Indentation Load-displacement Data Research Articles

Theoretical model for determining elastic modulus of ceramic materials by nanoindentation

In order to accurately determine the mechanical properties of ceramic materials with small size specimens by the nanoindentation experiment, an effective work ratio of indentation method is proposed based on the dimensional analysis and finite element simulation to extract elastic modulus of ceramic materials from sharp indentation load-displacement data. Results indicate that the influence of strain hardening exponent of materials on elastic modulus is very weak and can be ignored in this model. Moreover, the elastic modulus of the investigated material can be expressed as a simple function of the work ratio of indentation, plane strain elastic modulus of the indenter, as well as the nominal hardness of the investigated material. Additionally, the effectiveness and accuracy of this proposed method were verified by instrumented indentation tests on two typical certified standard fused silica and borosilicate crown glass samples with Berkovich indenter. After comparison with conventional Oliver-Pharr method, it is shown that the work ratio of indentation method has advantages including high accuracy and small standard deviation.Graphical abstract [Display omitted]

Investigation of the mechanical behaviour of lithium-ion batteries by an indentation technique

Indentation is an alternative technique for the measurement of a material׳s elastoplastic properties. It can be used when the classical tensile test approach is not feasible (thin film, very small components, etc.). This paper presents the results of experiments in which this technique has been exploited to investigate the mechanical properties of the multi-layered structure of lithium-ion batteries with the aim of gaining a better understanding of their mechanical integrity. Indentation tests were performed separately on different layers of a lithium-ion battery using a Berkovich indenter. In order to perform the tests, fused silica substrate (which has well-known mechanical properties) was used to constrain the samples. The elasticity of the anode and the current collectors were obtained from the unloading curve of the measured indentation load–displacement data. Also, the individual stress–strain curves were calculated through reverse engineering of the loading curve. A commercial finite element software (ABAQUS) was used to perform numerical simulations comprising axisymmetric elements representing the Al and Cu foil current collectors. Micro-tensile tests were also carried out on these foils. Agreement was obtained between the outcomes of the micro-tensile and the results of the reverse engineering of the indentation tests. A micro-structure analysis was also performed to give an insight into the structure of the battery components which is necessary for small scale mechanical characterization.

Determination of the properties of viscoelastic materials using spherical nanoindentation

The article is devoted to determining the properties of linearly viscoelastic isotropic materials from the experiment on the introduction of a spherical indenter at a constant-rate displacement in a viscoelastic sample. The results are based on the Lee–Radok (J. Appl. Mech. 27:438–444, 1960) solution of the viscoelastic contact problem. An exact formula is obtained for calculation of the relaxation function using indentation load–displacement data. To illustrate the application of this formula, it is used to find the relaxation function of polymethyl methacrylate (PMMA). The relaxation function found in the article is compared with data measured in a conventional test to evaluate the suitability of the proposed method.

Study of SiC’s Mechanical Property Variance Caused by Film Thickness

The mechanical properties of SiC thin films deposited by chemical vapor deposition process on silicon substrate are studied using nanoindentation techniques. The SiC thin films are of three different thicknesses: 1.6μm、4.5μm、9μm. In this study, nanoindentation method is preferred due to its reliability and accuracy on determining mechanical properties from indentation load-displacement data. The mechanical properties of elastic modulus and hardness are characterized. 1.6μm SiC thin film has the following values: E=345.73Gpa, H=33.71Gpa; 4.5μm SiC thin film has the following values: E=170.18Gpa, H=10.33Gpa; 9μm SiC thin film: E=167.96Gpa, H=9.48Gpa

Effect of Pile-Up on the Mechanical Characteristics of Steel by Depth Sensing Indentation

Mechanical properties by depth sensing indentation are derived from the indentation load-displacement data used a micromechanical model developed by Oliver & Pharr (O&P). However, O&P analysis on the indentation unloading curve is developed from a purely elastic contact mechanics (sink-in). The applicability of O&P analysis is limited by the materials pile-up. However, when it does, the contact area is larger than that predicted by elastic contact theory (material sinks-in during purely elastic contact), and both hardness H and Youngs modulus E are overestimated, because their evaluation depends on the contact area deduced from the load-displacement data. H can be overestimated by up to 60 % and E by up to 30 % depending on the extent of pile-up [1,2]. It is therefore important to determine the effect of pile-up on obtained mechanical characteristics of the material by depth sensing indentation. The work experimentally analyses the effect of pile-up height on mechanical characteristics H and E, which are determined by O&P analysis. Pile-up height was measured by atomic force microscopy (AFM).

