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
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
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 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
This paper develops the adhesive contact theory for a one-dimensional hexagonal quasicrystal half-space punched by a spherical indenter on the basis of the classical adhesive contact models involving the Johnson–Kend...This paper develops the adhesive contact theory for a one-dimensional hexagonal quasicrystal half-space punched by a spherical indenter on the basis of the classical adhesive contact models involving the Johnson–Kendall–Roberts(JKR)model,the Maugis–Dugdale(MD)model and the Derjaguin–Muller–Toporov(DMT)model.By using the superposition principle combined with the Griffith energy balance,all the significant physical quantities for adhesive contact,such as the energy release rate,indentation force,penetration depth,contact radius and pull-out force,are obtained for different models.The result for the DMT model is derived from the MD solution through a limiting procedure.A numerical calculation is carried out to verify the present analytical solutions,to compare different contact models,and to analyze the influence of the phason field on the results.It is indicated that the effect of the phason field on the result for the MD model is pronounced,especially for a small contact radius.However,the phason effect on the JKR and DMT results is not significant.The present solution can serve as a theoretical basis for nano-indentation and atomic force microscopy to measure the material properties of quasicrystals.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
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></span><span style="white-space:normal;"><span style="font-family:"">, both to the surface and internally. Their volumes add to the depression volume. These volumes are essential for the exemplified pile-up management. Phase-transitions produce polymorph interfaces that are nucleation sites for cracks. Technical materials must be developed with onset forces higher than the highest thinkable stresses (at airliners, bridges</span></span><span style="white-space:normal;"><span style="font-family:"">,</span></span><span style="white-space:normal;"><span style="font-family:""> etc</span></span><span style="white-space:normal;"><span style="font-family:"">.</span></span><span style="white-space:normal;"><span style="font-family:"">). This requires urgent revision of ISO 14577-ASTM stan</span></span><span style="white-space:normal;"><span style="font-family:"">dards.展开更多
Surface effects often play a significant role in the mechanical properties of soft materials such as hydrogels and biological tissues.In this paper,we investigate the plane-strain indentation of a soft elastic layer b...Surface effects often play a significant role in the mechanical properties of soft materials such as hydrogels and biological tissues.In this paper,we investigate the plane-strain indentation of a soft elastic layer bonded to a rigid substrate.The surface effects on the indentation behavior of the elastic layer-substrate system are theoretically analyzed.Indentation tests using indenters with different elliptical shapes are compared.Analytical expressions are derived for the indentation force-displacement relation using the Kerr model with the effect of surface tension.The theoretical solution is verified by finite element simulations.The dependence of surface effects on the ratio of the indenter’s major and minor elliptical axes is also examined.This work helps understand the size effects on the indentation behaviors of soft materials and guides the design of corresponding measurement tests.展开更多
Nix and Gao established an important relation between the microindentation hardness and indentation depth. Such a relation has been verified by many microindentation experiments （indentation depths in the micrometer ...Nix and Gao established an important relation between the microindentation hardness and indentation depth. Such a relation has been verified by many microindentation experiments （indentation depths in the micrometer range）, but it does not always hold in nanoindentation experiments （indentation depths approaching the nanometer range）. Indenter tip radius effect has been proposed by Qu et al. and others as possibly the main factor that causes the deviation from Nix and Gao＇s relationship. We have developed an indentation model for micro- and nanoindentation, which accounts for two indenter shapes, a sharp, conical indenter and a conical indenter with a spherical tip. The analysis is based on the conventional theory of mechanism-based strain gradient plasticity established from the Taylor dislocation model to account for the effect of geometrically necessary dislocations. The comparison between numerical result and Feng and Nix＇s experimental data shows that the indenter tip radius effect indeed causes the deviation from Nix-Gao relation, but it seems not be the main factor.展开更多
