Wedge Indentation Research Articles

Inclined indentation of smooth wedge in rock mass

The article focuses on the inclined rigid wedge indentation into a rigid-plastic half-plane of rocks with the Mohr–Coulomb-Mohr plasticity. The limiting loads on different sides of the wedge are determined versus the internal friction angle, cohesion and wedge angle. It is shown that when the force is applied along the symmetry axis of the wedge, the zone of plasticity is formed only on one wedge side. In order to form the plasticity zone on both sides of the wedge, it is necessary to apply the force asymmetrically relative to the wedge symmetry axis. An engineering solution for the asymmetrical case implementation is suggested.

Analytic relations for two-dimensional indentations with surface tension

Surface tension plays a significant role in micro- and nanoindentation tests. Based on the solution of a concentrated force acting on an elastic half-plane with surface tension, the two-dimensional indentations of an elastic half-plane by a cylindrical indenter, a wedge indenter and a flat-ended indenter are formulated, and by employing the Gauss–Chebyshev quadrature formula, the corresponding singular integral equations are numerically solved. For each indentation, the analytic solutions of two limit cases considering only bulk elasticity or surface tension are derived. Then through simple combinations of the results of two limit cases, the analytic relations between load and contact half-width or indent depth are formulated for the general case, and compared with the numerical results. The analytic relations established in this paper facilitate better characterization of mechanical properties of materials by micro/nanoindentation tests.

“Effect of Underlay Dimension to Cutting characteristics of Polystyrene Bars Subjected to Wedge Indentation”

“Effect of Underlay Dimension to Cutting characteristics of Polystyrene Bars Subjected to Wedge Indentation”

A novel numerical framework for self-similarity in plasticity: Wedge indentation in single crystals

A novel numerical framework for analyzing self-similar problems in plasticity is developed and demonstrated. Self-similar problems of this kind include processes such as stationary cracks, void growth, indentation etc. The proposed technique offers a simple and efficient method for handling this class of complex problems by avoiding issues related to traditional Lagrangian procedures. Moreover, the proposed technique allows for focusing the mesh in the region of interest. In the present paper, the technique is exploited to analyze the well-known wedge indentation problem of an elastic–viscoplastic single crystal. However, the framework may be readily adapted to any constitutive law of interest. The main focus herein is the development of the self-similar framework, while the indentation study serves primarily as verification of the technique by comparing to existing numerical and analytical studies. In this study, the three most common metal crystal structures will be investigated, namely the face-centered cubic (FCC), body-centered cubic (BCC), and hexagonal close packed (HCP) crystal structures, where the stress and slip rate fields around the moving contact point singularity are presented.

Geometrically necessary dislocation density measurements at a grain boundary due to wedge indentation into an aluminum bicrystal

An aluminum bicrystal with a symmetric tilt Σ43 (3 3 5)[1 1 0] coincident site lattice grain boundary was deformed plastically via wedge indentation under conditions that led to a plane strain deformation state. Plastic deformation is induced into both crystals and the initially straight grain boundary developed a significant curvature. The resulting lattice rotation field was measured via Electron Backscatter Diffraction (EBSD). The Nye dislocation density tensor and the associated Geometrically Necessary Dislocation (GND) densities introduced by the plastic deformation were calculated. The grain boundary served as an impediment to plastic deformation as quantified through a smaller lattice rotation magnitude and smaller GND density magnitudes in one of the crystals. There is evidence that the lattice rotations in one grain brought a slip system in that grain into alignment with a slip system in the other grain, upon which the impediment to dislocation transmission across the grain boundary was reduced. This allowed the two slip systems to rotate together in tandem at later stages of the deformation. Finite element crystal plasticity simulations using classical constitutive hardening relationship capture the general features observed in the experiments.