Flexoelectric properties of ferroelectrics and the nanoindentation size-effect

Recent works have established the critical role of flexoelectricity in a variety of size-dependent physical phenomena related to ferroelectrics including giant piezoelectricity at the nanoscale, dead-layer effect in nanocapacitors, dielectric properties of nanostructures among others. Flexoelectricity couples strain gradients to polarization in both ordinary and piezoelectric dielectrics. Relatively few experimental works exist that have determined flexoelectric properties and they all generally involve some sort of bending tests on micro-specimens. In this work, we present a straightforward method based on nanoindentation that allows the evaluation of flexoelectric properties in a facile manner. The key contribution is the development of an analytical model that, in conjunction with indentation load–displacement data, allows an estimate of the flexoelectric constants. In particular, we confirm the experimental results of other groups on BaTiO 3 which differ by three orders of magnitude from atomistic predictions. Our analytical model predicts (duly confirmed by our experiments) a strong indentation size-effect due to flexoelectricity.

Representative Strain of Indentation Analysis

Indentation analysis based on the concept of representative strain offers an effective way of obtaining mechanical properties, especially work-hardening behavior of metals, from reverse analysis of indentation load–displacement data, and does not require measuring of the projected contact area. The definition of representative strain adopted in previous studies [e.g., Dao et al., Acta Mater.49, 3899 (2001)] has a weak physical basis, and it works only for a limited range in some sense of engineering materials. A new indentation stress-state based formulation of representation is proposed in this study, which is defined as the plastic strain during equi-biaxial loading. Extensive numerical analysis based on the finite element method has shown that with the new formulation of representative strain and representative stress, the critical normalized relationship between load and material parameters is essentially independent of the work-hardening exponent for all engineering materials, and the results also hold for three distinct indenter angles. The new technique is used for four materials with mechanical properties outside the applicable regime of previous studies, and the reverse analysis has validated the present analysis. The new formulation based on indentation stress-state based definition of representative strain has the potential to quickly and effectively measure the mechanical properties of essentially all engineering materials as long as their constitutive behavior can be approximated into a power-law form.

Nanoindentation with spherical indenters: finite element studies of deformation in the elastic–plastic transition regime

Finite element simulation techniques were used to examine spherical indentation in the elastic–plastic transition regime and characterize the development of the constraint factor—the ratio of the mean pressure to the flow stress—with penetration depth for a wide variety of materials with different yield strengths and work hardening behavior. The simulations showed that the initial portion of the transition at small penetration depths is essentially independent of the work hardening behavior because plastic deformation in the subsurface plastic zone is constrained by surrounding elastic material. This is a potentially useful result in that it implies that some material properties may be measured from the indentation load–displacement data without prior knowledge of the work hardening behavior. At larger depths, the constraint factor diverges and the indentation behavior becomes dependent on the work hardening characteristics. These observations serve to divide the elastic–plastic transition into elastically-dominated and plastically-dominated parts. Insights gained about the behavior are presented and discussed.

Mechanical properties from instrumented indentation: Uncertainties due to tip-shape correction

The quality of hardness H and indentation modulus E* measurements from instrumented indentation is investigated. Load-displacement data from glass and sapphire are obtained by Vickers indentation and converted to H and E* through a series of equations, including those for tip-shape correction. The quality of H and E* is determined by calculating the statistical uncertainty at each step and propagating the uncertainty to the next step. Conventional tip-shape corrections, assuming either constant hardness or constant modulus, introduce significant errors in H and E* when single, continuous correction functions are used. Piecewise correction functions are shown to improve the quality of H and E*. This investigation demonstrates the importance of calculating and propagating uncertainty at each step when converting instrumented indentation load-displacement data to mechanical properties.

Micromechanical properties of epiphyseal trabecular bone and primary spongiosa around the physis: an in situ nanoindentation study.

