A review of rock macro-indentation:Theories,experiments,simulations,and applications

Rock macro-indentation plays a fundamental role in mechanical rock breaking for various rock engineering application,such as drilling,tunneling,cutting,and sawing.Over the past decades,extensive research has been conducted to understand the indentation mechanisms and responses through various approaches.This review aims to provide an overview of the current status and recent advancements in theories,experiments,numerical simulations,and applications of macro-indentation in rock engineering.It starts with elaborating on the mechanisms of macro-indentation,followed by a discussion of the merits and limitations of commonly used models.Influence factors and their effects on indentation test results are then summarized.Various numerical simulation methods for rock macro-indentation are highlighted,along with their advantages and disadvantages.Subsequently,the applications of indentation tests and indentation indices in characterizing rock properties are explored.It reveals that compression-tension,compression-shear,and composite models are widely employed in rock macroindentation.While the compression-tension model is straightforward to use,it may overlook the anisotropic properties of rocks.On the other hand,the composite model provides a more comprehensive description of rock indentation but requires complex calculations.Additionally,factors,such as indentation rate,indenter geometry,rock type,specimen size,and confining pressure,can significantly influence the indentation results.Simulation methods for macro-indentation encompass continuous medium,discontinuous medium,and continuous-discontinuous medium methods,with selection based on their differences in principle.Furthermore,rock macro-indentation can be practically applied to mining engineering,tunneling engineering,and petroleum drilling engineering.Indentation indices serve as valuable tools for characterizing rock strength,brittleness,and drillability.This review sheds light on the development of rock macro-indentation and its extensive application in engineering practice.Specialists in the field can gain a comprehensive understanding of the indentation process and its potential in various rock engineering endeavors.

Indentation behavior of a semi-infinite piezoelectric semiconductor under a rigid flat-ended cylindrical indenter

This paper theoretically studies the axisymmetric frictionless indentation of a transversely isotropic piezoelectric semiconductor(PSC)half-space subject to a rigid flatended cylindrical indenter.The contact area and other surface of the PSC half-space are assumed to be electrically insulating.By the Hankel integral transformation,the problem is reduced to the Fredholm integral equation of the second kind.This equation is solved numerically to obtain the indentation behaviors of the PSC half-space,mainly including the indentation force-depth relation and the electric potential-depth relation.The results show that the effect of the semiconductor property on the indentation responses is limited within a certain range of variation of the steady carrier concentration.The dependence of indentation behavior on material properties is also analyzed by two different kinds of PSCs.Finite element simulations are conducted to verify the results calculated by the integral equation technique,and good agreement is demonstrated.

Study of damage behavior and repair effectiveness of patch repaired carbon fiber laminate under quasi-static indentation loading

Damage caused due to low-velocity impacts in composites leads to substantial deterioration in their residual strength and eventually provokes structural failure.This work presents an experimental investigation on the effects of different patch and parent laminate stacking sequences on the enhancement of impact strength of Carbon Fiber Reinforced Polymers(CFRP)composites by utilising the adhesively bonded external patch repair technique.Damage evolution study is also performed with the aid of Acoustic Emission(AE).Two different quasi-isotropic configurations were selected for the parent laminate,viz.,[45°/45°/0°/0°]s and[45°/0°/45°/0°]s.Quasi Static Indentation(QSI)test was performed on both the pristine laminates,and damage areas were detected by using the C-scan inspection technique.Damaged laminates were repaired by using a single-sided patch of two different configurations,viz.,[45°/45°/45°/45°]and[45°/0°/0°/45°],and employing a circular plug to fill the damaged hole.Four different combinations of repaired laminates with two configurations of each parent and patch laminate were produced,which were further subjected to the QSI test.The results reveal the effectiveness of the repair method,as all the repaired laminates show higher impact resistance compared to the respective pristine laminates.Patches of[45°/0°/0°/45°]configuration when repaired by taking[45°/45°/0°/0°]s and[45°/0°/45°/0°]s as parents exhibited 68%and 73%higher peak loads,respectively,than the respective pristine laminates.Furthermore,parent and patch of configuration[45°/0°/45°/0°]s and[45°/0°/0°/45°],respectively,attain the highest peak load,whereas[45°/45°/0°/0°]s and[45°/45°/45°/45°]combinations possess the most gradual decrease in the load.

