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
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 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
Rock macro-indentation plays a fundamental role in mechanical rock breaking for various rock engineering application,such as drilling,tunneling,cutting,and sawing.Over the past decades,extensive research has been cond...Rock macro-indentation plays a fundamental role in mechanical rock breaking for various rock engineering application,such as drilling,tunneling,cutting,and sawing.Over the past decades,extensive research has been conducted to understand the indentation mechanisms and responses through various approaches.This review aims to provide an overview of the current status and recent advancements in theories,experiments,numerical simulations,and applications of macro-indentation in rock engineering.It starts with elaborating on the mechanisms of macro-indentation,followed by a discussion of the merits and limitations of commonly used models.Influence factors and their effects on indentation test results are then summarized.Various numerical simulation methods for rock macro-indentation are highlighted,along with their advantages and disadvantages.Subsequently,the applications of indentation tests and indentation indices in characterizing rock properties are explored.It reveals that compression-tension,compression-shear,and composite models are widely employed in rock macroindentation.While the compression-tension model is straightforward to use,it may overlook the anisotropic properties of rocks.On the other hand,the composite model provides a more comprehensive description of rock indentation but requires complex calculations.Additionally,factors,such as indentation rate,indenter geometry,rock type,specimen size,and confining pressure,can significantly influence the indentation results.Simulation methods for macro-indentation encompass continuous medium,discontinuous medium,and continuous-discontinuous medium methods,with selection based on their differences in principle.Furthermore,rock macro-indentation can be practically applied to mining engineering,tunneling engineering,and petroleum drilling engineering.Indentation indices serve as valuable tools for characterizing rock strength,brittleness,and drillability.This review sheds light on the development of rock macro-indentation and its extensive application in engineering practice.Specialists in the field can gain a comprehensive understanding of the indentation process and its potential in various rock engineering endeavors.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
The indentation method is useful in determining the residual stress according to the elastic-plastic properties of materials.So the effect of the residual stress on the elastic-plastic indentation properties of materi...The indentation method is useful in determining the residual stress according to the elastic-plastic properties of materials.So the effect of the residual stress on the elastic-plastic indentation properties of materials was studied by using the finite element method to find better indentation parameters which are strongly induced by the residual stress.The results show that load-depth curve,plastic pile-up,indentation shape,indentation contact stress and indentation residual stress are affected by different residual stress,and these parameters can be used to deduce the residual stress.Also,a special indentation equipment was developed to analyze the elastic-plastic properties of materials with different residual stress,and the experimental results show a good agreement with the FEM results.For practical application,the elastic-plastic indentation properties of materials with unknown residual stress could be obtained by the developed equipment to deduce the residual stress comprehensively.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
A new area function is introduced and applied to a Berkovich tip in order tocharacterize the contact projected area between an indenter and indented material. The function canbe related directly to tip-rounding, there...A new area function is introduced and applied to a Berkovich tip in order tocharacterize the contact projected area between an indenter and indented material. The function canbe related directly to tip-rounding, thereby having obviously physical meaning. Nanoindentationexperiments are performed on a commercial Nano Indenter XP^R system. The other two area functionsintroduced by Oliver and Pharr and by Thurn and Cook respectively are involved in this paper forcomparison. By comparison from experimental results among different area functions, the indenter tipdescribed by the proposed area function here is very close to the experimental indenter.展开更多
