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.

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.

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.

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. 【

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.

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.

Indentation size effect of germanium single crystal with different crystal orientations

In order to study the indentation size effect(ISE)of germanium single crystals,nano-indentation experiments were carried out on the(100),(110)and(111)plane-orientated germanium single crystals.The true hardness of each crystal plane of germanium single crystals was calculated based on the Meyer equation,proportional sample resistance(PSR)model and Nix-Gao model,and the indentation size effect(ISE)factor of each crystal plane was calculated.Results show that,the germanium single crystals experience elastic deformation,plastic deformation and brittle fracture during the loading process,and the three crystal planes all show obvious ISE phenomenon.All three models can effectively describe the ISE of germanium single crystals,and the calculated value of Nix-Gao model is the most accurate.Compared with the other two crystal planes,Ge(110)has the highest size effect factor m and the highest hardness,which indicates that Ge(110)has the worst plasticity.

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.

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.

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.

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.

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.

Determination of Elastic and Creep Properties of Thin-film Systems from indentation Experiments

Based on the detailed computer simulation of the indentation testing on the thin-film systems, the present paper explores the detailed procedure of determining elastic properties (elastic modulusE^(f) and Poisson ratio v(f)) and creep parameters (CCREEP^(f) and nCREEP^(f)) for a simple Norton law (ε=CCREEP^(f)σ^n CREE^(f), where e is creep strain rate, and a is the stress) material for a thin film coated on a creep substrate, whose elastic properties(E^(s) and v^(s)) and creep properties (CCREEP^(s) and nCREEP^(s)) of the substrate are known, from indentation elastic and creep testing,respectively. The influences of the thickness of the thin-film and the size of the indenter on the indentation behavior have been discussed. It is shown that the boundary between the thin film and the substrate has great influence on the indentation creep behavior. The relative sizes of indentation systems are chosen so that the behavior of the indentation on the film is influenced by the substrate. The two elastic parameters E^(f) and v^(f) of the film are coupled on the influence of the elastic behavior of indentation. With the two different size indenters, the two elastic parameters E^(f) and v^(f) of the film can be uniquely determined by the indentation experimental slopes of depth to applied net section stress results. The procedure of determining of the two Norton law parameters CCREEP^(f) and nCREEP^(f) includes the following steps by the steady indentation rate d. The first step to calculate the creep indentation rate on certain loads of the two different sizes of indenters on a set of assumed values of CCREEP^(f) and nCREEP^(f)Then to build relationship between the creep indentation rate and the assumed CCREEP^(f) and nCREEP^(f) With the experimental creep indentation rate to intersect two sets of which have the same values of d. The last step is to build the CCREEP^(f) and nCREEP^(f)curves from the intersection points for the two indenters. These two curves CCREEP^(f) and nCREEP^(f)

Experimental investigation on hard rock fragmentation of inserted tooth cutter using a newly designed indentation testing apparatus

This investigation aims to explore the effects of stress conditions and rock cutting rates on hard rock fragmentation through indentation tests on a newly designed triaxial testing apparatus.This apparatus was designed to realize a triaxial loading and indentation test of cylindrical specimens using inserted tooth cutter.The boreability and crushing efficiency of granite rock was investigated by analyzing the change rules of the thrusting force,penetration depth,characteristics of chippings and failure patterns.Several quantitative indexes were used to evaluate rock boreability in this investigation.The granite rock samples all had a chiselled pit and a crushed rock core.Under initial stress conditions,only flat-shape chippings were stripped from the rock surface when the thrusting force reached 20 kN.The rock cutting special energy had a close correlation with the initial stress conditions and inserted tooth shape.Moreover,a thrusting force prediction model was proposed in this paper.The contribution of this study is that for the first time the influence mechanism of the initial triaxial stress conditions on rock fragmentation is investigated using an inserted tooth and the newly designed testing apparatus.This study has a crucial importance for practical underground hard rock crushing in geoengineering.

An inverse problem in film/substrate indentation:extracting both the Young's modulus and thickness of films

In an indentation test,the effective Young's modulus of a film/substrate bilayer heterostructure varies with the indentation depth,a phenomenon known as the substrate effect.In previous studies investigating this,only the Young's modulus of the film was unknown.Once the effective Young's modulus of a film/substrate structure is determined at a given contact depth,the Young's modulus of the film can be uniquely determined,i.e.,there is a one-to-one relation between the Young's modulus of the film and the film/substrate effective Young's modulus.However,at times it is extremely challenging or even impossible to measure the film thickness.Furthermore,the precise definition of the layer/film thickness for a two-dimensional material can be problematic.In the current study,therefore,the thickness of the film and its Young's modulus are treated as two unknowns that must be determined.Unlike the case with one unknown,there are infinite combinations of film thickness and Young's modulus which can yield the same effective Young's modulus for the film/substrate.An inverse problem is formulated and solved to extract the Young's modulus and thickness of the film from the indentation depth-load curve.The accuracy and robustness of the inverse problem-solving method are also demonstrated.