Unexpected Twinning and Phase-Transition of the Indentation Standards, Their Transition Energies, and Scientific Dichotomy

The general use of aluminium as an indentation standard for the iteration of contact heights for the determination of ISO-14577 hardness and elastic modulus is challenged because of as yet not appreciated phase-changes in the physical force-depth standard curve that seemed to be secured by claims from 1992. The physical and mathematical analyses with closed formulas avoid the still world-wide standardized energy-law violation by not reserving 33.33% (h2 belief) (or 20% h3/2 physical law) of the loading force and thus energy for all not depth producing events but using 100% for the depth formation is a severe violation of the energy law. The not depth producing part of the indentation work cannot be done with zero energy! Both twinning and structural phase-transition onsets and normalized phase-transition energies are now calculated without iterations but with physically correct closed arithmetic equations. These are reported for Berkovich and cubecorner indentations, including their comparison on geometric grounds and an indentation standard without mechanical twinning is proposed. Characteristic data are reported. This is the first detection of the indentation twinning of aluminium at room temperature and the mechanical twinning of fused quartz is also new. Their disqualification as indentation standards is established. Also, the again found higher load phase-transitions disqualify aluminium and fused quartz as ISO-ASTM 14577 (International Standardization Organization and American Society for Testing and Materials) standards for the contact depth “hc” iterations. The incorrect and still world-wide used black-box values for H- and Er-values (the latter are still falsely called “Young’s moduli” even though they are not directional) and all mechanical properties that depend on them. They lack relation to bulk moduli from compression experiments. Experimentally obtained and so published force vs depth parabolas always follow the linear FN = kh3/2 + Fa equation, where Fa is the axis-cut before and after the phase-transition branches (never “h2” as falsely enforced and used for H, Er and giving incorrectly calculated parameters). The regression slopes k are the precise physical hardness values, which for the first time allow for precise calculation of the mechanical qualities by indentation in relation to the geometry of the indenter tip. Exactly 20% of the applied force and thus energy is not available for the indentation depth. Only these scientific k-values must be used for AI-advises at the expense of falsely iterated indentation hardness H-values. Any incorrect H-ISO-ASTM and also the iterated Er-ISO-ASTM modulus values of technical materials in artificial intelligence will be a disaster for the daily safety. The AI must be told that these are unscientific and must therefore be replaced by physical data. Iterated data (3 and 8 free parameters!) cannot be transformed into physical data. One has to start with real experimental loading curves and an absolute ZerodurR standard that must be calibrated with standard force and standard length to create absolute indentation results. .

Microstructure and indentation toughness of Cr/CrN multilayer coatings by arc ion plating

Cr/CrN multilayer coatings with bilayer periods in the range from 1351 to 260 nm were prepared on 304 stainless steel substrates by arc ion plating to study the microstructure and properties of multilayer coatings and stimulate their application.SEM results confirm the clear periodicity of the Cr/CrN multilayer coatings and the clear interface between individual layers.XRD patterns reveal that these multilayer coatings contain Cr,CrN and Cr_2N phases.Because Cr layer is softer than its nitride layer,the hardness decreases with the shortening of the bilayer period(or increasing volume fraction of Cr layer).The Cr/CrN multilayer coating with 862 nm period possesses the highest indentation toughness due to a proper individual Cr and nitride layer thickness.However,for the Cr/CrN multilayer with the bilayer period of 1351 nm,it possesses the lowest toughness due to more nitride phase.The indentation toughness of Cr/CrN multilayer coatings is related with their bilayer period.A coating with a proper individual Cr and nitride layer thickness possesses the highest indentation toughness.

Indentation of sandwich beams with metal foam core

The quasi-static indentation behavior of sandwich beams with a metal foam core was investigated. An analytical model was developed to predict the large deflections of indention of the sandwich beams with a metal foam core subjected to a concentrated loading. The interaction of plastic bending and stretching in the local deformation regions of the face sheet was considered in the analytical model. Moreover, the effects of the shear strength of the foam core on the indentation behavior were discussed in detail. The finite element simulations were preformed to validate the theoretical model. Comparisons between the analytical predictions and finite element results were conducted and good agreement was achieved. The results show that the membrane force dominates indentation behavior of the sandwich beams when the maximum deflection exceeds the thickness of the face sheet.

