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.

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.

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. .

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.

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.

A Reverse Numerical Approach to Determine Elastic-plastic Properties of Multi-layer Material Systems with Flat Cylindrical Indenters

In the present study, the indentation testing with a flat cylindrical indenter on typical multi-layer material systems was simulated successfully by finite element method. The emphasis was put on the methods of extracting the yield stresses and strain-hardening modulus of upper and middle-layers of three-layer material systems from the indentation testing. The slope of the indentation depth to the applied indentation stress curve was found to have a turning point, which can be used to determine the yield stress of the upper-layer. Then, a different method was also presented to determine the yield stress of the middle-layer. This method was based on a set of assumed applied indentation stresses which were to be intersected by the experimental results in order to meet the requirement of having the experimental indentation depth. At last, a reverse numerical algorithm was explored to determine the yield stresses of upper and middle-layers simultaneously by using the indentation testing with two different size indenters. This method assumed two ranges of yield stresses to simulate the indentation behavior. The experimental depth behavior was used to intersect the simulated indentation behavior. And the intersection corresponded to the values of yield stresses of upper and middle-layers. This method was also used further to determine the strain-hardening modulus of upper and middle-layers simultaneously.

Analytical solution of axisymmetric contact problem about indentation of a circular indenter into a soft functionally graded elastic layer

The paper addresses a contact problem of the theory of elasticity,i.e.,the penetration of a circular indenter with a flat base into a soft functionally graded elastic layer.The elastic properties of a functionally graded layer arbitrarily vary with depth,and the foundation is assumed to be elastic,yet much harder than a layer.Approximated analytical solution is constructed,and it is shown that the solutions are asymptotically exact both for large and small values of characteristic dimensionless geometrical parameter of the problem.Numerical examples are analyzed for the cases of monotonic and nonmonotonic variations of elastic properties.Numerical results for the case of homogeneous layer are compared with the results for nondeformable foundation.

Volume, Side-Area, and Force Direction of Berkovich and Cubecorner Indenters, Novel Important Insights

The iteration-free physical description of pyramidal indentations with closed mathematical equations is comprehensively described and extended for creating new insights in this important field of research and applications. All calculations are easily repeatable and should be programmed by instrument builders for even easier general use. Formulas for the volumes and side-areas of Berkovich and cubecorner as a function of depth are deduced and provided, as are the resulting forces and force directions. All of these allow for the detailed comparison of the different indenters on the mathematical reality. The pyramidal values differ remarkably from the ones of so-called “equivalent cones”. The worldwide use of such pseudo-cones is in severe error. The earlier claimed and used 3 times higher displaced volume with cube corner than with Berkovich is disproved. Both displace the same amount at the same applied force. The unprecedented mathematical results are experimentally confirmed for the physical indentation hardness and for the sharp-onset phase-transi- tions with calculated transition energy. The comparison of both indenters provides novel basic insights. Isotropic materials exhibit the same phase transition onset force, but the transition energy is larger with the cube corner, due to higher force and flatter force direction. This qualifies the cube corner for fracture toughness studies. Pile-up is not from the claimed “friction with the indenter”. Anisotropic materials with cleavage planes and channels undergo sliding along these under pressure, both to the surface and internally. Their volumes add to the depression volume. These volumes are essential for the exemplified pile-up management. Phase-transitions produce polymorph interfaces that are nucleation sites for cracks. Technical materials must be developed with onset forces higher than the highest thinkable stresses (at airliners, bridges, etc.). This requires urgent revision of ISO 14577-ASTM standards.

DETERMINATION OF CREEP PROPERTIES OF THERMAL BARRIER COATING(TBC)SYSTEMS FROM THE INDENTATION CREEP TESTING WITH ROUND FLAT INDENTERS

Indentation creep behavior with cylindrical flat indenters on the thermal barrier coating (TBC) was studied by finite element method (FEM). On ike constant applied indentation creep stress, there is a steady creep rate for each case studied for different creep properties of the TBC system. The steady creep depth rate depends on the applied indentation creep stress and size of the indenters as well as the creep properties of the bond coat of the TBC and the substrate. The possibilities to determine the creep properties of a thermal barrier system from indention creep testing were discussed. As an example, with two different size indenters, the creep properties of bond coat of the TBC system can be derived by an inverse FEM method. This study not only provides a numerical method to obtain the creep properties of the TBC system, but also extends the application of indentation creep method with cylindrical flat indenters.

