Numerical Study on the Effects of Equi-biaxial Residual Stress on Mechanical Properties of Nickel Film by Means of Nanoindentation

In this paper,mechanical properties of Nickel film under residual stress have been systematically examined by finite element method in nanoindentation.It was found that load-displacement curves shifted under elastic residual stress and residual stress exceeded the yield stress for fixed indentation depth.Indentation profiles changed monotonously with compressive and tensile stresses at peak force which determinates contact area observed directly by finite element modeling (FEM).The elastic residual stress h...     

Measurement of residual stress in quenched 1045 steel by the nanoindentation method

In this paper, the residual stress in quenched AISI 1045 steel was measured by a recently developed nanoindentation technique. Depth control mode was adopted to measure the residual stress. It was found that residual compressive stress was generated in the quenched steel. The material around nanoindents exhibits significant pile-up deformation. A new method was proposed to determine the real contact area for pile-up material on the basis of invariant pile-up morphology of the loaded or unloaded states. The results obtained by the new method were in good agreement with the residual stresses measured by the classical X-ray diffraction (XRD) method.     

试样倾斜对熔融石英硅三棱锥纳米压痕测试的影响

使用三棱锥压头对不同倾斜角下的熔融石英硅进行纳米压痕实验。结果表明,试样倾斜会影响加载曲线的形状。在相同的载荷下,随着试样倾斜角的增加,压痕最大深度、残余深度及接触深度逐渐减小,但卸载曲线不受影响,彼此保持平行,卸载曲线的拟合参数m及接触刚度值保持恒定。另外,试样倾斜将导致测量的压痕接触面积偏小,从而使得测量的硬度和弹性模量偏大。     

两种微纳米硬度测试方法的比较

在对材料微纳米硬度测试中,可利用纳米压痕方法得到载荷-位移曲线,并用相关算法得到接触面积和硬度值;也可通过原子力显微镜测出压痕残余面积,由残余面积和最大载荷得到材料的硬度值.利用这两种方法对塑性材料单晶铝和脆性材料单晶硅做微纳米硬度测试试验,经过比较分析,这两种方法各有优势和不足,得到的材料微纳米硬度都有压痕尺寸效应,但第二种方法得到的微纳米硬度尺寸效应比第一种明显.     

Plastic material parameters and plastic anisotropy of tungsten single crystal: a spherical micro-indentation study

Enhancement of toughness is currently a critical engineering issue in tungsten metallurgy. The inherent toughness of tungsten single crystals is closely related to the capacity for local plastic slip. In this study we have investigated the plastic behavior of tungsten single crystals by means of micro-indentation experiments performed on specimens exposing (100), (110), and (111) surfaces. In parallel, FEM simulations were carried out with the Peirce–Asaro–Needleman crystal plasticity model considering both {110} 〈111〉 and {112} 〈111〉 slip systems. Plastic material parameters were identified by comparing the measured and predicted load–displacement curves as well as pile-up profiles. It is found that both measured and simulated plastic pile-up patterns on the indented surfaces exhibit significant anisotropy and orientation dependence, although the measured and simulated load–displacement curves manifest no such orientation dependence. The height and extension of pile-ups differ strongly as a function of surface orientation. The FEM simulations are able to reproduce the observed features of spherical indentation both qualitatively and quantitatively.     

Application of the work of indentation approach for the characterization of aluminium 2024-T351 and Al cladding by nanoindentation

Nanoindentation has been used to characterize the mechanical properties of aerospace-grade Al2024-T351 with and without a clad layer of pure aluminium. The clad layer is introduced by means of a roll-bonding process which can cause significant work-hardening of the material in the clad layer. The hardness and Young’s modulus of the pure aluminium and the Al2024 have been determined by a number of methods, including the traditional Oliver and Pharr method, and a number of other methods, including direct measurement of the indentation by atomic force microscopy, and evaluation of the work of indentation. The Oliver and Pharr method was found to underestimate the area of contact as it did not include the area of piled-up material around the indentation periphery. This gave a corresponding overestimation of both hardness and modulus. The area of the indentation measured by atomic force microscopy was similarly found to underestimate the contact area owing to relaxation of material around the indent between indentation and imaging. The work of indentation approach was found to give good agreement between the hardness calculated by nanoindentation and those found in the literature.     

