Indentation Theory Research Articles

A cross-scale material removal prediction model for magnetorheological shear thickening polishing

Conventional polishing methods face significant challenges for achieving excellent performance on complex surfaces. The magnetorheological shear thickening polishing (MRSTP) method, with its dual-stimulus response of shear thickening and magnetization enhancement, offers an effective solution for polishing complex surfaces. However, existing models fail to elucidate the cross-scale material removal mechanisms in MRSTP owing to the coupling of magnetic and flow fields. In this study, a comprehensive model was proposed to address the the challenge of predicting the cross-scale material removal rate (MRR) in MRSTP for complex surfaces. Analytical and finite difference methods were employed to solve the pressure distribution during the MRSTP process using magnetohydrodynamics. By incorporating the pressure distribution, an MRR predictive model was developed for arbitrary points on the workpiece surface based on the indentation theory for active abrasive grains. The material removal mechanism was explored by considering elastic and plastic deformation under fluid pressure. The experimental validation showed a relative error of 14.9 % between the theoretical and experimental MRR. Experiments on aero-engine blade tenons demonstrated that the established MRR model is well suited for application to complex surfaces. This study ultimately reveals the material removal mechanism of MRSTP with coupled magnetic and flow field, providing a new foundation for predicting MRR on complex surfaces.

Effective characterization for the dynamic indentation and plastic parameters acquisition of metals

As a fundamental test technique for the mechanical properties of materials, indentation shows broad application prospects. Compared to the well-studied quasi-static indentation, relatively few and incomplete studies on the dynamic indentation test and characterization have been performed. In this work, a dynamic indentation test technique based on the split Hopkinson pressure bar system is developed, and the corresponding “three-wave method” is proposed to effectively acquire the time-resolved dynamic indentation load and depth. Systematic indentation tests under different loading rates and indenter cone angles are conducted on typical metal materials such as Cu, α-Fe, and α-Ti. Based on the dynamic indentation contact stiffness analysis and indentation theory the indentation hardness under different loading conditions are determined. A procedure for plastic parameter inversion of metal materials, including strain hardening and strain rate strengthening terms based on dynamic indentation, is provided. The effectiveness is verified by the traditional compression test results, providing a new method for characterizing the dynamic mechanical properties of metal materials.

Theoretical and experimental investigation on magnetorheological shear thickening polishing force using multi-pole coupling magnetic field

The magnetorheological shear thickening polishing method, with its dual-stimulus response of shear thickening and magnetization enhancement, has emerged as a promising magnetic field-assisted polishing technology. However, in existing theories and experimental studies on polishing forces, the phenomenon of magnetization enhancement was mainly considered. The shear thickening effect has not yet to be incorporated into. Furthermore, there have been few systematic investigations on the polishing mechanism considering variations of force characteristics. The study aims to fill in these research gaps by developing theoretical models for both normal and tangential forces, and revealing the microscopic polishing mechanism during the magnetorheological shear thickening polishing process. Both normal and tangential polishing force models were established through taking the rheological properties of polishing media under magnetic field and plastic indentation theory into account. Polishing force measurement experiments under a multi-pole coupling magnetic field were conducted to reveal the variations of the polishing forces with different polishing parameters and to validate the established models. Furthermore, the microstructural evolutions of the polishing media components and the surface morphologies after polishing were combined with in-depth analysis to elucidate the polishing mechanism. The polished surface quality was significantly improved without visible scratches. The surface roughness of 48 nm was achieved from the initial value of 245 nm under the normal force of 3.36 N and the tangential force of 2.42 N. The study provides deep insights into the polishing forces characteristics and the polishing mechanism, which contributes to a theoretical guidance for optimizing polishing parameters and improving polishing quality.

Obstructed swelling and fracture of hydrogels.

Obstructions influence the growth and expansion of bodies in a wide range of settings-but isolating and understanding their impact can be difficult in complex environments. Here, we study obstructed growth/expansion in a model system accessible to experiments, simulations, and theory: hydrogels swelling around fixed cylindrical obstacles with varying geometries. When the obstacles are large and widely-spaced, hydrogels swell around them and remain intact. In contrast, our experiments reveal that when the obstacles are narrow and closely-spaced, hydrogels fracture as they swell. We use finite element simulations to map the magnitude and spatial distribution of stresses that build up during swelling at equilibrium in a 2D model, providing a route toward predicting when this phenomenon of self-fracturing is likely to arise. Applying lessons from indentation theory, poroelasticity, and nonlinear continuum mechanics, we also develop a theoretical framework for understanding how the maximum principal tensile and compressive stresses that develop during swelling are controlled by obstacle geometry and material parameters. These results thus help to shed light on the mechanical principles underlying growth/expansion in environments with obstructions.

