The role of friction on sharp indentation

Frictional effects on sharp indentation of strain hardening solids are examined in this paper. The results of finite element simulations in a wide range of solids allow us to derive two simplified equations, accounting for the influence of the friction coefficient on hardness. Comparisons between the simulations and instrumented micro-indentation experiments are undertaken to ensure the validity of the former to metallic materials. Quantitative estimates of the role of friction on the development of pileup and sinking-in around the contact boundary are also given in the paper. These results provide a physical insight into the plastic flow features of distinctly different solids brought into contact with sharp indenters. Overall, the investigation shows that the amount of pileup can be used to set the range of validity of the two hardness equations indicated above. Friction has the largest influence on the contact response of solids exhibiting considerable piling-up effects (whose parameter , see text for details), whereas materials developing moderate pileup or sinking-in are less sensitive to friction. Finally, a methodology is devised to assess the influence of the friction coefficient on mechanical properties extracted through indentation experiments.     

Thermoelastic contact problem of two rotating bodies with frictional heat generation in annular region

Summary An axisymmetric contact problem with frictional heating is considered in which a parabolic annular punch is pressed into a plane surface and rotates about its axis of symmetry at constant speed. The problem is formulated in terms of one governing equation with unknown pressure. This equation is solved numerically. The change of the geometry of the contact region and pressure has been investigated. Received 21 May 1997; accepted for publication 23 June 1997     

The scale behavior of fillers in elastomers by means of indentation tests

 Indentation tests were carried out on a carbon black filled rubber sample on different length scales. The experiments covered the range from aggregation of particles on the submicron scale up to structures which represent the bulk properties of the sample on the millimeter scale. The local stiffness was used to visualize the areas investigated; therefore, mechanical images were obtained for all length scales. So-called “mechanical units” were defined for every scale. The size distribution curves for the mechanical units were analyzed and they were found to be non-Gaussian-shaped for every scale. Moreover, the distribution curves of the mechanical units are similar to the distribution curves of particles and aggregates obtained by electron microscopy reported in the literature. Evaluation by means of fractal analysis led to fractal dimensions for the mechanical units. It could be shown in the present case that the fractal dimension D≈1.24 of the mechanical units in the range of submicrons up to several hundred microns is in good agreement with that of the filler aggregates proposed in the literature. Furthermore, D is constant over a wide range of about 6 decades in area scale starting from aggregates up to the size of agglomerates. This leads to the conclusion that the local arrangement of the filler ensembles seems to be self-similar from the smallest scale of aggregation of particles up to the largest formation observed by indentation testing on the millimeter scale. Received: 15 May 2001 Accepted: 18 August 2001     

Instrumented Macroindentation Techniques for Polymers and Composites – Mechanical Properties,Fracture Toughness and Time-Dependent Behaviour as a Function of the Temperature

An innovative cooling and heating device has been successfully applied to an instrumented macrohardness testing machine in close collaboration with the company Zwick/Roell. The prototype allows the local time-dependent analysis of mechanical properties such as Martens hardness and indentation modulus, as well as fracture toughness and creep and relaxation behaviour at temperatures ranging from −100 °C to +100 °C. On the basis of load–indentation depth, load–time or indentation depth–time diagrams, the indentation behaviour as a function of test speed and/or temperature (which has rarely been done for polymers in the macro-range of loading) depending on matrix and materials composition (amorphous/semicrystalline thermoplastics, epoxy resins, micro- and nanocomposites) has been analysed. Martens-hardness, indentation modulus on the one hand and creep compliance and relaxation modulus on the other have been found to be strongly temperature dependent. Adequate methods of indentation fracture mechanics have been enhanced for polymers and applied to determine the fracture toughness of very different polymer-based materials.     

Ordering effect on the mechanical,electronic and magnetic properties of the β-based non-canonical approximant phases: β-Al50Cu33Fe17, η-Al50Cu44Fe6 and φ-Al47.5Cu49.5Fe3

Abstract

Using transmission electron microscopy and X-ray diffraction, we established that the ordered η1-Al₅₀Cu₄₄Fe₆ and φ-Al_47.5Cu_49.5Fe₃ (Fmm2) alloys with nano-sized domain structure are formed by slowly cooling, whereas β-solid solutions with a short-range order were found in quenched states. The φ′-modification which exhibits the additional long-period superstructure was also observed in Al_47.5Cu_49.5Fe₃. The studies of low temperature magnetic susceptibility and heat capacity did not reveal any another phase transitions in these alloys. The indentation test showed that hardness and Young’s modulus consistently grow as β-Al₅₀Cu₃₃Fe₁₇ → η1-Al₅₀Cu₄₄Fe₆ → (φ+φ′)-Al_47.5Cu_49.5Fe₃ and approach to those in icosahedral phase. The same trend in the Young’s modulus was obtained for alloys containing β-solid solution with a short-range order. Ab initio calculations, however, predicted the opposite tendency in cubic β-Al₅₀Cu_50?xFe_x with a decrease in x, which was explained by the weakening of the covalent Fe 3d – Al sp bonding. This discrepancy between the results for β- and ordered phases, we related to a crucial effect of ordering which is accompanied by a progressive distortion of cubic local structure in the series β-Al₅₀Cu₃₃Fe₁₇ → η1-Al₅₀Cu₄₄Fe₆ → φ-Al_47.5Cu_49.5Fe_3. As we demonstrated for η-Al(Cu, Fe), these distortions lead to the strengthening of the both covalent Fe–Al and Cu–Al bonds and the higher modules.     