Numerical Crack Analysis of Blunt Rock Indenters by an Indirect Boundary Element Method

Linear elastic fracture mechanics principles are widely applied for the analysis of crack problems in rock fracture mechanics. Rock indentation is an important and complicated problem among rock engineering issues. In this paper, in addition to the fracture criterion of maximum tangential stress adjacent to crack tip, the higher order displacement discontinuity method (which is a version of the indirect boundary element method) has been used for modeling the crack propagation mechanism under blunt indenters. In order to achieve more accurate results, higher order boundary elements i.e. quadratic elements, has been used to calculate displacement discontinuities and also to reduce the singularities of stress and displacement fields near the crack tip, the special crack tip elements has been used to calculate the stress intensity factors (SIF) at the crack tips. In this modeling, the effect of crack angle on stress intensity factors has been investigated. The numerical results of stress intensity factors obtained from some example problems were compared to the theoretical and experimental results cited in the literature which always show a percentage error less than one percent. The simulated results may pave the way for increasing the efficiency of mining and drilling by improving the design of tools and indentation equipments.

Effects of elastic-plastic properties of materials on residual indentation impressions in nano-indentation using sharp indenter

One of the primary features of nano-indentation technique is that the contact area induced by an indenter is indirectly measured by a relationship between the penetration depth and the known geometry of the indenter.However,this indirect measurement occasionally leads to inaccurate properties of the indented material.The objective of this study is to investigate the effects of E/σr and the strain hardening exponents n of materials on the behaviors of pile-up and sink-in in nano-indentation and to predict n values of materials from the residual indentation impressions.The relations between the residual indentation profile and n value of the indented material were identified by dimensional analysis.Also,they were numerically formulated using FE analysis of nano-indentation for 140 different combinations of elastic-plastic parameters such as E,σy and n.The parameters of hrp/hm,herp/hm,Rr/hm and HO&P/Hreal were introduced as various dimensionless parameters to represent and quantify the residual indentation profile after indentation.They were subsequently characterized as dimensionless functions using n and E/σr values.Finally,the validity of these functions was verified through 3D FE analysis of nano-indentation for Al 6061-T6 and AISI 1010 materials.

Mechanism and Method of Testing Fracture Toughness and Impact Absorbed Energy of Ductile Metals by Spherical Indentation Tests

To address the problem of conventional approaches for mechanical property determination requiring destructive sampling, which may be unsuitable for in-service structures, the authors proposed a method for determining the quasi-static fracture toughness and impact absorbed energy of ductile metals from spherical indentation tests (SITs). The stress status and damage mechanism of SIT, mode I fracture, Charpy impact tests, and related tests were frst investigated through fnite element (FE) calculations and scanning electron microscopy (SEM) observations, respectively. It was found that the damage mechanism of SITs is diferent from that of mode I fractures, while mode I fractures and Charpy impact tests share the same damage mechanism. Considering the diference between SIT and mode I fractures, uniaxial tension and pure shear were introduced to correlate SIT with mode I fractures. Based on this, the widely used critical indentation energy (CIE) model for fracture toughness determination using SITs was modifed. The quasi-static fracture toughness determined from the modifed CIE model was used to evaluate the impact absorbed energy using the dynamic fracture toughness and energy for crack initiation. The efectiveness of the newly proposed method was verifed through experiments on four types of steels: Q345R, SA508-3, 18MnMoNbR, and S30408.

