Conditions of applying Oliver–Pharr method to the nanoindentation of particles in composites

The indentation test is a popular experimental method to measure a material’s mechanical properties such as elastic modulus and hardness, and the Oliver–Pharr method is commonly used in commercial indentation instruments to obtain these two quantities. To apply the Oliver–Pharr method correctly in all of these cases, it is essential to know the limitations of this method. The present study focuses on the applicability of the Oliver–Pharr method to measure the mechanical properties of particles in composites. The finite element method is used to undertake virtual indentation tests on a particle embedded in a matrix. In our numerical studies, the indentation “pile-up” phenomenon is generally observed in our numerical case studies, which indicates that the contact area used for predicting the elastic modulus should be measured directly, not be estimated from the indentation curve. The Oliver–Pharr method based on the real contact area is applied to estimate the elastic modulus of the particles by using the indentation curve from the numerical simulation, with the estimated elastic modulus being compared with the input value. Applying the real contact area value (not the one predicted from the indentation curve) we show that the Oliver–Pharr method can still be applied to measure the elastic modulus of the particle with sufficient accuracy if the indentation depth is smaller than the particle-dominated depth, a value defined in this work. The influences of the matrix and particle properties on the particle-dominated depth are studied using a dimensional analysis and parametric study. Our results provide guidelines to allow the practical application of the Oliver–Pharr method to measure the elastic modulus of particles in composites. This could be particularly important where particles are formed in situ in a matrix (as opposed to being preformed and subsequently incorporated in a matrix), or when the modulus of individual performed particles is required such as for subsequent modelling, but the modulus of individual material particles (or its material) cannot readily be determined.     

Elastic properties of powders during compaction. Part 1: Pseudo-isotropic moduli

The elastic moduli of powdered materials undergoing uniaxial compaction was investigated, paying particular attention to effects of solid phase material properties and initial particle shape. Elastic properties were characterised by the isotropic elastic moduli Poisson’s ratio and Young’s modulus, calculated from elastic wave speeds measured in the axial (pressing direction). To isolate material property effects, three different ductile metal powders (copper, stainless steel, and aluminium) with equivalent particle shape (spheroidal) were tested. Comparison with similar measurements for a brittle spheroidal powder (glass) illustrated that solid phase yield mechanism affects the evolution of pore character, and hence bulk elastic properties of the powder compact. Pore character was also studied separately by comparing copper powders with differing particle shapes (spheroidal, irregular, and dendritic). For all powders, Young’s modulus increased monotonically with compaction (reducing porosity). For the ductile spheroidal powders, differences in evolution of Young’s modulus with compaction were accounted for by solid phase elastic properties. The different morphology copper powders showed an increase in compact compliance as particle (pore) ruggedness increased. Poisson’s ratio followed a concave porosity dependence: decreasing in the initial stages of compaction, then increasing as porosity approached zero. Comparison between powders indicated the initial decrease in Poisson’s ratio was insensitive to solid phase material properties. However, as the compact approached solid phase density, the Poisson’s ratio—porosity locus diverged towards corresponding solid phase values for each particle material, indicating an influence of solid phase elastic properties.     

Characterization of carbon nanotube/nanofiber-reinforced polymer composites using an instrumented indentation technique

An instrumented indentation technique was tested on three types of carbon nanotube/nanofiber-reinforced composites to investigate its applicability for measuring mechanical properties (elastic modulus and hardness). There was good agreement in the measured elastic modulus between the instrumented indentation and uniaxial tension tests for the case of a nanocomposite with a harder epoxy matrix material. In contrast, there was a considerable difference in elastic modulus between the two tests for the case of a nanocomposite with a softer polystyrene matrix material. A modified area function was then developed for the nanocomposite with the softer polystyrene matrix material, and this eliminated the difference in elastic modulus between the two test techniques. Thus, the instrumented indentation technique can be used for evaluating the mechanical properties of polymer matrix nanocomposites with an added advantage that a small sample size can be used. The instrumented indentation test was also utilized in the case of a patterned nanotube array-reinforced epoxy matrix composite. This clearly showed the modulus of the array nanocomposite improved considerably compared to that of the neat epoxy resin.     

