Spherical indentations that rely on original date are analyzed with the physically correct mathematical formula and its integration that take into account the radius over depth changes upon penetration. Linear plots, ...Spherical indentations that rely on original date are analyzed with the physically correct mathematical formula and its integration that take into account the radius over depth changes upon penetration. Linear plots, phase-transition onsets, energies, and pressures are algebraically obtained for germanium, zinc-oxide and gallium-nitride. There are low pressure phase-transitions that correspond to, or are not resolved by hydrostatic anvil onset pressures. This enables the attribution of polymorph structures, by comparing with known structures from pulsed laser deposition or molecular beam epitaxy and twinning. The spherical indentation is the easiest way for the synthesis and further characterization of polymorphs, now available in pure form under diamond calotte and in contact with their corresponding less dense polymorph. The unprecedented results and new possibilities require loading curves from experimental data. These are now easily distinguished from data that are “fitted” to make them concur with widely used unphysical Johnson’s formula for spheres (“<span style="white-space:nowrap;"><em>P</em> = (4/3)<em>h</em><sup>3/2</sup><em>R</em><sup>1/2</sup><em>E</em><sup><span style="white-space:nowrap;">∗</span></sup></span>”) not taking care of the <em>R/h</em> variation. Its challenge is indispensable, because its use involves “fitting equations” for making the data concur. These faked reports (no “experimental” data) provide dangerous false moduli and theories. The fitted spherical indentation reports with radii ranging from 4 to 250 μm are identified for PDMS, GaAs, Al, Si, SiC, MgO, and Steel. The detailed analysis reveals characteristic features.展开更多
A modified five-axis cutting system using a force control cutting strategy was to machine indentations in different annuli on the entire surface of a target ball.The relationship between the cutting depths and the app...A modified five-axis cutting system using a force control cutting strategy was to machine indentations in different annuli on the entire surface of a target ball.The relationship between the cutting depths and the applied load as well as the microsphere rotation speed were studied experimentally to reveal the micromachining mechanism.In particular,aligning the rotating center of the high precision spindle with the microsphere center is essential for guaranteeing the machining accuracy of indentations.The distance between adjacent indentations on the same annulus and the vertical distance between adjacent annuli were determined by the rotating speed of the micro-ball and the controllable movement of the high-precision stage,respectively.In order to verify the feasibility and effect of the proposed cutting strategy,indentations with constant and expected depths were conducted on the entire surface of a hollow thin-walled micro-ball with a diameter of 1 mm.The results imply that this machining methodology has the potential to provide the target ball with desired modulated defects for simulating the inertial confinement fusion implosion experiment.展开更多
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...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. <展开更多
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 ...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 F<sub>N</sub>h<sup>3/2 </sup>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.展开更多
This paper describes the phase-transition energies from published loading curves on the basis of the physically deduced F<sub>N</sub> = k-h<sup>3/2</sup> law that does not violate the energy la...This paper describes the phase-transition energies from published loading curves on the basis of the physically deduced F<sub>N</sub> = k-h<sup>3/2</sup> law that does not violate the energy law by assuming h<sup>2</sup> 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 F<sub>N</sub> 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 F<sub>N</sub> = k-h<sup>3/2</sup> relation that does not violate the energy law. Nevertheless, the old-fashioned authors stubbornly assume h<sup>2</sup>instead of h<sup>3/2</sup> 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 F<sub>N</sub> = k-h<sup>3/2</sup> 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.展开更多
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...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. 【展开更多
Instrumented indentation has been developed for determining the mechanical properties of materials but an accurate determination of these properties requires attention on contact stiffness analysis, indentation size e...Instrumented indentation has been developed for determining the mechanical properties of materials but an accurate determination of these properties requires attention on contact stiffness analysis, indentation size effect, elastic modulus mode of calculation, role of stress distribution around the indent and its introduction in expanding cavity models for tensile mechanical properties determination. In the present work, models for hardness, elastic modulus and plastic properties determination by indentation are briefly reviewed and applied for the characterization of a porosity-free β-TCP bioceramic. As a main result the elastic modulus is found to be equal to 162 GPa resulting from the application of different approaches based on the use of various sharp and spherical indenters. Additionally, Martens and contact macrohardnesses were found to be independent on the dwell-time and equals to 4.1 and 6.3 GPa, respectively. Finally, models based on Hollomon’s and Ludwik’s laws as well as expanding cavity models were critically analyzed in light of their capacity to determine the yield stress and to represent the behavior law of the material. As a main result, the yield stress of the β-TCP is found to be equal to 2 GPa.展开更多