Exciting News from Indentations onto Silicon, Copper, and Tungsten

Indentations onto crystalline silicon and copper with various indenter geometries, loading forces at room temperature belong to the widest interests in the field, because of the physical detection of structural phase transitions. By using the mathematically deduced FNh3/2 relation for conical and pyramidal indentations we have a toolbox for deciding between faked and experimental loading curves. Four printed silicon indentation loading curves (labelled with 292 K, 260 K, 240 K and 210 K) proved to be faked and not experimental. This is problematic for the AI (artificial intelligence) that will probably not be able to sort faked data out by itself but must be told to do so. High risks arise, when published faked indentation reports remain unidentified and unreported for the mechanics engineers by reading, or via AI. For example, when AI recommends a faked quality such as “no phase changes” of a technical material that is therefore used, it might break down due to an actually present low force, low transition energy phase-change. This paper thus installed a tool box for the distinction of experimental and faked loading curves of indentations. We found experimental and faked loading curves of the same research group with overall 14 authoring co-workers in three publications where valid and faked ones were next to each other and I can thus only report on the experimental ones. The comparison of Si and Cu with W at 20-fold higher physical hardness shows its enormous influence to the energies of phase transition and of their transition energies. Thus, the commonly preferred ISO14577-ASTM hardness values HISO (these violate the energy law and are simulated!) leads to almost blind characterization and use of mechanically stressed technical materials (e.g. airplanes, windmills, bridges, etc). The reasons are carefully detected and reported to disprove that the coincidence or very close coincidence of all of the published loading curves from 150 K to 298 K are constructed but not experimental. A tool-box for distinction of experimental from faked indentation loading curves (simulations must be indicated) is established in view of protecting the AI from faked data, which it might not be able by itself to sort them out, so that technical materials with wrongly attributed mechanical properties might lead to catastrophic accidents such as all of us know of. There is also the risk that false theories might lead to discourage the design of important research projects or for not getting them granted. This might for example hamper or ill-fame new low temperature indentation projects. The various hints for identifying faked claims are thus presented in great detail. The low-temperature instrumental indentations onto silicon have been faked in two consecutive publications and their reporting in the third one, so that these are not available for the calculation of activation energies. Conversely, the same research group published an indentation loading curve of copper as taken at 150 K that could be tested for its validity with the therefore created tools of validity tests. The physical algebraic calculations provided the epochal detection of two highly exothermic phase transitions of copper that created two polymorphs with negative standard energy content. This is world-wide the second case and the first one far above the 77 K of liquid nitrogen. Its existence poses completely new thoughts for physics chemistry and perhaps techniques but all of them are open and unprepared for our comprehension. The first chemical reactions might be in-situ photolysis and the phase transitions can be calculated from experimental curves. But several further reported low temperature indentation loading curves of silicon were tested for their experimental reality. And the results are compared to new analyses with genuine room temperature results. A lot is to be learned from the differences at room and low temperature.

Phase-Transitions at High, Very High, and Very Low Temperatures upon Nano-Indentations: Onset Forces and Transition Energies

This paper describes the phase-transition energies from published loading curves on the basis of the physically deduced FN = k-h3/2 law that does not violate the energy law by assuming h2 instead, as still do ISO-ASTM 14,577 standards. This law is valid for all materials and all “one-point indentation” temperatures. It detects initial surface effects and phase-transition kink-unsteadiness. Why is that important? The mechanically induced phase-transitions form polymorph interfaces with increased risk of crash nucleation for example at the pickle forks of airliners. After our published crashing risk, as nucleated within microscopic polymorph-interfaces via pre-cracks, had finally appeared (we presented microscopic images (5000×) from a model system), 550 airliners were all at once grounded for 18 months due to such microscopic pre-cracks at their pickle forks (connection device for wing to body). These pre-cracks at phase-transition interfaces were previously not complained at the (semi)yearlycheckups of all airliners. But materials with higher compliance against phase- transitions must be developed for everybody’s safety, most easily by checking with nanoindentations, using their physically correct analyses. Unfortunately, non-physical analyses, as based on the after all incredible exponent 2 on h for the FN versus h loading curve are still enforced by ISO-ASTM standards that cannot detect phase-transitions. These standards propagate that all of the force, as applied to the penetrating cone or pyramid shall be used for the depth formation, but not also in part for the pressure to the indenter environment. However, the remaining part of pressure (that was not consumed for migrations, etc.) is always used for the elastic modulus detection routine. That severely violates the energy-law! Furthermore, the now physically analyzed published loading curves contain the phase-transition onsets and energies information, because these old-fashioned authors innocently (?) published (of course correct) experimental loading curves. These follow as ever the physically deduced FN = k-h3/2 relation that does not violate the energy law. Nevertheless, the old-fashioned authors stubbornly assume h2instead of h3/2 as still do ISO-ASTM 14,577 standards according to an Oliver-Pharr publication of 1992 and textbooks. The present work contributes to understanding the temperature dependence of phase-transitions under mechanical load, not only for aviation and space flights, which is important. The physical calculations use exclusively regressions and pure algebra (no iterations, no fittings, and no simulations) in a series of straightforward steps by correcting for unavoidable initial effects from the axis cuts of the linear branches from the above equation exhibiting sharp kink unsteadiness at the onset of phase transitions. The test loading curves are from Molybdenum and Al 7075 alloy. The valid published loading curves strictly follow the FN = k-h3/2 relation. Full applied work, conversion work, and conversion work per depth unit show reliable overall comparable order of magnitude values at temperature increase by 150°C (Al 7075) and 980°C (Mo) when also considering different physical hardnesses and penetration depths. It turns out how much the normalized endothermic phase-transition energy decreases upon temperature increase. For the only known 1000°C indentation we provide reason that the presented loading curves changes are only to a minor degree caused by the thermal expansion. The results with Al 7075 up to 170°C are successfully compared. Al 7075 alloy is also checked by indentation with liquid nitrogen cooling (77 K). It gives two endothermic and one very prominent exothermic phase transition with particularly high normalized phase-transition energy. This indentation loading curve at liquid nitrogen temperature reveals epochal novelties. The energy requiring endothermic phase transitions (already seen at 20°C and above) at 77 K is shortly after the start of the second polymorph (sharply at 19.53 N loading force) followed by a strongly exothermic phase-transition by producing (that is losing) energy-content. Both processes at 77 K are totally unexpected. The produced energy per depth unit is much higher energy than the one required for the previous endothermic conversions. This exothermic phase-transition profits from the inability to provide further energy for the formation of the third polymorph as endothermic obtained at 70°C and above. That is only possible because the very cold crystal can no longer support endothermic events but supports exothermic ones. Both endothermic and exothermic phase-transitions at 77 K under load are unprecedented and were not expected before. While the energetic support at 77 K for endothermic processes under mechanical load is unusual but still understandable (there are also further means to produce lower temperatures). But strongly exothermicphase-transition under mechanical load for the production of new modification with negative energy content (less than the energy content of the ambient polymorph) at very low temperature is an epochal event here on earth. It leads to new global thinking and promises important new applications. The energy content of strongly exothermic transformed material is less than the thermodynamic standard zero energy-content on earth. And it can only be reached when there is no possibility left to produce an endothermic phase-transition. Such less than zero-energy-content materials should be isolated, using appropriate equipment. Their properties must be investigated by chemists, crystallographers, and physicists for cosmological reasons. It could be that such materials will require cooling despite their low energy content (higher stability!) and not survive at ambient temperatures and pressures on earth, but only because we do not know of such negative-energy-content materials with our arbitrary thermodynamic standard zeros on earth. At first one will have to study how far we can go up with temperature for keeping them stable. Thus, the apparently never before considered unprecedented result opens up new thinking for the search of new polymorphs that can, of course, not be reached by heating. Various further applications including cosmology and space flight explorations are profiting from it.

