A nanoindentation analysis of the effects of microstructure on elastic properties of Al2O3/SiC composites

Nanoindentation tests were carried out to investigate certain elastic properties of Al2O3/SiCp composites at microscopic scales (nm up to mu m) and under ultra-low loads from 3 mN to 250 mN, with special attention paid to effects caused by SiC particles and pores. The measured Young's modulus depends on the volume fraction of SiC particles and on the composite porosity and it can compare with that of alumina. The Young's modulus exhibits large scatters at small penetrations, but it tends to be constant with lesser dispersion as the indentation depth increases. Further analysis indicated that the scatter results from specific microstructural heterogeneities. The measured Young's moduli are in agreement with predictions, provided the actual role of the microstructure is taken into account. (C) 2007 Elsevier Ltd. All rights reserved.

Evaluation of the Effectiveness of Representative Methods for Determining Young's Modulus and Hardness from Instrumented Indentation Data

The effectiveness of Oliver & Pharr's (O&P's) method, Cheng & Cheng's (C&C's) method, and a new method developed by our group for estimating Young's modulus and hardness based on instrumented indentation was evaluated for the case of yield stress to reduced Young's modulus ratio (sigma(y)/E-r) >= 4.55 x 10(-4) and hardening coefficient (n) <= 0.45. Dimensional theorem and finite element simulations were applied to produce reference results for this purpose. Both O&P's and C&C's methods overestimated the Young's modulus under some conditions, whereas the error can be controlled within +/- 16% if the formulation was modified with appropriate correction functions. Similar modification was not introduced to our method for determining Young's modulus, while the maximum error of results was around +/- 13%. The errors of hardness values obtained from all the three methods could be even larger and were irreducible with any correction scheme. It is therefore suggested that when hardness values of different materials are concerned, relative comparison of the data obtained from a single standard measurement technique would be more practically useful. It is noted that the ranges of error derived from the analysis could be different if different ranges of material parameters sigma(y)/E-r and n are considered.

An Improved Energy Method For Determining Young'S Modulus By Instrumented Indentation Using A Berkovich Tip

We previously proposed a method for estimating Young's modulus from instrumented nanoindentation data based on a model assuming that the indenter had a spherical-capped Berkovich geometry to take account of the bluntness effect. The method is now further improved by releasing the constraint on the tip shape, allowing it to have a much broader arbitrariness to range from a conical-tipped shape to a flat-ended shape, whereas the spherical-capped shape is just a special case in between. This method requires two parameters to specify a tip geometry, namely, a volume bluntness ratio V-r and a height bluntness ratio h(r). A set of functional relationships correlating nominal hardness/reduced elastic modulus ratio (H-n/E-r) and elastic work/total work ratio (W-e/W) were established based on dimensional analysis and finite element simulations, with each relationship specified by a set of V-r and h(r). Young's modulus of an indented material can be estimated from these relationships. The method was shown to be valid when applied to S45C carbon steel and 6061 aluminum alloy.

Nanoindentation of thin-film-substrate system: Determination of film hardness and Young's modulus

In the present paper, the hardness and Young's modulus of film-substrate systems are determined by means of nanoindentation experiments and modified models. Aluminum film and two kinds of substrates; i.e. glass and silicon, are studied. Nanoindentation XP II and continuous stiffness mode are used during the experiments. In order to avoid the influence of the Oliver and Pharr method used in the experiments, the experiment data are analyzed with the constant Young's modulus assumption and the equal hardness assumption. The volume fraction model (CZ model) proposed by Fabes et al. (1992) is used and modified to analyze the measured hardness. The method proposed by Doerner and Nix (DN formula) (1986) is modified to analyze the measured Young's modulus. Two kinds of modified empirical formula are used to predict the present experiment results and those in the literature, which include the results of two kinds of systems, i.e., a soft film on a hard substrate and a hard film on a soft substrate. In the modified CZ model, the indentation influence angle, phi, is considered as a relevant physical parameter, which embodies the effects of the indenter tip radius, pile-up or sink-in phenomena and deformation of film and substrate.