Finite element analysis was carried out to investigate the conical indentation response of elastic-plastic solids within the framework of the hydrostatic pressure dependence and the power law strain hardening. A large...Finite element analysis was carried out to investigate the conical indentation response of elastic-plastic solids within the framework of the hydrostatic pressure dependence and the power law strain hardening. A large number of 40 difierent combinations of elasto-plastic properties with n ranging from 0 to 0.5 and σy/E ranging from 0.0014 to 0.03 were used in the computations. The loading curvature C and the average contact pressure Pave were considered within the concept of representative strains and the dimensional analysis.Dimensionless functions associated with these two parameters were formulated for each studied value of the pressure sensitivity. The results for pressure sensitive materials lie between those for Von Mises materials and the elastic model.展开更多
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-w...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.展开更多
In this study,the sliding friction contact problems associated with the indentation of an elastic half-plane by rigid cylindrical and flat punches were investigated within the context of the micropolar theory.The micr...In this study,the sliding friction contact problems associated with the indentation of an elastic half-plane by rigid cylindrical and flat punches were investigated within the context of the micropolar theory.The micropolar theory of elasticity introduces the characteristic material length and the dimensionless coupling number to describe the size effect.Coulomb’s friction law is satisfied by a punch when it is subjected to both normal and tangential forces.Using the Fourier integral transformation technique,these mixed-boundary value problems were reduced to singular integral equations of the second kind in which the unknown quantity is the contact stress on the contact surface.The collocation method was utilized to solve the integral equations numerically.An extensive parametric study was conducted to investigate the effects of the friction coefficient,the characteristic material length,and the dimensionless coupling number on the normal and in-plane stresses.The results show that the contact stress predicted by the micropolar theory differs significantly from those predicted by the couple stress theory and the classical elasticity theory.展开更多
In the past decades,residual stresses have attracted wide attention due to their significant influences on material’s strength,fatigue life,and dimensional stability.Various residual stress measurement methods have b...In the past decades,residual stresses have attracted wide attention due to their significant influences on material’s strength,fatigue life,and dimensional stability.Various residual stress measurement methods have been developed such as X-ray diffraction,neutron diffraction,crack compliance,and hole drilling.These methods may suffer from different disadvantages including radiation,high cost,destructive,unportable,etc.In this work,an in situ residual stress measurement method was proposed based on instrumented indentation using a piezoelectric bimorph cantilever.A Vickers’indenter was fabricated onto the free end of the cantilever for pressing into the sample and a strain gauge was bonded on the cantilever to monitor the indentation load.During testing,the contact area was extracted by tracking the cantilever’s contact resonance frequency based on the electromechanical impendence method.Different from traditional indentation-based methods that use a single hardness value to compute the residual stress,here the indentation force-contact area(F-S)curves with and without residual stresses were measured to derive the residual stress based on an empirical model.Experiments were then conducted on a specially designed CrMnCu specimen with different applied stresses.Results show that the measured residual stress values agreed well with the applied stresses monitored by a strain gauge.The proposed residual stress measurement method holds great promise for in situ residual stress estimation due to its portable apparatus,simple operation procedure and insensitiveness to testing environment.展开更多
This work investigates the indentation response of an elastic plate resting upon a thin,transversely isotropic elastic layer supported by a rigid substrate.Such a scenario is encountered across a range of length scale...This work investigates the indentation response of an elastic plate resting upon a thin,transversely isotropic elastic layer supported by a rigid substrate.Such a scenario is encountered across a range of length scales from piezoresistive tests on graphite nanoflakes to the bending of floating ice shelves atop seabed,where the elastic layer commonly exhibits certain anisotropy.We first develop an approximate model to describe the elastic response of a transversely isotropic layer by exploiting the slenderness of the layer.We show that this approximate model can be reduced to the classic compressible Winkler foundation model as the elastic constants of the layer are set isotropic.We then investigate the combined response of an elastic plate on the transversely isotropic elastic layer.Facilitated by the simplicity of our proposed approximate model,we can derive simple analytical solutions for the cases of small and large indenter radi.The analytical results agree well with numerical calculations obtained via finite element methods,as long as the system is sufficiently slender in a mechanical sense.These results offer quantitative insights into the mechanical behavior of numerous semiconductor materials characterized by transverse isotropy and employed with slender geometries in various practical applications where the thin layer works as conductive and functional layers.展开更多