氧化物光学薄膜的压入硬度研究

为了评价离子源辅助对不同氧化物薄膜的影响,采用不同的镀膜设备沉积了TiO_(2)、Ta_(2)O_(5)、ZrO_(2)、SiO_(2)氧化物单层膜,用椭偏仪测量了其折射率和厚度,并用纳米压痕仪测量了不同载荷下材料的杨氏模量和纳米硬度,比较了不同离子源沉积条件下膜层这两个参数的变化。结果表明,离子源辅助能有效增加膜层杨氏模量和压入硬度,TiO_(2)增加了2 GPa,Ta_(2)O_(5)增加了4 GPa,ZrO_(2)增加了2 GPa,和膜层的折射率变化趋势是一致的。纳米压痕法也可作为评价离子源轰击能力的一种手段。

Physical Macrohardness of the Kinetic Indentation of the Material: Function and Universal Unit of Measure (Part 1)

Three directions of development of kinetic indentation methods.Physical-energetic analysis of the indentation force diagram according to ISO 14577.Physical theory and universal criterion for the macrohardness of a material.Model of the physical process,thermomechanical potential,function of the state of the kinetic macroindentation process.Method for determining the physical function and unit of measurement of the kinetic macrohardness of a material.The ratio of the values of the empirical(standard)and physical macrohardness of the material.Physical reason for the appearance of the size effect in empirical indentation methods.The principle of determining the standard value of physical macrohardness.

基于压痕试验的岩石力学参数的卡尔曼滤波反演

压痕试验是间接评估岩体力学特性的重要方法,为了更好地利用压痕试验评估岩体力学参数,本研究采用一种基于扩展卡尔曼滤波算法的参数反演方法。基于室内压痕试验获得的荷载-压入深度曲线数据,通过弹塑性数值仿真模型构建岩体弹塑性参数与压痕曲线的响应关系,进而利用卡尔曼滤波算法实现对岩石弹塑性参数的反演和优化分析。结果表明,本研究方法具有较好的收敛性和较高的识别精度,反演得到的岩石弹性参数均值的相对误差在10%左右,塑性参数的反演结果相对误差小于20%。较传统单一经验公式方法,本研究方法具有更高的预测精度,对多种不同岩性岩体都有较好的适用性。