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 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
Uniaxial strain hardening exponent is not suitable for describing the strain hardening behaviors of the anisotropic materials, especially when material deforms in the multi-axial stress states. In this work, a novel m...Uniaxial strain hardening exponent is not suitable for describing the strain hardening behaviors of the anisotropic materials, especially when material deforms in the multi-axial stress states. In this work, a novel method was proposed to estimate the equivalent strain hardening exponent of anisotropic materials based on an equivalent energy method. By performing extensive finite element (FE) simulations of the spherical indentation on anisotropic materials, dimensionless function was proposed to correlate the strain hardening exponent of anisotropic materials with the indentation imprint parameters. And then, a mathematic expression on the strain hardening exponent of anisotropic materials with the indentation imprint was established to estimate the equivalent strain hardening exponent of anisotropic materials by directly solving this dimensionless function. Additionally, Meyer equation was modified to determine the yield stress of anisotropic materials. The effectiveness and reliability of the new method were verified by the numerical examples and by its application on the TC1M engineering material.展开更多
The spherical indentation test has been successfully applied to inversely derive the tensile properties of small regions in a non-destructive way.Current inverse methods mainly rely on extensive iterative calculations...The spherical indentation test has been successfully applied to inversely derive the tensile properties of small regions in a non-destructive way.Current inverse methods mainly rely on extensive iterative calculations,which yield a considerable computational costs.In this paper,a database method is proposed to determine tensile flow properties from a single indentation force-depth curves to avoid iterative simulations.Firstly,a database that contain numerous indentation force-depth curves is established by inputting varied Ludwic material parameters into the indentation finite elements model.Secondly,for a given experimental indentation curve,a mean square error(MSE)is designated to evaluate the deviation between the experimental curve and each curve in the database.Finally,the true stresses at a series of plastic strain can be acquired by analyzing these deviations.To validate this new method,three different steels,i.e.A508,2.25Cr1 Mo and 316L are selected.Both simulated indentation curves and experimental indentation curves are used as inputs of the database to inversely acquire the flow properties.The result indicates that the pro-posed approach provides impressive accuracy when simulated indentation curves are used,but is less accurate when experimental curves are used.This new method can derive tensile properties in a much higher efficiency compared with traditional inverse method and are therefore more adaptive to engineering application.展开更多
Spherical indentations that rely on original date are analyzed with the physically correct mathematical formula and its integration that take into account the radius over depth changes upon penetration. Linear plots, ...Spherical indentations that rely on original date are analyzed with the physically correct mathematical formula and its integration that take into account the radius over depth changes upon penetration. Linear plots, phase-transition onsets, energies, and pressures are algebraically obtained for germanium, zinc-oxide and gallium-nitride. There are low pressure phase-transitions that correspond to, or are not resolved by hydrostatic anvil onset pressures. This enables the attribution of polymorph structures, by comparing with known structures from pulsed laser deposition or molecular beam epitaxy and twinning. The spherical indentation is the easiest way for the synthesis and further characterization of polymorphs, now available in pure form under diamond calotte and in contact with their corresponding less dense polymorph. The unprecedented results and new possibilities require loading curves from experimental data. These are now easily distinguished from data that are “fitted” to make them concur with widely used unphysical Johnson’s formula for spheres (“<span style="white-space:nowrap;"><em>P</em> = (4/3)<em>h</em><sup>3/2</sup><em>R</em><sup>1/2</sup><em>E</em><sup><span style="white-space:nowrap;">∗</span></sup></span>”) not taking care of the <em>R/h</em> variation. Its challenge is indispensable, because its use involves “fitting equations” for making the data concur. These faked reports (no “experimental” data) provide dangerous false moduli and theories. The fitted spherical indentation reports with radii ranging from 4 to 250 μm are identified for PDMS, GaAs, Al, Si, SiC, MgO, and Steel. The detailed analysis reveals characteristic features.展开更多