A comparative study of Young's modulus of single-walled carbon nanotube by CPMD, MD, and first principle simulations

Carbon nanotubes (CNTs), due to their exceptional magnetic, electrical and mechanical properties, are promising candidates for several technical applications ranging from nanoelectronic devices to composites. Young's modulus holds the special status in material properties and micro/nano-electromechanical systems (MEMS/NEMS) design. The excellently regular structures of CNTs facilitate accurate simulation of CNTs' behavior by applying a variety of theoretical methods. Here, three representative numerical methods, i.e., Car-Parrinello molecular dynamics (CPMD), density functional theory (DFT) and molecular dynamics (MD), were applied to calculate Young's modulus of single-walled carbon nanotube (SWCNT) with chirality (3,3). The comparative studies showed that the most accurate result is offered by time consuming DFT simulation. MID simulation produced a less accurate result due to neglecting electronic motions. Compared to the two preceding methods the best performance, with a balance between efficiency and precision, was deduced by CPMD.

An Instrumented Indentation Method for Young's Modulus Measurement with Accuracy Estimation

The relationships between indentation responses and Young's modulus of an indented material were investigated by employing dimensional analysis and finite element method. Three representative tip bluntness geometries were introduced to describe the shape of a real Berkovich indenter. It was demonstrated that for each of these bluntness geometries, a set of approximate indentation relationships correlating the ratio of nominal hardness/reduced Young's modulus H (n) /E (r) and the ratio of elastic work/total work W (e)/W can be derived. Consequently, a method for Young's modulus measurement combined with its accuracy estimation was established on basis of these relationships. The effectiveness of this approach was verified by performing nanoindentation tests on S45C carbon steel and 6061 aluminum alloy and microindentation tests on aluminum single crystal, GCr15 bearing steel and fused silica.

Study of elastic modulus and yield strength of polymer thin films using atomic force microscopy

Nanometer-scale elastic moduli and yield strengths of polycarbonate (PC) and polystyrene (PS) thin films were measured with atomic force microscopy (AFM) indentation measurements. By analysis of the AFM indentation force curves with the method by Oliver and Pharr, Young's moduli of PC and PS thin films could be obtained as 2.2 +/- 0.1 and 2.6 +/- 0.1 GPa, respectively, which agree well with the literature values. By fitting Johnson's conical spherical cavity model to the measured plastic zone sizes, we obtained yield strengths of 141.2 MPa for PC thin films and 178.7 MPa for PS thin films, which are similar to2 times the values expected from the literature. We propose that it is due to the AFM indentation being asymmetric, which was not accounted for in Johnson's model. A correction factor, epsilon, of similar to0.72 was introduced to rescale the plastic zone size, whereupon good agreement between theory and experiment was achieved.

MECHANICAL-PROPERTIES OF PHENOLPHTHALEIN POLYETHER KETONE - YIELD STRESS, YOUNGS MODULUS, AND FRACTURE-TOUGHNESS

A series of tensile and three-point bending studies was conducted at various temperatures and loading rates using phenolphthalein polyether ketone (PEK-C). Yield stress, Young's modulus, fracture toughness, and crack opening displacement data were obtained for various conditions. In general, both yield stress and Young's modulus increase with decreasing temperature. However, the relationships between fracture toughness, loading rate, and temperature are very complex. This behavior is due to the simultaneous intersection of viscoelasticity and localized plastic deformation. The increased yield stress is the main factor contributing to the reduction in fracture toughness and crack opening displacement. The relationship between fracture toughness and yield stress are discussed. (C) 1995 John Wiley and Sons, Inc.

Stiffness behaviour of injection moulded short glass fibre/impact modifier/polypropylene hybrid composites

The stiffness behaviour of injection moulded short glass fibre/impact modifier/polypropylene hybrid composites has been investigated in this work by theoretical predictions and experiments. Predictions from the self-consistent method were found to be in good agreement with test results for the impact modifier/polypropylene blends. By taking into account of the fibre orientation distributions in the skin and core layers, the values of Young's modulus for the skin and core layers were predicted by employing Eshelby's equivalent inclusion method and the average induced strain approach. The prediction of the values of Young's modulus for the whole sample was obtained by applying the simple mixture theory of laminated composites to the predicted results for the skin and core layers. Good correlation between predicted and experimental Young's modulus values were found.

Effects of 'sinking in' and 'piling up' on estimating the contact area under load in indentation

The phenomena of the 'piling up' and 'sinking-in' of surface profiles in conical indentation in elastic-plastic solids with work hardening are studied using dimensional and finite-element analysis. The degree of sinking in and piling up is shown to depend on the ratio of the initial yield strength Y to Young's modulus E and on the work-hardening exponent n. The widely used procedure proposed by Oliver and Pharr for estimating contact depth is then evaluated systematically. By comparing the contact depth obtained directly from finite-element calculations with that obtained from the initial unloading slope using the Oliver-Pharr procedure, the applicability of the procedure is discussed.