We study the axisymmetric frictionless indentation problem of a piezoelectric semiconductor(PSC)thin film perfectly bonded to a semi-infinite isotropic elastic substrate by a rigid and insulating spherical indenter.Th...We study the axisymmetric frictionless indentation problem of a piezoelectric semiconductor(PSC)thin film perfectly bonded to a semi-infinite isotropic elastic substrate by a rigid and insulating spherical indenter.The Hankel integral transformation is first employed to derive the general solutions for the governing differential equations of the PSC film and elastic substrate.Then,using the boundary and interface conditions,the complicated indentation problem is reduced to numerically solve a Fredholm integral equation of the second kind.Numerical results are given to demonstrate the effects of semiconducting property,film thickness as well as Young’s modulus and Poisson’s ratio of the substrate on the indentation responses.The obtained findings will contribute to the establishment of indentation experiments for PSC film/substrate systems.展开更多
The accurate characterization of anisotropy for additively manufactured materials is of vital importance for both highperformance structural design and printing processing optimization.To avoid the repetitive and redu...The accurate characterization of anisotropy for additively manufactured materials is of vital importance for both highperformance structural design and printing processing optimization.To avoid the repetitive and redundant tensile testing on specimens prepared along diverse directions,this study proposes an instrumented indentation-based inverse identification method for the efficient characterization of additively manufactured materials.In the present work,a 3D finite element model of indentation test is first established for the printed material,for which an anisotropic material constitutive model is incorporated.We have demonstrated that the indentation responses are information-rich,and material anisotropy along different directions can be interpreted by a single indentation imprint.Subsequently,an inverse identification framework is built,in which an Euclidean error norm between simulated and experimental indentation responses is minimized via optimization algorithms such as the Globally Convergent Method of Moving Asymptotes(GCMMA).The developed method has been verified on diverse printed materials referring to either the indentation curve or the residual imprint,and the superiority of this latter over the former is confirmed by a better and faster convergence of inverse identification.Experimental validations on 3D printed materials(including stainless steel 316L,aluminum alloy AlSi10Mg,and titanium alloy TC4)reveal that the developed method is both accurate and reliable when compared with material constitutive behaviors obtained from uni-axial tensile tests,regardless of the degree of anisotropy among different materials.展开更多
The presence of residual stresses in materials or engineering structures can significantly influence their mechanical per-formance.Accurate measurement of residual stresses is of great importance to ensure their in-se...The presence of residual stresses in materials or engineering structures can significantly influence their mechanical per-formance.Accurate measurement of residual stresses is of great importance to ensure their in-service reliability.Although numerous instrumented indentation methods have been proposed to evaluate residual stresses,the majority of them require a stress-free reference sample as a comparison benchmark,thereby limiting their applicability in scenarios where obtaining stress-free reference samples is challenging.In this work,through a number of finite element simulations,it was found that the loading exponent of the loading load-depth curve and the recovered depth during unloading are insensitive to residual stresses.The loading curve of the stress-free specimen was virtually reconstructed using such stress-insensitive parameters extracted from the load-depth curves of the stressed state,thus eliminating the requirement for stress-free reference samples.The residual stress was then correlated with the fractional change in loading work between stressed and stress-free loading curves through dimensional analysis and finite element simulations.Based on this correlation,an instrumented sharp indentation method for measuring equibiaxial residual stress without requiring a stress-free specimen was established.Both numerical and experimental verifications were carried out to demonstrate the accuracy and reliability of the newly proposed method.The maximum relative error and absolute error in measured residual stresses are typically within±20%and±20 MPa,respectively.展开更多
A dimensionless load-displacement model based on the energy-density equivalence principle is proposed to obtain the stress-strain relationships of metallic materials under monotonic indentations with various diameters...A dimensionless load-displacement model based on the energy-density equivalence principle is proposed to obtain the stress-strain relationships of metallic materials under monotonic indentations with various diameters of spherical indenters.Finite element simulations are carried out to verify the constitutive relations from the new model,involving indentations made with various spherical indenters.For each indenter,some quasi-static spherical indentation tests are conducted on the materials with 40 preset constitutive relationships.The results indicate that the stress-strain curves predicted by the model align with the preset curves under 200 loading conditions.Moreover,the goodness-of-fit between the predicted stress-strain curves and the preset curves exceeds0.96 for all indenters and materials.In the end,the indentation tests are conducted by the spherical indenters with the diameters of 1.587 mm for fifteen metallic materials and1 mm for eight metallic materials.The results show that the stress-strain curves obtained by the spherical indentation based on the new model closely match those obtained from the uniaxial tensile tests.The relative errors for both the proof strength at 0.2%plastic extension and the tensile strength are below 5%.展开更多
