A dual conical indentation technique based on FEA solutions for property evaluation

The sharp indenters such as Berkovich and conical indenters have a geometrical self-similarity so that we can obtain only one parameter from an indentation loading curve, which makes different materials have the same load-displacement relation. Most studies to evaluate elastic-plastic properties by using the geometrical self-similar indenter have therefore tried to use dual/plural indentation techniques, on the basis of the concept of representative strain/stress varying with the indenter angle. However, any suggested representative concept is not universally operative for real materials. In this work, we suggest a method of material property evaluation without using the concept of representative strain. We begin the work by studying the characteristics of load-depth curves of conical indenters via finite element (FE) method. From FE analyses of dual-conical indentation, we investigate the relationships between indentation parameters and load-depth curves. The projected contact diameter is expressed as a function of the indenter angle, tip-radius, and material properties, which allows us to simply predict the elastic modulus. Two mapping functions for two indenter angles (45° and 70.3°) are presented to find the two unknowns (yield strain and strain-hardening exponent) via dual indentation technique. The method provides elastic modulus, yield strength and strain-hardening exponent with an average error of less than 5%. The method is valid for any elastically deforming indenters. We also discuss the sensitivity of measured properties to the load-displacement curve variation, and the difference between conical and Berkovich indenters.     

Deformation and fracture of rocks loaded with spherical indenters

The response of four rocks, namely granite, rhyolite, limestone and schist, to indentation by blunt cutting tools is discussed from a contact mechanics point of view. Contact forces between 0.1 kN and 2.45 kN are applied; indenter sizes are 1.0 and 5.0 mm, respectively. A transition from elastic to elastic-plastic response exists which depends on rock hardness and on indenter size. Blunt indenters promote elastic response; soft rocks tend to elastic-plastic response. In the elastic-plastic range, depression radius has a linear relationship to the indenter radius. Radial cracking occurs in soft rocks leading to strength degradation in the near surface regions. Sharp indenters promote radial cracking. The relationship between length of radial cracks and contact force is non-linear. Lateral cracking occurs in soft rocks leading to material removal. Sharp indenters promote lateral fractures. Anisotropy and non-homogeneity affect the material response notably. The ratio between fracture toughness and hardness (`index of brittleness') is a promising parameter to evaluate the behaviour of rock materials in excavation, drilling and fragmentation processes.     

Low-force AFM nanomechanics with higher-eigenmode contact resonance spectroscopy

Atomic force microscopy (AFM) methods for quantitative measurements of elastic modulus on stiff (>10?GPa) materials typically require tip-sample contact forces in the range from hundreds of nanonewtons to a few micronewtons. Such large forces can cause sample damage and preclude direct measurement of ultrathin films or nanofeatures. Here, we present a contact resonance spectroscopy AFM technique that utilizes a cantilever's higher flexural eigenmodes to enable modulus measurements with contact forces as low as 10?nN, even on stiff materials. Analysis with a simple analytical beam model of spectra for a compliant cantilever's fourth and fifth flexural eigenmodes in contact yielded good agreement with bulk measurements of modulus on glass samples in the 50-75?GPa range. In contrast, corresponding analysis of the conventionally used first and second eigenmode spectra gave poor agreement under the experimental conditions. We used finite element analysis to understand the dynamic contact response of a cantilever with a physically realistic geometry. Compared to lower eigenmodes, the results from higher modes are less affected by model parameters such as lateral stiffness that are either unknown or not considered in the analytical model. Overall, the technique enables local mechanical characterization of materials previously inaccessible to AFM-based nanomechanics methods.     

Characterization of stress-strain relationships of elastoplastic materials: An improved method with conical and pyramidal indenters

The load-displacement curve in indentation is widely used to extract elastoplastic properties of materials. It is believed that such a measurement is non-unique and a full stress-strain curve cannot be obtained with a sharp indenter or even plural and spherical indenters. By introducing a ratio of the additional residual area to the area of a profile indenter, we proposed a new set of dimensionless functions. Based on these functions and finite element simulations, analytical expressions were derived between indentation data and elastoplastic properties. It is shown that this method can effectively distinguish highly elastic and plastic solids (Cheng and Cheng, 1999) and mystical materials (Chen et al., 2007), which provides a useful guideline for properly using the indentation technique to measure elastoplastic properties of materials with conical and pyramidal indenters.     