In the present study, the indentation testing with a flat cylindrical indenter on typical multi-layer material systems was simulated successfully by finite element method. The emphasis was put on the methods of extrac...In the present study, the indentation testing with a flat cylindrical indenter on typical multi-layer material systems was simulated successfully by finite element method. The emphasis was put on the methods of extracting the yield stresses and strain-hardening modulus of upper and middle-layers of three-layer material systems from the indentation testing. The slope of the indentation depth to the applied indentation stress curve was found to have a turning point, which can be used to determine the yield stress of the upper-layer. Then, a different method was also presented to determine the yield stress of the middle-layer. This method was based on a set of assumed applied indentation stresses which were to be intersected by the experimental results in order to meet the requirement of having the experimental indentation depth. At last, a reverse numerical algorithm was explored to determine the yield stresses of upper and middle-layers simultaneously by using the indentation testing with two different size indenters. This method assumed two ranges of yield stresses to simulate the indentation behavior. The experimental depth behavior was used to intersect the simulated indentation behavior. And the intersection corresponded to the values of yield stresses of upper and middle-layers. This method was also used further to determine the strain-hardening modulus of upper and middle-layers simultaneously.展开更多
The paper addresses a contact problem of the theory of elasticity,i.e.,the penetration of a circular indenter with a flat base into a soft functionally graded elastic layer.The elastic properties of a functionally gra...The paper addresses a contact problem of the theory of elasticity,i.e.,the penetration of a circular indenter with a flat base into a soft functionally graded elastic layer.The elastic properties of a functionally graded layer arbitrarily vary with depth,and the foundation is assumed to be elastic,yet much harder than a layer.Approximated analytical solution is constructed,and it is shown that the solutions are asymptotically exact both for large and small values of characteristic dimensionless geometrical parameter of the problem.Numerical examples are analyzed for the cases of monotonic and nonmonotonic variations of elastic properties.Numerical results for the case of homogeneous layer are compared with the results for nondeformable foundation.展开更多
Nanovesicles have been demonstrated to be the key agents in therapeutic encapsulations for drug delivery and diagnostic area,and the effectiveness and efficiency of these applications strongly depend on the mechanical...Nanovesicles have been demonstrated to be the key agents in therapeutic encapsulations for drug delivery and diagnostic area,and the effectiveness and efficiency of these applications strongly depend on the mechanical properties of nanovesicles.Based on the Helfrich membrane theory,a theoretical investigation is conducted to explore the mechanical behaviors of pressurized elastic fluid nanovesicles during the indentation by a rigid cylindrical indenter.The effects of osmotic pressure,membrane bending rigidity,energy of adhesion bet ween the vesicle and substrate on the mechanical responses of the vesicle to the indentation are analyzed.It is found that the osmotic pressure dominates the mechanical behaviors of strongly pressurized nanovesicles as well as the effective vesicle stiffness and Young's modulus.Our results may have important implications on regulating the mechanical behaviors of inter-and intracellular nanovesicles which are crucial for particle-based drug delivery systems.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
Linear elastic fracture mechanics principles are widely applied for the analysis of crack problems in rock fracture mechanics. Rock indentation is an important and complicated problem among rock engineering issues. In...Linear elastic fracture mechanics principles are widely applied for the analysis of crack problems in rock fracture mechanics. Rock indentation is an important and complicated problem among rock engineering issues. In this paper, in addition to the fracture criterion of maximum tangential stress adjacent to crack tip, the higher order displacement discontinuity method (which is a version of the indirect boundary element method) has been used for modeling the crack propagation mechanism under blunt indenters. In order to achieve more accurate results, higher order boundary elements i.e. quadratic elements, has been used to calculate displacement discontinuities and also to reduce the singularities of stress and displacement fields near the crack tip, the special crack tip elements has been used to calculate the stress intensity factors (SIF) at the crack tips. In this modeling, the effect of crack angle on stress intensity factors has been investigated. The numerical results of stress intensity factors obtained from some example problems were compared to the theoretical and experimental results cited in the literature which always show a percentage error less than one percent. The simulated results may pave the way for increasing the efficiency of mining and drilling by improving the design of tools and indentation equipments.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
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
Indentation hardness is found to be related to indentation depth when indentation test is applied on homogeneous materials under small indentation depth, which shows strong size effect in the indentation. While in con...Indentation hardness is found to be related to indentation depth when indentation test is applied on homogeneous materials under small indentation depth, which shows strong size effect in the indentation. While in contrast, indentation hardness has a very limited relationship with indentation depth when it is large, showing distinct scaling relationships between hardness and material properties. Previous studies on scaling relationships under deep indentation condition of elastic-perfectly plastic homogeneous materials have been carried out systematically by finite element analysis. In this paper, a heterogeneous material, particlereinforced matrix composite is detailed studied to investigate its scaling relationships under deep indentation with different particle positions and material properties by finite element analysis.展开更多
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.
