scispace - formally typeset
Search or ask a question
Dissertation

Sources of error in relating nanoindentation results to material properties

TL;DR: In this article, the effect of sample tilt on results of nanoindentation tests was investigated, and it was shown that for materials that sink-in and those that pile-up, the projected contact area of a tilted sample is higher than that estimated by the standard area function, which leads to overestimation of the hardness and elastic modulus.
Abstract: This dissertation consists of four submission-ready papers that address some of the key error sources that affect the accuracy of interpretation of nanoindentation test results to obtain material properties for elastoplastic materials. The first part of the work is a study of the effect of sample tilt on results of nanoindentation tests. Geometrical relations are used to develop a correction to account for the effect of tilt angle on the contact area. 3D FEA (Finite Element Analysis) shows that the assumptions made in deriving the geometric correction are valid, and the results for contact area, hardness and modulus match the predictions of the analytical model. It is shown that for both materials that sink-in and those that pile-up, the projected contact area for nanoindentation on tilted sample is higher than that estimated by the standard area function, which leads to overestimation of the hardness and elastic modulus. Experimental nanoindentation tests on tilted samples show lower sensitivity to sample tilt compared to FEA results because the compliance of the indenter holder causes the indenter tip to displace in the direction of the surface tilt, reducing the total penetration of the tip into the surface. For tips with very high compliance, this may even lead to significant underestimation of the hardness and modulus. The second part discusses the various factors that affect the accuracy of FEA of nanoindentation. With the understanding that contact area error arising from discretization of the continuum is a key contributor to noise in the hardness data, a self similar mesh is designed that results in a known amount of maximum error in contact area over a range of depths of penetration of the indenter. Based on the fact that contact area increases in discrete jumps, it is argued that the maximum force that a given area of contact can support, before the next element comes into contact, is the best measure of the true hardness of the material that can be obtained with a given mesh. FEA simulations carried out with meshes of different amounts of error in contact area show that as the discretization becomes coarser, the estimate of the true hardness increases, due to the inability of the mesh to resolve the steep gradients in stress and strain near the end point of contact. It is also shown that results obtained from different meshes with different error percentages can be extrapolated to determine the exact value of hardness that will be obtained with infinitesimally small elements. It is shown that other sources of error, such as the convergence tolerance of the iterative solution process, are small in comparison to the discretization errors. The third part is a study aimed at identifying the size of the volume underneath a nanoindentation that influences the hardness and modulus measured. FEA simulations of the indentation of a hemispherical particle embedded in a matrix reveal that the hardness of particle can be measured accurately by nanoindentation as long as vii the plastically…
Citations
More filters
Journal ArticleDOI
TL;DR: In this article, an innovative approach through micro-nano-indentation testing with a cylindrical flat-tip indenter and coupled with computer modeling was proposed to characterize the material's elastic-plastic properties.
Abstract: Material property measurements at the micro-/nanoscale are required for within many materials systems, such as thin-films, coatings, nanostructured materials, and interface/interphase. An innovative approach through micro-/nano-indentation testing with a cylindrical flat-tip indenter and coupled with computer modeling was proposed to characterize the material’s elastic–plastic properties. A mechanical model proposed for directly extracting the yield strength of the tested materials, based on the hemi-spherical stress–strain distribution assumption, was analytically derived and numerically validated. Specimens being tested are aluminum alloy, low carbon steel, and alloy steel. A micro-/nano-indentation solid model was constructed and computer modeling was conducted. The load point in the indentation load–depth curve and the modifier for extracting the yield strength were identified through computer modeling and validated by indentation tests. The material properties measured by indentation were compared with tensile tests. The indentation testing errors induced by residual stresses in specimens were investigated by a residual stress measurement system.

36 citations

Journal ArticleDOI
TL;DR: In this article, an innovative approach through nanoindentation testing using a Berkovich sharp-tip and a cylindrical flat-tip, coupled with computer modeling is proposed as a means of characterizing the elastic-plastic properties of materials within micro/nanoscale.
Abstract: In this paper, an innovative approach through nanoindentation testing using a Berkovich sharp-tip and a cylindrical flat-tip, respectively, and coupled with computer modeling is proposed as a means of characterizing the elastic–plastic properties of materials within micro/nanoscale. Low carbon steel was selected as a case study material. Nanoindentation tests were carried out to obtain load–depth graphs. For cylindrical flat-tip indentation, a mechanical model was proposed for directly extracting yield strength of the testing material from the corresponding load points, considering a modifier k . Young's modulus was derived from the indentation tests using both tips. The final indentation sites were measured and analyzed using a 3D laser scanning microscope. The nanoindentation solid models were developed, and computer modeling based on finite element analysis was conducted to find the effects of indentation depth, yield strength and strain hardening coefficient on the load–depth graph and the final indentation pileup profiles, taking into account the effects of friction on nanoindentation. The computer modeling nanoindentation data was compared with and validated by the nanoindentation tests.