Investigation of the Mechanical Properties of Thin Films by Nanoindentation, Considering the Effects of Thickness and Different Coating-Substrate Combinations

In order to further investigate nanoindentation data of film-substrate systems and to learn more about the mechanical properties of nanometer film-substrate systems, two kinds of films on different substrate systems have been tested with a systematic variation in film thickness and substrate characteristics. The two kinds of films are aluminum and tungsten, which have been sputtered on to glass and silicon substrates, respectively. Indentation experiments were performed with a Nano Indent XP II with indenter displacements typically about two times the nominal film thicknesses. The resulting data are analyzed in terms of load-displacement curves and various comparative parameters, such as hardness, Young's modulus, unloading stiffness and elastic recovery. Hardness and Young's modulus are investigated when the substrate effects are considered. The results show how the composite hardness and Young's modulus are different for different substrates, different films and different film thicknesses. An assumption of constant Young's modulus is used for the film-substrate system, in which the film and substrate have similar Young's moduli. Composite hardness obtained by the Joslin and Oliver method is compared with the directly measured hardness obtained by the Oliver and Pharr method.

Saturated duration for dynamic structural plastic response and fundamental periods of elastic vibration

The relationship is determined between saturated duration of rectangular pressure pulses applied to rigid, perfectly plastic structures and their fundamental periods of elastic vibration. It is shown that the ratio between the saturated duration and the fundamental period of elastic vibration of a structure is dependent upon two factors: the first one is the slenderness or thinness ratio of the structure; and the second one is the square root of ratio between the Young's elastic modulus and the yield stress of the structural material. Dimensional analysis shows that the aforementioned ratio is one of the basic similarity parameters for elastic-plastic modeling under dynamic loading.

Experimental Studies of the Material Properties of the Forewing of Cicada (Homoptera, Cicadidae)

Detailed investigations on the structural and mechanical properties of the forewing of the cicada were carried out. Measurement of the structures of the wings showed that the thickness of the membrane of each cell and the diameter of each vein were non-uniform in both the longitudinal and transverse directions, and their means were approximately 12.2 and 133.3 mum, respectively. However, the aspect ratios of the wings and the bodies were quite uniform and were approximately equal to 2.98 and 2.13, respectively. Based on the measured thickness, mass and area of the membranes of the cells, the mean density and the mean area density of the wing were approximately 2.3 g cm(-3) and 2.8 x 10(-3) g cm(-2), respectively. In addition, the diameters of the veins of the wings, including the diameters of the holes in the vein of the leading edge, were examined. The mechanical properties of the wing were investigated separately by nanoindentation and tensile testing. The results indicated that the mean Young's modulus, hardness and yield stress of the membranes of the wings were approximately 3.7 Gpa, 0.2 Gpa and 29 Mpa, respectively, and the mean Young's modulus and strength of the veins along the direction of the venation of wings were approximately 1.9 Gpa and 52 Mpa, respectively. Finally, the relevant results were briefly analyzed and discussed, providing a guideline to the biomimetic design of the aerofoil materials of micro air vehicles.

Relationships between hardness, elastic modulus, and the work of indentation

The work done during indentation is examined using dimensional analysis and finite element calculations for conical indentation in elastic-plastic solids with work hardening. An approximate relationship between the ratio of hardness to elastic modulus and the ratio of irreversible work to total work in indentation is found. Consequently, the ratio of hardness to elastic modulus may be obtained directly from measuring the work of indentation. Together with a well-known relationship between elastic modulus, initial unloading slope, and contact area, a new method is then suggested for estimating the hardness and modulus of solids using instrumented indentation with conical or pyramidal indenters.

Impact response and failure mechanisms of ultrahigh modulus polyethylene fiber composites and polyethylene fiber-carbon fiber hybrid composites

The impact response and failure mechanisms of ultrahigh modulus polyethylene (UHMPE) fiber composites and UHMPE fiber-carbon fiber hybrid composites have been investigated. Charpy impact, drop weight impact and high strain rate impact experiments have been performed in order to study the impact resistance, notch sensitivity, strain rate sensitivity and hybrid effects. Results obtained from dynamic and quasi-static measurements have been compared. Because of the ductility of UHMPE fibers, the impact energy absorption of UHMPE fiber composites is very high, thereby leading to excellent damage tolerance. By hybridizing with UHMPE fibers, the impact properties of carbon fiber composites can be greatly improved. The impact and shock failure mechanisms of these composites are discussed.