PIEZOSPECTROSCOPIC STUDY OF RESIDUAL STRESSES AROUND INDENTATIONS IN SiC/Al_O_3 NANOCOMPOSITE

A new experimental measurement of residual stresses around Vickers′ indentations on the surface of the SiC/Al 2O 3 nanocomposites is proposed with the aid of a Raman microprobe. Results s how that the shifts of R lines in the fluorescence spectra va ry with the distance from the centre of indentation. The magnitude of load appli ed on the surface of the materials through the indenter influences the shifts of R lines to great extent. The luminescence of R lines of the materials before indenting is used to determine the residual stresses around the indentation in the materials, assuming that the stress tensor is transversely isotropic. Final ly, the term of hydrostatic stress is adopted to explain and compare different residual stresses around indentations with the increase of the indenting load an d the distance from the centre of indentations. <

Effect of indentation size and grain/sub-grain size on microhardness of high purity tungsten

Hardness of materials depends significantly on the indentation size and grain/sub-grain size via microindentation and nanoindentation tests of high-purity tungsten with different structures.The grain boundary effect and indentation size effect were explored.The indentation hardness was fitted using the Nix-Gao model by considering the scaling factor.The results show that the scaling factor is barely correlated with the grain/sub-grain size.The interaction between the plastically deformed zone（PDZ） boundary and the grain/sub-grain boundary is believed to be the reason that leads to an increase of the measured hardness at the specific depths.Results also indicate that the area of the PDZ is barely correlated with the grain/sub-grain size,and the indentation hardness starts to stabilize once the PDZ expands to the dimension of an individual grain/sub-grain.

PIEZOSPECTROSCOPIC STUDY OF RESIDUAL STRESSES AROUND INDENTATIONS IN SiC/AlO3 NANOCOMPOSITE

A new experimental measurement of residual stresses around Vickers′ indentations on the surface of the SiC/Al 2O 3 nanocomposites is proposed with the aid of a Raman microprobe. Results s how that the shifts of R lines in the fluorescence spectra va ry with the distance from the centre of indentation. The magnitude of load appli ed on the surface of the materials through the indenter influences the shifts of R lines to great extent. The luminescence of R lines of the materials before indenting is used to determine the residual stresses around the indentation in the materials, assuming that the stress tensor is transversely isotropic. Final ly, the term of hydrostatic stress is adopted to explain and compare different residual stresses around indentations with the increase of the indenting load an d the distance from the centre of indentations. 【

An New Area Function for Sharp Indenter Tips in Nanoindentation

A new area function is introduced and applied to a Berkovich tip in order tocharacterize the contact projected area between an indenter and indented material. The function canbe related directly to tip-rounding, thereby having obviously physical meaning. Nanoindentationexperiments are performed on a commercial Nano Indenter XP^R system. The other two area functionsintroduced by Oliver and Pharr and by Thurn and Cook respectively are involved in this paper forcomparison. By comparison from experimental results among different area functions, the indenter tipdescribed by the proposed area function here is very close to the experimental indenter.

Dynamic characteristics of nanoindentation in Ni:A molecular dynamics simulation study

In this work, three-dimensional molecular dynamics simulation is carried out to elucidate the nanoindentation behaviour of single crystal Ni. The substrate indenter system is modelled using hybrid interatomic potentials including the manybody potential （embedded atom method） and two-body Morse potential. The spherical indenter is chosen, and the simulation is performed for different loading rates from 10 m/s to 200 m/s. Results show that the maximum indentation load and hardness of the system increase with the increase of velocity. The effect of indenter size on the nanoindentation response is also analysed. It is found that the maximum indentation load is higher for the large indenter whereas the hardness is higher for the smaller indenter. Dynamic nanoindentation is carried out to investigate the behaviour of Ni substrate to multiple loading-unloading cycles. It is observed from the results that the increase in the number of loading unloading cycles reduces the maximum load and hardness of the Ni substrate. This is attributed to the decrease in recovery force due to defects and dislocations produced after each indentation cycle.