Fracture toughness is one of the crucial mechanical properties of brittle materials such as glasses and ceramics which demonstrate catastrophic failure modes. Conventional stan- dardized testing methods adopted for fr...Fracture toughness is one of the crucial mechanical properties of brittle materials such as glasses and ceramics which demonstrate catastrophic failure modes. Conventional stan- dardized testing methods adopted for fracture toughness determination require large specimens to satisfy the plane strain condition. As for small specimens, indentation is a popular, sometimes exclusive testing mode to determine fracture toughness for it can be performed on a small flat area of the specimen surface. This review focuses on the development of indentation fracture theories and the representative testing methods. Cracking pattern dependent on indenter geometry and material property plays an important role in modeling, and is the main reason for the diversity of indentation fracture theories and testing methods. Along with the simplicity of specimen require- ment is the complexity of modeling and analysis which accounts for the semi-empirical features of indentation fracture tests. Some unresolved issues shaping the gap between indentation fracture tests and standardization are also discussed.展开更多
In this paper,the nanoindentation simulation on the two models of neat polyethylene（PE） and the polyethylene incorporated with 25wt% POSS（POSS-PE） is performed to reveal the reinforcing mechanism of the mechanical...In this paper,the nanoindentation simulation on the two models of neat polyethylene（PE） and the polyethylene incorporated with 25wt% POSS（POSS-PE） is performed to reveal the reinforcing mechanism of the mechanical properties.The influence of the indenter shapes on nanoindentation is researched by using three different shapes of diamond indenters（cube-corner indenter,cylindrical indenter with spherical tip and cylindrical indenter with flat tip）.The molecular mechanics method is adopted to eliminate the temperature effects.Under different indenters,the load-displacement responses,hardnesses（indentation hardness and Martens hardness） and Young＇s moduli of PE and POSS-PE are obtained.Compared with PE,all the mechanical properties are improved dramatically.Then,we analyze the source of loading drop phenomena and the enhancement mechanism of POSS.Furthermore,the result shows that the different shapes of indenters cause a large impact on indentation hardness,but a little impact on Martens hardness.And Young＇s modulus of the flat indenter is much larger than that of cube-corner indenter and spherical indenter.展开更多
In this paper,NiCr-Cr3C2 coating was deposited onto AISI 1045 steel substrate by employing supersonic plasma spraying technique.The surface and cross-section morphologies of the NiCr-Cr3C2 coating were observed by SEM...In this paper,NiCr-Cr3C2 coating was deposited onto AISI 1045 steel substrate by employing supersonic plasma spraying technique.The surface and cross-section morphologies of the NiCr-Cr3C2 coating were observed by SEM.The phase constituents of the coating were identified by XRD.The SEM images showed that the coating was very dense,and it had a low porosity structure.The XRD pattern implied that the coating was mainly composed of NiCr,Cr3C2 and Cr7C2.Nanoindentation tests were performed on the coating surface by a Nano indenter.The widely used Oliver-Pharr method was adopted to extract the mechanical properties of the coating.The hardness exhibited a strong peak-load-dependence,i.e.indentation size effect;the elastic modulus was not affected by indentation size effect.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
The finite element method for the conventional theory of mechanism-based strain gradient plasticity is used to study the indentation size effect. For small indenters （e.g., radii on the order of 10μm）, the maximum ...The finite element method for the conventional theory of mechanism-based strain gradient plasticity is used to study the indentation size effect. For small indenters （e.g., radii on the order of 10μm）, the maximum allowable geometrically necessary dislocation （GND） density is introduced to cap the GND density such that the latter does not become unrealistically high. The numerical results agree well with the indentation hardness data of iridium. The GND density is much larger than the density of statistically stored dislocations （SSD） underneath the indenter, but this trend reverses away from the indenter. As the indentation depth （or equivalently, contact radius） increases, the GND density decreases but the SSD density increases.展开更多
Nanoindentation size effect was investigated under very low loads on type 316 stainless steel. Nanoindentation measurements were carried out on the samples surfaces with a Berkovich pyramidal diamond indenter applying...Nanoindentation size effect was investigated under very low loads on type 316 stainless steel. Nanoindentation measurements were carried out on the samples surfaces with a Berkovich pyramidal diamond indenter applying loads in the range of 25-1000μN. Simultaneously, AFM images of the sample surface were recorded before and after indentation process .For type 316 stainless steel, the indentation size effect was found. The results were discussed in the terms of the model of geometrically necessary dislocations proposed to interpret the indentation size effect.It can be seen that the square of the nanohardness, H 2, vs the inverse of indentation depth, 1/h, is linearly dependent on the indented depth in the range of 25-150nm,which is a good qualitative agreement with the predictions of the model. However, for shallow indents, the slope of the line severely changes.Some possible mechanisms for this change were proposed.展开更多
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%.