Investigation of impact load and erosion behaviors on Ti-Ta alloy surface through the synergistic effect of ultrasonic cavitation and micro-abrasive particles

Ti–Ta alloy micro-nano surface processing is crucial for achieving biocompatibility. To investigate the cavitation and micro-abrasive particle damage characteristics, and the deformation mechanism of Ti–Ta alloy material surface, indentation theory, and the J-C constitutive model were adopted. Numerical load prediction models for ultrasonic cavitation and micro-abrasive particles' impact on Ti–Ta alloy surfaces were developed, and the erosion behaviors of ultrasonic cavitation and micro-abrasive particles’ impact on Ti–Ta alloy surfaces individually and in synergy were experimentally investigated. The inversion analysis shows that the range of ultrasonic cavitation impact load is 0.025–1.015 N, and there are material peeling and interconnection phenomena in the cavitation erosion pit. On the other hand, the impact load range of 10 μm spherical smooth SiO2 micro-abrasive particles is 0.107–0.814 N, and there is no material peeling or interconnection phenomenon in the micro-abrasive particle erosion pit. Additionally, the cavitation erosion rate is determined through changes in roughness and depression volume, resulting in a rate of 38.6%. In contrast, the cavitation-induced micro-abrasive particle erosion rate reached 166.4%. The results show that the impact load and erosion rate of ultrasonic cavitation-induced micro-abrasive particles are greater than those of cavitation impact load and erosion rate. Furthermore, ultrasonic cavitation-induced micro-abrasive particles impact is found to be more conducive to achieving micro-nano processing of Ti–Ta alloy surface.

Numerical and experimental studies of the interface characteristics and wave formation mechanism of Hastelloy/stainless steel explosive welding composite plate

In this paper, Hastelloy UNS N10276 was joined to stainless steel UNS S30403 by explosive welding. Theoretical analysis, computer simulation, and experiment results are combined to study the interface characteristics and wave formation mechanism of the Hastelloy/stainless steel explosive welding composite plate. The macro morphology and microstructure of the composite plate’s interface were studied based on experimental research. And the explosive welding process was numerically simulated by ANSYS/AUTODYN. The formation mechanism of the wave interface was studied, and the physical quantities of the interface were analyzed, such as the temperature, the pressure, the heating rate, and the cooling rate. It was shown that the formation of microstructure in the melting zone was related to the temperature change history of the interface. The generation of the jet was the key factor to achieving explosive welding, and the formation mechanism of the wave interface was close to the indentation theory. Additionally, some significant phenomena in explosive welding have been studied.

Chemically-induced active micro-nano bubbles assisting chemical mechanical polishing: Modeling and experiments

The material loss caused by bubble collapse during the micro-nano bubbles auxiliary chemical mechanical polishing (CMP) process cannot be ignored. In this study, the material removal mechanism of cavitation in the polishing process was investigated in detail. Based on the mixed lubrication or thin film lubrication, bubble-wafer plastic deformation, spherical indentation theory, Johnson-Cook (J-C) constitutive model, and the assumption of periodic distribution of pad asperities, a new model suitable for micro-nano bubble auxiliary material removal in CMP was developed. The model integrates many parameters, including the reactant concentration, wafer hardness, polishing pad roughness, strain hardening, strain rate, micro-jet radius, and bubble radius. The model reflects the influence of active bubbles on material removal. A new and simple chemical reaction method was used to form a controllable number of micro-nano bubbles during the polishing process to assist in polishing silicon oxide wafers. The experimental results show that micro-nano bubbles can greatly increase the material removal rate (MRR) by about 400% and result in a lower surface roughness of 0.17 nm. The experimental results are consistent with the established model. In the process of verifying the model, a better understanding of the material removal mechanism involved in micro-nano bubbles in CMP was obtained.