高频热压杨木单板层积材纵向弹性模量和泊松比的测定与分析

基于四点弯曲法,对一种基于高频热压技术的厚型杨木单板层积材的纵向弹性模量和纵横向泊松比进行了试验测定。其中纵向弹性模量的测定,分别采用了挠度法和应变片法。实验结果表明,2种测量方法所得纵向弹性模量数值比较接近,但又存在一定的差异,并对其差异的影响因素进行了探讨。基于高频热压技术的杨木单板层积材纵向弹性模量的测定结果表明,其纵向弹性模量接近甚至超过杨木单板,为该材料引入重型产品包装箱领域甚至结构用材料,从而替代原木,提供了一定的参考价值。     

Modulus measurements in discontinuous reinforced aluminum composites

Discontinuous Reinforced Composites generally show low elastic limits which results in large difficulty in determining the elastic modulus. However, a simple and convenient method to overcome the difficulty is by conducting intermittent unloading tests during a conventional tensile test and by measuring the modulus from the unloading curve. It is demonstrated that the measurements are very consistent and insensitive to the unloading strain.     

The adhesive contact of a flat punch on a hyperelastic substrate subject to a pull-out force or a bending moment

In the last decade, instrumented macro- and nano-indentation tests have become useful tools for probing mechanical properties of materials. In this context, little in-depth work has been done for soft bio-materials like biofilms, tissues, gels, cells, etc. Such materials show large elastic strains when subjected to relatively fast loading (excluding viscoelastic phenomena). The present work focuses on the adhesive contact of such materials. Flat punches of circular imprint are used and are subjected to pullout normal forces or bending moments. The materials are modeled as hyperelastic (fast-testing conditions), using the Mooney-Rivlin (M-R) strain energy density function. We examine both incompressibility and compressibility issues. The contact problem of half-space materials interacting with rigid indenters is solved explicitly for moderate deformations and is compared with finite element results. Experiments are conducted with an artificial material (gel, reinforced with talc powder) that is modeled as a hyperelastic material. The present work is expected to extend indentation testing to important technologies like medical applications (health monitoring of tissues) and food industries (quality control of various production stages). It is concluded that the adhesive contact can be used to estimate the initial elastic modulus of soft substrates, but not all the material constants required by the hyperelastic models.     

Influence of visco-elasto-plastic properties of magnetite on the elastic modulus: Multicyclic indentation and theoretical studies

In the present work, we study the indentation behaviour of the magnetite coexisting with hematite in a natural dual-phase crystal. In particular we show the influence of cycling indentation conditions on the elastic modulus measurement in relation to the visco-elasto-plastic properties of the material. Elastic properties of Fe₃O₄ are investigated using Oliver and Pharr's technique, which is based on depth-sensing indentation (DSI) analysis. Depending on the visco-elasto-plastic properties of the material, the indentation test conditions (monotonic, cyclic, loading and unloading rates, dwell time at peak load, …) can modify the shape of the load–depth curve and, subsequently, the results. Molecular dynamics simulation based on shell model potential, is used to determine elastic quantities including elastic modulus, bulk modulus and Young modulus.     

Effect of volume fraction and wall thickness on the elastic properties of hollow particle filled composites

Hollow particle filled composites, called syntactic foams, are widely used in applications requiring high damage tolerance and low density. The understanding of the mechanics of these materials is largely based on experimental studies. Predictive models that are capable of estimating the elastic properties of these materials over wide variation of particle wall thickness, size, and volume fraction are not yet fully developed. The present study is focused on developing a modeling scheme to estimate the elastic constants for such materials. The elastic properties of an infinitely dilute dispersion of microballoons in a matrix material are first computed by solving a dilatation and a shear problem. A differential scheme is then used to extrapolate the elastic properties of composites with high volume fractions of microballoons. The results show that the model is successful in predicting the Young’s modulus for syntactic foams containing microballoons of a wide range of wall thickness and volume fraction.     

