Abstract： An effective approach was conducted for estimating fracture toughness using the crack opening displacement （COD） method for plasma enhanced chemical vapor deposition （PECVD） coating materials. For this ...Abstract： An effective approach was conducted for estimating fracture toughness using the crack opening displacement （COD） method for plasma enhanced chemical vapor deposition （PECVD） coating materials. For this evaluation, an elastoplastic analysis was used to estimate critical COD values for single edge notched bending （SENB） specimens. The relationship between fracture toughness （Kic） and critical COD for SENB specimens was obtained. Microstructure of the interface between AleO3-TiO2 composite ceramic coatings and AISI 1045 steel substrates was studied by using scanning electron microscope （SEM）. Chemical compositions were clarified by energy-dispersive X-ray spectroscopy （EDS）. The results show that the interface between of Al203-TiO2 and substrate has mechanical combining. The nanohardness of the coatings can reach 1 200 GPa examined by nanoindentation. The Klc was calculated according to this relationship from critical COD. The bending process produces a significant relationship of COD independent of the axial force applied. Fractographic analysis was conducted to determine the crack length. From the physical analysis of nanoindentation curves, the elastic modulus of 1045/AI2O3-TiO2 is 180 GPa for the 50 μm film. The highest value of fracture toughness for 1045/A1203-TiO2-250 μm is 348 MPa·mv2.展开更多
Seismic prediction of cracks is of great significance in many disciplines,for which the rock physics model is indispensable.However,up to now,multitudinous analytical models focus primarily on the cracked rock with th...Seismic prediction of cracks is of great significance in many disciplines,for which the rock physics model is indispensable.However,up to now,multitudinous analytical models focus primarily on the cracked rock with the isotropic background,while the explicit model for the cracked rock with the anisotropic background is rarely investigated in spite of such case being often encountered in the earth.Hence,we first studied dependences of the crack opening displacement tensors on the crack dip angle in the coordinate systems formed by symmetry planes of the crack and the background anisotropy,respectively,by forty groups of numerical experiments.Based on the conclusion from the experiments,the analytical solution was derived for the effective elastic properties of the rock with the inclined penny-shaped cracks in the transversely isotropic background.Further,we comprehensively analyzed,according to the developed model,effects of the crack dip angle,background anisotropy,filling fluid and crack density on the effective elastic properties of the cracked rock.The analysis results indicate that the dip angle and background anisotropy can significantly either enhance or weaken the anisotropy degrees of the P-and SH-wave velocities,whereas they have relatively small effects on the SV-wave velocity anisotropy.Moreover,the filling fluid can increase the stiffness coefficients related to the compressional modulus by reducing crack compliance parameters,while its effects on shear coefficients depend on the crack dip angle.The increasing crack density reduces velocities of the dry rock,and decreasing rates of the velocities are affected by the crack dip angle.By comparing with exact numerical results and experimental data,it was demonstrated that the proposed model can achieve high-precision estimations of stiffness coefficients.Moreover,the assumption of the weakly anisotropic background results in the consistency between the proposed model and Hudson's published theory for the orthorhombic rock.展开更多
Critical crack tip opening displacement (CTODc) of concrete using experimental and analytical evaluation with seven different compressive strengths ranging from 30 up to 150 MPa was studied based on two types of fract...Critical crack tip opening displacement (CTODc) of concrete using experimental and analytical evaluation with seven different compressive strengths ranging from 30 up to 150 MPa was studied based on two types of fracture tests:three-point bending (TPB) and wedge splitting (WS).In the tests,the values of CTODc were experimentally recorded using a novel technique,in which fiber Bragg grating (FBG) sensors were used,and two traditional techniques,in which strain gauges and clip gauges were deployed.The values of CTODc of tested concrete were also predicted using two existing analytical formulae proposed by JENQ & SHAH and XU,respectively.It is found that the values of CTODc obtained by both experimental measurements and analytical formulae exhibit a negligible variation as the compressive strength of concrete increases,and the test geometry adopted has little impact on the value of CTODc.Regarding the experimental measurement of CTODc,the clip gauge method generally leads to a larger value of CTODc and shows a more significant scatter as compared with the other two methods,while the strain gauge method leads to a slightly lower CTODc as compared with the FBG sensor method.The analytical formula proposed by JENQ and SHAH is found to generally lead to an overestimation,while the analytical formula proposed by XU shows a good accuracy.展开更多