Directionality of residual stress evaluated by instrumented indentation testing using wedge indenter

In instrumented indentation testing (IIT), residual stress can be evaluated by shift in indentation load-depth curves for stress-free and stressed states. Although the average surface residual stress is able to be evaluated with Vickers indenter, in order to know stress directionality, another indentation tests with two-fold symmetric indenter, for example, Knoop indenter, are needed. As some necessities for evaluating nonequibiaxial residual stress within small indent area, we suggest a novel way to evaluate directionality of residual stress, p, using wedge indenter characterized by two parameters, edge length and inclined angle. We develop wedge-indentation-mechanics model based on predetermined conversion factors which are determined by IITs for various uniaxial stressed states combining with finite element analysis simulations. By utilizing the developed model, directionality of residual stress is evaluated through two serial wedge IITs with respect to principal directions. We find good agreements between applied residual stress and residual stress evaluated by the developed model for biaxial tensile stress states.

Re-Examination of Correlation between Hardness and Tensile Properties by Numerical Analysis

Contact, singular-field, and large-deformation numerical analyses were performed to re-examine the correlation between hardness and tensile properties. Materials have single hardness values, but continuous changes in stress-strain diagrams; it is impossible, in principle, to correlate the hardness to one stress-strain value. Therefore, there must exist an application limit, which is discussed in this study. Because discretization error is unavoidable in such analyses, a method for leveling the discretization error regardless of the analysis condition was introduced. Moreover, in order to generalize the analysis results, the stress-strain diagram used for this analysis was considered as a dimensionless expression in arranging the results. From the analytical results, the following conclusions were deduced. The range in which the empirical equation between hardness and tensile strength is applicable depends on only the value of the work hardening exponent. Moreover, for the 0.05–0.2 range of the work hardening exponent for general steel, the prediction of tensile strength from the hardness is possible with 10% error at indenter face angles between 110° and 136° in case of the wedge indentation.

Analyzing the effect of hydration on the wedge indentation fracture behavior of cortical bone

Hydration directly affects the mechanical properties of bone. An initial and basic procedure shows both wedge indentation fracture experiments under plane strain conditions in cortical bone and numerical simulation with finite elements agree that dry bone fractures much more easily than fully hydrated bone submerged in an aqueous environment, such as in the body of an animal. The wedge indentation experiments were performed with high speed video microscopy, under dry and fully hydrated (submerged) conditions. The numerical simulation, specifically finite element analysis using cohesive elements to simulate fracture, was utilized to capture plasticity, fracture initiation and propagation, and to study the applicability of brittle material based indentation fracture theory. Experiment and theory give similar results for the dependence of depth of fracture initiation, and size of plastic zone, on hydration state. Comparison of fracture propagation characteristics between wet and dry bone are examined and discussed. This research demonstrates the ability to quantitatively assess the effect of hydration on the fracture initiation, propagation, and plastic zone size of cortical bone, through an approach using simple wedge indentation, with important implications for efforts in developing methods to understand clinical diagnostic testing and general fracture behavior of living bone in the ultimate interest of health care purposes.

Estimation of Wedge Indentation Resistance and Plane Compressive Characteristics of Acrylic PSA

This paper aims to estimate the compressive characteristics and indentation resistance of the acrylic Pressure Sensitive Adhesive (PSA) sheet subjected to the plane plate compression and/or the wedge indentation. These two compressive loading tests with the acrylic PSA sheet were carried out experimentally and numerically. Through the experimental tests, it was found that the indentation velocity affected the cutting line force and the compressive velocity as the compressive strain rate affected the compressive pressure. In addition, a Finite Element Method (FEM) analysis of those two loading tests was carried out using a linear viscoelastic model. It was revealed that the elastic modulus estimated by compressive test is appropriate to simulate the wedge indentation.

ポリプロピレン材のくさび押抜き特性における刃先形状の影響

ポリプロピレン材のくさび押抜き特性における刃先形状の影響

Plane strain indentation on finite thickness bonded layer in couple stress elasticity

Contact of flat, cylindrical and wedge indenter on a finite thickness layer obeying couple stress elasticity and bonded to a rigid base under plane strain conditions is solved. The method of stress functions and Fourier transforms is employed to reduce the mixed boundary value contact problem to a singular integral equation in terms of the unknown contact pressure and contact size. For a given load on the indenter, the solution is obtained iteratively through numerical inversion of the integral equation and the effect of layer thickness and intrinsic length inherent in couple stress elastic material on the contact pressure and contact size is studied. Finally a map described in terms of the intrinsic length and layer thickness is proposed which can be used as a guiding tool to decide appropriate combination of geometry i.e. layer or half space and material behavior i.e. classical elasticity or couple stress elasticity to obtain accurate indentation response for a given system.