Identification of Viscoelastic Parameters for Composite Propellant by Indentation Technique

AbstractA method for identifying the relaxation modulus or creep compliance of composite propellant based on indentation technique is proposed, which can rapidly and nondestructively measure the mechanical properties of solid rocket motor grain in storage. According to viscoelastic indentation theories, a constitutive model for conical indentation is derived to predict the mechanical parameters of composite propellants. The indentation test with different loading rates and the traditional tensile stress relaxation test for a certain PBT composite propellant were carried out to verify the feasibility of the proposed method. The results show that the prediction results calculated by the constitutive model are in good agreement with the load‐displacement curves of the indentation test, and the mechanical parameters identified by the constitutive model are similar to those parameters fitted by the tensile stress relaxation test. Relevant methods and conclusions can provide a reference for structural analysis and storage life prediction of solid rocket motors.

Effect of Poisson's ratio on the indentation of open cell foam

We tested whether conventional and auxetic (negative Poisson's ratio) foam indentation response fits with classical indentation theory. We first made foam cubes with 20–25 mm sides, and Poisson's ratios spanning negative and positive values (−0.35 to 0.3). These foam cubes were compression tested, and indented by the curved face of two cylinders (10 and 50 mm diameters) and a stud (12 mm diameter), to 20% of their thickness. Full-field true strains were measured by digital image correlation, to obtain Poisson's ratios and to study foam deformation during indentation. Indentation force vs. displacement was measured and calculated using incremental Poisson's ratios and tangent moduli. Normalised root mean square errors between measured and calculated indentation forces were ∼5% of measured values. Foam densification during indentation, and compression towards sample edges, increased with the magnitude of negative Poisson's ratio; these may both increase indentation resistance beyond predictions from indentation theory.

Integrated Prediction Method of Plastic Parameters and Hardness of Materials Based on VICKERS Indentation Theory Model

Integrated Prediction Method of Plastic Parameters and Hardness of Materials Based on VICKERS Indentation Theory Model

Revisiting the theory behind AFM indentation procedures. Exploring the physical significance of fundamental equations

Fundamental contact mechanics models concerning the interaction of an axisymmetric indenter and an elastic half-space are usually employed in atomic force microscopy (AFM) indentation methods. In this paper, a simplified ‘equivalent’ physical system is used to correlate basic magnitudes such as the applied force on an elastic half space, the Young’s modulus, the contact radius and the indentation depth. More specifically, the equations correlating the above magnitudes are derived using fundamental physics instead of the typical rigorous mathematical process with a small error. In addition, the relation between a force-indentation curve and the indenter’s shape is also presented in detail in order to help students and non-specialists in contact mechanics to obtain a strong background to the AFM indentation theory.

Analytical modelling of the trans-scale cutting forces in diamond cutting of polycrystalline metals considering material microstructure and size effect

In diamond cutting of polycrystalline metals, the influence of size effect and microstructure on the cutting force is prominent due to the trans-scale variation of undeformed chip thickness (UDCT) from microscale to nanoscale. This study proposes a trans-scale cutting force model for diamond cutting of polycrystalline metals with the full consideration of microstructure, material elastic recovery, size effect and round-tool-edge effect. Specifically, by corelating micro-forming theory and crystal plastic theory, a hybrid slip-line model (HSLM) is developed to determine the flow stress in the primary deformation zone, which can quantify the influence of size effect and microstructure, such as grain size, grain boundary and crystal anisotropy, on flow stress. Then, the normal cutting force and frictional cutting force are determined by analysing the stress distribution and frictional states at tool-chip interface using a tool-chip contact model. The rubbing force induced by material elastic recovery at very small UDCT is determined based on indentation theory. Through diamond cutting of polycrystalline copper with different grain sizes, it is experimentally demonstrated that the proposed HSLM can capture the cutting mechanism transformation phenomenon from shearing (tensile stress) to ploughing (compressive stress) with increasing size factor. Besides, the proposed force model has the improved estimation accuracy compared with the conventional force models developed based on Johnson-Cook constitutive equation.

Material Removal Model for Lapping Process Based on Spiral Groove Density

The increasing demand for single-crystal wafers combined with the increase in diameter of semiconductor wafers has warranted further improvements in thickness variation and material removal rate during lapping to ensure price competitiveness of wafers; consequently, the lapping process has gained the attention of researchers. However, there is insufficient research on the effect of platen grooves on the lapping process. In this study, the parameters to describe grooves were defined in order to understand their influence on the lapping process, and a material removal model was suggested based on indentation theory and subsequently experimentally validated. The results indicate that changes in groove density affect the lubrication condition at the contact interface as well as the probability of abrasive participation by varying the oil film thickness. When fabricating the groove for a lapping platen, a groove density at the critical groove density (CGD) or higher should be selected. The higher the groove density, the easier it is to avoid the CGD, and the higher is the material removal rate. The results of this study will enable engineers to design lapping platen grooves that are suitable for the production of modern semiconductor wafers.

