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
In two recent papers,approximate solutions for compact non-axisymmetric contact problems of homogeneous and power-law graded elastic bodies have been suggested,which provide explicit analytical relations for the force...In two recent papers,approximate solutions for compact non-axisymmetric contact problems of homogeneous and power-law graded elastic bodies have been suggested,which provide explicit analytical relations for the force–approach relation,the size and the shape of the contact area,as well as for the pressure distribution therein.These solutions were derived for profiles,which only slightly deviate from the axisymmetric shape.In the present paper,they undergo an extensive testing and validation by comparison of solutions with a great variety of profile shapes with numerical solutions obtained by the fast Fourier transform(FFT)-assisted boundary element method(BEM).Examples are given with quite significant deviations from axial symmetry and show surprisingly good agreement with numerical solutions.展开更多
This paper theoretically studies the axisymmetric frictionless indentation of a transversely isotropic piezoelectric semiconductor(PSC)half-space subject to a rigid flatended cylindrical indenter.The contact area and ...This paper theoretically studies the axisymmetric frictionless indentation of a transversely isotropic piezoelectric semiconductor(PSC)half-space subject to a rigid flatended cylindrical indenter.The contact area and other surface of the PSC half-space are assumed to be electrically insulating.By the Hankel integral transformation,the problem is reduced to the Fredholm integral equation of the second kind.This equation is solved numerically to obtain the indentation behaviors of the PSC half-space,mainly including the indentation force-depth relation and the electric potential-depth relation.The results show that the effect of the semiconductor property on the indentation responses is limited within a certain range of variation of the steady carrier concentration.The dependence of indentation behavior on material properties is also analyzed by two different kinds of PSCs.Finite element simulations are conducted to verify the results calculated by the integral equation technique,and good agreement is demonstrated.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
A theoretical model of relationship between subsurface damage and surface roughness was established to realize rapid and non-destructive measurement of subsurface damage of ground optical materials.Postulated conditio...A theoretical model of relationship between subsurface damage and surface roughness was established to realize rapid and non-destructive measurement of subsurface damage of ground optical materials.Postulated condition of the model was that subsurface damage depth and peak-to-valley surface roughness are equal to depth of radial and lateral cracks in brittle surface induced by small-radius(radius≤200 μm)spherical indenter,respectively.And contribution of elastic stress field to the radial cracks propagation was also considered in the loading cycle.Subsurface damage depth of ground BK7 glasses was measured by magnetorheological finishing spot technique to validate theoretical ratio of subsurface damage to surface roughness.The results show that the ratio is directly proportional to load of abrasive grains and hardness of optical materials,while inversely proportional to granularity of abrasive grains and fracture toughness of optical materials.Moreover,the influence of the load and fracture toughness on the ratio is more significant than the granularity and hardness,respectively.The measured ratios of 80 grit and 120 grit fixed abrasive grinding of BK7 glasses are 5.8 and 5.4,respectively.展开更多
Three-dimensional finite element modeling of the contact between a rigid spherical indenter and a rough surface is presented when considering both the loading and unloading phases. The relationships among the indentat...Three-dimensional finite element modeling of the contact between a rigid spherical indenter and a rough surface is presented when considering both the loading and unloading phases. The relationships among the indentation load, displacement, contact area, and mean contact pressure for both loading and unloading are established through a curve fitting using sigmoid logistic and power law functions. The contact load is proportional to the contact area, and the mean contact pressure is related to the characteristic stress, which is dependent on the material properties. The residual displacement is proportional to the maximum indentation displacement. A proportional relationship also exists for plastically dissipated energy and work conducted during loading. The surface roughness results in an effective elastic modulus calculated from an initial unloading stiffness several times larger than the true value of elastic modulus. Nonetheless, the calculated modulus under a shallow spherical indentation can still be applied for a relative comparison.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
Pile-up around indenter is usually observed during instrumented indentation tests on bulk metallic glass. Neglecting the pile-up effect may lead to errors in evaluating hardness,Young’s modulus,stress-strain response...Pile-up around indenter is usually observed during instrumented indentation tests on bulk metallic glass. Neglecting the pile-up effect may lead to errors in evaluating hardness,Young’s modulus,stress-strain response,etc. Finite element analysis was employed to implement numerical simulation of spherical indentation tests on bulk metallic glass. A new model was proposed to describe the pile-up effect. By using this new model,the contact radius and hardness of Zr41.2Ti13.8Cu12.5Ni10Be22.5 bulk metallic glass were obtained under several different indenter loads with pile-up,and the results agree well with the data generated by numerical simulation.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-r展开更多