Effects of Blade Tip Geometry on Cutting Characteristics of Lead Alloy Sheet Subjected to Wedge Indentation

This research work was carried out aiming to investigate the cutting characteristics of a soft metallic sheet subjected to the wedge blade indentation. The indentation of a lead alloy worksheet was conducted, experimentally using a center bevel blade in order to reveal the experimental background of the indentation. In addition, to investigate the effects of the blade tip geometry, the bevel angle of the wedge blade, on the cutting characteristics of the worksheet, the finite element method (FEM) analysis was conducted. By varying the bevel angle, the critical levels of stresses for the necking of the worksheet were detected. Also, it was found that the bevel angle affected the cutting load resistance, the necking of the worksheet and the final feature of the wedged edge.

Mechanical properties of pentaerythritol tetranitrate(PETN) single crystals from nano‐indentation: Depth dependent response at the nano meter scale

The current work presents the results from an investigation of the mechanical behavior of single crystals of the energetic material pentaerythritol tetranitrate (PETN) using a nano‐indentation technique. The indentation tests have been performed on the maximum growth habit face (110) of the PETN, using a spherical, Berkovich and an anisometric (wedge‐shaped) tip. The load displacement curves along with analysis have been used to extract the mechanical properties and identify the anisotropic indentation modulus for the PETN. The indentation moduli of the PETN single crystal were found to decrease as indentation depth increases and become independent of indentation depth for depths greater than 200 nm for the spherical indenter and 300 nm for the anisometric wedge indenter and Berkovich tip. The indentation modulus obtained from spherical tip indentation is compared with the results calculated by using literature values of the elastic constants. The wedge indenter measurements and Berkovich indentation at various tip orientations are different due to the anisotropy of the PETN. The yield behaviors of the PETN single crystal were also explored using both spherical and wedge tip indentation and the differences are discussed.

Porosity and geometry control ductile to brittle deformation in indentation of porous solids

We report a series of plane strain wedge indentation experiments on a model porous brittle solid (soft rock) and study the effect of porosity and the indenter geometry on the mechanics of indentation. A series of images of the region surrounding the indenter were captured during indentation and were analysed using a particle image velocimetry algorithm. From the image analyses, deformation parameters were analysed as functions of porosity, including velocity fields and localization features such as compaction bands and fractures. The initiation of fracture during indentation was observed in the transition from brittle to ductile behaviour as a function of indentation depth. Higher ductility of the rock during indentation was observed for samples of high porosity and for indentation utilizing sharper wedges. The implications of these results for controlling deformation and fracture in rock drilling by tool geometry and rock porosity control are briefly discussed.

Assessing strain mapping by electron backscatter diffraction and confocal Raman microscopy using wedge-indented Si

The accuracy of electron backscatter diffraction (EBSD) and confocal Raman microscopy (CRM) for small-scale strain mapping are assessed using the multi-axial strain field surrounding a wedge indentation in Si as a test vehicle. The strain field is modeled using finite element analysis (FEA) that is adapted to the near-indentation surface profile measured by atomic force microscopy (AFM). The assessment consists of (1) direct experimental comparisons of strain and deformation and (2) comparisons in which the modeled strain field is used as an intermediate step. Direct experimental methods (1) consist of comparisons of surface elevation and gradient measured by AFM and EBSD and of Raman shifts measured and predicted by CRM and EBSD, respectively. Comparisons that utilize the combined FEA–AFM model (2) consist of predictions of distortion, strain, and rotation for comparison with EBSD measurements and predictions of Raman shift for comparison with CRM measurements. For both EBSD and CRM, convolution of measurements in depth-varying strain fields is considered. The interconnected comparisons suggest that EBSD was able to provide an accurate assessment of the wedge indentation deformation field to within the precision of the measurements, approximately 2×10−4 in strain. CRM was similarly precise, but was limited in accuracy to several times this value.

