Triangular Pyramidal Indenters Research Articles

Nanoindentation of Fused Quartz at Loads Near the Cracking Threshold

Nanoindentation with triangular pyramidal indenters with centerline-to-face angles of 35.3°, 45°, 55°, 65.3° and 75° at loads in the range 1–500 mN was conducted on fused quartz to explore how cracks first form and develop in brittle materials during sharp indentation contact. The cracking behavior was documented using high resolution scanning electron microscopy and serial cross sectioning by focused ion beam milling. Results show that cracking is enhanced by sharper indenters and that there is a distinct threshold load below which no cracking is observed. The threshold increases rapidly with indenter angle. A series of indentations made at increasing load with the 45° indenter shows that the first cracks to form are relatively straight radials that emanate outward from the corners of the indentation. However, underneath the indent they do not connect to the hardness impression but rather terminate at what appears to be the elastic-plastic boundary. With increasing load, the radial cracks extend outward and downward, but at an intermediate load they branch to the sides beneath the hardness impression to form lateral cracks. Cracking does not appear to initiate from pre-existing flaws, but is generated from processes associated with plastic deformation beneath the indenter. Results are discussed in terms of prevailing ideas on the origin of the cracking threshold.

Loop energy: A useful indicator of the hardness of minerals from depth-sensing indentation tests

Depth-sensing indentation tests were performed to obtain the loop energy (equivalent to the energy consumed to produce the indentation) and the residual depth of the indentation using a triangular pyramidal diamond indenter for the minerals in Mohs hardness scale except for diamond, as well as other minerals (apophyllite, forsterite, and tourmaline), at a maximum load ranging from 30 to 100 mN. A new graphic presentation is proposed that shows the hardness of minerals in log(penetration depth)−log(loop energy) space. The data for each mineral under different loads give a straight regression line with a slope of 2.6–2.9 (except for talc, which yields a slope of 2.2), while the data for different minerals under a given load yield a straight regression line with a slope of 1.1–1.2. A theoretical analysis of ideal materials, in terms of log(penetration depth)−log(loop energy) space, shows the existence of two series of parallel regression lines with slopes of 3 (data for each mineral at different loads) and 1 (data for different minerals under a given load). The results show a slight deviation between the measured and theoretical slopes, probably reflecting a progressive change in the mechanical properties of the minerals during the indentation tests.

Effects of indenter angle on micro‐scale fracture toughness measurement by pillar splitting

AbstractWe present improvements to a recently developed pillar splitting technique that can be used to characterize the fracture toughness of materials at the micrometer scale. Micro‐pillars with different aspect ratios were milled from bulk Si (100) and TiN and CrN thin films, and pillar splitting tests were carried out using four different triangular pyramidal indenters with centerline‐to‐face angles varying from 35.3° to 65.3°. Cohesive zone finite element modeling (CZ‐FEM) was used to evaluate the effect of different material parameters and indenter geometries on the splitting behavior. Pillar splitting experiments revealed a linear relationship between the splitting load and the indenter angle, while CZ‐FEM simulations provided the dimensionless coefficients needed to estimate the fracture toughness from the splitting load. The results provide novel insights into the fracture toughness of materials at small‐scales using the pillar spitting technique and provide a simple and reliable way to measure fracture toughness over a broad range of material properties.

Evaluation of wear suppression for phospholipid polymer-grafted ultra-high molecular weight polyethylene at concentrated contact

The wear resistance of cross-linked polyethylene grafted with poly(2-methacryloyloxyethyl phosphorylcholine) (PMPC-grafted CLPE) and unmodified CLPE loaded by an alumina roller were evaluated in a simulated synovial fluid (0.5wt% hyaluronate solution containing 30vol% fetal bovine serum). To evaluate the wear depth distribution within the wear scar, we compared the projected area of wear and non-wear for indents on polyethylene surfaces produced by a triangular pyramidal indenter and estimated the local wear depths on the basis of the changes in the projected area. The worn depth of PMPC-grafted CLPE was almost a third lower than that on CLPE.