The search for mechanical properties of materials reached a highly acclaimed level, when indentations could be analysed on the basis of elastic theory for hardness and elastic modulus. The mathematical formulas proved...The search for mechanical properties of materials reached a highly acclaimed level, when indentations could be analysed on the basis of elastic theory for hardness and elastic modulus. The mathematical formulas proved to be very complicated, and various trials were published between the 1900s and 2000s. The development of indentation instruments and the wish to make the application in numerous steps easier, led in 1992 to trials with iterations by using relative values instead of absolute ones. Excessive iterations of computers with 3 + 8 free parameters of the loading and unloading curves became possible and were implemented into the instruments and worldwide standards. The physical formula for hardness was defined as force over area. For the conical, pyramidal, and spherical indenters, one simply took the projected area for the calculation of the indentation depth from the projected area, adjusted it later by the iterations with respect to fused quartz or aluminium as standard materials, and called it “contact height”. Continuously measured indentation loading curves were formulated as loading force over depth square. The unloading curves after release of the indenter used the initial steepness of the pressure relief for the calculation of what was (and is) incorrectly called “Young’s modulus”. But it is not unidirectional. And for the spherical indentations’ loading curve, they defined the indentation force over depth raised to 3/2 (but without R/h correction). They till now (2025) violate the energy law, because they use all applied force for the indenter depth and ignore the obvious sidewise force upon indentation (cf. e.g. the wood cleaving). The various refinements led to more and more complicated formulas that could not be reasonably calculated with them. One decided to use 3 + 8 free-parameter iterations for fitting to the (poor) standards of fused quartz or aluminium. The mechanical values of these were considered to be “true”. This is till now the worldwide standard of DIN-ISO-ASTM-14577, avoiding overcomplicated formulas with their complexity. Some of these are shown in the Introduction Section. By doing so, one avoided the understanding of indentation results on a physical basis. However, we open a simple way to obtain absolute values (though still on the blackbox instrument’s unsuitable force calibration). We do not iterate but calculate algebraically on the basis of the correct, physically deduced exponent of the loading force parabolas with h3/2 instead of false “h2” (for the spherical indentation, there is a calotte-radius over depth correction), and we reveal the physical errors taken up in the official worldwide “14577-Standard”. Importantly, we reveal the hitherto fully overlooked phase transitions under load that are not detectable with the false exponent. Phase-transition twinning is even present and falsifies the iteration standards. Instead of elasticity theory, we use the well-defined geometry of these indentations. By doing so, we reach simple algebraically calculable formulas and find the physical indentation hardness of materials with their onset depth, onset force and energy, as well as their phase-transition energy (temperature dependent also its activation energy). The most important phase transitions are our absolute algebraically calculated results. The now most easily obtained phase transitions under load are very dangerous because they produce polymorph interfaces between the changed and the unchanged material. It was found and published by high-enlargement microscopy (5000-fold) that these trouble spots are the sites for the development of stable, 1 to 2 µm long, micro-cracks (stable for months). If however, a force higher than the one of their formation occurs to them, these grow to catastrophic crash. That works equally with turbulences at the pickle fork of airliners. After the publication of these facts and after three fatal crashing had occurred in a short sequence, FAA (Federal Aviation Agency) reacted by rechecking all airplanes for such micro cracks. These were now found in a new fleet of airliners from where the three crashed ones came. These were previously overlooked. FAA became aware of that risk and grounded 290 (certainly all) of them, because the material of these did not have higher phase-transition onset and energy than other airplanes with better material. They did so despite the 14577-Standard that does not find (and thus formally forbids) phase transitions under indenter load with the false exponent on the indentation parabola. However, this “Standard” will, despite the present author’s well-founded petition, not be corrected for the next 5 years.展开更多
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...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.展开更多