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supported primarily by the National Natural Science Foundation of China(Nos.12172237,12002273 and 11832007)The supports from Sichuan Science and Technology Program(No.2021YJ0513-BG)+1 种基金2022 Open Project of Failure Mechanics and Engineering Disaster Prevention,Key Lab of Sichuan Provence(No.FMEDP202211)are also gratefully acknowledged.
文摘This paper develops the adhesive contact theory for a one-dimensional hexagonal quasicrystal half-space punched by a spherical indenter on the basis of the classical adhesive contact models involving the Johnson–Kendall–Roberts(JKR)model,the Maugis–Dugdale(MD)model and the Derjaguin–Muller–Toporov(DMT)model.By using the superposition principle combined with the Griffith energy balance,all the significant physical quantities for adhesive contact,such as the energy release rate,indentation force,penetration depth,contact radius and pull-out force,are obtained for different models.The result for the DMT model is derived from the MD solution through a limiting procedure.A numerical calculation is carried out to verify the present analytical solutions,to compare different contact models,and to analyze the influence of the phason field on the results.It is indicated that the effect of the phason field on the result for the MD model is pronounced,especially for a small contact radius.However,the phason effect on the JKR and DMT results is not significant.The present solution can serve as a theoretical basis for nano-indentation and atomic force microscopy to measure the material properties of quasicrystals.
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.
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></span><span style="white-space:normal;"><span style="font-family:"">, both to the surface and internally. Their volumes add to the depression volume. These volumes are essential for the exemplified pile-up management. Phase-transitions produce polymorph interfaces that are nucleation sites for cracks. Technical materials must be developed with onset forces higher than the highest thinkable stresses (at airliners, bridges</span></span><span style="white-space:normal;"><span style="font-family:"">,</span></span><span style="white-space:normal;"><span style="font-family:""> etc</span></span><span style="white-space:normal;"><span style="font-family:"">.</span></span><span style="white-space:normal;"><span style="font-family:"">). This requires urgent revision of ISO 14577-ASTM stan</span></span><span style="white-space:normal;"><span style="font-family:"">dards.
基金This work was supported by the National Natural Science Foundation of China(Grant Nos.11802225 and 11921002).
文摘Surface effects often play a significant role in the mechanical properties of soft materials such as hydrogels and biological tissues.In this paper,we investigate the plane-strain indentation of a soft elastic layer bonded to a rigid substrate.The surface effects on the indentation behavior of the elastic layer-substrate system are theoretically analyzed.Indentation tests using indenters with different elliptical shapes are compared.Analytical expressions are derived for the indentation force-displacement relation using the Kerr model with the effect of surface tension.The theoretical solution is verified by finite element simulations.The dependence of surface effects on the ratio of the indenter’s major and minor elliptical axes is also examined.This work helps understand the size effects on the indentation behaviors of soft materials and guides the design of corresponding measurement tests.
基金The project supported by the National Natural Science Foundation of China (10121202)the Ministry of Education of China (20020003023)
文摘Nix and Gao established an important relation between the microindentation hardness and indentation depth. Such a relation has been verified by many microindentation experiments （indentation depths in the micrometer range）, but it does not always hold in nanoindentation experiments （indentation depths approaching the nanometer range）. Indenter tip radius effect has been proposed by Qu et al. and others as possibly the main factor that causes the deviation from Nix and Gao＇s relationship. We have developed an indentation model for micro- and nanoindentation, which accounts for two indenter shapes, a sharp, conical indenter and a conical indenter with a spherical tip. The analysis is based on the conventional theory of mechanism-based strain gradient plasticity established from the Taylor dislocation model to account for the effect of geometrically necessary dislocations. The comparison between numerical result and Feng and Nix＇s experimental data shows that the indenter tip radius effect indeed causes the deviation from Nix-Gao relation, but it seems not be the main factor.
基金the National Natural Science Foundation of China （No. 10472094） the Research Fund for the Doctoral Program of Higher Education （N6CJ0001） Doctorate Fund of Northwestern Polytechnical University.