To address the problem of conventional approaches for mechanical property determination requiring destructive sampling, which may be unsuitable for in-service structures, the authors proposed a method for determining ...To address the problem of conventional approaches for mechanical property determination requiring destructive sampling, which may be unsuitable for in-service structures, the authors proposed a method for determining the quasi-static fracture toughness and impact absorbed energy of ductile metals from spherical indentation tests (SITs). The stress status and damage mechanism of SIT, mode I fracture, Charpy impact tests, and related tests were frst investigated through fnite element (FE) calculations and scanning electron microscopy (SEM) observations, respectively. It was found that the damage mechanism of SITs is diferent from that of mode I fractures, while mode I fractures and Charpy impact tests share the same damage mechanism. Considering the diference between SIT and mode I fractures, uniaxial tension and pure shear were introduced to correlate SIT with mode I fractures. Based on this, the widely used critical indentation energy (CIE) model for fracture toughness determination using SITs was modifed. The quasi-static fracture toughness determined from the modifed CIE model was used to evaluate the impact absorbed energy using the dynamic fracture toughness and energy for crack initiation. The efectiveness of the newly proposed method was verifed through experiments on four types of steels: Q345R, SA508-3, 18MnMoNbR, and S30408.展开更多
At great depth ratio, two methodologies based on the representative strain were improved to extract mechanical properties of metallic engineering structural materials from P-h curve of an indentation response. The imp...At great depth ratio, two methodologies based on the representative strain were improved to extract mechanical properties of metallic engineering structural materials from P-h curve of an indentation response. The improved aspects include： the com- bination of great ratio h1/R=0.1 and h2/R=0.4 replaced h1/R=0.01 and h2/R=0.06 （Cao＇s method） and h1/R=0.1 and h2/R=0.3 （Ogasawara＇s method）; three types of metallic engineering structural materials with obviously different elastic modulus were dealt with to get their calculation parameters, respectively; a new parameter reflecting the effect of work-hardening exponent n was introduced to get the dimensionless function which is independent of n and a relationship between W/（h3σrS） and E^＊/（σrS） at great depth ratio. By using the results of finite element simulation, the efficiency and accuracy of the improved method have been proved, and it showed that the accuracv of the improved method is much better than the former method.展开更多
The introduction of residual stress during the processing of materials has an important impact on the properties of the materials, so it is important to accurately measure the residual stress of the material. This pap...The introduction of residual stress during the processing of materials has an important impact on the properties of the materials, so it is important to accurately measure the residual stress of the material. This paper established a finite element model of spherical indentation under the action of non-equivalent biaxial residual stress. Then we extracted the full-field accumulation state near the indentation under different stress states from the simulation results and summarized the pile height distribution near the indentation under different stress states. From the simulation, we found that the maximum pile-up height near the indentation point presented a regular trend.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
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.
基金Project(51675431)supported by the National Natural Science Foundation of China
文摘Uniaxial strain hardening exponent is not suitable for describing the strain hardening behaviors of the anisotropic materials, especially when material deforms in the multi-axial stress states. In this work, a novel method was proposed to estimate the equivalent strain hardening exponent of anisotropic materials based on an equivalent energy method. By performing extensive finite element (FE) simulations of the spherical indentation on anisotropic materials, dimensionless function was proposed to correlate the strain hardening exponent of anisotropic materials with the indentation imprint parameters. And then, a mathematic expression on the strain hardening exponent of anisotropic materials with the indentation imprint was established to estimate the equivalent strain hardening exponent of anisotropic materials by directly solving this dimensionless function. Additionally, Meyer equation was modified to determine the yield stress of anisotropic materials. The effectiveness and reliability of the new method were verified by the numerical examples and by its application on the TC1M engineering material.
基金Supported by China Postdoctoral Science Foundation(Grant No.2019M661406).
文摘The spherical indentation test has been successfully applied to inversely derive the tensile properties of small regions in a non-destructive way.Current inverse methods mainly rely on extensive iterative calculations,which yield a considerable computational costs.In this paper,a database method is proposed to determine tensile flow properties from a single indentation force-depth curves to avoid iterative simulations.Firstly,a database that contain numerous indentation force-depth curves is established by inputting varied Ludwic material parameters into the indentation finite elements model.Secondly,for a given experimental indentation curve,a mean square error(MSE)is designated to evaluate the deviation between the experimental curve and each curve in the database.Finally,the true stresses at a series of plastic strain can be acquired by analyzing these deviations.To validate this new method,three different steels,i.e.A508,2.25Cr1 Mo and 316L are selected.Both simulated indentation curves and experimental indentation curves are used as inputs of the database to inversely acquire the flow properties.The result indicates that the pro-posed approach provides impressive accuracy when simulated indentation curves are used,but is less accurate when experimental curves are used.This new method can derive tensile properties in a much higher efficiency compared with traditional inverse method and are therefore more adaptive to engineering application.