The concept of eigen crack opening displacement （COD） can be defined as the COD of a crack in infinite plate under the tractions acting on the crack surface. By introducing this concept, the eigen COD formulation of...The concept of eigen crack opening displacement （COD） can be defined as the COD of a crack in infinite plate under the tractions acting on the crack surface. By introducing this concept, the eigen COD formulation of boundary integral equation is proposed in this paper, together with the solution procedures for multiple crack problems in plane elasticity. With the proposed approach, the multiple crack problems can be solved with the conventional displacement discontinuity boundary integral equations in an iterative fashion with a small size of system matrix as that in the numerical Green’s function （NGF） approach but without the trouble to determine the complementary solutions since the standard boundary element discretization on the crack surface is no longer required with the proposed approach. Some numerical examples computing the stress intensity factors are presented and compared with those in literature to show the accuracy and the effectiveness of the proposed approach.展开更多
Backfill mining is one of the most important technical means for controlling strata movement and reducing surface subsidence and environmental damage during exploitation of underground coal resources. Ensuring the sta...Backfill mining is one of the most important technical means for controlling strata movement and reducing surface subsidence and environmental damage during exploitation of underground coal resources. Ensuring the stability of the backfill bodies is the primary prerequisite for maintaining the safety of the backfilling working face, and the loading characteristics of backfill are closely related to the deformation and subsidence of the roof. Elastic thin plate model was used to explore the non-uniform subsidence law of the roof, and then the non-uniform distribution characteristics of backfill bodies’ load were revealed. Through a self-developed non-uniform loading device combined with acoustic emission (AE) and digital image correlation (DIC) monitoring technology, the synergistic dynamic evolution law of the bearing capacity, apparent crack, and internal fracture of cemented coal gangue backfills (CCGBs) under loads with different degrees of non-uniformity was deeply explored. The results showed that: 1) The uniaxial compressive strength (UCS) of CCGB increased and then decreased with an increase in the degree of non-uniformity of load (DNL). About 40% of DNL was the inflection point of DNL-UCS curve and when DNL exceeded 40%, the strength decreased in a cliff-like manner;2) A positive correlation was observed between the AE ringing count and UCS during the loading process of the specimen, which was manifested by a higher AE ringing count of the high-strength specimen. 3) Shear cracks gradually increased and failure mode of specimens gradually changed from “X” type dominated by tension cracks to inverted “Y” type dominated by shear cracks with an increase in DNL, and the crack opening displacement at the peak stress decreased and then increased. The crack opening displacement at 40% of the DNL was the smallest. This was consistent with the judgment of crack size based on the AE b-value, i. e., it showed the typical characteristics of “small b-value-large crack and large b-value-small crack”. The research results are of significance for preventing the instability and failure of backfill.展开更多
An accurate crack surface opening displacement formula for edge cracks in finite bodies has been derived,and was subsequently used to develop wide-range closed-form weight functions for edge cracks. The analytical wei...An accurate crack surface opening displacement formula for edge cracks in finite bodies has been derived,and was subsequently used to develop wide-range closed-form weight functions for edge cracks. The analytical weight function is general and can be easily used to determine accurate stress intensity factors and crack surface opening displacements for arbitrarily loaded edge cracks with high efficiency.Examples have been given for problems of edge crack(s)with a number of typical load conditions for illustration.展开更多
In this paper, a mathematical strip-saturation model is proposed for a poled transversely isotropic piezoelectric plate weakened by two impermeable unequal-collinear hairline straight cracks. Remotely applied in-plane...In this paper, a mathematical strip-saturation model is proposed for a poled transversely isotropic piezoelectric plate weakened by two impermeable unequal-collinear hairline straight cracks. Remotely applied in-plane unidirectional electromechanical loads open the cracks in mode-I such that the saturation zone developed at the interior tips of cracks gets coalesced. The developed saturation zones are arrested by distributing over their rims in-plane normal cohesive electrical displacement. The problem is solved using the Stroh formalism and the complex variable technique. The expressions are derived for the stress intensity factors （SIFs）, the lengths of the saturation zones developed, the crack opening displacement （COD）, and the energy release rate. An illustrative numerical case study is presented for the poled PZT-5H ceramic to investigate the effect of prescribed electromechanical loads on parameters affecting crack arrest. Also, the effect of different lengths of cracks on the SIFs and the local energy release rate （LERR） has been studied. The results obtained are graphically presented and analyzed.展开更多
