An Energy-Based Method for Analyzing Instrumented Spherical Indentation Experiments

Using dimensional analysis and finite element calculation, we studied spherical indentation in elastic-plastic solids with work hardening. We report two previously unknown relationships between hardness, reduced modulus, indentation depth, indenter radius, and work of indentation. These relationships, together with the relationship between initial unloading stiffness and reduced modulus, provide an energy-based method for determining contact area, reduced modulus, and hardness of materials from instrumented spherical indentation measurements. This method also provides a means for calibrating the effective radius of imperfectly shaped spherical indenters. Finally, the method is applied to the analysis of instrumented spherical indentation experiments on copper, aluminum, tungsten, and fused silica.

Interface crack problems with strain gradient effects

In this paper, the strain gradient theory proposed by Chen and Wang (2001 a, 2002b) is used to analyze an interface crack tip field at micron scales. Numerical results show that at a distance much larger than the dislocation spacing the classical continuum plasticity is applicable; but the stress level with the strain gradient effect is significantly higher than that in classical plasticity immediately ahead of the crack tip. The singularity of stresses in the strain gradient theory is higher than that in HRR field and it slightly exceeds or equals to the square root singularity and has no relation with the material hardening exponents. Several kinds of interface crack fields are calculated and compared. The interface crack tip field between an elastic-plastic material and a rigid substrate is different from that between two elastic-plastic solids. This study provides explanations for the crack growth in materials by decohesion at the atomic scale.

激光硬化基体对镀铬层组织和结合的影响

采用激光相变硬化的方法在电镀前对基体表层预先进行处理，以改善镀层与基体的结合强度，提高其承载能力。借助扫描电镜（SEM）分析镀铬层的组织和界面，对镀层、相变硬化区和基体的硬度变化进行分析，对镀层抗高温烧蚀能力进行测试。结果表明，基体经激光相变硬化处理后，既可以促进镀层外延生长，又可以在镀层和基体之间实现硬度的梯度过渡，从而可以改善结合，缓解应力，提高承载能力，镀层的抗剥落能力和使用寿命得到显著提高。激光相变硬化得到细小的淬火马氏体，位错密度显著增加，表面活性增强，是促进镀层外延生长的主要原因。

What is indentation hardness?

Using dimensional analysis and finite element calculations, we derive simple scaling relationships for loading and unloading curve, contact depth, and hardness. The relationship between hardness and the basic mechanical properties of solids, such as Young's modulus, initial yield strength, and work-hardening exponent, is then obtained. The conditions for 'piling-up' and 'sinking-in' of surface profiles during indentation are determined. A method for estimating contact depth from initial unloading slope is examined. The work done during indentation is also studied. A relationship between the ratio of hardness to elastic modulus and the ratio of irreversible work to total work is discovered. This relationship offers a new method for obtaining hardness and elastic modulus. Finally, a scaling theory for indentation in power-law creep solids using self-similar indenters is developed. A connection between creep and 'indentation size effect' is established.

A New Modified Expanding Cavity Model for Characterizing the Spherical Indentation Behaviour of Bulk Metallic Glass with Pile-up

Spherical nanoindentation tests were performed on Zr41.2Ti13.8Cu12.5Ni10Be22.5 bulk metallic glass and pile-ups were observed around the indenter. A new modified expanding cavity model was developed to characterize the indentation deformation behavior of strain-hardening and pressure-dependent materials. By using this model, the representative stress-strain response of this bulk metallic glass to hardness and indentation in the elastic-plastic regime were obtained taking into consideration the effect of pile-up.

