Load-indentation Curves Research Articles

Analytical Modeling of Circular Glare Laminated Plates under Lateral Indentation

In this paper analytical solutions are derived to predict the static response of thin circular clamped GLARE fibre-metal laminated plates under the action of a lateral hemispherical indentor. The load-indentation curve is calculated along with the first failure load and deflection due to glass-epoxy tensile fracture. The Ritz method is employed with one, two and three-parameter Ritz approximation functions. The derived formulas are applied to GLARE 2-2/1-0.3 and to GLARE 3-3/2-0.4 circular plates with various diameters. The results converge satisfactorily in all examined cases. The calculated load-indentation curve and the first failure agree well with published experimental data for the case of a GLARE 2-2/1-0.3 plate with a radius of 40 mm (failure load within 7% and failure deflection within 3%). The same load-indentation curves are also calculated using ANSYS and by comparison to FEM results the validity of the analytical model is further verified. No analytical solution of this problem is known to the authors.

Experimental and numerical nano-characterisation of two phases in concrete

Concrete is the most used material in construction worldwide. Concrete is a composite material including three phases: cement paste, aggregate and interfacial transition zone (ITZ). Previous research has demonstrated that the macro behaviour of concrete represents the integration of its constituent phases. Here, we present a methodology to experimentally and numerically characterise the mechanical performance of individual points within these constituent phases. Concrete samples made of high performance concrete are indented using state of the art nano-characterisation system. Using nano-positioning technique load-indentation curves are recorded at two individual points at the cement paste (CP) phase and at the ITZ phase. The load-indentation relationship showed a significant difference between the mechanical behaviours at both points. The finite element (FE) method is used to simulate behaviour at both phases. It is shown that the load-indentation curves can be simulated accurately using FE providing insight on intrinsic constitutive models.

The effect of friction on indentation test results

A smooth contact analysis is commonly adopted in simulated indentation. Limited studies have been performed to investigate the possibility of deviation due to this simplification. This study involves the finite element simulation of indentation by conical indenters and the Berkovich family of indenters with three different apex angles of indenter tips of 50°, 60° and 70.3°. Loading curvatures and the ratio of the remaining work done to the total work done of the load-indentation curves resulting from the simulated indentation tests considering friction and smooth contact surfaces were compared and discussed. A wide range of elasto-plastic materials obeying the power law strain hardening model were considered in this study. The results as presented herein demonstrate that the effect of friction on the two essential basic parameters from the load–indentation curves, namely, the loading curvatures and the ratio of the work done, varies depending on both mechanical properties of the target materials and the geometries of the indenter tips adopted in the investigation.

Evaluation of the Interfacial Strength of Layered Structures by Indentation Method

The delamination of thin coating films from substrates is a critical issue for the reliability of micro- and nanoelectronic devices. Indentation methods have the potential to measure interfacial strength in micro- and nanofilm thickness coating films. In this paper, indentation tests of layered structures are simulated using the damage-based cohesive zone model. When the delamination initiates, the indentation load and depth curve tend to deviate from the indentation load and depth curve for the perfectly bonded case. When the interface is stiffer than the coating film, a brittlelike delamination occurs on the interface; when the stiffness of the interface is smaller than that of the coating layer, a ductilelike delamination occurs on the interface. The ratio of shear moduli, μint∕μPI, characterizes the delamination behavior on the interface during indentation tests. Focusing on the discontinuous point during the indentation tests and introducing the balance of energy before and after the onset of delamination, the evaluation method of the interfacial strength is proposed. The proposed method can be used to estimate the interfacial strength when the ratio of hardness and the yield stress of the coating film is 3.5<HA∕σy<4.5.