A dual triangular pyramidal indentation technique for material property evaluation

Abstract

Correction of indentation load–depth curve based on elastic deformation of sharp indenter

Indenters in numerical analyses are usually assumed rigid. For rigid indenters, the ratios of Kick’s law coefficient to elastic modulus (C/E) are equal for materials with equal values of yield strain (εo) and strain hardening coefficient (n). However, this is not the case for elastic indenters as indenter deformation leads to a shift of the load–depth (P–h) curve.In this study, we employ conical indenters with half-included angle θ=70.3°, tip radius R=0.025mm to derive a corrected P–h curve; maximum indentation depth is set to hmax=0.05mm. Applying finite element analysis (FEA), we show that materials with equal εo and n give equal C/E-values for rigid indenters but different C/E-values for elastic indenters. To account for the elastic deformation of the indenter, we establish a method by introducing a correction factor κ so that equal C/E-values are obtained. It is found that for a given θ, κ does not change when varying indenter size, indentation depth and indenter tip-radius. For a different indenter angle θ, a different value of κ is obtained, yet by following the same correction procedure.We further demonstrate that corresponding κ values for triangular pyramidal indenters are different from those of conical ones, due to the difference in actual projected contact areas. Consequently, the proposed method is applicable to any indenter shape.

유한요소해에 기초한 이중 삼각뿔 압입 물성평가법

In this study, we suggest a method for material property evaluation by dual-triangular pyramidal indenters using the reverse analysis. First, we demonstrated that load-displacement curves of conical and triangular pyramidal indenters are different for the same material. For this reason, an independent research on the triangular pyramidal indenter is needed. From FE indentation analyses on various materials, we then investigated the relationships among material properties, indentation parameters and load-displacement curves. From this, we established property evaluation formula using dual-triangular pyramidal indenters having two different half-included-angles. The approach provides the values of elastic modulus, yield strength and strain-hardening exponent within an average error of 3% for various materials.

Ultra-high residual compressive stress (>2 GPa) in a very small volume (<1 m3) of indented quartz

Indentation testing of natural single-crystal α-quartz parallel to the crystallographic c axis, using a triangular pyramidal diamond indenter at a maximum load of 500 mN, produced a very small residual volume of less than 1 μm 3 in which α-quartz is highly stressed. Laser Raman microspectroscopy across the indentation at room temperature and pressure revealed a shift in the Raman bands, interpreted to reflect the residual stress field generated within the α-quartz. Based on the observed Raman shift, we identified a steep gradient in the residual non-hydrostatic stress field after complete unloading in quartz near the impression formed by indentation. At the center of the indentation, the maximum compressive stress and tensile stress were inferred to be higher than 2.2 and 0.1 GPa, respectively.

A method for evaluating the stress–strain relationship of materials in the microstructural region using a triangular pyramidal indenter

A method for evaluating the microstructural stress–strain relationship of materials, using a triangular pyramidal indenter, is proposed in order to investigate the mechanical properties of steels and weld zones. An existing evaluation method, using a ball indenter, is correspondingly applied to the evaluation method using a triangular pyramidal indenter because the strain distribution under the indenter or the indentation curve on the unloading process between the ball and pyramidal indentation has a similarity. A corresponding ball indenter whose projection area is equal to that of the triangular pyramidal indenter is used to replace the triangular pyramidal indentation with the ball indentation, and the representative stress and strain that express the complicated deformation under the indenter are determined. The stress–strain relationships of single-phase steels in microstructural size are estimated by the proposed method, and on average correspond with those measured by macro-tensile tests. The difference in the stress–strain relationships due to the difference of the crystal orientation of each grain is possibly negligible with this method. It is expected to clearly estimate the difference in the stress–strain relationship of each phase in, for example, dual-phase steels by the proposed method.

S0302-1-4 微小押込み試験による純チタン結晶方位評価法の提案(実験力学における計測・解析法の新展開(1))

Most characteristics of metallic materials are influenced by crystallographic orientation of grains. Measurement of crystal orientation is therefore important for effective use of metallic materials. However, the most methods employed for orientation measurement require expensive apparatus and technical skills. Meanwhile, indentation testing is easy to perform and the imposed micro-indentation geometry on a grain is possible to reflect its crystallographic orientation. The present study aims to establish the method to evaluate crystallographic orientation of grain in polycrystalline metal, based on the indentation geometry. The indentation tests with triangular pyramidal indenter were carried out on pure titanium grains, of which crystal orientations were premeasured by electron backscattered diffraction method. Thus, the relationship between the crystallographic orientation and the indentation geometry was discussed. The results indicated that the directions of <0001> axis and <21^^-1^^-0> axis projected on sample surface were well-correlated with the deviation of te indentation shape from the ideal one. This fact suggests the possibility to evaluate crystallographic orientation by the imposed indentation geometry.