Flat-Top Cylinder Indenter for Mechanical Characterization: A Report of Industrial Applications.

FIMEC (flat-top cylinder indenter for mechanical characterisation) is an instrumented indentation test employing a cylindrical punch. It has been used to determine the mechanical properties of metallic materials in several applications of industrial interest. This work briefly describes the technique and the theory of indentation with a flat-ended punch. The flat indentation of metals has been investigated through experimental tests, and an equation has been derived to calculate the yield stress from the experimental data in deep indentation. The approach is supported by many data on various metals and alloys. Some selected case studies are presented in the paper: (i) crank manufacturing through pin squeeze casting; (ii) the evaluation of the local mechanical properties in a carter of complex geometry; (iii) the qualification of Al billets for extrusion; (iv) stress–relaxation tests on CuCrZr heat sinks; (v) the characterization of thick W coatings on CuCrZr alloy; (vi) the measure of the local mechanical properties of the molten-zone (MZ) and the heat-affected zone (HAZ) in welded joints. The case studies demonstrate the great versatility of the FIMEC test which provides information not available by employing conventional experimental techniques such as tensile, bending, and hardness tests. On the basis of theoretical knowledge and large amount of experimental data, FIMEC has become a mature technique for application on a large scale in industrial practice.

ПРИБЛИЖЕННОЕ ОПРЕДЕЛЕНИЕ ГЕОМЕТРИЧЕСКИХ ПАРАМЕТРОВ НАПЛЫВА ПРИ ВНЕДРЕНИИ ПАРАБОЛОИДНОГО ИНДЕНТОРА В ПОЛУПРОСТРАНСТВО

The problem of the indenter embedding into a half-space is formulated and solved. A concept of the elastic contact is used, which implies the uniformity of the stress-strain state in a surface layer. The process of the surface layer formation after mechanical treatment is studied. Based on the general theory of indenter penetration into a half-space, numerical and analytical solutions, determining the length and depth of penetration of a paraboloid into elastoplastic space, are obtained. According to the theory of indentation, the problem is reduced to the use of the method of approximate determination of geometric parameters of a bead, when a paraboloid is being embedded into elastoplastic space. An exact solution to the formulated problem allows one to obtain analytical dependences for calculating the velocities and to study the stress-strain state of the material in the half-space surface layer during the processing. The reliability of the obtained analytical solution is confirmed by numerical calculations without introducing additional hypotheses. Based on the analytical solution, the geometric parameters of the influx from the penetration depth are determined. Calculations can be performed at any embedding depth. Sag formation during the indenter embedding by 18 mm into plasticine specimens is considered as an example. It is shown that the rigid zone is insignificant or absent.

Characterizing poroelasticity of biological tissues by spherical indentation: An improved theory for large relaxation

Flow of fluids within biological tissues often meets with resistance that causes a rate- and size-dependent material behavior known as poroelasticity. Characterizing poroelasticity can provide insight into a broad range of physiological functions, and is done qualitatively in the clinic by palpation. Indentation has been widely used for characterizing poroelasticity of soft materials, where quantitative interpretation of indentation requires a model of the underlying physics, and such existing models are well established for cases of small strain and modest force relaxation. We showed here that existing models are inadequate for large relaxation, where the force on the indenter at a prescribed depth at long-time scale drops to below half of the initially peak force (i.e., F(0)/F(∞) > 2). We developed an indentation theory for such cases of large relaxation, based on Biot theory and a generalized Hertz contact model. We demonstrated that our proposed theory is suitable for biological tissues (e.g., porcine liver, spleen, kidney, skin and human cirrhosis liver) with both small and large relaxations. The proposed method would be a powerful tool to characterize poroelastic properties of biological materials for various applications such as pathological study and disease diagnosis.