Viscoplastic Parameter Identification for Lead-Free Solder Alloy by Micro-Indentation, FE Simulation and Optimization

A system for material parameter identification by depth-sensing micro-indentation, Finite Element (FE) simulation and optimization has been developed. In this system, the material parameter identification is treated as an optimization problem by minimizing the difference between experimentally obtained indentation load vs. penetration (P-h) curves and the corresponding FE simulation results. To reduce the computation time, a multipoint approximation response surface methodology (MARS) is used in combination with the interaction of high- and low-fidelity analysis algorithms. Using this system, the viscoplastic properties of a lead-free solder (Sn-3.5Ag-0.75Cu) were identified. This identification method has been confirmed by comparing the obtained material parameters with those determined from uniaxial compression tests.

Study of Delamination of Thin Film Coating on Cyclic Nano-Indentation Test

The aim of this paper is to evaluate the cyclic interfacial strength between thin film and its substrate by cyclic nano-indentation tests. The specimen used in this study is PET substrate/ITO coatings layered specimen. From the indentation load and displacement curve, we proposed an evaluation method for the interfacial strength. The results are good agreement with the interfacial strength evaluated by peel test. After cyclic indentations, the surface profile was observed by atomic force microscope. The number of elongates increased with indentation cycles when the indentation load is low, whereas elongates number is almost constant under high load cases. These phenomena can be explained by simple models. In this study, two types of fracture modes are proposed. They are “subsidiary fracture mode” and “buckling mode”.

An inversion method for identification of elastoplastic properties for engineering materials from limited spherical indentation measurements

In this article, a new method for determination of elastoplastic properties from an indentation loading curve is proposed. Mathematical model, based on deformation theory, leads to quasi-static elastoplastic contact problem, given by the monotonically increasing values αi>0 of the indentation depth. The identification problem is formulated as an inverse problem of determining the stress–strain curve from an experimentally given indentation curve . The inversion method is based on the parameterization of the stress–strain curve, according to the discrete values of the indentation depth, and uses only a priori information as monotonicity of the unknown function . It is shown that the ill-conditionedness of the identification problems depends on the state discretization parameter Δei. An algorithm of optimal selection of state discretization parameters is proposed as a new regularization scheme. Numerical examples with noise free and noisy data illustrate applicability and high accuracy of the proposed method.

Scaling functions in conical indentation of elastic-plastic solids

The finite element method was used to simulate the conical indentation of elastic-plastic solids with work hardening. The ratio of the initial yield strength to the Young's modulus Y/E ranged from 0 to 0.02. Based on the calculation results, two sets of scaling functions for non-dimensional hardness H/K and indenter penetration h are presented in the paper, which have closed simple mathematical form and can be used easily for engineering application. Using the present scaling functions, indentation hardness and indentation loading curves can be easily obtained for a given set of material properties. Meanwhile one can use these scaling functions to obtain material parameters by an instrumented indentation load-displacement curve for loading and unloading if Young's modulus E and Poisson's ratio nu are known.

Determination of Residual Stress and Yield Stress Simultaneously by Indentation Method with Dual Indenters

AbstractIn general, the method of obtaining residual stress from indentation test requires calculating the contact area of indenter and indented material, and also needs to know yield stress of indented material in advance. In this work, the dimensional analysis of indentation loading curve was first analyzed, and then a reverse numerical procedure was explored to show a possibility of determining residual stress and yield stress of materials simultaneously from indentation test. Besides, the calculation of contact area can be also avoided.

Characterization of Elastoplastic Properties Based on Inverse Analysis and Finite Element Modeling of Two Separate Indenters

A method that can determine uniquely the elastoplastic properties from indentation loading and unloading curves has been developed. It is based on finite element modeling and inverse analysis of two separate indenters. The approach was validated by numerical experiments using a fictitious material. It was demonstrated that the proposed method can uniquely recover the elastoplastic properties using only indentation load-displacement curves of two indenters. Although the proposed procedure has been used to predict elastoplastic strain hardening behavior, it is also applicable to estimate other mechanical properties where there are more than two unknown parameters, such as rate-dependent behavior.