Numerical simulation of rock fragmentation mechanisms subject to wedge penetration for TBMs

The rock fragmentation mechanism and failure process induced by a wedge indenter for TBMs are numerically simulated utilizing the discrete element method (DEM) in the present study. A novel clustered assembly approach with irregular boundaries for grain-based brittle rock is incorporated into the particle flow code (PFC) to calibrate the macro-responses such as the low tensile to compressive strength ratio observed in laboratory tests. The simulation results are compared with laboratory tests which were conducted to reveal the rock indentation process and rock-tool interactions. The numerical analysis can be divided to two main parts. Part one is to investigate the crack propagation and damage evolution at meso-scale associated with the force–indentation curve. The stress field distributions with respect to indentation time are depicted. It is revealed that the tensile cracks are resulted from the chipping process and the shear cracks are induced by the crushing force with the orientation angle ranging from 45° to 55°, which is in good agreement with macro-observations. In Part two, the fragmentation efficiency and penetration rate under different cases are analyzed with several parameters such as the wedge angle, the confinement stress and the penetration velocity. Meanwhile, the blunt indenter is taken as a special case for analysis and comparison of the fragmentation mechanism.

Characterization of the compressive deformation behavior with strain rate effect of low-density polymeric foams

This study investigates the compressive deformation behavior of a low-density polymeric foam at different strain rates. The material tested has micron-sized pores with a closed cell structure. The porosity is about 94%. During a uni-axial compressive test, the macroscopic stress–strain curve indicates a plateau region during plastic deformation. Finite Element Method (FEM) simulation was carried out, in which the yield criterion considered both components of Mises stress and hydrostatic stress. By using the present FEM and experimental data, we established a computational model for the plastic deformation behavior of porous material. To verify our model, several indentation experiments with different indenters (spherical indentation and wedge indentation) were carried out to generate various tri-axial stress states. From the series of experiments and computations, we observed good agreement between the experimental data and that generated by the computational model. In addition, the strain rate effect is examined for a more reliable prediction of plastic deformation. Therefore, the present computational model can predict the plastic deformation behavior (including time-dependent properties) of porous material subjected to uni-axial compression and indentation loadings.

Dislocation structure during microindentation

Within the recently proposed continuum dislocation theory, numerical simulations of the displacement controlled wedge indentation for single crystals using the finite elements are provided. Under the assumption of plane strain deformation of the crystal having only one active slip system on each side of the wedge the load–displacement curve as well as the dislocation density are computed for the loading and unloading path in terms of the indentation depth. The results of numerical simulations are compared with those obtained from the experiments which shows qualitative agreement.

In situ analysis of flow dynamics and deformation fields in cutting and sliding of metals

The flow dynamics, deformation fields and chip-particle formation in cutting and sliding of metals are analysed, in situ , using high-speed imaging and particle image velocimetry. The model system is a brass workpiece loaded against a wedge indenter at low speeds. At large negative rake angles, the flow is steady with a prow of material forming ahead of the indenter. There is no material removal and a uniformly strained layer develops on the workpiece surface—the pure sliding regime. When the rake angle is less negative, the flow becomes unsteady, triggered by formation of a crack on the prow free surface and material removal ensuing—the cutting regime. The strain on the prow surface at crack initiation is found to be constant. Chip morphologies, such as discrete particle, segmented chip and continuous chip with mesoscale roughness, are shown to arise from a universal mechanism involving propagation of the prow crack, but to different distances towards the indenter tip. The simple shear deformation in continuous chip formation shows small-angle oscillations also linked to the prow crack. Implications for material removal processes and ductile failure are discussed.

Deformation field evolution in indentation of a porous brittle solid

An experimental study of plane strain wedge indentation of a model porous brittle solid has been made to understand the effect of indentation parameters on the evolution of the deformation field and the accompanying volume change. A series of high-speed, high-resolution images of the indentation region and simultaneous measurements of load response were captured through the progression of the indentation process. Particle image velocimetry analysis of the images facilitated in situ measurement of the evolution of the resulting plastic zone in terms of incremental material displacement (velocity), strain rate, strain and volume change (e.g., local pore collapse). These measurements revealed initiation and propagation of flow localizations and fractures, as well as enabled estimate of volume changes occurring in the deformation zone. The results were directly compared with theoretical estimates of indentation pressure and deformation zone geometry and were used to validate a modified cavity expansion solution that incorporates effects of volume changes in the plastic zone.