文摘In the present study, the indentation testing with a flat cylindrical indenter on typical multi-layer material systems was simulated successfully by finite element method. The emphasis was put on the methods of extracting the yield stresses and strain-hardening modulus of upper and middle-layers of three-layer material systems from the indentation testing. The slope of the indentation depth to the applied indentation stress curve was found to have a turning point, which can be used to determine the yield stress of the upper-layer. Then, a different method was also presented to determine the yield stress of the middle-layer. This method was based on a set of assumed applied indentation stresses which were to be intersected by the experimental results in order to meet the requirement of having the experimental indentation depth. At last, a reverse numerical algorithm was explored to determine the yield stresses of upper and middle-layers simultaneously by using the indentation testing with two different size indenters. This method assumed two ranges of yield stresses to simulate the indentation behavior. The experimental depth behavior was used to intersect the simulated indentation behavior. And the intersection corresponded to the values of yield stresses of upper and middle-layers. This method was also used further to determine the strain-hardening modulus of upper and middle-layers simultaneously.
基金supports of the Ministry of Education and Science of Russia (11.519.11.3028,14.B37.21.1131,14.B7.21.1632)Russian Foundation of Basic Research (11-08-91168-GFEN a)
文摘The paper addresses a contact problem of the theory of elasticity,i.e.,the penetration of a circular indenter with a flat base into a soft functionally graded elastic layer.The elastic properties of a functionally graded layer arbitrarily vary with depth,and the foundation is assumed to be elastic,yet much harder than a layer.Approximated analytical solution is constructed,and it is shown that the solutions are asymptotically exact both for large and small values of characteristic dimensionless geometrical parameter of the problem.Numerical examples are analyzed for the cases of monotonic and nonmonotonic variations of elastic properties.Numerical results for the case of homogeneous layer are compared with the results for nondeformable foundation.
基金Financial support for this work was provided by the National Natural Science Foundation of China(Grant Nos.11872005 and 11521202).
文摘Nanovesicles have been demonstrated to be the key agents in therapeutic encapsulations for drug delivery and diagnostic area,and the effectiveness and efficiency of these applications strongly depend on the mechanical properties of nanovesicles.Based on the Helfrich membrane theory,a theoretical investigation is conducted to explore the mechanical behaviors of pressurized elastic fluid nanovesicles during the indentation by a rigid cylindrical indenter.The effects of osmotic pressure,membrane bending rigidity,energy of adhesion bet ween the vesicle and substrate on the mechanical responses of the vesicle to the indentation are analyzed.It is found that the osmotic pressure dominates the mechanical behaviors of strongly pressurized nanovesicles as well as the effective vesicle stiffness and Young's modulus.Our results may have important implications on regulating the mechanical behaviors of inter-and intracellular nanovesicles which are crucial for particle-based drug delivery systems.
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.
文摘Linear elastic fracture mechanics principles are widely applied for the analysis of crack problems in rock fracture mechanics. Rock indentation is an important and complicated problem among rock engineering issues. In this paper, in addition to the fracture criterion of maximum tangential stress adjacent to crack tip, the higher order displacement discontinuity method (which is a version of the indirect boundary element method) has been used for modeling the crack propagation mechanism under blunt indenters. In order to achieve more accurate results, higher order boundary elements i.e. quadratic elements, has been used to calculate displacement discontinuities and also to reduce the singularities of stress and displacement fields near the crack tip, the special crack tip elements has been used to calculate the stress intensity factors (SIF) at the crack tips. In this modeling, the effect of crack angle on stress intensity factors has been investigated. The numerical results of stress intensity factors obtained from some example problems were compared to the theoretical and experimental results cited in the literature which always show a percentage error less than one percent. The simulated results may pave the way for increasing the efficiency of mining and drilling by improving the design of tools and indentation equipments.
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.
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supported by the National Natural Science Foundation of China(Grant Nos.11432014,11672301,11521202,11890681)
文摘Indentation hardness is found to be related to indentation depth when indentation test is applied on homogeneous materials under small indentation depth, which shows strong size effect in the indentation. While in contrast, indentation hardness has a very limited relationship with indentation depth when it is large, showing distinct scaling relationships between hardness and material properties. Previous studies on scaling relationships under deep indentation condition of elastic-perfectly plastic homogeneous materials have been carried out systematically by finite element analysis. In this paper, a heterogeneous material, particlereinforced matrix composite is detailed studied to investigate its scaling relationships under deep indentation with different particle positions and material properties by finite element analysis.
