The purpose of this paper is the physical deduction of the loading curves for spherical and flat punch indentations, in particular as the parabola assumption for not self-similar spherical impressions appears impossib...The purpose of this paper is the physical deduction of the loading curves for spherical and flat punch indentations, in particular as the parabola assumption for not self-similar spherical impressions appears impossible. These deductions avoid the still common first energy law violations of ISO 14577 by consideration of the work done by elastic and plastic pressure work. The hitherto generally accepted “parabolas’” exponents on the depth h (“2 for cone, 3/2 for spheres, and 1 for flat punches”) are still the unchanged basis of ISO 14577 standards that also enforce the up to 3 + 8 free iteration parameters for ISO hardness and ISO elastic indentation modulus. Almost all of these common practices are now challenged by physical mathematical proof of exponent 3/2 for cones by removing the misconceptions with indentation against a projected surface (contact) area with violation of the first energy law, because the elastic and inelastic pressure work cannot be obtained from nothing. Physically correct is the impression of a volume that is coupled with pressure formation that creates elastic deformation and numerous types of plastic deformations. It follows the exponent 3/2 only for the cones/pyramids/wedges loading parabola. It appears impossible that the geometrically not self-similar sphere loading curve is an h3/2 parabola. Hertz did only deduce the touching of the sphere and Sneddon did not get a parabola for the sphere. The radius over depth ratio is not constant with the sphere. The apparently good correlation of such parabola plots at large R/h ratios and low h-values does not withstand against the deduced physical equation for the spherical indentation loading curve. Such plots are unphysical for the sphere and so tried regression results indicate data-treatments. The closed physical deduction result consists of the exponential factor h and a dimensionless correction factor that is depth dependent. The non-parabola against force plot using published data is concavely bent even for large radius/depth-ratios at the shallow indents. The capabilities of conical/pyramidal/wedged indentations are thus lost. These facts are outlined for experimental nano- and micro-indentations. Spherical indentations reveal that linear data regression is suspicious and worthless if it does not correspond with physical reality. This stresses the necessity of the straightforward deductions of the correct relations on the basis of iteration-less and fitting-less undeniable calculation rules on a undeniable basic physical understanding. The straightforward physical deduction of the flat punch indentation is therefore also presented, together with formulas for the physical indentation hardness, indentation work, and applied work for these geometrically self-similar indentations. It is exemplified with a macroindentation.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
Some factors that affect the experimental results in nanoindentation tests such as the contact depth,contact area,load and loading duration are analyzed in this article. Combining with the results of finite element nu...Some factors that affect the experimental results in nanoindentation tests such as the contact depth,contact area,load and loading duration are analyzed in this article. Combining with the results of finite element numerical simulation,we find that the creep property of the tested material is one of the important factors causing the micron indentation hardness descending with the increase of indentation depth. The analysis of experimental results with different indentation depths demonstrates that the hardn...展开更多
The quasi-static indentation behavior of sandwich beams with a metal foam core was investigated. An analytical model was developed to predict the large deflections of indention of the sandwich beams with a metal foam ...The quasi-static indentation behavior of sandwich beams with a metal foam core was investigated. An analytical model was developed to predict the large deflections of indention of the sandwich beams with a metal foam core subjected to a concentrated loading. The interaction of plastic bending and stretching in the local deformation regions of the face sheet was considered in the analytical model. Moreover, the effects of the shear strength of the foam core on the indentation behavior were discussed in detail. The finite element simulations were preformed to validate the theoretical model. Comparisons between the analytical predictions and finite element results were conducted and good agreement was achieved. The results show that the membrane force dominates indentation behavior of the sandwich beams when the maximum deflection exceeds the thickness of the face sheet.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
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 rat...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.展开更多
Hardness of materials depends significantly on the indentation size and grain/sub-grain size via microindentation and nanoindentation tests of high-purity tungsten with different structures.The grain boundary effect a...Hardness of materials depends significantly on the indentation size and grain/sub-grain size via microindentation and nanoindentation tests of high-purity tungsten with different structures.The grain boundary effect and indentation size effect were explored.The indentation hardness was fitted using the Nix-Gao model by considering the scaling factor.The results show that the scaling factor is barely correlated with the grain/sub-grain size.The interaction between the plastically deformed zone（PDZ） boundary and the grain/sub-grain boundary is believed to be the reason that leads to an increase of the measured hardness at the specific depths.Results also indicate that the area of the PDZ is barely correlated with the grain/sub-grain size,and the indentation hardness starts to stabilize once the PDZ expands to the dimension of an individual grain/sub-grain.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
The increasing use of small material components in a wide range of industrial fields necessitates the development of an accurate and robust indentation testing method.To this end,this paper proposes an Energy-density-...The increasing use of small material components in a wide range of industrial fields necessitates the development of an accurate and robust indentation testing method.To this end,this paper proposes an Energy-density-equivalence for a Flat Indentation(E-FI)model based on the energy density equivalent principle.The proposed model describes the relationships among the material parameters of Hollomon's power law(H-law),flat indenter diameter,energy,and indentation displacement.An E-FI Method(E-FIM)that determines the H-law parameters of materials through the indentation test is also developed.The energy-displacement curves forward-predicted by the E-FI model(based on known H-law parameters of materials)and the H-law parameters of materials given by the E-FIM(based on known energy-displacement curves)are consistent with the results of Finite Element Analysis(FEA)and the H-law parameters of materials used as the input for FEA,respectively.Using E-FIM,the goodness of fit for both stress–strain curves with H-law,predicted based on the displacement with 2%signal interference,and that for stress–strain curves without interference is more than 0.98.The stress–strain relations predicted by E-FIM were consistent with the results obtained via uniaxial tensile tests of ten ductile materials.展开更多