On the measurement of pile-up corrected hardness based on the early Hertzian loading analysis

Nanoindentation has been used to gain insight into the elastic/plastic contact responses of material at very small scales. The Oliver and Pharr's analysis (W.C. Oliver and G.M. Pharr, J. Mater. Res. 7 (1992) 1564) on the nanoindentation curve, however, can be meaningless when plastically deformed material piles around the indented points. This study suggests a measuring methodology of the real contact area enlarged by the material pile-up and its corresponding mechanical properties; the pile-up corrected contact area can be calculated inversely from the reduced modulus formulation with input information of the independently determined Young's modulus based on the Hertzian loading analysis. This contact correction relaxed overestimates in the elastic modulus and hardness interpreted from the nanoindentation curve and yielded actual mechanical properties comparable to the literature values of a (100) tungsten monocrystal. In addition, theoretically estimated upheaval amount of the contact boundary in this study was nearly consistent with the average pile-up height measured from an atomic-force microscope.     

The indentation of hard metals: the role of residual stresses

Experimental evidence to support Johnson's [6] analysis of the residual surface stress distribution produced in a flat surface by a spherical indenter is presented. The theory suggests that high residual stresses develop just outside the contact area as a result of the superposition of elastic unloading stresses onto the stresses at maximum load when the specimen has deformed plastically. The experiments involved the use of a semi-brittle steel, sufficiently hardened so that, while tensile stresses in the surface produced cracks, the substrate deformed plastically under the triaxial stress system beneath the indenter. Radial cracks produced by the indenter frequently extended after load removal, implying the presence of the high tensile circumferential residual stresses predicted by the theory. This work and recent studies of indentation loading of glasses show that there are important situations where residual stresses can contribute to their failure and wear.     

Nanoindentation and residual stress measurements of yttria-stablized zirconia composite coatings produced by electrophoretic deposition

Yttria stabilized zirconia (YSZ)/Al₂O₃ composite coatings were prepared by an electrophoretic deposition (EPD) method. The mechanical properties of the coatings were determined by nanoindentation and residual stresses were measured by Cr³⁺ fluorescence spectroscopy. It was found that the nanoindentation was sensitive to the presence of sub-micrometer pores. In order to determine the macroscopic mechanical properties, a penetration depth of > 1000 nm was required due to the porous and inhomogeneous nature of the materials. Both microstress and mechanical properties exhibited a gradient across the coating thickness, which can be attributed to the density gradient caused by constrained sintering of the coatings. It has been confirmed that the mechanical properties determined by nanoindentation are not affected by the external applied stress. AFM examination confirmed there was no impression pile-up during indentation.     

Approach to determine stress strain curves by FEM supported nanoindentation

Nanoindentation is an often used method to characterize the hardness and the elastic modulus of thin coatings. Finding a method to determine the flow curve of thin coatings using analytical or numerical methods is one goal of actual nanoindenter research. In this work an approach is presented to determine the flow curve of materials using nanoindentation and finite element simulation (FEM). This method uses a FEM model of the indentation process. The determination of the flow curve is achieved by iteratively comparing experimental and simulated load‐displacement curves and adapting the modelled plastic behaviour until both curves match. Analytical methods are used to determine boundary conditions for the flow curve and therefore reduce the number of possible solutions. The method is validated on material samples with known flow curves. The forecasted flow curves uniformly show good agreement with experimental measured flow curves. A critical discussion of the results and the future prospects is made.     

Measurement of mechanical properties of 1045 steel with significant pile-up by sharp indentation

The Oliver–Pharr method has extensively been adopted for measuring hardness and elastic modulus by indentation techniques. However, the method assumes that the contact periphery sinks in, which limits the applicability to the materials pile up. This study proposed an improved methodology to calculate the real contact area of 1045 steel with significant pile-up. The contact boundary between indenter and specimen was assumed to overlap with the top points on the residual surface profile, and the real contact depth was defined by a sum of the indentation depth at maximum load, h _max, and average pile-up height, h_{\textpile - up}^\textave h_{\text{pile - up}}^{\text{ave}} , measured from the analysis on the residual indent morphology with atomic force microscope (AFM). The mechanical properties calculated by the newly proposed method were compared with those by the Oliver–Pharr method.     

Measurements of Viscoelastic Functions of Polymers in the Frequency-Domain Using Nanoindentation

A method to measure the complex compliance (or modulus) of linearly viscoelastic materials is presented using nanoindentation with a spherical indenter. The Hertzian solution for an elastic indentation problem, in combination with a hereditary integral operator proposed by Lee and Radok (Journal of Applied Mechanics 27, 1960, 438–444) for the situation of non-decreasing indentation contact area, was used to derive formulas for the complex viscoelastic functions in the frequency-domain. The formulas are most suitable for frequencies lower than a frequency limit such that the condition of non-decreasing contact area holds; they are reasonably good approximation at higher frequencies under which decreasing contact area occurs and the Ting (Journal of Applied Mechanics 33, 1966, 845–854) approach for arbitrary contact area history is needed. Nanoindentation tests were conducted on both polycarbonate and polymethyl methacrylate under a harmonic indentation load superimposed on either step or ramp indentation load, while the resulting displacement under steady state was recorded. The load and displacement data at each frequency were processed using the derived formulas to determine the viscoelastic functions in the frequency-domain. The same materials were also tested using a dynamic mechanical analysis (DMA) apparatus to determine the complex viscoelastic functions. The DMA and nanoindentation results were compared and found in a good agreement, indicating the validity of the new method presented.     