Indentation Theory for Identification of Solid Surface Tension and Its Numerical Proof by FE simulation

Indentation Theory for Identification of Solid Surface Tension and Its Numerical Proof by FE simulation

Valid Geometric Solutions for Indentations with Algebraic Calculations

This paper analyzes the force vs depth loading curves of conical, pyramidal, wedged and for spherical indentations on a strict mathematical basis by explicit use of the indenter geometries rather than on still world-wide used iterated “contact depths” with elastic theory and violation of the energy law. The now correctly analyzed loading curves provide as yet undetectable phase-transition. For the spherical indentations, this includes an obvious correction for the varying depth/radius ratio, which had previously been disregarded. Only algebraic formulas are now used for the calculation of material’s properties without data-fittings, or simplifications, or false simulations. Penetration resistance differences of materials’ polymorphs provide precise intersection values as kink unsteadiness by equalization of linear regression lines from mathematically linearized loading curves. These intersections indicate phase transition onset values for depth and force. The precise and correct determination of phase-transition onsets allows for energy and phase-transition energy calculations. The unprecedented algebraic equations are most simply and mathematically reproducibly deduced. There are no restrictions for elastic and/or plastic behavior and no use of different formulas for different force ranges. The novel indentation formulas reveal unprecedented access to the onset, energy and transition energy of phase-transitions. This is now also achieved for spherical indentations. Their formula as deduced for plotting is reformulated for integrations. The distinction of applied work (Wapplied) and indentation work (Windent) allows now for comparing spherical with pyramidal indentation phase-transitions. Only low energy phase-transitions from pyramidal indentation may be missed in spherical indentations. The rather low penetration depths of sphere calottes calculate very close for cap and flat area values. This allows for the calculation of the indentation phase-transition onset pressure and thus the successful comparison with hydrostatic anvil pressurizing results. This is very helpful for their interpretations, as low energy phase-transitions are often missed under the anvil, and it further strengthens the unparalleled ease of the indentation techniques. Exemplification is reported for pyramidal, spherical, and hydrostatic anvil stressing by the numerical analysis of published germanium data. The previous widely accepted historical indentation theories and standards are challenged. Falsely simulated and even published so-called “experimental” indentation data from the literature can most easily be checked. They are mathematically unsound and their correction is urgently necessary for scientific reasons and daily safety with stressed materials. The motivation for this paper is the challenge of worldwide incorrect ISO 14577 standards for false and incomplete characterization of materials. The minimization of catastrophic failures e.g. in aviation requires the strengthening and the advancements of the mathematical truth by using our closed formulas that are based on undeniable geometric and algebraic calculation rules.

Scaling laws and snap-through events in indentation of perforated membranes

We revisit the classical theory of indentation for very soft materials. Many experiments consist in extracting the stiffness of a membrane from the cubic answer of the force versus indentation depth. However, this law is restricted to a perfect membrane under a sharp point loading. In biophysical experiments, where this technique recovers some success at low scales thanks to AFM, the thin samples are highly deformable, hyper-elastic, pre-stretched and often attached to a substrate which cannot be neglected. In addition microscopic tiny pores may exist or may be created by the indenter. This diversity requires specific studies with the correct elasticity: here we choose the neo-Hookean elastic model at large membrane deformations. We show that, the weak loading regime is extremely sensitive to any physical properties of the thin layer but also of the indenter geometry. In addition, when a hole exists, at finite forcing or finite indentation depth, we discover a topological bifurcation with abrupt dynamical jump variation of typical quantities such as the hole size. This bifurcation is similar to the famous catenoid instabilities which are also due to a topological bifurcation, when the two rings of support are pulled apart. This bifurcation is robust in the sense that it always exists whatever the physical properties of the sample.

3D Axisymmetric exact solutions of the piezo-coating sensors for coating/substrate system under charged conical contact

A complete set of frictionless conical contact (indentation) theory of the piezoelectric contact mechanics (PCM) for transversely isotropic piezoelectric elasticity coated system (TIPECS) under charged conical contact is established. 3D exact solutions for the stresses, displacements, electric displacements and electric potential are derived. The contact radius VS the total load relation is obtained, which is valuable to develop the technology of indentation. The relations of coating thickness VS voltage and coating thickness VS voltage are studied. The optimal thickness can be determined with an optimization procedure. Interfacial delamination area of the TIPECS can be predicted with interfacial failure criterion. The theoretical results are helpful for the prediction of some transient electrical effects, which can be combined with experiments to estimate some elastic constants, dielectric constants and piezoelectric constants in the indentation process.