Characterization of microstructural damage during plastic strain of a particulate-reinforced metal matrix composite at elevated temperature

The evolution of damage in a SiC-reinforced 2618 AI alloy during plastic strain has been investigated by elastic modulus reduction and direct observations of the microstructure at room temperature and temperatures up to 220 °C. Particle fracture increases as a function of strain at all temperatures but the total number of fractured particles at any given strain is lower at higher test temperatures. The dependence of fracture on particle size and aspect ratio was recorded. Normalized elastic modulus measurements decrease as a function of strain at the same rate for tests at 25,110 and 220 °C with an anomalous set of measurements at 165 °C showing a reduced damage rate. There is no universal correlation between the number of damaged particles and reduced modulus with each test temperature showing a different relation. This indicates the different temperature dependence of void nucleation and subsequent growth. The results are used to interpret different models of load sharing between reinforcement and matrix during straining.[/p]     

地震模拟振动台试验模型相似设计中的材料弹性模量取值问题研究

为了提高结构地震模拟振动台试验的精度,采用实常用模型材料的力学性能试验与规范计算理论分析相结合的方式,对混凝土结构、砌体结构及钢结构地震模拟振动台试验模型相似关系设计中的材料弹性模量取值方法进行了系统研究,推荐了混凝土结构、砌体结构及钢结构地震模拟相似关系设计中材料弹性模量的合理取值方法。试验与分析结果表明：模型材料弹性模量的试验值与原型材料弹性模量的规范值可能会存在较大差异,造成模型相似关系中的模型与原型弹性模量比过小,使振动台试验结果失真。因此,当混凝土结构振动台试验模型采用微粒混凝土或砂浆材料浇筑时,模型材料与原型混凝土材料的弹性模型应统一采用规范提供的拟合公式根据材料立方体抗压强度计算得到;当砌体结构振动台试验模型采用小型混凝土砌块制作时,模型材料弹性模量应采用规范拟合公式由材料试验确定的砌体抗压强度设计值计算得到;钢结构地震模拟相似关系中的弹性模量比可采用1.0。以上结论可为不同结构地震模拟振动台试验的模型相似关系设计提供理论依据。     

Comparison of Dynamic Young’s Modulus of Thin Concrete Disks to Stress Wave–Based Nondestructive Evaluation Findings

Stress wave–based nondestructive evaluation (NDE) techniques are frequently used for in-situ evaluation of concrete. Stress wave velocity in a material is related to Young’s modulus of elasticity. Cores for in-situ compressive strength are subject to a minimum length-to-diameter ratio requirement that enforce large specimen sizes. Thin circular disks sawn from cylinders or cores are widely used in measurement of chloride or air permeability of concrete. While these methods provide useful information on concrete properties with depth, the capability of measuring changes in mechanical properties such as elastic Young’s modulus in small depth increments is of value to both researchers and consulting engineers conducting condition assessment or NDE, particularly when damage gradients exist. Changes in properties over relatively small depths may be undetected otherwise due to limitations of test method, equipment, or imposed specimen size. This study presents applications of Young’s modulus of thin concrete disks to structural assessment projects involving damage and damage gradients. In-situ nondestructive ultrasonic pulse velocity (UPV) testing was used in identification of affected areas. Young’s modulus of thin concrete disks was used in interpretation of the NDE results and provided an improved understanding of the extent of damage that was indicated using NDE. Two different case studies are discussed: exposure to fire and exposure to thermal shock and cryogenic temperatures. The use of thin disks enabled determination of mechanical properties of relatively thin layers of concrete and, therefore, provided a means to quantitatively assess the extent of damage gradients. Confirmation of NDE results using modulus data and analytical modeling using the relationship between Young’s modulus and pulse velocity provided improved understanding of NDE findings reducing uncertainty in engineering analysis and improving repair recommendations.     