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...
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the Yunlong Lake Laboratory of Deep Underground Science and Engineering(Grant No.104023005)the National Natural Science Foundation of China(Grant No.52308403)China Postdoctoral Science Foundation(Grant No.2023M731998)for funding provided to this work.
文摘Rock macro-indentation plays a fundamental role in mechanical rock breaking for various rock engineering application,such as drilling,tunneling,cutting,and sawing.Over the past decades,extensive research has been conducted to understand the indentation mechanisms and responses through various approaches.This review aims to provide an overview of the current status and recent advancements in theories,experiments,numerical simulations,and applications of macro-indentation in rock engineering.It starts with elaborating on the mechanisms of macro-indentation,followed by a discussion of the merits and limitations of commonly used models.Influence factors and their effects on indentation test results are then summarized.Various numerical simulation methods for rock macro-indentation are highlighted,along with their advantages and disadvantages.Subsequently,the applications of indentation tests and indentation indices in characterizing rock properties are explored.It reveals that compression-tension,compression-shear,and composite models are widely employed in rock macroindentation.While the compression-tension model is straightforward to use,it may overlook the anisotropic properties of rocks.On the other hand,the composite model provides a more comprehensive description of rock indentation but requires complex calculations.Additionally,factors,such as indentation rate,indenter geometry,rock type,specimen size,and confining pressure,can significantly influence the indentation results.Simulation methods for macro-indentation encompass continuous medium,discontinuous medium,and continuous-discontinuous medium methods,with selection based on their differences in principle.Furthermore,rock macro-indentation can be practically applied to mining engineering,tunneling engineering,and petroleum drilling engineering.Indentation indices serve as valuable tools for characterizing rock strength,brittleness,and drillability.This review sheds light on the development of rock macro-indentation and its extensive application in engineering practice.Specialists in the field can gain a comprehensive understanding of the indentation process and its potential in various rock engineering endeavors.
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.
基金Supported by the Science Research Fund of Shanghai Education Council(No.06VZ004)
文摘The indentation method is useful in determining the residual stress according to the elastic-plastic properties of materials.So the effect of the residual stress on the elastic-plastic indentation properties of materials was studied by using the finite element method to find better indentation parameters which are strongly induced by the residual stress.The results show that load-depth curve,plastic pile-up,indentation shape,indentation contact stress and indentation residual stress are affected by different residual stress,and these parameters can be used to deduce the residual stress.Also,a special indentation equipment was developed to analyze the elastic-plastic properties of materials with different residual stress,and the experimental results show a good agreement with the FEM results.For practical application,the elastic-plastic indentation properties of materials with unknown residual stress could be obtained by the developed equipment to deduce the residual stress comprehensively.
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.
文摘A new area function is introduced and applied to a Berkovich tip in order tocharacterize the contact projected area between an indenter and indented material. The function canbe related directly to tip-rounding, thereby having obviously physical meaning. Nanoindentationexperiments are performed on a commercial Nano Indenter XP^R system. The other two area functionsintroduced by Oliver and Pharr and by Thurn and Cook respectively are involved in this paper forcomparison. By comparison from experimental results among different area functions, the indenter tipdescribed by the proposed area function here is very close to the experimental indenter.
基金Project supported by the National Natural Science Foundation of China(Nos.11302231,11025212 and 11272318)
文摘Fracture toughness is one of the crucial mechanical properties of brittle materials such as glasses and ceramics which demonstrate catastrophic failure modes. Conventional stan- dardized testing methods adopted for fracture toughness determination require large specimens to satisfy the plane strain condition. As for small specimens, indentation is a popular, sometimes exclusive testing mode to determine fracture toughness for it can be performed on a small flat area of the specimen surface. This review focuses on the development of indentation fracture theories and the representative testing methods. Cracking pattern dependent on indenter geometry and material property plays an important role in modeling, and is the main reason for the diversity of indentation fracture theories and testing methods. Along with the simplicity of specimen require- ment is the complexity of modeling and analysis which accounts for the semi-empirical features of indentation fracture tests. Some unresolved issues shaping the gap between indentation fracture tests and standardization are also discussed.