Vickers indentation was introduced into the originally in-plane and out-of-plane poled PLZT ceramics.The Raman spectra were in-situ recorded at selected crack tips before and after the indentations,as well as after th...Vickers indentation was introduced into the originally in-plane and out-of-plane poled PLZT ceramics.The Raman spectra were in-situ recorded at selected crack tips before and after the indentations,as well as after the applications of external electric field.The results show that the changes in Raman intensities of optical modes could be sensitively related to 90° domain switching around the crack tips which are strongly dependent on the directions of original polarization and geometric locations.When the direction of electric field was perpendicular to the direction of original polarization,the 90° domain switching at crack tips of the Vickers indentation on the originally in-plane poled PLZT ceramics caused most significant change in the Raman intensity,which inhibited the crack growth.However,when the direction of electric field was parallel to the direction of original polarization,the growth of crack tips became predominantly without the 90° domain switching,which led to the crack growth.展开更多
文摘Spherical indentations that rely on original date are analyzed with the physically correct mathematical formula and its integration that take into account the radius over depth changes upon penetration. Linear plots, phase-transition onsets, energies, and pressures are algebraically obtained for germanium, zinc-oxide and gallium-nitride. There are low pressure phase-transitions that correspond to, or are not resolved by hydrostatic anvil onset pressures. This enables the attribution of polymorph structures, by comparing with known structures from pulsed laser deposition or molecular beam epitaxy and twinning. The spherical indentation is the easiest way for the synthesis and further characterization of polymorphs, now available in pure form under diamond calotte and in contact with their corresponding less dense polymorph. The unprecedented results and new possibilities require loading curves from experimental data. These are now easily distinguished from data that are “fitted” to make them concur with widely used unphysical Johnson’s formula for spheres (“<span style="white-space:nowrap;"><em>P</em> = (4/3)<em>h</em><sup>3/2</sup><em>R</em><sup>1/2</sup><em>E</em><sup><span style="white-space:nowrap;">∗</span></sup></span>”) not taking care of the <em>R/h</em> variation. Its challenge is indispensable, because its use involves “fitting equations” for making the data concur. These faked reports (no “experimental” data) provide dangerous false moduli and theories. The fitted spherical indentation reports with radii ranging from 4 to 250 μm are identified for PDMS, GaAs, Al, Si, SiC, MgO, and Steel. The detailed analysis reveals characteristic features.
基金the financial support of the National Natural Science Foundation of China(52035004,21827802)Natural Science Foundation of Heilongjiang Province of China(YQ2020E015)+1 种基金Self-Planned Task(No.SKLRS202001C)of State Key Laboratory of Robotics and System(HIT)‘Youth Talent Support Project’of the Chinese Association for Science and Technology。
文摘A modified five-axis cutting system using a force control cutting strategy was to machine indentations in different annuli on the entire surface of a target ball.The relationship between the cutting depths and the applied load as well as the microsphere rotation speed were studied experimentally to reveal the micromachining mechanism.In particular,aligning the rotating center of the high precision spindle with the microsphere center is essential for guaranteeing the machining accuracy of indentations.The distance between adjacent indentations on the same annulus and the vertical distance between adjacent annuli were determined by the rotating speed of the micro-ball and the controllable movement of the high-precision stage,respectively.In order to verify the feasibility and effect of the proposed cutting strategy,indentations with constant and expected depths were conducted on the entire surface of a hollow thin-walled micro-ball with a diameter of 1 mm.The results imply that this machining methodology has the potential to provide the target ball with desired modulated defects for simulating the inertial confinement fusion implosion experiment.
文摘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. <
文摘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 F<sub>N</sub>h<sup>3/2 </sup>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.
文摘This paper describes the phase-transition energies from published loading curves on the basis of the physically deduced F<sub>N</sub> = k-h<sup>3/2</sup> law that does not violate the energy law by assuming h<sup>2</sup> 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 F<sub>N</sub> 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 F<sub>N</sub> = k-h<sup>3/2</sup> relation that does not violate the energy law. Nevertheless, the old-fashioned authors stubbornly assume h<sup>2</sup>instead of h<sup>3/2</sup> 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 F<sub>N</sub> = k-h<sup>3/2</sup> 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.
文摘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. 【
文摘Instrumented indentation has been developed for determining the mechanical properties of materials but an accurate determination of these properties requires attention on contact stiffness analysis, indentation size effect, elastic modulus mode of calculation, role of stress distribution around the indent and its introduction in expanding cavity models for tensile mechanical properties determination. In the present work, models for hardness, elastic modulus and plastic properties determination by indentation are briefly reviewed and applied for the characterization of a porosity-free β-TCP bioceramic. As a main result the elastic modulus is found to be equal to 162 GPa resulting from the application of different approaches based on the use of various sharp and spherical indenters. Additionally, Martens and contact macrohardnesses were found to be independent on the dwell-time and equals to 4.1 and 6.3 GPa, respectively. Finally, models based on Hollomon’s and Ludwik’s laws as well as expanding cavity models were critically analyzed in light of their capacity to determine the yield stress and to represent the behavior law of the material. As a main result, the yield stress of the β-TCP is found to be equal to 2 GPa.