pH Dependent Elasticity of Polystyrene‐block‐poly(acrylic acid) Vesicle Shell Membranes by Atomic Force Microscopy

We assess the elastic properties of PS‐b‐PAA vesicle membranes under different pH values by AFM force measurements. We find that based on the shell deformation theory, the values of the estimated apparent Young's modulus of the vesicle membranes decrease as the pH of the solution increases. The onset of the decrease of E coincides with the surface pK_a determined from ζ‐potential measurements. This decrease of E at higher pH is attributed to electrostatic repulsion between the deprotonated PAA chains resulting in the thinning of the vesicle membrane.

     

Spherical indentation of incompressible rubber-like materials

In recent years, indentation tests have been proven very useful in probing mechanical properties of small volumes of materials. However, a class of materials that very little has been done in this direction is rubber-like materials (elastomers). The present work investigates the spherical indentation of incompressible rubber-like materials. The analysis is performed in the context of second-order hyperelasticity and is accompanied by finite element computations and an extensive experimental program with spherical indentors of different radii. Uniaxial tensile tests were also performed and it was found that the initial elastic modulus correlates well with the indentation response. The experiments suggest stiffer indentation response than that predicted by linear elasticity, which is somehow counter-intuitive, if the uniaxial material response is to be considered. Regarding the uniqueness of the inverse problem, that is to establish material properties from spherical indentation tests, the answer is disappointing. We prove that the inverse problem does not give unique answer regarding the constitutive relation, except for the initial stiffness.     

光学元件亚表层裂纹成核临界条件研究

基于压痕实验和连续刚度测量法得到了熔石英材料硬度和弹性模量随压入深度的变化曲线, 系统分析了材料由延性到脆性转变的过程, 确定了熔石英晶体在静态/准静态印压和动态刻划时产生裂纹的临界载荷和临界深度。渐变载荷刻划实验结果表明, 划痕过程诱发的裂纹对法向载荷有很强的依赖性, 载荷较小时材料去除方式为延性域去除。随着法向载荷的增加, 首先产生垂直于试件表面的中位裂纹和平行于试件表面方向扩展的侧向裂纹, 而在试件表面上并没有产生明显的特征。载荷进一步增加后, 侧向裂纹扩展并形成了明亮区域, 最终诱发了沿垂直于或近似垂直于压头运动方向扩展的径向裂纹, 实现了材料的脆性去除。     

Young's modulus of ZnO microwires determined by various mechanical measurement methods

The mechanical properties of ZnO microwires have been studied using three different methods: quasi-static flexural measurements using atomic force microscopy, static measurements using a nano indenter, and dynamic flexural measurements using optical interferometry. ZnO microwires were synthesized by chemical vapor deposition method, and the crystal structure and quality were examined using x-ray diffraction and photoluminescence spectroscopy. The Young's moduli were estimated using the measurement results from the three methods, and they showed consistent values in the range 67.5–79.4 GPa for microwires with diameters of 1.8 μm ± 100 nm.     

Size-dependent sharp indentation-II: a reverse algorithm to identify plastic properties of metallic materials

In part I of this paper (Cao and Lu, J. Mech. Phys. Solids, in press), a closed-form expression of the size-dependent sharp indentation loading curve has been proposed. In this second part, which concerns the direct application of the analytical model, a reverse algorithm has first been established to extract the plastic properties of metallic materials on a small scale where the size effect caused by geometrically necessary dislocations is significant. Second, from the viewpoint of the mathematical theory of inverse problems, the properties of the present inverse problem i.e. the existence, uniqueness and stability of the solution, have been investigated systematically. The results have identified the extent to which the plastic properties of ductile materials can be determined effectively using the present method. Third, experimental verifications of the reverse algorithm using a standard Berkovich indenter have been carried out for 316 stainless steel and pure titanium, respectively. The results show that, by taking a maximum indentation depth of 1.5 and , respectively for the two materials, a good engineering estimation of the representative stresses, σ_0.033, in the absence of a strain gradient can be made using the present method, which can be used in conjunction with the representative stress corresponding to another indenter with a different tip apex angle to determine the plastic properties of metallic materials, i.e. the yield strength σ_y and the strain hardening exponent n. The material length scale can also be identified by using the present algorithm. Experimental results show that it has the correct order of magnitude, but is more sensitive to data errors than the identified representative stress.