A plastic indentation model for sandwich beams with metallic foam cores

Light weight high performance sandwich composite structures have been used extensively in various load bearing applications.Experiments have shown that the indentation significantly reduces the load bearing capacity of sandwiched beams.In this paper,the indentation behavior of foam core sandwich beams without considering the globally axial and flexural deformation was analyzed using the principle of virtual velocities.A concisely theoretical solution of loading capacity and denting profile was presented.The denting load was found to be proportional to the square root of the denting depth.A finite element model was established to verify the prediction of the model.The load-indentation curves and the profiles of the dented zone predicted by theoretical model and numerical simulation are in good agreement.

Indentation of elastically soft and plastically compressible solids

The effect of soft elasticity, i.e., a relatively small value of the ratio of Young＇s modulus to yield strength and plastic compressibility on the indentation of isotropically hardening elastic-viscoplastic solids is investigated. Calcu- lations are carried out for indentation of a perfectly sticking rigid sharp indenter into a cylinder modeling indentation of a half space. The material is characterized by a finite strain elastic-viscoplastic constitutive relation that allows for plas- tic as well as elastic compressibility. Both soft elasticity and plastic compressibility significantly reduce the ratio of nomi- nal indentation hardness to yield strength. A linear relation is found between the nominal indentation hardness and the log- arithm of the ratio of Young＇s modulus to yield strength, but with a different coefficient than reported in previous studies. The nominal indentation hardness decreases rapidly for small deviations from plastic incompressibility and then decreases rather slowly for values of the plastic Poisson＇s ratio less than 0.25. For both soft elasticity and plastic compressibility, the main reason for the lower values of indentation hardness is related to the reduction in the hydrostatic stress level in the material below the indenter.

The indenter tip radius effect in micro- and nanoindentation hardness experiments

Nix and Gao established an important relation between the microindentation hardness and indentation depth. Such a relation has been verified by many microindentation experiments （indentation depths in the micrometer range）, but it does not always hold in nanoindentation experiments （indentation depths approaching the nanometer range）. Indenter tip radius effect has been proposed by Qu et al. and others as possibly the main factor that causes the deviation from Nix and Gao＇s relationship. We have developed an indentation model for micro- and nanoindentation, which accounts for two indenter shapes, a sharp, conical indenter and a conical indenter with a spherical tip. The analysis is based on the conventional theory of mechanism-based strain gradient plasticity established from the Taylor dislocation model to account for the effect of geometrically necessary dislocations. The comparison between numerical result and Feng and Nix＇s experimental data shows that the indenter tip radius effect indeed causes the deviation from Nix-Gao relation, but it seems not be the main factor.

Micro/nano Indentation and Single Grit Diamond Grinding Mechanism on Ultra Pure Fused Silica

The existing research about ductile grinding of fused silica glass was mainly focused on how to carry out ductile regime material removal for generating very ＂smoothed＂ surface and investigate the machining-induced damage in the grinding in order to reduce or eliminate the subsurface damage.The brittle/ductile transition behavior of optical glass materials and the wear of diamond wheel are the most important factors for ductile grinding of optical glass.In this paper,the critical brittle/ductile depth,the influence factors on brittle/ductile transition behavior,the wear of diamond grits in diamond grinding of ultra pure fused silica（UPFS） are investigated by means of micro/nano indentation technique,as well as single grit diamond grinding on an ultra-stiff machine tool,Tetraform ＂C＂.The single grit grinding processes are in-process monitored using acoustic emission（AE） and force dynamometer simultaneously.The wear of diamond grits,morphology and subsurface integrity of the machined groves are examined with atomic force microscope（AFM） and scanning electron microscope（SEM）.The critical brittle/ductile depth of more than 0.5 μm is achieved.When compared to the using roof-like grits,by using pyramidal diamonds leads to higher critical depths of scratch with identical grinding parameters.However,the influence of grit shapes on the critical depth is not significant as supposed.The grinding force increased linearly with depth of cut in the ductile removal regime,but in brittle removal regime,there are large fluctuations instead of forces increase.The SEM photographs of the cross-section profile show that the median cracks dominate the crack patterns beneath the single grooves.Furthermore,The SEM photographs show multi worn patterns of diamond grits,indicating an inhomogeneous wear mechanism of diamond grits in grinding of fused silica with diamond grinding wheels.The proposed research provides the basal technical theory for improving the ultra-precision grinding of UPFS.