A contact problem for an infinitely long hollow cylinder is considered. The cylinder is compressed by an outer rigid ring with a circular profile. The material of the cylinder is linearly elastic and isotropic. The ex...A contact problem for an infinitely long hollow cylinder is considered. The cylinder is compressed by an outer rigid ring with a circular profile. The material of the cylinder is linearly elastic and isotropic. The extent of the contact region and the pressure distribution are sought. Governing equations of the elasticity theory for the axisymmetric problem in cylindrical coordinates are solved by Fourier transforms and general expressions for the displacements are obtained. Using the boundary conditions, the formulation is reduced to a singular integral equation. This equation is solved by using the Gaussian quadrature. Then the pressure distribution on the contact region is determined. Numerical results for the contact pressure and the distance characterizing the contact area are given in graphical form.展开更多
The iteration-free physical description of pyramidal indentations with closed mathematical equations is comprehensively described and extended for creating new insights in this important field of research and app...The iteration-free physical description of pyramidal indentations with closed mathematical equations is comprehensively described and extended for creating new insights in this important field of research and applications. All calculations are easily repeatable and should be programmed by instrument builders for even easier general use. Formulas for the volumes and side-areas of Berkovich and cubecorner as a function of depth are deduced and provided, as are the resulting forces and force directions. All of these allow for the detailed comparison of the different indenters on the mathematical reality. The pyramidal values differ remarkably from the ones of so-called “equivalent cones”. The worldwide use of such pseudo-cones is in severe error. The earlier claimed and used 3 times higher displaced volume with cube corner than with Berkovich is disproved. Both displace the same amount at the same applied force. The unprecedented mathematical results are experimentally confirmed for the physical indentation hardness and for the sharp-onset phase-transi</span></span><span style="white-space:normal;"><span style="font-family:"">- </span></span><span style="white-space:normal;"><span style="font-family:"">tions with calculated transition energy. The comparison of both indenters pro</span></span><span style="white-space:normal;"><span style="font-family:"">vides novel basic insights. Isotropic materials exhibit the same phase transition onset force, but the transition energy is larger with the cube corner, due to higher force and flatter force direction. This qualifies the cube</span></span><span style="white-space:normal;"><span style="font-family:""> </span></span><span style="white-space:normal;"><span style="font-family:"">corner for fracture toughness studies. Pile-up is not from the claimed “friction with the indenter”. Anisotropic materials with cleavage planes and channels undergo sliding along these</span></span><span style="white-space:normal;"><span style="font-family:""> under pressure</span></展开更多
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financial support from Deutsche Forschungsgemeinschaft(DFG)(Grant Nos.PO 810/66-1 and LI 3064/2-1)。
文摘In two recent papers,approximate solutions for compact non-axisymmetric contact problems of homogeneous and power-law graded elastic bodies have been suggested,which provide explicit analytical relations for the force–approach relation,the size and the shape of the contact area,as well as for the pressure distribution therein.These solutions were derived for profiles,which only slightly deviate from the axisymmetric shape.In the present paper,they undergo an extensive testing and validation by comparison of solutions with a great variety of profile shapes with numerical solutions obtained by the fast Fourier transform(FFT)-assisted boundary element method(BEM).Examples are given with quite significant deviations from axial symmetry and show surprisingly good agreement with numerical solutions.
基金Project supported by the National Natural Science Foundation of China(Nos.12072209,U21A2043012192211)+1 种基金the Natural Science Foundation of Hebei Province of China(No.A2020210009)the S&T Program of Hebei Province of China(No.225676162GH)。
文摘This paper theoretically studies the axisymmetric frictionless indentation of a transversely isotropic piezoelectric semiconductor(PSC)half-space subject to a rigid flatended cylindrical indenter.The contact area and other surface of the PSC half-space are assumed to be electrically insulating.By the Hankel integral transformation,the problem is reduced to the Fredholm integral equation of the second kind.This equation is solved numerically to obtain the indentation behaviors of the PSC half-space,mainly including the indentation force-depth relation and the electric potential-depth relation.The results show that the effect of the semiconductor property on the indentation responses is limited within a certain range of variation of the steady carrier concentration.The dependence of indentation behavior on material properties is also analyzed by two different kinds of PSCs.Finite element simulations are conducted to verify the results calculated by the integral equation technique,and good agreement is demonstrated.