35 citations

Journal ArticleDOI
TL;DR: In this article, the effects of angular misalignment on the nanoindentation testing with a cylindrical flat-tip indenter were numerically analyzed, and computer modeling based on finite element analysis was conducted.
Abstract: Nanoindentation techniques are commonly used to characterize nanomechanical properties of microscaled and nanoscaled materials. Nanoindentation using a cylindrical flat-tip indenter has a constant contact area which makes it a reliable source to find material’s yield strength as well as other mechanical properties. However, an angular misalignment of the indenter with the specimen results in experimental error. In this work, the effects of angular misalignment on the nanoindentation testing with a cylindrical flat-tip indenter were numerically analyzed. A three-dimensional nanoindentation solid model was generated, computer modeling based on finite element analysis was conducted. The angle of misalignment ranged from 0° to 1°. Young’s modulus and hardness were evaluated. Based on the hemispherical stress–strain distribution assumption of an elastic plastic indentation, corrected depths and modifiers were proposed for adjusting material’s 0.1% offset and 0.2% offset yield strengths. Low carbon steel AISI 1018 was selected as sample material for indentation testing and modeling validation.

13 citations

Book ChapterDOI
01 Jan 2017
TL;DR: In this paper, the authors introduce the concepts that define the mechanical properties characterized by nanoindentation, the fundamentals of nano-indentations, and applications in materials and composites, especially applications in nanostructured materials and thin films.
Abstract: This chapter introduces the concepts that define the mechanical properties characterized by nanoindentation, the fundamentals of nanoindentation, nanoindentation applications in materials and composites, and especially applications in nanostructured materials and thin films. Also introduced are experimental, theoretical, and computational approaches to revealing the mechanisms and fundamentals of nanoindentation. This chapter reviews frontier research on the use of experimental and computer modeling to find the mechanical properties of materials, composites, nanomaterials, and thin films by nanoindentation.

10 citations

References
More filters
Journal ArticleDOI
TL;DR: In this paper, the authors used a Berkovich indenter to determine hardness and elastic modulus from indentation load-displacement data, and showed that the curve of the curve is not linear, even in the initial stages of the unloading process.
Abstract: 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%.

22,557 citations

Journal ArticleDOI
TL;DR: In this paper, the effects of the substrate on the determination of mechanical properties of thin films by nanoindentation were examined, and the properties of aluminum and tungsten films on the following substrates: aluminum, glass, silicon and sapphire.

1,410 citations

Journal ArticleDOI
TL;DR: In this article, the authors used finite element simulation of conical indentation of a wide variety of elastic-plastic materials 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.
Abstract: 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.

847 citations


"Sources of error in relating nanoin..." refers background or methods in this paper

  • ...It was also noticed that several studies reported FEA result of nanoindentation containing clearly perceivable noise (Antunes et al., 2007; Bolshakov and Pharr, 1998; Chen and Vlassak, 2001; Larsson et al., 1996)....

    [...]

  • ...The other source that was limiting our ability to quantify the change of mechanical properties was the inability of the widely used method (Oliver and Pharr, 1992) to estimate the contact area accurately when the material piles up around the indenter (Bolshakov, 1996; Bolshakov and Pharr, 1998; Cheng and Cheng, 1998, 2000)....

    [...]

  • ...…limiting our ability to quantify the change of mechanical properties was the inability of the widely used method (Oliver and Pharr, 1992) to estimate the contact area accurately when the material piles up around the indenter (Bolshakov, 1996; Bolshakov and Pharr, 1998; Cheng and Cheng, 1998, 2000)....

    [...]

Journal ArticleDOI
R.B. King1
TL;DR: In this article, the problem of flat-ended cylindrical, quadrilateral, and triangular punches indenting a layered isotropic elastic half-space is considered, and solutions are obtained numerically.

816 citations

Journal ArticleDOI
TL;DR: In this paper, a detailed analysis of Sneddon's solution for indentation by a rigid cone reveals several largely ignored features that have important implications for nanoindentation property measurement.
Abstract: Methods for analyzing nanoindentation load-displacement data to determine hardness and elastic modulus are based on analytical solutions for the indentation of an elastic half-space by rigid axisymmetric indenters. Careful examination of Sneddon's solution for indentation by a rigid cone reveals several largely ignored features that have important implications for nanoindentation property measurement. Finite element and analytical results are presented that show corrections to Sneddon's equations are needed if accurate results are to be obtained. Without the corrections, the equations underestimate the load and contact stiffness in a manner that leads to errors in the measured hardness and modulus, with the magnitudes of the errors depending on the angle of the indenter and Poisson's ratio of the half-space. First order corrections are derived, and general implications for the interpretation of nanoindentation data are discussed.

403 citations


"Sources of error in relating nanoin..." refers background or methods in this paper

  • ...For example Hay et al. (1999) have reported results of axisymmetric FEA of conical indentation by four different cones with half-included angles of 42.28º, 60º, 70.32º, and 80º. Noting that their mesh consisted of square elements 5nm on a side in the region of contact, the possible error in contact…...

    [...]

  • ...72, suggested by Sneddon for conical indentation (Hay et al., 1999)....

    [...]

  • ...Comprehensive studies of various aspects of nanoindentation using FEA are available in the literature (Bolshakov, 1996; Hay et al., 1999; Shim, 2007)....

    [...]

  • ...Comprehensive studies of various aspects of nanoindentation using FEA are available in the literature (Bolshakov, 1996; Hay et al., 1999; Shim, 2007)....

    [...]

  • ...For conical indentation of fused silica, β can be obtained from analytical equation given by Hay et al. (1999) which is equal to 1.072....

    [...]