文摘Finite element analysis was carried out to investigate the conical indentation response of elastic-plastic solids within the framework of the hydrostatic pressure dependence and the power law strain hardening. A large number of 40 difierent combinations of elasto-plastic properties with n ranging from 0 to 0.5 and σy/E ranging from 0.0014 to 0.03 were used in the computations. The loading curvature C and the average contact pressure Pave were considered within the concept of representative strains and the dimensional analysis.Dimensionless functions associated with these two parameters were formulated for each studied value of the pressure sensitivity. The results for pressure sensitive materials lie between those for Von Mises materials and the elastic model.
文摘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.
基金supported by the National Natural Science Foundation of China(Grant No.12062019)the Natural Science Foundation of Inner Mongolia(Grant Nos.2024QN01013 and 2024MS01007).
文摘In this study,the sliding friction contact problems associated with the indentation of an elastic half-plane by rigid cylindrical and flat punches were investigated within the context of the micropolar theory.The micropolar theory of elasticity introduces the characteristic material length and the dimensionless coupling number to describe the size effect.Coulomb’s friction law is satisfied by a punch when it is subjected to both normal and tangential forces.Using the Fourier integral transformation technique,these mixed-boundary value problems were reduced to singular integral equations of the second kind in which the unknown quantity is the contact stress on the contact surface.The collocation method was utilized to solve the integral equations numerically.An extensive parametric study was conducted to investigate the effects of the friction coefficient,the characteristic material length,and the dimensionless coupling number on the normal and in-plane stresses.The results show that the contact stress predicted by the micropolar theory differs significantly from those predicted by the couple stress theory and the classical elasticity theory.
基金supported by the National Key R&D Program of China(Grant No.2023YFF0716800)National Natural Science Foundation of China(Grant No.12102393).
文摘In the past decades,residual stresses have attracted wide attention due to their significant influences on material’s strength,fatigue life,and dimensional stability.Various residual stress measurement methods have been developed such as X-ray diffraction,neutron diffraction,crack compliance,and hole drilling.These methods may suffer from different disadvantages including radiation,high cost,destructive,unportable,etc.In this work,an in situ residual stress measurement method was proposed based on instrumented indentation using a piezoelectric bimorph cantilever.A Vickers’indenter was fabricated onto the free end of the cantilever for pressing into the sample and a strain gauge was bonded on the cantilever to monitor the indentation load.During testing,the contact area was extracted by tracking the cantilever’s contact resonance frequency based on the electromechanical impendence method.Different from traditional indentation-based methods that use a single hardness value to compute the residual stress,here the indentation force-contact area(F-S)curves with and without residual stresses were measured to derive the residual stress based on an empirical model.Experiments were then conducted on a specially designed CrMnCu specimen with different applied stresses.Results show that the measured residual stress values agreed well with the applied stresses monitored by a strain gauge.The proposed residual stress measurement method holds great promise for in situ residual stress estimation due to its portable apparatus,simple operation procedure and insensitiveness to testing environment.
基金supported by the National Natural Science Foundation of China(12372103)the Opening Fund of State Key Laboratory of Nonlinear Mechanics(Institute of Mechanics,CAS)the Fundamental Research Funds for Central Universities(Peking University).
文摘This work investigates the indentation response of an elastic plate resting upon a thin,transversely isotropic elastic layer supported by a rigid substrate.Such a scenario is encountered across a range of length scales from piezoresistive tests on graphite nanoflakes to the bending of floating ice shelves atop seabed,where the elastic layer commonly exhibits certain anisotropy.We first develop an approximate model to describe the elastic response of a transversely isotropic layer by exploiting the slenderness of the layer.We show that this approximate model can be reduced to the classic compressible Winkler foundation model as the elastic constants of the layer are set isotropic.We then investigate the combined response of an elastic plate on the transversely isotropic elastic layer.Facilitated by the simplicity of our proposed approximate model,we can derive simple analytical solutions for the cases of small and large indenter radi.The analytical results agree well with numerical calculations obtained via finite element methods,as long as the system is sufficiently slender in a mechanical sense.These results offer quantitative insights into the mechanical behavior of numerous semiconductor materials characterized by transverse isotropy and employed with slender geometries in various practical applications where the thin layer works as conductive and functional layers.
基金supported by the National Natural Science Foundation of China(Nos.12072209,U21A20430,12192211,12472155)the S&T Program of Hebei(225676162GH).