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Project(50375156) supported by the National Natural Science Foundation of China
文摘A theoretical model of relationship between subsurface damage and surface roughness was established to realize rapid and non-destructive measurement of subsurface damage of ground optical materials.Postulated condition of the model was that subsurface damage depth and peak-to-valley surface roughness are equal to depth of radial and lateral cracks in brittle surface induced by small-radius(radius≤200 μm)spherical indenter,respectively.And contribution of elastic stress field to the radial cracks propagation was also considered in the loading cycle.Subsurface damage depth of ground BK7 glasses was measured by magnetorheological finishing spot technique to validate theoretical ratio of subsurface damage to surface roughness.The results show that the ratio is directly proportional to load of abrasive grains and hardness of optical materials,while inversely proportional to granularity of abrasive grains and fracture toughness of optical materials.Moreover,the influence of the load and fracture toughness on the ratio is more significant than the granularity and hardness,respectively.The measured ratios of 80 grit and 120 grit fixed abrasive grinding of BK7 glasses are 5.8 and 5.4,respectively.
基金supported by National Natural Science Foundation of China (Grant Nos. 51705082, 51875016)Fujian Provincial Minjiang Scholar (No. 0020-510486)Fujian Provincial Collaborative Innovation Center for High-end Equipment Manufacturing (No. 002050006103)
文摘Three-dimensional finite element modeling of the contact between a rigid spherical indenter and a rough surface is presented when considering both the loading and unloading phases. The relationships among the indentation load, displacement, contact area, and mean contact pressure for both loading and unloading are established through a curve fitting using sigmoid logistic and power law functions. The contact load is proportional to the contact area, and the mean contact pressure is related to the characteristic stress, which is dependent on the material properties. The residual displacement is proportional to the maximum indentation displacement. A proportional relationship also exists for plastically dissipated energy and work conducted during loading. The surface roughness results in an effective elastic modulus calculated from an initial unloading stiffness several times larger than the true value of elastic modulus. Nonetheless, the calculated modulus under a shallow spherical indentation can still be applied for a relative comparison.
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the National Natural Science Foundation of China (Grant Nos. 10725211, 10721202 and 10472119) the Key Project of Chinese Academy of Sciences (Grant Nos. KJCX2-YW-M04 and KJCX-SW-L08)
文摘Pile-up around indenter is usually observed during instrumented indentation tests on bulk metallic glass. Neglecting the pile-up effect may lead to errors in evaluating hardness,Young’s modulus,stress-strain response,etc. Finite element analysis was employed to implement numerical simulation of spherical indentation tests on bulk metallic glass. A new model was proposed to describe the pile-up effect. By using this new model,the contact radius and hardness of Zr41.2Ti13.8Cu12.5Ni10Be22.5 bulk metallic glass were obtained under several different indenter loads with pile-up,and the results agree well with the data generated by numerical simulation.
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-r
文摘A contact problem for an infinitely long hollow cylinder is considered. The cylinder is compressed by an outer rigid ring with a circular profile. The material of the cylinder is linearly elastic and isotropic. The extent of the contact region and the pressure distribution are sought. Governing equations of the elasticity theory for the axisymmetric problem in cylindrical coordinates are solved by Fourier transforms and general expressions for the displacements are obtained. Using the boundary conditions, the formulation is reduced to a singular integral equation. This equation is solved by using the Gaussian quadrature. Then the pressure distribution on the contact region is determined. Numerical results for the contact pressure and the distance characterizing the contact area are given in graphical form.
文摘The iteration-free physical description of pyramidal indentations with closed mathematical equations is comprehensively described and extended for creating new insights in this important field of research and applications. All calculations are easily repeatable and should be programmed by instrument builders for even easier general use. Formulas for the volumes and side-areas of Berkovich and cubecorner as a function of depth are deduced and provided, as are the resulting forces and force directions. All of these allow for the detailed comparison of the different indenters on the mathematical reality. The pyramidal values differ remarkably from the ones of so-called “equivalent cones”. The worldwide use of such pseudo-cones is in severe error. The earlier claimed and used 3 times higher displaced volume with cube corner than with Berkovich is disproved. Both displace the same amount at the same applied force. The unprecedented mathematical results are experimentally confirmed for the physical indentation hardness and for the sharp-onset phase-transi</span></span><span style="white-space:normal;"><span style="font-family:"">- </span></span><span style="white-space:normal;"><span style="font-family:"">tions with calculated transition energy. The comparison of both indenters pro</span></span><span style="white-space:normal;"><span style="font-family:"">vides novel basic insights. Isotropic materials exhibit the same phase transition onset force, but the transition energy is larger with the cube corner, due to higher force and flatter force direction. This qualifies the cube</span></span><span style="white-space:normal;"><span style="font-family:""> </span></span><span style="white-space:normal;"><span style="font-family:"">corner for fracture toughness studies. Pile-up is not from the claimed “friction with the indenter”. Anisotropic materials with cleavage planes and channels undergo sliding along these</span></span><span style="white-space:normal;"><span style="font-family:""> under pressure</span></