Influence of indenter angle on cracking in Si and Ge during nanoindentation

The influence of indenter angle on the nanoindentation cracking behavior of single crystal Si and Ge was systematically explored through nanoindentation experiments with a series of triangular pyramidal indenters with different centerline-to-face angles in the range 35.3–85.0°. The relationships between indentation load, crack length and indentation size and their dependence on indenter angle were carefully examined and compared with previous indentation cracking studies. The results are discussed in terms of ways to estimate fracture toughness and indentation cracking threshold loads more precisely through nanoindentation.

Extraction of flow properties of single-crystal silicon carbide by nanoindentation and finite-element simulation

A method is presented for estimating the plastic flow behavior of single-crystal silicon carbide by nanoindentation experiments using a series of triangular pyramidal indenters with five different centerline-to-face angles in combination with two-dimensional axisymmetric finite-element (FE) simulations. The method is based on Tabor’s concepts of characteristic strain and constraint factor, which allow indentation hardness values obtained with indenters of different angles to be related to the flow properties of the indented material. The procedure utilizes FE simulations applied in an iterative manner in order to establish the yield strength and work-hardening exponent from the experimentally measured dependence of the hardness on indenter angle. The methodology is applied to a hard, brittle ceramic material, 6H–SiC, whose flow behavior cannot be determined by conventional tension or compression testing. It is shown that the friction between the indenter and the material plays a significant role, especially for very sharp indenters.

A comparison of 3D finite element simulations for Berkovich and conical indentation of fused silica

Much of our understanding of elastic-plastic contact mechanics as it relates to the interpretation of nanoindentation data comes from two-dimensional, axisymmetric finite element simulations of conical indentation. In many instances, conical results adequately describe real experimental results; however, there are instances where conical simulations fail to capture important behaviour. Three-dimensional finite element simulations of Berkovich triangular pyramidal indentation of fused silica are compared to similar simulations with a 70.3° cone. It is shown that a potentially significant difference between the two indenters exists for the contact areas and contact stiffnesses. Implications for the interpretation of nanoindentation data are discussed.

An experimental evaluation of the constant β relating the contact stiffness to the contact area in nanoindentation

Measurements of mechanical properties by nanoindentation with triangular pyramidal indenters like the Berkovich rely heavily upon the relationship between the contact stiffness, S, the contact area, A, and the reduced elastic modulus, Er . This relationship is often written in the form S=2βEr (A/π)1/2, where β is a constant that depends on the geometry of the indenter. Although the most common values for β used in experimental measurements are 1.000 and 1.034, various theoretical analyses have yielded values as small as 1.00 or as large as 1.20, depending on the assumptions made to model the deformation. Here, the most appropriate value of β is explored by performing careful experiments in fused quartz with thin gold coatings applied to the surface to reveal the actual contact area when observed in the scanning electron microscope. Experiments were performed not only with the Berkovich indenter, but with five other three-sided pyramidal indenters with centreline-to-face angles ranging from 35.3° (cube corner) to 85.0°. The results are important in the accurate measurement of mechanical properties by nanoindentation

Nanoindentation-Induced Phase Transformations in Ge Studied by Electron Microscopy and Raman Spectroscopy

The sequences of hydrostatic pressure-induced phase transformations in Si and Ge have been established in diamond anvil studies. At sufficient pressure the normal diamond-cubic structure Si-I/Ge-I transforms to the metallic {beta}-tin structure; upon unloading, several metastable phases can form depending on the maximum load and/or unloading rate. In the case of Ge, the metastable phases are Ge-III(ST12) or Ge-IV(BC8). Since microstructural investigations of Si indents have revealed metastable crystalline phases, it was expected that Ge indents could demonstrate similar phenomena. However, there is no prior evidence of phase transformations from indentation load-displacement (P-h) curves or electron microscopy. In this study, nanoindentations were made on undoped (100) Ge at room temperature with triangular pyramidal indenters with centerline-to-face angles of 35{sup o} (cube-corner) and 65{sup o} (Berkovich) at loads of 10, 50 and 80 mN and a loading/unloading rate of 5mN/s. The indents were examined by SEM, micro-Raman analyses and TEM of cross-sections prepared by dual-beam FIB milling.