Scaling, Dimensional Analysis, and Indentation Measurements

We provide an overview of the basic concepts of scaling and dimensional analysis, followed by a review of some of the recent work on applying these concepts to modeling instrumented indentation measurements. Specifically, we examine conical and pyramidal indentation in elastic-plastic solids with power-law work-hardening, in power-law creep solids, and in linear viscoelastic materials. We show that the scaling approach to indentation modeling provides new insights into several basic questions in instrumented indentation, including, what information is contained in the indentation load-displacement curves? How does hardness depend on the mechanical properties and indenter geometry? What are the factors determining piling-up and sinking-in of surface profiles around indents? Can stress-strain relationships be obtained from indentation load-displacement curves? How to measure time dependent mechanical properties from indentation? How to detect or confirm indentation size effects? The scaling approach also helps organize knowledge and provides a framework for bridging micro- and macroscales. We hope that this review will accomplish two purposes: (1) introducing the basic concepts of scaling and dimensional analysis to materials scientists and engineers, and (2) providing a better understanding of instrumented indentation measurements.

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.

Mode I crack tip field with strain gradient effects

A plane strain mode I crack tip field with strain gradient effects is investigated. A new strain gradient theory is used. An elastic-power law hardening strain gradient material is considered and two hardening laws, i.e. a separation law and an integration Law are used respectively. As for the material with the separation law hardening, the angular distributions of stresses are consistent with the HRR field, which differs from the stress results([19]); the angular distributions of couple stresses are the same as the couple stress results([19]). For the material with the integration law hardening, the stress field and the couple stress field can not exist simultaneously, which is the same as the conclusion([19]), but for the stress dominated field, the angular distributions of stresses are consistent with the HRR field; for the couple stress dominated field, the angular distributions of couple stresses are consistent with those in Ref. [19]. However, the increase in stresses is not observed in strain gradient plasticity because the present theory is based on the rotation gradient of the deformation only, while the crack tip field of mode I is dominated by the tension gradient, which will be shown in another paper.

Deformation behavior and microstructure effect in 2124Al/SiCp composite

Dynamic compression tests were performed by means of a Split Hopkinson Pressure Bar (SHPB). Test materials were 2124Al alloys reinforced with 17% volume fraction of 3, 13 and 37 μm SiC particles, respectively. Under strain rate ε = 2100 l/s, SiC particles have a strong effect on σ_0.2 of the composites and the σ_0.2 increases with different SiC particle size in the following order: 2124Al-alloy → 124Al/SiC_p (37 μm) → 2124Al/SiC_p (13 μm) → 2124Al/SiC_p (3 μm), and the strain hardening of the composites depends mainly on the strain hardening of matrix, 2124A1 alloy. The results of dimensional analysis present that the flow stress of these composites not only depends on the property of reinforcement and matrix but also relates to the microstructure scale, matrix grain size, reinforcement size, the distance between reinforcements and dislocations in matrix. The normalized flow stress here is a function of inverse power of the edge-edge particle spacing, dislocation density and matrix grain size. Close-up observation shows that, in the composite containing SiC particles (3 μm), localized deformation formed readily comparing with other materials under the same loading condition. Microscopic observations indicate that different plastic flow patterns occur within the matrix due to the presence of hard particles with different sizes.

Particulate Size Effects in the Particle-Reinforced Metal-Matrix Composites

The influences of I,article size on the mechanical properties of the particulate metal matrix composite;are obviously displayed in the experimental observations. However, the phenomenon can not be predicted directly using the conventional elastic-plastic theory. It is because that no length scale parameters are involved in the conventional theory. In the present research, using the strain gradient plasticity theory, a systematic research of the particle size effect in the particulate metal matrix composite is carried out. The roles of many composite factors, such as: the particle size, the Young's modulus of the particle, the particle aspect ratio and volume fraction, as well as the plastic strain hardening exponent of the matrix material, are studied in detail. In order to obtain a general understanding for the composite behavior, two kinds of particle shapes, ellipsoid and cylinder, are considered to check the strength dependence of the smooth or non-smooth particle surface. Finally, the prediction results will be applied to the several experiments about the ceramic particle-reinforced metal-matrix composites. The material length scale parameter is predicted.