文摘Spherical indentations that rely on original date are analyzed with the physically correct mathematical formula and its integration that take into account the radius over depth changes upon penetration. Linear plots, phase-transition onsets, energies, and pressures are algebraically obtained for germanium, zinc-oxide and gallium-nitride. There are low pressure phase-transitions that correspond to, or are not resolved by hydrostatic anvil onset pressures. This enables the attribution of polymorph structures, by comparing with known structures from pulsed laser deposition or molecular beam epitaxy and twinning. The spherical indentation is the easiest way for the synthesis and further characterization of polymorphs, now available in pure form under diamond calotte and in contact with their corresponding less dense polymorph. The unprecedented results and new possibilities require loading curves from experimental data. These are now easily distinguished from data that are “fitted” to make them concur with widely used unphysical Johnson’s formula for spheres (“<span style="white-space:nowrap;"><em>P</em> = (4/3)<em>h</em><sup>3/2</sup><em>R</em><sup>1/2</sup><em>E</em><sup><span style="white-space:nowrap;">∗</span></sup></span>”) not taking care of the <em>R/h</em> variation. Its challenge is indispensable, because its use involves “fitting equations” for making the data concur. These faked reports (no “experimental” data) provide dangerous false moduli and theories. The fitted spherical indentation reports with radii ranging from 4 to 250 μm are identified for PDMS, GaAs, Al, Si, SiC, MgO, and Steel. The detailed analysis reveals characteristic features.
基金Supported by National Natural Science Foundation of China(Grant No.52275154)National Key Research and Development Project of China(Grant No.2016YFF0203005).
文摘To address the problem of conventional approaches for mechanical property determination requiring destructive sampling, which may be unsuitable for in-service structures, the authors proposed a method for determining the quasi-static fracture toughness and impact absorbed energy of ductile metals from spherical indentation tests (SITs). The stress status and damage mechanism of SIT, mode I fracture, Charpy impact tests, and related tests were frst investigated through fnite element (FE) calculations and scanning electron microscopy (SEM) observations, respectively. It was found that the damage mechanism of SITs is diferent from that of mode I fractures, while mode I fractures and Charpy impact tests share the same damage mechanism. Considering the diference between SIT and mode I fractures, uniaxial tension and pure shear were introduced to correlate SIT with mode I fractures. Based on this, the widely used critical indentation energy (CIE) model for fracture toughness determination using SITs was modifed. The quasi-static fracture toughness determined from the modifed CIE model was used to evaluate the impact absorbed energy using the dynamic fracture toughness and energy for crack initiation. The efectiveness of the newly proposed method was verifed through experiments on four types of steels: Q345R, SA508-3, 18MnMoNbR, and S30408.
文摘At great depth ratio, two methodologies based on the representative strain were improved to extract mechanical properties of metallic engineering structural materials from P-h curve of an indentation response. The improved aspects include： the com- bination of great ratio h1/R=0.1 and h2/R=0.4 replaced h1/R=0.01 and h2/R=0.06 （Cao＇s method） and h1/R=0.1 and h2/R=0.3 （Ogasawara＇s method）; three types of metallic engineering structural materials with obviously different elastic modulus were dealt with to get their calculation parameters, respectively; a new parameter reflecting the effect of work-hardening exponent n was introduced to get the dimensionless function which is independent of n and a relationship between W/（h3σrS） and E^＊/（σrS） at great depth ratio. By using the results of finite element simulation, the efficiency and accuracy of the improved method have been proved, and it showed that the accuracv of the improved method is much better than the former method.
文摘The introduction of residual stress during the processing of materials has an important impact on the properties of the materials, so it is important to accurately measure the residual stress of the material. This paper established a finite element model of spherical indentation under the action of non-equivalent biaxial residual stress. Then we extracted the full-field accumulation state near the indentation under different stress states from the simulation results and summarized the pile height distribution near the indentation under different stress states. From the simulation, we found that the maximum pile-up height near the indentation point presented a regular trend.
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.