基金supported by the National Natural Science Foundation of China (No. 10972066)the Doctoral Program Foundation of Institutions of Higher Education of China (No. 20070213054)+1 种基金the Natural Science Foundation of the Heilongjiang Province of China (A2007-10)the Fundamental Research Funds for the Central Universities (No. HIT.NSRIF. 2010070)
文摘In this paper,the nanoindentation simulation on the two models of neat polyethylene（PE） and the polyethylene incorporated with 25wt% POSS（POSS-PE） is performed to reveal the reinforcing mechanism of the mechanical properties.The influence of the indenter shapes on nanoindentation is researched by using three different shapes of diamond indenters（cube-corner indenter,cylindrical indenter with spherical tip and cylindrical indenter with flat tip）.The molecular mechanics method is adopted to eliminate the temperature effects.Under different indenters,the load-displacement responses,hardnesses（indentation hardness and Martens hardness） and Young＇s moduli of PE and POSS-PE are obtained.Compared with PE,all the mechanical properties are improved dramatically.Then,we analyze the source of loading drop phenomena and the enhancement mechanism of POSS.Furthermore,the result shows that the different shapes of indenters cause a large impact on indentation hardness,but a little impact on Martens hardness.And Young＇s modulus of the flat indenter is much larger than that of cube-corner indenter and spherical indenter.
基金Advanced Maintenance Research Project(9140A270304090C8501)National Natural Science Foundations of China(50975285,50735006)Equipment Research Project,and Fundamental Research Funds for the Central Universities(2009PY08)
文摘In this paper,NiCr-Cr3C2 coating was deposited onto AISI 1045 steel substrate by employing supersonic plasma spraying technique.The surface and cross-section morphologies of the NiCr-Cr3C2 coating were observed by SEM.The phase constituents of the coating were identified by XRD.The SEM images showed that the coating was very dense,and it had a low porosity structure.The XRD pattern implied that the coating was mainly composed of NiCr,Cr3C2 and Cr7C2.Nanoindentation tests were performed on the coating surface by a Nano indenter.The widely used Oliver-Pharr method was adopted to extract the mechanical properties of the coating.The hardness exhibited a strong peak-load-dependence,i.e.indentation size effect;the elastic modulus was not affected by indentation size effect.
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.
基金Project supported by the National Science Foundation （No. CMS-0084980） ONR （No. N00014-01-1-0205, program officer Dr. Y.D.S. Rajapakse）, by the Foundation for the Author of National Excellent Doctoral Dissertation of China （FANEDD） （No. 2007B30）.
文摘The finite element method for the conventional theory of mechanism-based strain gradient plasticity is used to study the indentation size effect. For small indenters （e.g., radii on the order of 10μm）, the maximum allowable geometrically necessary dislocation （GND） density is introduced to cap the GND density such that the latter does not become unrealistically high. The numerical results agree well with the indentation hardness data of iridium. The GND density is much larger than the density of statistically stored dislocations （SSD） underneath the indenter, but this trend reverses away from the indenter. As the indentation depth （or equivalently, contact radius） increases, the GND density decreases but the SSD density increases.
基金FundedbytheNationalNaturalScienceFoundationofChi na (No .5 0 1710 13)andtheSpecialFoundationfortheNationalStateBasicResearchProject(No.G19990 6 5 0 )
文摘Nanoindentation size effect was investigated under very low loads on type 316 stainless steel. Nanoindentation measurements were carried out on the samples surfaces with a Berkovich pyramidal diamond indenter applying loads in the range of 25-1000μN. Simultaneously, AFM images of the sample surface were recorded before and after indentation process .For type 316 stainless steel, the indentation size effect was found. The results were discussed in the terms of the model of geometrically necessary dislocations proposed to interpret the indentation size effect.It can be seen that the square of the nanohardness, H 2, vs the inverse of indentation depth, 1/h, is linearly dependent on the indented depth in the range of 25-150nm,which is a good qualitative agreement with the predictions of the model. However, for shallow indents, the slope of the line severely changes.Some possible mechanisms for this change were proposed.
