Nonlinear Analysis of Oscillatory Indentation in Elastic and Viscoelastic Solids

Determining the mechanical properties at micro- and nanometer length scales using nanoindentation or atomic force microscopy is important to many areas of science and engineering. Here we establish equations for obtaining storage and loss modulus from oscillatory indentations by performing a nonlinear analysis of conical and spherical indentation in elastic and viscoelastic solids. We show that, when the conical indenter is driven by a sinusoidal force, the square of displacement is a sinusoidal function of time, not the displacement itself, which is commonly assumed. Similar conclusions hold for spherical indentations. Well-known difficulties associated with measuring contact area and correcting thermal drift may be circumvented using the newly derived equations. These results may help improve methods of using oscillatory indentation for determining elastic and viscoelastic properties of solids.

Finite Element Solutions for Plane Strain Mode I Crack with Strain Grading Effect

In this paper, a new phenomenological theory with strain gradient effects is proposed to account for the size dependence of plastic deformation at micro- and submicro-length scales. The theory fits within the framework of general couple stress theory and three rotational degrees of freedom omega(i) are introduced in addition to the conventional three translational degrees of freedom mu(i). omega(i) is called micro-rotation and is the sum of material rotation plus the particles' relative rotation. While the new theory is used to analyze the crack tip field or the indentation problems, the stretch gradient is considered through a new hardening law. The key features of the theory are that the rotation gradient influences the material character through the interaction between the Cauchy stresses and the couple stresses; the term of stretch gradient is represented as an internal variable to increase the tangent modulus. In fact the present new strain gradient theory is the combination of the strain gradient theory proposed by Chen and Wang (Int. J. Plast., in press) and the hardening law given by Chen and Wang (Acta Mater. 48 (2000a) 3997). In this paper we focus on the finite element method to investigate material fracture for an elastic-power law hardening solid. With remotely imposed classical K fields, the full field solutions are obtained numerically. It is found that the size of the strain gradient dominance zone is characterized by the intrinsic material length l(1). Outside the strain gradient dominance zone, the computed stress field tends to be a classical plasticity field and then K field. The singularity of stresses ahead of the crack tip is higher than that of the classical field and tends to the square root singularity, which has important consequences for crack growth in materials by decohesion at the atomic scale. (C) 2002 Elsevier Science Ltd. All rights reserved.

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.

A New Version of Smoothed Point Method to Simulate Linear Elastic Wave Propagation

By using the kernel function of the smoothed particle hydrodynamics (SPH) and modification of statistical volumes of the boundary points and their kernel functions, a new version of smoothed point method is established for simulating elastic waves in solid. With the simplicity of SPH kept, the method is easy to handle stress boundary conditions, especially for the transmitting boundary condition. A result improving by de-convolution is also proposed to achieve high accuracy under a relatively large smooth length. A numerical example is given and compared favorably with the analytical solution.

Comparison between weight loss of bends in a pneumatic conveyor and erosion rate obtained in a centrifugal erosion tester for the same materials

In order to find a link between results obtained from a laboratory erosion tester and tests carried out on a pneumatic conveyor, a comparison has been made between weight loss from bends on an industrial-scale pneumatic conveyor and erosion rates obtained in a small centrifugal erosion tester, for the same materials. Identical test conditions have been applied to both experiments so that comparable test results have been obtained. The erosion rate of mild steel commonly used as the wall material of conveyor pipes and pipe bends was determined individually on both test rigs. A relationship between weight loss from the bends and erosion rate determined from the tester has been developed. A discussion based on the results and their applicability to the prediction of wear in pneumatic conveyors concludes the paper. © 2004 Elsevier B.V. All rights reserved.

Theermal Stress and Fracture in Transparent Optical Materials due to Laser Energy-Absorption by a Defect

利用热弹性理论分析了在光学材料中由于缺陷吸收激光能量引起的温度和热应力分布,并且针对一个简单的裂纹模型分析了热应力产生的应力强度因子,给出了一些主要参数对于应力强度因子的影响的规律。

Nonuniformity Effect of Surface-Nanocrystalline Materials in Nanoindentation Test

In the present research, microstructures of the surface-nanocrystalline Al alloy material are observed and measured based on the transmission electron microscopy (TEM) technique, and the corresponding mechanical behaviors are investigated experimentally and theoretically. In the experimental research, the nanoindentation test method is used, and the load and microhardness curves are measured, which strongly depend on the grain size and grain size nonuniformity. Two kinds of the nanoindentation test methods are adopted: the randomly selected loading point method and the continuous stiffness method. In the theoretical modeling, based on the microstructure characteristics of the surface-nanocrystalline Al alloy material, a dislocation pile-up model considering the grain size effect and based on the Mott theory is presented and used. The hardness-indent depth curves are predicted and modeled.

The Size-Dependent Elastic Properties of Nanofilms with Surface Effects

Size-dependent elastic constants are investigated theoretically with reference to a nanoscale single-crystal thin film. A three-dimensional _3D_ model is presented with the relaxation on the surface of the nanofilm taken into consideration. The constitutive relation of the 3D model is derived by using the energy approach, and analytical expressions for the four nonzero elastic constants of the nanofilm are obtained. The size effects of the four elastic constants are then discussed, and the dependence of these elastic constants on the surface relaxation and the ambiguity in the definition of the thickness of the nanofilm are also analyzed. In addition, the elastic moduli of the nanofilm in two kinds of plane problem are obtained and discussed in the case of a special boundary condition.

An elasto-plastic constitutive relation of whisker-reinforced metal-matrix composite

A material model for whisker-reinforced metal-matrix composites is constructed that consists of three kinds of essential elements: elastic medium, equivalent slip system, and fiber-bundle. The heterogeneity of material constituents in position is averaged, while the orientation distribution of whiskers and slip systems is considered in the structure of the material model. Crystal and interface sliding criteria are addressed. Based on the stress-strain response of the model material, an elasto-plastic constitutive relation is derived to discuss the initial and deformation induced anisotropy as well as other fundamental features. Predictions of the present theory for unidirectional-fiber-reinforced aluminum matrix composites are favorably compared with FEM results.

Creep response of sandwich beams with a metallic foam core

The creep response of metallic foam sandwich beams in 3-point bend is investigated numerically for the case of a metallic foam core and two steel faces. The face sheets are treated as elastic, while the foam core is modeled by a viscoplastic extension of the Deshpande-Fleck yield surface. This power-law creeping constitutive law has been implemented within the commercial finite element code ABAQUS. It is found that the beams creep by a variety of competing mechanisms, depending upon the choice of material properties and the geometric parameters. A failure map is constructed and effect of rate dependence on the load-deflection curves is quantified, and compared against the available experimental data.

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.

Using internal fibre geometry to improve the performance of pin-loaded holes in composite materials

The anisotropic nature of fibre reinforced composites leads to large stress concentrations around pin-loaded holes through standard weave cloths. Proper understanding of how this anisotropic nature affects the load distribution around holes can be utilised to reduce these con-centrations if sufficient thought is given to the internal fibre geometry near to the hole. Such local reinforcements need not be highly complex and can be readily produced without excessive effort, producing significant improvements in performance. © 1996 Kluwer Academic Publishers.