文摘We study the axisymmetric frictionless indentation problem of a piezoelectric semiconductor(PSC)thin film perfectly bonded to a semi-infinite isotropic elastic substrate by a rigid and insulating spherical indenter.The Hankel integral transformation is first employed to derive the general solutions for the governing differential equations of the PSC film and elastic substrate.Then,using the boundary and interface conditions,the complicated indentation problem is reduced to numerically solve a Fredholm integral equation of the second kind.Numerical results are given to demonstrate the effects of semiconducting property,film thickness as well as Young’s modulus and Poisson’s ratio of the substrate on the indentation responses.The obtained findings will contribute to the establishment of indentation experiments for PSC film/substrate systems.
基金Supported by National Key R&D Program of China(Grant Nos.2022YFB4603101,2022YFB3402200)Key Project of NSFC of China(Grant No.92271205)Sichuan Provincial Science and Technology Program and Fundamental Research Funds for the Central Universities of China(Grant No.D5000230049).
文摘The accurate characterization of anisotropy for additively manufactured materials is of vital importance for both highperformance structural design and printing processing optimization.To avoid the repetitive and redundant tensile testing on specimens prepared along diverse directions,this study proposes an instrumented indentation-based inverse identification method for the efficient characterization of additively manufactured materials.In the present work,a 3D finite element model of indentation test is first established for the printed material,for which an anisotropic material constitutive model is incorporated.We have demonstrated that the indentation responses are information-rich,and material anisotropy along different directions can be interpreted by a single indentation imprint.Subsequently,an inverse identification framework is built,in which an Euclidean error norm between simulated and experimental indentation responses is minimized via optimization algorithms such as the Globally Convergent Method of Moving Asymptotes(GCMMA).The developed method has been verified on diverse printed materials referring to either the indentation curve or the residual imprint,and the superiority of this latter over the former is confirmed by a better and faster convergence of inverse identification.Experimental validations on 3D printed materials(including stainless steel 316L,aluminum alloy AlSi10Mg,and titanium alloy TC4)reveal that the developed method is both accurate and reliable when compared with material constitutive behaviors obtained from uni-axial tensile tests,regardless of the degree of anisotropy among different materials.
基金support from the National Natural Science Foundation of China(Grant Nos.12172332,11727803 and 12072009)the Zhejiang Provincial Natural Science Foundation of China(Grant No.LZ23A020007)the Fundamental Research Funds for the Provincial Universities of Zhejiang(Grant No.RF-C2022003).
文摘The presence of residual stresses in materials or engineering structures can significantly influence their mechanical per-formance.Accurate measurement of residual stresses is of great importance to ensure their in-service reliability.Although numerous instrumented indentation methods have been proposed to evaluate residual stresses,the majority of them require a stress-free reference sample as a comparison benchmark,thereby limiting their applicability in scenarios where obtaining stress-free reference samples is challenging.In this work,through a number of finite element simulations,it was found that the loading exponent of the loading load-depth curve and the recovered depth during unloading are insensitive to residual stresses.The loading curve of the stress-free specimen was virtually reconstructed using such stress-insensitive parameters extracted from the load-depth curves of the stressed state,thus eliminating the requirement for stress-free reference samples.The residual stress was then correlated with the fractional change in loading work between stressed and stress-free loading curves through dimensional analysis and finite element simulations.Based on this correlation,an instrumented sharp indentation method for measuring equibiaxial residual stress without requiring a stress-free specimen was established.Both numerical and experimental verifications were carried out to demonstrate the accuracy and reliability of the newly proposed method.The maximum relative error and absolute error in measured residual stresses are typically within±20%and±20 MPa,respectively.
基金Project supported by the National Natural Science Foundation of China(Nos.11872320 and 12072294)。
文摘A dimensionless load-displacement model based on the energy-density equivalence principle is proposed to obtain the stress-strain relationships of metallic materials under monotonic indentations with various diameters of spherical indenters.Finite element simulations are carried out to verify the constitutive relations from the new model,involving indentations made with various spherical indenters.For each indenter,some quasi-static spherical indentation tests are conducted on the materials with 40 preset constitutive relationships.The results indicate that the stress-strain curves predicted by the model align with the preset curves under 200 loading conditions.Moreover,the goodness-of-fit between the predicted stress-strain curves and the preset curves exceeds0.96 for all indenters and materials.In the end,the indentation tests are conducted by the spherical indenters with the diameters of 1.587 mm for fifteen metallic materials and1 mm for eight metallic materials.The results show that the stress-strain curves obtained by the spherical indentation based on the new model closely match those obtained from the uniaxial tensile tests.The relative errors for both the proof strength at 0.2%plastic extension and the tensile strength are below 5%.