Evaluation of the tensile properties of a material through spherical indentation: definition of an average representative strain and a confidence domain

In the present article, a new method for the determination of the hardening law using the load displacement curve, F–h, of a spherical indentation test is developed. This method is based on the study of the error between an experimental indentation curve and a number of finite elements simulation curves. For the smaller values of these errors, the error distribution shape is a valley, which is defined with an analytic equation. Except for the fact that the identified hardening law is a Hollomon type, no assumption was made for the proposed identification method. A new representative strain of the spherical indentation, called “average representative strain,” ε _aR was defined in the proposed article. In the bottom of the valley, all the stress–strain curves that intersect at a point of abscissa ε _aR lead to very similar indentation curves. Thus, the average representative strain indicates the part of the hardening law that is the better identified from spherical indentation test. The results show that a unique material parameter set (yield stress σ _y, strain hardening exponent n) is identified when using a single spherical indentation curve. However, for the experimental cases, the experimental imprecision and the material heterogeneity lead to different indentation curves, which makes the uniqueness of solution impossible. Therefore, the identified solution is not a single curve but a domain that is called “solution domain” in the yield stress–work hardening exponent diagram, and “confidence domain” in the stress–strain diagram. The confidence domain gives clear answers to the question of uniqueness of the solution and on the sensitivity of the indentation test to the identified hardening laws parameters.     

Deformation and fracture of a mudflat-cracked laser-fabricated oxide on Ti

Concentrated heating of titanium by a focused laser beam in ambient atmosphere produces unique dielectric layers with characteristic colors dictated by film thickness and optical properties. A combination of microscopy and diffraction techniques employed to study the phase and microstructure of the oxide coatings showed that nanosecond-pulsed laser irradiation produces polycrystalline TiO films and underlying Ti₆O interfacial layers. Mudflat cracking was prevalent in all coatings with most cracks extending through thickness to the metal substrate. Deformation and fracture behavior were probed by traditional nanoindentation methods with accompanying electron microscopy. These mixed titanium oxide coatings have moduli (~200 GPa) and hardnesses (~16 GPa) that are larger than the underlying metallic substrates. Fracture energies and residual stress have also been determined from pre-cracked films; fracture toughness and residual stress tend to decrease with decreasing laser fluence. Electrical contact resistance, measured with conductive nanoindentation, indicates a correlation between laser exposure, current–voltage behavior at constant load, and indentation response. Film conductance increases with decreasing laser fluence, likely due to the presence of defects, which act as a conduction path. Combining techniques provide a unique approach for defining electromechanical behavior and the resulting performance of the films in conditions that cause wear.     

Residual stress release characteristics of hole-drilling determined by in-plane three-directional optical interference moiré

By adopting a new stress calibration method, a grating rosette moiré interferometry and incremental hole-drilling combined system is developed to determine the magnitud of the residual stress in aluminium plate subjected to a uniform uniaxial tensile load. Performing in-plane three-directional fringe analysis, the optical data contained in the moiré interferograms are converted into values of the strains in three directions corresponding to the grating rosette. The evaluation is carried out through the measurement of the in-plane displacement field in three directions generated by the introduction of the small incremental hole. The in-plane three-directional displacement fields are determined from the calculation of the optical in-plane three-directional phase distribution by means of a phase-shifting method. A new finite element calibration analysis that is general axisymmetric elements instead of 3-D block element and harmonic axisymmetric element is adopted to relate the relieved displacement field to the magnitude of the residual stress. The magnitude of the principal stresses is finally evaluated through a least-squares calculation and is also compared with the stress value applied to the specimen measured with strain gauges.     