Calculating the elastic moduli of steel-fiber reinforced concrete using a dedicated empirical formula

The equivalent inclusion method (EIM) is adopted to study the characteristics of the equivalent material properties of steel-fiber reinforced concrete as a function of the volume fraction and the length to diameter ratio of the fibers. It is found that the equivalent material moduli of concrete reinforce with randomly orientated and distributed fibers are insensitive to the length to diameter ratio of the steel fibers. A set of empirical formulae is then proposed for the purposes of engineering applications. The proposed empirical model can simplify the calculation of the equivalent material moduli. Verifications of the proposed empirical formulae with the EIM model and with experimental data are performed with two examples. The first is a compression test. The second is 4 point bending test. The empirical formulae, based on the equivalent inclusion method proposed in this study, represent an alternative means of quickly calculating the effective elastic modulus of steel-fiber reinforced concrete materials.     

An elastic mechanics model and computation method for geotechnical material

岩土材料内摩擦性质是岩土的基本力学性质之一,无论岩土处于何种受力状态,都应考虑岩土体的内摩擦力。然而,至今只有岩土极限分析与塑性力学中考虑岩土体的内摩擦力,而在弹性理论与能量理论等诸方面均未体现。认为岩土体无论是处于塑性状态还是弹性状态,都存在着内摩擦力,为此建立岩土材料弹性力学的摩擦体力学单元。基于土体试验提出黏聚力先发挥,摩擦力随变形逐渐发挥,并假设摩擦因数与应变成正比,由此确定摩擦力的计算,最后仿效线弹性力学计算方法,但此时摩擦体的剪切模量G已非常数,从而形成摩擦体的非线性弹性力学计算方法。算例表明,按该方法计算出的弹性地基上的位移和剪应力小于传统方法计算出的位移和应力值,这比较符合实际情况,表明采用摩擦体力学单元对岩土材料是合适的。     

Elastic properties of thin poly(vinyl alcohol)-cellulose nanocrystal membranes

In spite of extensive studies on the preparation and characterization of nanocomposite materials, the correlation of their properties at the nanoscale with those in bulk is a relatively unexplored area. This is of great importance, especially for materials with potential biomedical applications, where surface properties are as important in determining their applicability as bulk characteristics. In this study, the nanomechanical characteristics of thin poly(vinyl alcohol) (PVOH)-poly(acrylic acid) (PAA)-cellulose nanocrystal (CNC) membranes were studied using the nanoindentation module in an atomic force microscope (AFM) and the properties were compared with the macro-scale properties obtained by tensile tests. In general, the elastic properties measured by nanoindentation followed the same trend as macro-scale tensile tests except for the PVOH 85-PAA 0-CNC 15 sample. In comparison to the macro-scale elastic properties, the measured elastic moduli with AFM were higher. Macro-scale tensile test results indicated that, in the presence of PAA, incorporation of CNCs up to 20?wt% improved the elastic modulus of PVOH, but when no PAA was added, increasing the CNC content above 10?wt% resulted in their agglomeration and degradation in mechanical properties of PVOH. The discrepancy between macro-scale tensile tests and nanoindentation in the PVOH 85-PAA 0-CNC 15 sample was correlated to the high degree of inhomogeneity of CNC dispersion in the matrix. It was found that the composites reinforced with cellulose nanocrystals had smaller indentation imprints and the pile-up effect increased with the increase of cellulose nanocrystal content.     

Dynamic mechanical analysis of prestrained Al2O3/Al metal-matrix composite

The effect of prestraining on the elastic modulus,E, and damping capacity, tan, of 10 and 20 vol% Al₂O₃ particle-reinforced composites has been investigated as function of temperature using dynamic mechanical analysis. Both elastic modulus and damping capacity were found to increase with volume fraction. At 10 vol% the modulus and damping were relatively insensitive to prestrain. However, at 20 vol% it was observed that the modulus decreased with increasing prestrain while damping increased significantly. These results are discussed in terms of fraction of broken particles, particle size, and differential in thermal expansion between the matrix and Al₂O₃ particulate.     

Ancestrally high elastic modulus of gecko setal beta-keratin.