脉冲激光表面强化数值模拟及热物性参量影响

建立了包含脉冲激光束时空分布、依赖于温度的材料参量、组织演化历史以及多次相变特征在内的脉冲激光表面强化三维有限元模型。针对常热物性和变热物性并考虑相变潜热两种情况，温度场及其演化分别得到了解析解和通用有限元软件的验证，强化区层深和宽度得到了实验验证。研究了材料热物性对强化区的影响，得到了一定范围内强化区层深随材料热物性参量的变化规律，即：热传导系数不变时，强化区层深随热扩散率的增加而增加；比热容不变时，强化区层深随热扩散率的增加而减小；热扩散率一定时，强化区层深随热传导系数和比热容的增加而降低。以球铁、共析钢和巾碳钢为例，分析了两种确定材料热物性常数方法，即一定温度范围内的平均值法和选取奥氏体化温度附近参量方法的可行性，研究表明平均值法可以得到较好的结果。

球墨铸铁变换激光束淬火性能的研究

采用经过二元光学元件变换呈二维点阵7*7分布的脉冲激光束对球墨铸铁材料进行表面淬火处理，研究激光参数变化对铸铁表面的粗糙度、硬化层深度、显做硬度和耐磨性等的影响。结果表明，在一定的能量范围内，随着能量的增加，粗糙度略呈增长的趋势，硬化层深也略有增加，并存在一个硬化层深极限值。硬度峰值差别很小，而相变硬化区差别则很大。耐磨性试验表明，随着能量的增加，耐磨性有提高的趋势。

On the design of the piecewise linear vibration absorber

This paper explores the potential of the piecewise linear vibration absorber in a system subject to narrow band harmonic loading. Such a spring is chosen because the design of linear springs is common knowledge among engineers. The two-degrees-of-freedom system is solved by using the Incremental Harmonic Balance method, and response aspects such as stiffness crossing frequency and jump behaviour are discussed. The effects of mass, stiffness, natural frequency ratios, and stiffness crossing positions on the suppression zone are probed. It is shown that a hardening absorber can deliver a wider bandwidth than a linear one over a range of frequencies. The absorber parameters needed to produce good designs have been determined and the quality of the realized suppression zone is discussed. Design guidelines are formulated to aid the parameter selection process.

Nonequilibrium microstructures and phase evolutions of an iron-based laser clad coating

The microstructural and compositional features of the laser-solidified microstructures and phase evolutions occurring during high temperature tempering were investigated by using analytical electron microscopy with energy dispersive X-ray analysis. The cladded alloy, a powder mixture of Fe, Cr, W, Ni and C with a weight ratio of 10:5:1:1:1, was processed with a 3 kW continuous wave CO2 laser. The cladded coating possessed the hypoeutectic microstructure of the primary dendritic gamma-austenite and interdendritic eutectic consisting of (gamma+M7C3). The gamma-austenite is a nonequilibrium phase with extended solid solution of alloying elements. And, a great deal of fine structures, i.e., a high density of dislocations, twins, and stacking faults existed in austenite phase. During high temperature aging, the precipitation of M23C6, MC and M2C in austenite and in situ transformation of M7C3(+gamma) --> M23C6 and M7C3+gamma --> M6C occurred. The laser clad coating revealed an evident secondary hardening and superior impact wear resistance.

Rapidly solidified nonequilibrium microstructure and phase transformation of laser-synthesized iron-based alloy coating

The rapidly solidified microstructural and compositional features, the precipitation and transformation of carbides during tempering, and the impact wear resistance of an iron-based alloy coating prepared by laser cladding are investigated. The clad coating alloy, a powder mixture of Fe, Cr, W, Ni, and C with a weight ratio of 10:5:1.1.1, is processed using a continuous wave CO, laser. Microstructural studies demonstrate that the coating possesses the hypoeutectic microstructure comprising the primary dendritic gamma-austenite and interdendritic eutectic consisting of gamma-austenite and M7C3 carbides. gamma-Austenite is a non-equilibrium phase with an extended solid solution of alloying elements. During high temperature tempering at 963 K for 1 h, the precipitation of M23C6, MC and M2C carbides in austenite and in situ carbide transformation of M7C3 to M23C6 and M7C3 to M6C respectively are observed. In addition, the microstructure of the laser-clad coating reveals an evident secondary hardening and a superior impact wear resistance.