A simple mechanistic model to predict the macroscopic response of fibreglass–aluminium laminates under low-velocity impact

Low-velocity impact tests were carried out on fibreglass–aluminium laminates made of 2024 T3 sheets and S2-glass/epoxy prepreg layers, using an instrumented falling weight machine. In the tests, the impactor mass was held constant, whereas the energy was varied by adjusting the drop height. The load–displacement curves obtained were highly non-linear, with the specimen stiffness rapidly increasing with increasing the displacement. From the analysis of the data, the material response was unaffected by the actual speed adopted. Simple second-order polynomials, together with additional hypotheses supported by the results generated, were used to represent the load variation as a function of displacement during both the loading and the rebound phase. The resulting model, aiming to predict the contact history, consisted of three parameters, which could be determined by a minimum of experimental tests. From the model, the fundamental impact features, such as the overall force–time curve, dissipated energy, and contact duration, were effectively calculated. The damage progression with increasing the impact energy was assessed by ultrasonic C-scan and destructive analysis. Even when considerable failures were detected in the material, no clear sign of their occurrence was yielded by the fundamental impact parameters usually provided by an instrumented impact test, i.e. the force–time and force–displacement curves, the residual displacement, and the contact time. Only the extent of the damage area, plotted against the energy, underwent a sudden change in slope when a major damage took place.     

Nanoindentation-induced phase transformation in (1 1 0)-oriented Si single-crystals

Pressure-induced plastic deformation and phase transformations manifested as the discontinuities displayed in the loading and unloading segments of the load–displacement curves were investigated by performing the cyclic nanoindentation tests on the (1 1 0)-oriented Si single-crystal with a Berkovich diamond indenter. The resultant phases after indentation were examined by using the cross-sectional transmission electron microscopy (XTEM) technique. The behaviors of the discontinuities displayed on the loading and re-loading segments of the load–displacement curves are found to closely correlate to the formation of Si-II metallic phase, while those exhibiting on the unloading segments are relating to the formation of metastable phases of Si-III, Si-XII, and amorphous silicon as identified by TEM selected area diffraction (SAD) analyses. Results revealed that the primary indentation-induced deformation mechanism in Si is intimately depending on the detailed stress distributions, especially the reversible Si-II ? Si-XII/Si-III phase transformations might have further complicated the resultant phase distribution. In addition to the frequently observed stress-induced phase transformations and/or crack formations, evidence of dislocation slip bands was also observed in tests of Berkovich nanoindentation.     

Evaluation of the elastic modulus of thin film considering the substrate effect and geometry effect of indenter tip

A method using finite element method (FEM) is proposed to evaluate the geometry effect of indenter tip on indentation behavior of film/substrate system. For the nanoindentation of film/substrate system, the power function relationship is proposed to describe the loading curve of the thin film indentation process due to substrate effect. The exponent of the power function and the maximum indentation load can reflect the geometry effect of indenter and substrate effect. In the forward analysis, FEM is used to simulate the indentation behavior of thin film with different apex angles of numerical conical indenter tip, and maximum indentation load and loading curve exponent are obtained from the numerical loading curves. Meanwhile, the dimensionless equations between the loading curve exponent, the maximum load, elastic properties of film/substrate system and apex angle of indenter are established considering substrate effect. In the reverse analysis, a nanoindentation test was performed on thin film to obtain the maximum indentation load and the loading curve exponent, and then the experimental data is substituted into the dimensionless equations. The elastic modulus of thin film and the real apex angle of indenter can be obtained by solving the dimensionless equations. The results can be helpful to the measurement of the mechanical properties of thin films by means of nanoindentation.     

Indentation size effect of hardness of metallic glasses

It has been found that the hardness measured from different metallic glassy samples using the Oliver and Pharr scheme [Oliver WC, Pharr GM. An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. J Mater Res 1992;7:1564–83] [1] shows an apparent indentation size effect (ISE), i.e., the hardness decreases as indentation depth increases. A similar ISE of the pile-up ratio has also been found. A ribbon glassy sample fabricated at a larger cooling rate shows larger pile-up and lower hardness value than a bulk glassy sample under the same conditions. The ISE of hardness can be effectively eliminated by taking into account the different pile-up ratios at different indentation depths.     

Discrete dislocation simulation of nanoindentation

A methodology to describe nanoindentation by means of discrete dislocations is presented. A collocation method is used to calculate the arising contact stresses at each indentation step, which permits to realize an arbitrary shape of the indenter. Distributed dislocation sources are allowed to emit dislocations on predefined slip planes, when the critical value of the local shear stress for the emission is reached. After each indentation step, the newly emitted dislocations are brought to their equilibrium positions under the influence of the stresses induced by the contact stresses and the dislocations. As an application of our model, the plastic behavior of two materials with different densities of dislocation sources will be studied in detail.This work was financially supported by the FWF (Fonds zur Förderung der wissenschaftlichen Forschung) Project P13908-N07.