文摘The search for mechanical properties of materials reached a highly acclaimed level, when indentations could be analysed on the basis of elastic theory for hardness and elastic modulus. The mathematical formulas proved to be very complicated, and various trials were published between the 1900s and 2000s. The development of indentation instruments and the wish to make the application in numerous steps easier, led in 1992 to trials with iterations by using relative values instead of absolute ones. Excessive iterations of computers with 3 + 8 free parameters of the loading and unloading curves became possible and were implemented into the instruments and worldwide standards. The physical formula for hardness was defined as force over area. For the conical, pyramidal, and spherical indenters, one simply took the projected area for the calculation of the indentation depth from the projected area, adjusted it later by the iterations with respect to fused quartz or aluminium as standard materials, and called it “contact height”. Continuously measured indentation loading curves were formulated as loading force over depth square. The unloading curves after release of the indenter used the initial steepness of the pressure relief for the calculation of what was (and is) incorrectly called “Young’s modulus”. But it is not unidirectional. And for the spherical indentations’ loading curve, they defined the indentation force over depth raised to 3/2 (but without R/h correction). They till now (2025) violate the energy law, because they use all applied force for the indenter depth and ignore the obvious sidewise force upon indentation (cf. e.g. the wood cleaving). The various refinements led to more and more complicated formulas that could not be reasonably calculated with them. One decided to use 3 + 8 free-parameter iterations for fitting to the (poor) standards of fused quartz or aluminium. The mechanical values of these were considered to be “true”. This is till now the worldwide standard of DIN-ISO-ASTM-14577, avoiding overcomplicated formulas with their complexity. Some of these are shown in the Introduction Section. By doing so, one avoided the understanding of indentation results on a physical basis. However, we open a simple way to obtain absolute values (though still on the blackbox instrument’s unsuitable force calibration). We do not iterate but calculate algebraically on the basis of the correct, physically deduced exponent of the loading force parabolas with h3/2 instead of false “h2” (for the spherical indentation, there is a calotte-radius over depth correction), and we reveal the physical errors taken up in the official worldwide “14577-Standard”. Importantly, we reveal the hitherto fully overlooked phase transitions under load that are not detectable with the false exponent. Phase-transition twinning is even present and falsifies the iteration standards. Instead of elasticity theory, we use the well-defined geometry of these indentations. By doing so, we reach simple algebraically calculable formulas and find the physical indentation hardness of materials with their onset depth, onset force and energy, as well as their phase-transition energy (temperature dependent also its activation energy). The most important phase transitions are our absolute algebraically calculated results. The now most easily obtained phase transitions under load are very dangerous because they produce polymorph interfaces between the changed and the unchanged material. It was found and published by high-enlargement microscopy (5000-fold) that these trouble spots are the sites for the development of stable, 1 to 2 µm long, micro-cracks (stable for months). If however, a force higher than the one of their formation occurs to them, these grow to catastrophic crash. That works equally with turbulences at the pickle fork of airliners. After the publication of these facts and after three fatal crashing had occurred in a short sequence, FAA (Federal Aviation Agency) reacted by rechecking all airplanes for such micro cracks. These were now found in a new fleet of airliners from where the three crashed ones came. These were previously overlooked. FAA became aware of that risk and grounded 290 (certainly all) of them, because the material of these did not have higher phase-transition onset and energy than other airplanes with better material. They did so despite the 14577-Standard that does not find (and thus formally forbids) phase transitions under indenter load with the false exponent on the indentation parabola. However, this “Standard” will, despite the present author’s well-founded petition, not be corrected for the next 5 years.
基金Project(51171118)supported by the National Natural Science Foundation of ChinaProject(2012-4)supported by the Liaoning Provincial Key Laboratory of Advanced Materials,Shenyang University,China
文摘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.
基金Project(2006L2003)supported by the Fujian Key Laboratory of Advanced Materials,ChinaProject(10802070)supported by the National Natural Science Foundation of China
文摘Vickers indentation was introduced into the originally in-plane and out-of-plane poled PLZT ceramics.The Raman spectra were in-situ recorded at selected crack tips before and after the indentations,as well as after the applications of external electric field.The results show that the changes in Raman intensities of optical modes could be sensitively related to 90° domain switching around the crack tips which are strongly dependent on the directions of original polarization and geometric locations.When the direction of electric field was perpendicular to the direction of original polarization,the 90° domain switching at crack tips of the Vickers indentation on the originally in-plane poled PLZT ceramics caused most significant change in the Raman intensity,which inhibited the crack growth.However,when the direction of electric field was parallel to the direction of original polarization,the growth of crack tips became predominantly without the 90° domain switching,which led to the crack growth.