Nanoindentation of wood cell walls: Continuous stiffness and hardness measurements

The objective of this study was to measure the mechanical properties of individual, native wood fibers using the continuous nanoindentation measurement technique. The indentation depth profile exhibited a small length-scale effect, which was confirmed using the size-effect index derived from the indentation loading curve. The hardness (Hu) or stiffness (Eu) values determined from indentation unloading were also examined for 10 different annual rings of a loblolly pine, with microfibril angles (MFA) between 14° and 36°. A predictable pattern of Eu values was found as a function of MFA, and hence Eu can at least be considered a relative measure of the longitudinal stiffness properties of wood cell walls. For Hu values, a dependence on orientation was observed, and there is a preliminary indication that the dependence could be affected by cell-wall extractives. It is thus desirable, for cell-wall modification studies, to minimize any unintended variations by using samples that are from the same growth ring, so that any treatment-induced changes in the cell-wall hardness can be identified.

Post-yield characterisation of metals with significant pile-up through spherical indentations

Finite element simulations of spherical indentations accounting for frictional contact provide validated load–indentation output for assessing and improving existing methods used to determine the stress–strain curve of materials with significant pile-up. The importance of friction to the proper assessment of the pile-up effect is established. Weaknesses in current characterisation relations and procedures are also identified. Existing correction formulae accounting for pile-up are modified so that the contact area radius is more accurately determined. This modification is implemented in the context of a characterisation process that relies on analysing unloading portions of load–indentation curves. Post-yield material behaviour predictions from such analysis are found to be in very good agreement with the initial finite element material input.

Equivalency of Berkovich and conical load-indentation curves

The Berkovich indenter, which is one of the most commonly used indenter tips in instrumented indentation experiments, requires a tedious 3D finite element simulation. The indenter is widely idealized as a conical indenter of 70.3° half-angle to enable a substantially less demanding 2D axisymmetric modelling. Although the approach has been commonly adopted, limited studies have been performed to investigate possible deviations due to this simplification. The present study attempts to address the equivalency of the two indenters by performing extensively both 3D and 2D finite element analyses to simulate the load-displacement response of a wide range of elasto-plastic materials obeying power law strain-hardening during indentation for both Berkovich and conical indenters, respectively. It is demonstrated that the equivalency between these two indenters in terms of curvature of the loading curve is not valid across the range of material properties under study. However, it is established that if only the ratio of the remaining work done (WR) and the total work done (WT) of the load-indentation curve is of interest, this simplification can be adopted with satisfactory results.

3013 繰り返しナノインデンテーションによるコーティング薄膜のはく離(S38 皮膜の磨耗および残留応力特性(2),S38 コーティング材料の皮膜特性とその評価)

The aim of this paper is to evaluate the cyclic interfacial strength by cyclic nanoindentation tests. The specimen used in this study is PET substrate/ITO coatings layered specimen. In this study mono cycle nanoindentation test and 10 cycle nanoindentation were conducted on each load, and these results were compared. From indentation load and displacement curves, we classified those results into 3 types (A-C). These three types relate the maximum loads. After the cyclic indentation, we observed the surface profile by the function of atomic force microscope. On Type A, the deviations were observed on the edge on indentations. On Type B, some elongates were observed in the indentations. In addition the number of elongates increased by repeating nanoindentation. These phenomena can be explained by simple models. In this study, two types of fracture modes are proposed. They are "subsidiary fracture mode" and "buckling mode". From the deviation of indentation load and displacement curve, we proposed the method to estimate the energy used for thin film delamination and the interfacial strength was evaluated. The results are good agreement with the interfacial strength evaluated by peel test.