The elastic modulus and hardness of the mineralized bone around the growth plate was measured to determine its regional micromechanical properties. Multiple nanoindentation tests, >10 sessions, with depths ranging from 100 to 1,000 nm at loading rates of 12.5 and 750 microN/s, were performed on the trabecular bone in the epiphysis, trabecular bone at the junction of the physis and epiphysis, primary spongiosa in the metaphysis, and surrounding cortical bone of the distal femur of 300-gm Sprague-Dawley rats. The indentation load-displacement data obtained in these tests were analyzed to determine the elastic modulus and hardness of the tissues. The nanoindentation results highlighted the regional variations in the material properties of the mineralized tissues around the growth plate. The primary spongiosa had a lower elastic modulus and hardness than both epiphyseal trabecular and cortical bone (p < 0.01). A relatively well-defined thick trabecular band at the physeal-epiphyseal junction had modulus and hardness values comparable to those of cortical bone (p > 0.05). These findings support the hypothesis that the primary spongiosa has micromechanical properties that are significantly lower than the epiphyseal trabecular bone. On this basis, it is speculated that the fracture patterns commonly seen in patients with physeal injuries are influenced by the micromechanical properties of these tissues, as well as by the nature and direction of the applied force.

Influences of pileup on the measurement of mechanical properties by load and depth sensing indentation techniques

Finite element simulation of conical indentation of a wide variety of elastic-plastic materials has been used to investigate the influences of pileup on the accuracy with which hardness and elastic modulus can be measured by load and depth-sensing indentation techniques. The key parameter in the investigation is the contact area, which can be determined from the finite element results either by applying standard analysis procedures to the simulated indentation load-displacement data, as would be done in an experiment, or more directly, by examination of the contact profiles in the finite element mesh. Depending on the pileup behavior of the material, these two areas may be very different. When pileup is large, the areas deduced from analyses of the load-displacement curves underestimate the true contact areas by as much as 60%. This, in turn, leads to overestimations of the hardness and elastic modulus. The conditions under which the errors are significant are identified, and it is shown how parameters measured from the indentation load-displacement data can be used to identify when pileup is an important factor.

Between nanoindentation and scanning force microscopy: measuring mechanical properties in the nanometer regime

Interest in the properties of materials in small dimensions has led to the parallel development of nanoindentation and scanning force microscopy (SFM). Nanoindentation has extended indentation testing into the submicrometer regime via the development of suitable equipment and means of interpreting indentation load-displacement data which obviate the need to image such microscopic indentations. SFM, on the other hand, has been developed primarily as an imaging tool which depends on tip-surface interaction forces. Both of these methods depend on very low load mechanical contacts and can, in principle, be used to examine mechanical properties on a very fine, near atomic, dimensional scale. Indeed, efforts have been made to apply the technique of nanoindentation at ever smaller loads, while SFM-based techniques have been developed which enable one to assess mechanical properties. Nonetheless, approximately three orders of magnitude separate the commonly-used load ranges of these methods, and it is precisely in this load gap that one might like to work in order to investigate mechanical properties in the 1–10 nm regime. A review of recent work in this area is presented along with results obtained using SFM-based nanoindentation techniques on surfaces and thin coatings. Methods for interpreting the results of such experiments are evaluated, and some prospects for the future are outlined.

An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments

The indentation load-displacement behavior of six materials tested with a Berkovich indenter has been carefully documented to establish an improved method for determining hardness and elastic modulus from indentation load-displacement data. The materials included fused silica, soda–lime glass, and single crystals of aluminum, tungsten, quartz, and sapphire. It is shown that the load–displacement curves during unloading in these materials are not linear, even in the initial stages, thereby suggesting that the flat punch approximation used so often in the analysis of unloading data is not entirely adequate. An analysis technique is presented that accounts for the curvature in the unloading data and provides a physically justifiable procedure for determining the depth which should be used in conjunction with the indenter shape function to establish the contact area at peak load. The hardnesses and elastic moduli of the six materials are computed using the analysis procedure and compared with values determined by independent means to assess the accuracy of the method. The results show that with good technique, moduli can be measured to within 5%.