The influence of correlating material parameters of gradient foam core on free vibration of sandwich panel

For the sandwich panel with mass density gradient (DG) foam core, the Young's modulus of the core varies with the mass density along the thickness direction. To characterize the correlative effect of Young's modulus and mass density of the DG closed-cell foam material, a simplified formula is presented. Subsequently, based on a high-order sandwich plate theory for sandwich panel with homogeneous core, a new gradient sandwich model is developed by introducing a gradient expression of material properties. Finite element (FE) simulation is carried out in order to verify this model. The results show that the proposed model can predict well the free vibration of composite sandwich panel with the gradient core. Finally, the correlating effects of material parameters of the DG foam core on the natural frequencies of sandwich panel are investigated. It is found that the natural frequencies of sandwich panels decrease as the gradient changes of the DG foam cores increase under the condition of that the core masses keep constant.     

Characterization of single crystal silicon and electroplated nickel films by uniaxial tensile test with in situ X-ray diffraction measurement

In this study, mechanical properties of micron‐thick single crystalline silicon (Si) and electroplated nickel (Ni) films at intermediate temperatures are investigated by means of X‐ray diffraction (XRD) tensile testing. The developed tensile test technique enables us to directly measure lateral (out‐of‐plane) elastic strain of microscale crystalline specimen using XRD during tensile loading, and determines Young's modulus, Poisson's ratio and tensile strength of the Si and Ni specimens. The specimens, measuring 10 μm thick, 300 μm wide and 3 mm long, are prepared through a conventional micro‐machining process, and the ultraviolet lithographie galvanoformung abformung (UV‐LIGA) process including a molding and an electroplating. The Si specimens, showing brittle fracture at room temperature (R.T.), have average Young's modulus and Poisson's ratio of 169 GPa and 0.35, respectively, in very good agreement with analytical values. The Ni specimens, showing ductile fracture, have those of 190 GPa and 0.24, lower than bulk coarse grained Ni. Young's moduli of both the Si and Ni specimens decrease with increasing temperature, but Poisson's ratios are independent of temperature. The influence of specimen size on elastic‐plastic properties of the specimens is discussed.     

A comparison of indentations of different size and geometry in single-quasicrystalline AIPdMn

The study compares impressions into one and the same single-quasicrystalline Al₇₀Pd₂₀Mn₁₀ sample (surface of fivefold symmetry) that were performed by spherical and pointed indenters (Vickers- and corner-of-a-cube-geometry) and investigated using Atomic Force Microscopy (AFM). The Meyer hardness number was found to vary with indentation size in a manner similar to materials that work harden, though this behavior must have a different physical origin: for spherical indentations the hardness number slightly increases with increasing load (Meyer hardness evolution), whereas for pyramid-shaped indenters a considerable hardness increase in case of decreasing load can be stated. Spherical indentations show little piling-up only in contrast to pointed indentations where huge elevations surrounding the indent developed. Different degrees of lateral cracking can account for this observation. In case of Vickers indentations the material breaks into segments which display mutual shearing. Distinct differences can also be noticed with respect to the volume balance between the apparent piled-up volume around the impression and the volume of the displaced material. This balance proves positive for pyramidal and negative for spherical impressions.     

Computational study of the effect of carbon vacancy defects on the Young's modulus of (6, 6) single wall carbon nanotube

Most molecular dynamics (MD) simulations for single wall carbon nanotubes (SWCNT) are based on a perfect molecular material structure. The presence of vacancy defects in SWCNTs could lead to deviations from this perfect structure thus affecting the predicted properties. The present paper investigates the effect of carbon vacancy defects in the molecular structure of SWCNT on the Young's modulus of the SWCNT using MD simulations performed via Accelrys and Materials Studio. The effect of the position of the defects in the nanotube ring and the effect of the number of defects on the Young's modulus are studied. The studies indicate that for an enclosed defect with the same shape in a SWCNT structure, its position did not cause any change in the Young's modulus. However, as the number of defects increased, the predicted Young's modulus was found to decrease. For a 10 ring (6, 6) SWCNT, six vacancy defects (corresponding to a defect percentage of 2.5%) reduced the Young's modulus by 13.7%.     