The effect of large deformation and material nonlinearity on gel indentation

A gel, an aggregate of polymers with solvents, has dual attributes of solid and liquid as solvent migrates in and out of the polymer network. Indentation has recently been used to characterize the mechanical properties of gels. This paper evaluates the effects of large deformation and material nonlinearity on gel indentation through theoretical modeling and finite element analysis. It is found that large deformation significantly affects the interpretation of the experimen- tal observations and the classical relation between indenta- tion force and depth has limitations for large deformation. The material nonlinearity does not play a very important role on indentation experiment so that the poroelasticity is a good approximation. Based on these observations, this paper proposes an alternative approach to measure the mechanical properties of gels, namely, uniaxial compression experiment.

Modeling and Validation of Indentation Depth of Abrasive Grain into Lithium Niobate Wafer by Fixed-Abrasive Lapping

The prediction of indentation depth of abrasive grain in hydrophilic fixed-abrasive(FA)lapping is crucial for controlling material removal rate and surface quality of the work-piece being machined.By applying the theory of contact mechanics,a theoretical model of the indentation depth of abrasive grain was developed and the relationships between indentation depth and properties of contact pairs and abrasive back-off were studied.Also,the average surface roughness(Ra)of lapped wafer was approximately calculated according to the obtained indentation depth.To verify the rationality of the proposed model,a series of lapping experiments on lithium niobate(LN)wafers were carried out,whose average surface roughness Ra was measured by atomic force microscope(AFM).The experimental results were coincided with the theoretical predictions,verifying the rationality of the proposed model.It is concluded that the indentation depth of the fixed abrasive was primarily affected by the applied load,wafer micro hardness and pad Young′s modulus and so on.Moreover,the larger the applied load,the more significant the back-off of the abrasive grain.The model established in this paper is helpful to the design of FA pad and its machining parameters,and the prediction of Ra as well.

Analyses and predictions of rock cuttabilities under different confining stresses and rock properties based on rock indentation tests by conical pick

The rock indentation tests by a conical pick were conducted to investigate the rock cuttability correlated to confining stress conditions and rock strength.Based on the test results,the regression analyses,support vector machine(SVM)and generalized regression neural network(GRNN)were used to find the relationship among rock cuttability,uniaxial confining stress applied to rock,uniaxial compressive strength(UCS)and tensile strength of rock material.It was found that the regression and SVM-based models can accurately reflect the variation law of rock cuttability,which presented decreases followed by increases with the increase in uniaxial confining stress and the negative correlation to UCS and tensile strength of rock material.Based on prediction models for revealing the optimal stress condition and determining the cutting parameters,the axial boom roadheader with many conical picks mounted was satisfactorily utilized to perform rock cutting in hard phosphate rock around pillar.

A NUMERICAL STUDY OF INDENTATION WITH SMALL SPHERICAL INDENTERS

The finite element method for the conventional theory of mechanism-based strain gradient plasticity is used to study the indentation size effect. For small indenters （e.g., radii on the order of 10μm）, the maximum allowable geometrically necessary dislocation （GND） density is introduced to cap the GND density such that the latter does not become unrealistically high. The numerical results agree well with the indentation hardness data of iridium. The GND density is much larger than the density of statistically stored dislocations （SSD） underneath the indenter, but this trend reverses away from the indenter. As the indentation depth （or equivalently, contact radius） increases, the GND density decreases but the SSD density increases.

Element Analysis of Ceramic Coatings under Spherical Indentation with Metallic Interlayer: PartⅡRing Crack

Spherical indentation of ceramic coatings with metallic interlayer was performed by means of axisymmetric finite element analysis （FEA）. Two typical ceramic coatings with relatively high and low elastic modulus deposited on aluminum alloy and carbon steel were considered. The fracture mechanics of the ceramic coatings mechanisms due to occurrence of surface ring cracks extending traverse the coating thickness under spherical indentation are investigated within the framework of linear fracture mechanics. The J-integral associated to such cracks was computed. The evolution of J-integral vs the crack length and the indentation depth was studied. The effects of the interlayer, the coating and the substrate on the J-integral evolution were discussed. The results show that a suitable metallic interlayer can improve the fracture resistance of the coating systems under the same indentation conditions through reducing the J-integral.