Typical bulk adhesives are characterized by soft, tacky materials with elastic moduli well below 1MPa. Geckos possess subdigital adhesives composed mostly of beta-keratin, a relatively stiff material. Biological adhesives like those of geckos have inspired empirical and modelling research which predicts that even stiff materials can be effective adhesives if they take on a fibrillar form. The molecular structure of beta-keratin is highly conserved across birds and reptiles, suggesting that material properties of gecko setae should be similar to that of beta-keratin previously measured in birds, but this has yet to be established. We used a resonance technique to measure elastic bending modulus in two species of gecko from disparate habitats. We found no significant difference in elastic modulus between Gekko gecko (1.6 GPa +/- 0.15s.e.; n=24 setae) and Ptyodactylus hasselquistii (1.4 GPa +/- 0.15s.e.; n=24 setae). If the elastic modulus of setal keratin is conserved across species, it would suggest a design constraint that must be compensated for structurally, and possibly explain the remarkable variation in gecko adhesive morphology.     

Effect of particle packing structure on the elastic modulus of wet powder compacts analyzed by persistent homology

This study applies persistent homology (PH) to the structural analysis of wet powder compacts to clarify the effect of packing structure on the elastic modulus, and proposes an equation for the relationship between saturation and elastic modulus based on the index of structural homogeneity. The relationship between the saturation and the elastic modulus was experimentally obtained by compression tests of wet powder compacts. The elastic modulus decreased linearly with increasing saturation, but the slope was different depending on the packing structure of compacts which were made from high purity alumina with different particle size distributions. PH was applied to the packing structure of particles of different diameters calculated by DEM simulation to evaluate the packing structure. The features of each packing structure were extracted by PH, and the index of structural homogeneity was obtained. A new empirical equation is proposed which can predict the relationship between the elastic modulus and the saturation considering structural homogeneity, specific surface area, surface tension, and porosity as the main factors affecting the elastic modulus in the partially saturated state. These results indicate that PH analysis is effective to evaluate the packing structure and that this method may predict the mechanical properties of wet powder compacts.     

Influence of imperfect interface on the elastic moduli of syntactic foams

Syntactic foams are manufactured by dispersing microspheres in a polymeric matrix, and the macroscale material properties of these foams are estimated by analyzing a periodic distribution of the inclusions. The analysis in the simplest form, further assume that the inclusions are perfectly bonded to the matrix material. It has been shown in a previous study [P.R. Marur, Mater. Lett. 59 (2005) 1954–1957.] that analytical model overestimated the experimentally determined elastic moduli, and that the morphology of particle distribution has negligible influence on the elastic moduli. In this paper, the assumption of perfect adhesion between the inclusion and the matrix is relaxed to allow for possible localized slip and separation at the particle interface. The analytical results obtained considering imperfect interface well agree with the measured elastic modulus reported in the literature.     

Modeling elastic properties of short flax fiber-reinforced composites by orientation averaging

Natural fibers of plant origin, used as reinforcement in polymer matrix composite materials, exhibit highly anisotropic elastic properties due to their complex internal structure. Mechanical properties can be evaluated not only by tests but also by mechanical models reflecting the principal morphological features of fibers. Such a FEM model is applied to estimate the elastic properties of a unit cell of a short-fiber-reinforced composite, an elementary flax fiber embedded in a polymer matrix. Orientation averaging approach is used for prediction of the stiffness of short flax fiber reinforced polymer matrix composite. The numerical estimates of Young’s modulus are compared to the test results of extruded flax/polypropylene composite.     

Relationship between space and time characteristics of cavitation impact pressures and resulting pits in materials

Cavitation erosion studies require a well-defined measure of the aggressiveness of the subject cavitation field. One proposed method of cavitation field strength evaluation is to use pitting tests on a selected material sample subjected to the cavitation field. These relatively short duration tests record pits or permanent deformations from individual cavitation events during the cavitation incubation period. The pitting test results are dependent on the load and the material used in the tests and a good understanding of the pit formation mechanism is required to correlate the loads with the deformations. In this study, finite element numerical simulations are conducted to examine the response of several selected materials to imposed loads representing cavitation events. The magnitude, duration, and spatial extent of the loads are varied, and the effects of these on the material deformations are studied. Next, the effects of material properties, such as yield stress, Young’s modulus, and plastic modulus on the pitting characteristics are elucidated. Material responses are found to be drastically different between metals and compliant materials and to depend significantly on load duration and spatial extent in addition to the magnitude.