An engineering model for deformation of CFRP plates during penetration

The response of brittle CFRP laminated plates to penetration by cylindrical indenters has been studied using a combined experimental and analytical investigation. The two major damage modes caused by delamination and plugging are found to divide the plate response into three distinct stages. An analytical model, which accounts for the geometric parameters of the response, is developed to describe the deformation behaviour of the laminate in the post-delamination stage. Using the experimental measurements of strains and displacements at the centre, the model is used to estimate the size of the internal damage (delamination) and its effective bending modulus. The predicted delamination sizes for various laminate thicknesses are successfully correlated with those measured using C-scans. The agreement instills confidence in using the present analytical approach to reduce the number of tests required to characterize the penetration response of laminates.     

Elastoplastic analysis of functionally graded spherical pressure vessels

Purely elastic, partially plastic and fully plastic stress states of internally pressurized functionally graded spherical pressure vessels are investigated analytically in the framework of small deformation theory. The modulus of elasticity and the uniaxial yield limit of the spherical pressure vessel material are assumed to vary nonlinearly in the radial direction. The plastic model is based on Tresca’s yield criterion and ideal plastic material behavior. It is shown that, unlike in the case of a homogeneous spherical pressure vessel, different modes of plasticization may take place due to the radial variation of the functionally grading parameters.     

OPTIMAL DISTRIBUTION OF FILLER MATERIAL IN A CIRCULAR PLATE MADE OF PARTICULATE COMPOSITE

Optimal distribution of reinforcing particles in a continuous matrix is determined in order to maximize the stiffness of a simply supported and symmetrically loaded circular plate. The elastic constants are computed from a dilute suspensions model which relates the concentration of inclusions to material properties by assuming a low volume fraction of spherical particles within the matrix. A linear relationship between the concentration of inclusions and the Young's modulus is obtained by neglecting the higher order concentration terms in the expression for the elastic modulus. This procedure leads to a closed form solution of the design problem which is accurate for small volumes of the filler material. Efficiency of the design is assessed by comparing the maximum deflections of the optimal (nonhomogeneous) and the homogeneous plates. Numerical results are given in graphical form     

Relationship between structure and thermal fatigue in cast iron

Abstract

Thermal fatigue of a material is determined by rupture stress, the elasticity modulus, heat conductivity, and thermal expansion. In addition to thermal expansion, one has to consider also the volume changes as a result of phase transformations. It is known that high rupture stress and high heat conductivity result in high resistance to thermal fatigue. A high Young's modulus and high thermal expansion give low resistance to thermal fatigue. Cast iron is a composite material, consisting mostly of graphite, ferrite, and cementite. The graphite can occur in a number of different morphologies. It can be spherical, as in ductile cast iron, it can be flakelike, as in flake cast iron, but it can also be rodlike, as in vermicular or undercooled graphite. Many of the properties important for thermal fatigue are influenced by the shape of the graphite. By using various models to explain the properties of composite materials, the changes in the properties of cast iron as a function of graphite shape are analysed. The analytical results are compared with experimental results. It is shown that the elasticity modulus and thermal expansion are lowest for flake graphite and that thermal conductivity is highest for this material. The conclusion is that grey cast iron has a better resistance to thermal fatigue than vermicular as well as nodular cast irons, in spite of its lower rupture stress.

MST/783     

Mechanical behaviour of ferrocement composites: an experimental investigation

In-plane tension, compression and bending tests were conducted on plain mortar and ferrocement specimens with woven and welded meshes. Tension tests were also carried out on meshes. Bending tests were conducted using specimens with centre point loading. The objective of the study was to investigate the behaviour of material reinforced with varying number of mesh layers and orientations and to evolve a set of elastic and inelastic material properties. It is observed that the conventional empirical relations based on mortar crushing strength overestimate the mortar modulus. The elastic moduli obtained using the rule of mixtures compares well with the values evaluated from the tests on ferrocement specimens. The 45° orientation emerges as the weakest configuration both in terms of the Young's modulus and ultimate stress because of the lowest volume fraction of wire mesh in the direction of loading at this orientation.     

