use of a periodic, axisymmetric model representing two grains. A microcrack nucleated at the center in one grain is driven by a constant remotely applied stress towards the second grain. The cleavage planes of the grain in which the microcrack is nucleated coincide with the principal loading direction. In the adjacent grain, due to misalignment in possible cleavage planes, the propagation direction changes and separation occurs in mixed mode, involving both normal and shear separations. The temperature dependence of the mechanical properties of the material is accounted for by use of a temperature dependent elasto viscoplastic material model. The largest grain size that can arrest a rapidly propagating microcrack is defined as the critical grain size. The effects of stress state and temperature on the critical grain size are examined. The influence of mismatch in lattice orientation between two adjacent grains in terms of a tilt angle is both qualitatively and quantitatively described. It is shown that the critical grain size is influenced by plastic geometry change and prestraining, which depend on the applied stress state. The results also show that a microcrack can be arrested in an adjacent grain under specific conditions.     

Kinetic grain growth in Cu-Zn-Al shape memory alloys

Kinetic grain growth has been evaluated in Cu-Zn-Al shape memory alloys by the calculation of different grain size parameters (perimeter, area, minimal and maximal diameter) in different alloys, and at different temperatures and heat treatment times. The growth order values have been worked out and the activation energy estimated.     

Mechanical properties of hybrid composites using finite element method based micromechanics

A micromechanical analysis of the representative volume element of a unidirectional hybrid composite is performed using finite element method. The fibers are assumed to be circular and packed in a hexagonal array. The effects of volume fractions of the two different fibers used and also their relative locations within the unit cell are studied. Analytical results are obtained for all the elastic constants. Modified Halpin–Tsai equations are proposed for predicting the transverse and shear moduli of hybrid composites. Variability in mechanical properties due to different locations of the two fibers for the same volume fractions was studied. It is found that the variability in elastic constants and longitudinal strength properties was negligible. However, there was significant variability in the transverse strength properties. The results for hybrid composites are compared with single fiber composites.     

On modeling anisotropy in deformation processes involving textured polycrystals with distorted grain shape

A mathematical formulation is presented which uses rate-dependent polycrystalline plasticity to model the development of plastic anisotropy in bulk forming processes. The formulation assumes that underlying a material point on a continuum scale is a collection of anisotropic, contiguous grains. The mechanical response at a continuum level is derived from the response of individual grains suitably averaged over all grains in the aggregate. The effects of preferred orientation (texture) and of the evolving grain shape on the directionality to the flow properties of the polycrystal are included. A general numerical framework is described for incorporating this complex material behavior in a finite element formulation. As an application, texture development during the flat rolling of aluminum sheets is presented. The simulation predictions have been compared with reported experimental data and with a previous study where the effects of grain shape were neglected.     

The effect of grain orientation on the tensile‐compressive asymmetry of polycrystalline NiTi shape memory alloy

The purpose of the present study is to thoroughly understand the influence of crystallographic texture on the stress‐strain asymmetric behavior of polycrystalline NiTi shape memory alloy under tension and compression. To do this, a 3D thermo‐mechanical model has been implemented in a finite element program and textured and untextured polycrystalline NiTi have been considered. In our polycrystalline finite element model, each element represents one grain and a set of crystal orientations which approximate the initial crystallographic texture of the NiTi are assigned to the elements. From the calculated results, it is found that the crystallographic texture is the important reason for the tension‐compression asymmetry. For the textured polycrystal, the tension‐compression asymmetry can be observed clearly, but for the polycrystal containing randomly oriented grains, the stress‐strain curves show low levers of asymmetry between tensile and compressive loading, and the evolutions of martensite volume fractions are similar under two stress states.     

A three-dimensional micromechanics model for the damage of brittle materials based on the growth and unilateral effect of elliptic microcracks

Based on the analysis of a representative elliptic microcrack embedded in a RVE, the additional compliance tensor induced by an embedded opening/closed microcrack is derived, and that corresponding to the kinked growth of a closed elliptic microcrack is also derived by making use of its approximately equivalent simplification. The effect of the microcracks is analyzed with the Taylor’s scheme by introducing an appropriate probability density function. A three-dimensional micromechanics damage model is obtained for brittle materials, assuming numerous randomly distributed elliptic microcracks and taking into account their deformation, frictional sliding, growth and kinked growth.     

基于宏微观分析的碳纤维增强高分子复合材料强度性能表征

微观力学强度理论(MMF)是一种新型的基于物理失效模式的复合材料强度理论。通过对碳纤维/树脂(UTS50/E51)复合材料单向层合板进行纵向、横向静载拉伸、压缩和弯曲试验, 得到层合板的基本力学性能和宏观强度指标。建立了碳纤维增强树脂基复合材料微观力学模型, 获取树脂基体和纤维不同位置的机械载荷应力放大系数和热载荷应力放大系数。结合获取的应力放大系数及试验测得的单向层合板宏观强度, 计算出层合板组分的MMF强度特征值。绘制了基于MMF强度理论的层合板破坏包络线, 并与Tsai-Wu失效准则预测结果进行对比。实现了对UTS50/E51层合板MMF强度特征值的表征。     

The grain shape dependence of springback of integrated circuit leadframes

Anisotropy is known to be an important factor in affecting springback and deformation behaviour of cold rolled integrated circuit (IC) leadframes. Less work has been carried out to study the effect of grain shape on springback of IC leadframes, though it is considered to be a source of plastic anisotropy. In this paper, a plane stress model based on the concept of relaxed constraints has been developed to investigate the effect of grain shape on springback of a cold rolled copper alloy. Comparisons between the predictions by the relaxed constraint model and the conventional full constraints model and the experimental results have been made. It is found that significant improvement has been obtained by using the new model.