Indentation-induced phase transformations in silicon: influences of load, rate and indenter angle on the transformation behavior

Nanoindentation has been used widely to study pressure-induced phase transformations in Si. Here, a new aspect of the behavior is examined by making nanoindentations on (1 0 0) single crystals using a series of triangular pyramidal indenters with centerline-to-face angles varying from 35.3° to 85.0°. Effects of indenter angle, maximum load, and loading/unloading rate are systematically characterized from nanoindentation load–displacement data in conjunction with micro-Raman imaging spectroscopy of the residual hardness impressions. Results are discussed in terms of prevailing ideas and models for indentation-induced phase transformations in silicon.

An Experimental Evaluation of the Constant β Relating the Contact Stiffness to the Contact Area in Nanoindentation

ABSTRACTMeasurements of mechanical properties by nanoindentation with triangular pyramidal indenters like the Berkovich rely heavily upon the relationship between the contact stiffness, S, the contact area, A, and the reduced elastic modulus, Er. This relationship is often written in the form S = 2βEr(A/π)1/2, where β is a constant that depends on the geometry of the indenter. Although the most common values for β used in experimental measurements are 1.000 and 1.034, various theoretical analyses have yielded values as small as 1.00 or as large as 1.2, depending on the assumptions made to model the deformation. Here, we explore the most appropriate value of β by performing careful experiments in fused quartz with thin gold coatings applied to the surface to reveal the actual contact area when observed in the scanning electron microscope. Experiments were performed not only with the Berkovich indenter, but with five other three-sided pyramidal indenters with centerline-to-face angles ranging from 35.3° (cube corner) to 85°. Results are discussed as they apply to obtaining accurate measurements of mechanical properties by nanoindentation.

Micro-Raman Mapping and Analysis of Indentation-Induced Phase Transformations in Germanium

ABSTRACTAlthough it has been confirmed by diamond anvil cell experiments that germanium transforms under hydrostatic pressure from the normal diamond cubic phase (Ge-I) to the metallic β-tin phase (Ge-II) and re-transforms to Ge-III (ST12 structure) or Ge-IV (BC8 structure) during release of the pressure, there are still controversies about whether the same transformations occur during nanoindentation. Here, we present new evidence of indentation-induced phase transformations in germanium. Nanoindentation experiments were performed on a (100) Ge single crystal using two triangular pyramidal indenters with different tip angles - the common Berkovich and the sharper cube-corner. Although the indentation load-displacement curves do not show any of the characteristics of phase transformation that are well-known for silicon, micro-Raman spectroscopy in conjunction with scanning electron microscopy reveals that phase transformations to amorphous and metastable crystalline phases do indeed occur. However, the transformations are observed reproducibly only for the cube-corner indenter.

Micro-Raman Mapping and Analysis of Indentation-Induced Phase Transformations in Germanium

ABSTRACTAlthough it has been confirmed by diamond anvil cell experiments that germanium transforms under hydrostatic pressure from the normal diamond cubic phase (Ge-I) to the metallic β-tin phase (Ge-II) and re-transforms to Ge-III (ST12 structure) or Ge-IV (BC8 structure) during release of the pressure, there are still controversies about whether the same transformations occur during nanoindentation. Here, we present new evidence of indentation-induced phase transformations in germanium. Nanoindentation experiments were performed on a (100) Ge single crystal using two triangular pyramidal indenters with different tip angles - the common Berkovich and the sharper cube-corner. Although the indentation load-displacement curves do not show any of the characteristics of phase transformation that are well-known for silicon, micro-Raman spectroscopy in conjunction with scanning electron microscopy reveals that phase transformations to amorphous and metastable crystalline phases do indeed occur. However, the transformations are observed reproducibly only for the cube-corner indenter.

Cross-Sectional TEM Studies of Indentation-Induced Phase Transformations in Si: Indenter Angle Effects

ABSTRACTNanoindentations were made on a (100) single crystal Si wafer at room temperature with a series of triangular pyramidal indenters having centerline-to-face angles ranging from 35° to 85°. Indentations produced at high (80 mN) and low (10 mN) loads were examined in plan-view by scanning electron microscopy and in cross-section by transmission electron microscopy. Microstructural observations were correlated with the indentation load-displacement behavior. Cracking and extrusion are more prevalent for sharp indenters with small centerline-to-face angles, regardless of the load. At low loads, the transformed material is amorphous silicon for all indenter angles. For Berkovich indentations made at high-load, the transformed material is a nanocrystalline mix of Si-I and Si-III/Si-XII, as confirmed by selected area diffraction. Extrusion of material at high loads for the cube-corner indenter reduces the volume of transformed material remaining underneath the indenter, thereby eliminating the pop-out in the unloading curve.