Input error sensitivity of hardness and elastic modulus evaluated from indentation load-displacement records by Oliver and Pharr method

Due to its straightforwardness and the ease of implementation the Oliver-Pharr method [1] has been used in the analysis of load-displacement records for more than a decade now. This paper provides analytical expressions relating the errors in the hardness and elastic modulus obtained by this method to systematic calibration errors of measured depth, force and frame compliance for spherical and sharp indentation. While in systems with zero frame compliance the sensitivity ratios for depth and force measurement were found to be constant, in systems with a finite frame compliance the error sensitivity changes with the absolute values of applied force and measured depth. The analytical predictions are compared with the true variation in derived materials parameters and the ranges of validity of the expressions are established. The error sensitivity with respect to different input variables and its implications for the actual measurement are discussed.     

High-modulus steels reinforced with ceramic particles through ingot casting process

High Young's modulus steels can be fabricated based on the concept of metal matrix composites. In this paper, a number of reinforcing ceramic phases with high Young's modulus are assessed and selected to design compositions for high-modulus steels based on thermodynamic calculations. The steel matrix composites reinforced with boride and carbide phases are produced through ingot casting and are processed thermomechanically to strips following standard processing routes for automotive products. The results show that the Young's modulus of steels in the as-cast condition can be increased using borides and carbides. However, further down-stream processing via conventional thermomechanical processing leads to a gradual degradation of the Young's modulus due to extensive void formation. The opportunities and challenges of ceramic-reinforced high-modulus steels produced via conventional ingot casting and thermomechanical processing for the automotive market are discussed.     

Thermo-elastic/plastic semi-analytical solution of incompressible functionally graded spherical pressure vessel under thermo-mechanical loading

In this paper, numerical solutions to assess partially plastic and fully plastic deformation behavior of a functionally graded spherical pressure vessel are presented. The modulus of elasticity of the material is assumed to vary nonlinearly in the radial direction and axisymmetric displacements and stresses in the functionally graded spherical vessel subjected to thermal loading and uniform internal pressure are determined using plasticity theory. Tresca??s yield criterion and its associated flow rule are used to formulate different plastic regions for an ideal FG material. In this way, the material property varies by Young??s modulus that may be an arbitrary function of the radial coordinate. Therefore, the material is assumed to be functionally graded in the radial direction. Hence, the general analytical solutions of such equations are not available, the numerical method (semi-analytical) is applied and a new collection of equilibrium equations with small deflections is presented. Accordingly, the radial domain is divided into some virtual sub-domains in which the power-law distribution is used for the thermomechanical properties of the elemental components. By considering the necessary continuity conditions between adjacent sub-domains, jointly with the global boundary conditions, a set of linear differential equations is obtained. Solution of the linear differential equations yields the thermoelastic responses for each sub-domain as exponential functions of the radial coordinate. Subsequently, attributed to centrifugal force, results for the stress, strain, and displacement components along the radius in elastic and plastic area are presented.     

Simple cylindrical and spherical finite elements

Finite element approximations are developed for three‐dimensional domains naturally represented in either cylindrical or spherical coordinates. Lines of constant radius, axial length, or angle are used to represent the domain and cast approximations that are natural for these geometries. As opposed to general isoparametric three‐dimensional elements generated in conventional parent space, these elements can be evaluated analytically and do not generate geometric discretization error. They also allow for anisotropic material coefficients that are frequently aligned in either cylindrical or spherical coordinates. Several examples are provided that show convergence properties and comparison with analytical solutions of the Poisson equation.     

扫描探针显微技术测量血管内皮细胞的弹性

血管内皮细胞的功能与许多疾病间存在关联,但现在对其功能好坏的定量描述仍十分少见。该文以内皮细胞的弹性作为衡量其功能的一个标准。通过理论建立压痕测量杨氏模量的计算方法,并利用扫描探针显微镜从实验上得到了正常及过氧化氢处理过的人脐静脉内皮细胞的杨氏模量。发现过氧化氢处理后细胞的杨氏模量升高,表明通过杨氏模量来表征细胞活性是可行的。