文摘The purpose of this paper is the physical deduction of the loading curves for spherical and flat punch indentations, in particular as the parabola assumption for not self-similar spherical impressions appears impossible. These deductions avoid the still common first energy law violations of ISO 14577 by consideration of the work done by elastic and plastic pressure work. The hitherto generally accepted “parabolas’” exponents on the depth h (“2 for cone, 3/2 for spheres, and 1 for flat punches”) are still the unchanged basis of ISO 14577 standards that also enforce the up to 3 + 8 free iteration parameters for ISO hardness and ISO elastic indentation modulus. Almost all of these common practices are now challenged by physical mathematical proof of exponent 3/2 for cones by removing the misconceptions with indentation against a projected surface (contact) area with violation of the first energy law, because the elastic and inelastic pressure work cannot be obtained from nothing. Physically correct is the impression of a volume that is coupled with pressure formation that creates elastic deformation and numerous types of plastic deformations. It follows the exponent 3/2 only for the cones/pyramids/wedges loading parabola. It appears impossible that the geometrically not self-similar sphere loading curve is an h3/2 parabola. Hertz did only deduce the touching of the sphere and Sneddon did not get a parabola for the sphere. The radius over depth ratio is not constant with the sphere. The apparently good correlation of such parabola plots at large R/h ratios and low h-values does not withstand against the deduced physical equation for the spherical indentation loading curve. Such plots are unphysical for the sphere and so tried regression results indicate data-treatments. The closed physical deduction result consists of the exponential factor h and a dimensionless correction factor that is depth dependent. The non-parabola against force plot using published data is concavely bent even for large radius/depth-ratios at the shallow indents. The capabilities of conical/pyramidal/wedged indentations are thus lost. These facts are outlined for experimental nano- and micro-indentations. Spherical indentations reveal that linear data regression is suspicious and worthless if it does not correspond with physical reality. This stresses the necessity of the straightforward deductions of the correct relations on the basis of iteration-less and fitting-less undeniable calculation rules on a undeniable basic physical understanding. The straightforward physical deduction of the flat punch indentation is therefore also presented, together with formulas for the physical indentation hardness, indentation work, and applied work for these geometrically self-similar indentations. It is exemplified with a macroindentation.
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.
基金National Natural Science Foundation of China (10772183, 10532070)
文摘Some factors that affect the experimental results in nanoindentation tests such as the contact depth,contact area,load and loading duration are analyzed in this article. Combining with the results of finite element numerical simulation,we find that the creep property of the tested material is one of the important factors causing the micron indentation hardness descending with the increase of indentation depth. The analysis of experimental results with different indentation depths demonstrates that the hardn...
基金Projects(11102146,11372235,11272246,11021202,11002107)supported by the National Natural Science Foundation of ChinaProject(2011CB610301)supported by the National Basic Research Program of ChinaProject supported by the Fundamental Research Funds for the Central Universities,China
文摘The quasi-static indentation behavior of sandwich beams with a metal foam core was investigated. An analytical model was developed to predict the large deflections of indention of the sandwich beams with a metal foam core subjected to a concentrated loading. The interaction of plastic bending and stretching in the local deformation regions of the face sheet was considered in the analytical model. Moreover, the effects of the shear strength of the foam core on the indentation behavior were discussed in detail. The finite element simulations were preformed to validate the theoretical model. Comparisons between the analytical predictions and finite element results were conducted and good agreement was achieved. The results show that the membrane force dominates indentation behavior of the sandwich beams when the maximum deflection exceeds the thickness of the face sheet.
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. <
基金supported by the National Natural Science Foundation of China(50005016,50375124)China Aviation Foundation(02c53011,03B53003)as well as the Yangtze River Foundation.
文摘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.
基金Project(51174235)supported by the National Natural Science Foundation of China
文摘Hardness of materials depends significantly on the indentation size and grain/sub-grain size via microindentation and nanoindentation tests of high-purity tungsten with different structures.The grain boundary effect and indentation size effect were explored.The indentation hardness was fitted using the Nix-Gao model by considering the scaling factor.The results show that the scaling factor is barely correlated with the grain/sub-grain size.The interaction between the plastically deformed zone（PDZ） boundary and the grain/sub-grain boundary is believed to be the reason that leads to an increase of the measured hardness at the specific depths.Results also indicate that the area of the PDZ is barely correlated with the grain/sub-grain size,and the indentation hardness starts to stabilize once the PDZ expands to the dimension of an individual grain/sub-grain.
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. 【
基金co-supported by the National Natural Science Foundation of China(No.11872320)。
文摘The increasing use of small material components in a wide range of industrial fields necessitates the development of an accurate and robust indentation testing method.To this end,this paper proposes an Energy-density-equivalence for a Flat Indentation(E-FI)model based on the energy density equivalent principle.The proposed model describes the relationships among the material parameters of Hollomon's power law(H-law),flat indenter diameter,energy,and indentation displacement.An E-FI Method(E-FIM)that determines the H-law parameters of materials through the indentation test is also developed.The energy-displacement curves forward-predicted by the E-FI model(based on known H-law parameters of materials)and the H-law parameters of materials given by the E-FIM(based on known energy-displacement curves)are consistent with the results of Finite Element Analysis(FEA)and the H-law parameters of materials used as the input for FEA,respectively.Using E-FIM,the goodness of fit for both stress–strain curves with H-law,predicted based on the displacement with 2%signal interference,and that for stress–strain curves without interference is more than 0.98.The stress–strain relations predicted by E-FIM were consistent with the results obtained via uniaxial tensile tests of ten ductile materials.