On the determination of reduced Young's modulus and hardness of elastoplastic materials using a single sharp indenter

In this work, we analyzed the theoretical errors of reduced Young's modulus and hardness of materials provided by single sharp indenter algorithms. According to the analysis, two conclusions can be drawn. First, various methods that use only the indentation loading and unloading curves from a single sharp indenter and omit the effect of the strain hardening exponent own the same widths of the theoretical error bands defined here. They are WEb for reduced Young's modulus and WHb for hardness. Second, the upper-bounds, BUE and BUH, and lower-bounds, BLE and BLH, of theoretical errors of the measured reduced Young's modulus and hardness might be different for different methods. These conclusions, on the one hand, are relevant to the evaluation of various established single sharp indenter algorithms. On the other hand, they provide useful information (i.e., to optimize the theoretical error bounds) for correcting an established method and the development of new single sharp indenter algorithms. According to the conclusions, an energy-based method has been devised to determine reduced Young's modulus and hardness of materials from nanoindentation tests using a standard Berkovich or Vickers indenter (equivalent to a 70.3° cone). It has been shown that the present method owns the reasonable theoretical error bounds and can provide stable results in the presence of data errors.

Modeling Receptor-Ligand Mediated Adhesion in Nanoindentation of Cells

ABSTRACTThe specific adhesion mediated by receptor-ligand binding in the nanoindentation of cells was studied by using a continuum-kinetics approach. It was found that the adhesion force only causes a shift to the indentation loading curve whereas the unloading curve is tilted downward by the adhesion force, resulting in a hysteresis. Parametric studies were conducted to investigate how experimental conditions influence the adhesion force. It was found that the maximum adhesion force is sensitive to the geometry of the indenter but insensitive to the indentation depth and the mechanical properties of cells. It was also shown that the dependence of the adhesion force on the loading and unloading rates is controlled by the association rate of the receptor-ligand binding, leading to three well-defined regimes.

Plane strain indentation of a Zr-based metallic glass: Experiments and numerical simulation

The response of a Zr-based metallic glass in instrumented plane strain indentation with a cylindrical indenter tip is studied experimentally. A recently developed constitutive model and simulation capability for metallic glasses is used to numerically calculate indentation load versus depth curves, and the evolution of corresponding shear-band patterns under the indenter. The numerical simulations are shown to compare very favorably with the corresponding experimental results.

연속압입시험기법을 이용한 용접부 잔류응력 평가

Apparent mechanical properties in structural components can be different from the initially designed values due to the formation of the residual stress in metal forming and welding. Therefore, the evaluation of residual stress has great importance in the reliability diagnosis of structural components. A nondestructive continuous indentation technique has been proposed to evaluate various strength concerning mechanical properties from the analysis of load-depth curve. In this study, quantitative residual stress estimation on API X65 welded joints for natural gas pipeline was performed by analyzing the variation of indentation loading curve by residual stress through a new proposed theoretical model. The residual stress from the indentation method was compared with that from the saw-cutting method.

Material characterization via least squares support vector machines

Analytical methods to interpret the load indentation curves are difficult to formulate and execute directly due to material and geometric nonlinearities as well as complex contact interactions. In the present study, a new approach based on the least squares support vector machines (LS-SVMs) is adopted in the characterization of materials obeying power law strain-hardening. The input data for training and verification of the LS-SVM model are obtained from 1000 large strain–large deformation finite element analyses which were carried out earlier to simulate indentation tests. The proposed LS-SVM model relates the characteristics of the indentation load-displacement curve directly to the elasto-plastic material properties without resorting to any iterative schemes. The tuned LS-SVM model is able to accurately predict the material properties when presented with new sets of load-indentation curves which were not used in the training and verification of the model.

Identification of Viscoplastic Properties of Individual Phases in Lead-Free Solder Alloy by Depth-Sensing Microindentation

The viscoplastic properties of the Sn-rich phase and Sn–Ag–Cu eutectic constituent in a Sn–3.5Ag–0.75Cu lead-free solder were determined by performing microindentation tests on these individual phases. Material parameters in Norton’s law for each phase were successfully identified by fitting the experimentally obtained rate-dependent indentation load (P) vs penetration-depth (h) curves, as well as indentation-creep data, with the corresponding Finite Element (FE) simulation results. For this material parameter identification, an appropriate indenter-penetration depth for a given size of a phase, where the P–h response is not affected by the other neighboring phases, was determined by FE simulation.