The effect of pearlite interlamellar spacing(d)from 0.31 to 0.77 μm of T8 steel on fatigue crack propagation near threshold has been investigated at different stress ratios(R).The closure stress intensity factor(K_(c...The effect of pearlite interlamellar spacing(d)from 0.31 to 0.77 μm of T8 steel on fatigue crack propagation near threshold has been investigated at different stress ratios(R).The closure stress intensity factor(K_(cl)),the threshold value(ΔK_(th))and crack tip opening dis- placement range(ΔCOD)were measured.The results show that pearlite interlamellar spac- ing in this range has no effect on K_(cl),but has effect on the threshold value in low stress ratio. The threshold value is higher for materials with larger interlamellar spacing.No matter what the stress ratio is,during the propagation near threshold,the propagation rate will be the same,provieded the crack tip opening displacement range is the same. Metallurgical examinations were also carried out to show that the crack propagation path is sensitive to mierostructure.The crack always propagates along either boundary of pearlite colony or ferrite lamellar in pearlite.展开更多
By using Fourier transformation the boundary problem of periodical interfacial cracks in anisotropic elastoplastic bimaterial was transformed into a set of dual integral equations and then it was further reduced by me...By using Fourier transformation the boundary problem of periodical interfacial cracks in anisotropic elastoplastic bimaterial was transformed into a set of dual integral equations and then it was further reduced by means of definite integral transformation into a group of singular equations. Closed form of its solution was obtained and three corresponding problems of isotropic bimaterial, of a single anisotropic material and of a bimaterial of isotropy- anisotropy were treated as the specific cases. The plastic zone length of the crack tip and crack openning displacement ( COD) decline as the smaller yield limit of the two bonded materials rises, and they were also determined by crack length and the space between two neighboring cracks . In addition , COD also relates it with moduli of the materials .展开更多
基金Project supported by the National Research Foundation of Korea(2011-0030804)the Korea Research Foundation(KRF2009-0076450)funded by the Korea Government(MEST)
文摘Abstract： An effective approach was conducted for estimating fracture toughness using the crack opening displacement （COD） method for plasma enhanced chemical vapor deposition （PECVD） coating materials. For this evaluation, an elastoplastic analysis was used to estimate critical COD values for single edge notched bending （SENB） specimens. The relationship between fracture toughness （Kic） and critical COD for SENB specimens was obtained. Microstructure of the interface between AleO3-TiO2 composite ceramic coatings and AISI 1045 steel substrates was studied by using scanning electron microscope （SEM）. Chemical compositions were clarified by energy-dispersive X-ray spectroscopy （EDS）. The results show that the interface between of Al203-TiO2 and substrate has mechanical combining. The nanohardness of the coatings can reach 1 200 GPa examined by nanoindentation. The Klc was calculated according to this relationship from critical COD. The bending process produces a significant relationship of COD independent of the axial force applied. Fractographic analysis was conducted to determine the crack length. From the physical analysis of nanoindentation curves, the elastic modulus of 1045/AI2O3-TiO2 is 180 GPa for the 50 μm film. The highest value of fracture toughness for 1045/A1203-TiO2-250 μm is 348 MPa·mv2.
基金We would like to acknowledge all the reviewers and editors and the sponsorship of National Natural Science Foundation of China(42030103)the Marine S&T Fund of Shandong Province for Pilot National Laboratory for Marine Science and Technology(Qingdao)(2021QNLM020001-6)the Laoshan National Laboratory of Science and Technology Foundation(LSKJ202203400).
文摘Seismic prediction of cracks is of great significance in many disciplines,for which the rock physics model is indispensable.However,up to now,multitudinous analytical models focus primarily on the cracked rock with the isotropic background,while the explicit model for the cracked rock with the anisotropic background is rarely investigated in spite of such case being often encountered in the earth.Hence,we first studied dependences of the crack opening displacement tensors on the crack dip angle in the coordinate systems formed by symmetry planes of the crack and the background anisotropy,respectively,by forty groups of numerical experiments.Based on the conclusion from the experiments,the analytical solution was derived for the effective elastic properties of the rock with the inclined penny-shaped cracks in the transversely isotropic background.Further,we comprehensively analyzed,according to the developed model,effects of the crack dip angle,background anisotropy,filling fluid and crack density on the effective elastic properties of the cracked rock.The analysis results indicate that the dip angle and background anisotropy can significantly either enhance or weaken the anisotropy degrees of the P-and SH-wave velocities,whereas they have relatively small effects on the SV-wave velocity anisotropy.Moreover,the filling fluid can increase the stiffness coefficients related to the compressional modulus by reducing crack compliance parameters,while its effects on shear coefficients depend on the crack dip angle.The increasing crack density reduces velocities of the dry rock,and decreasing rates of the velocities are affected by the crack dip angle.By comparing with exact numerical results and experimental data,it was demonstrated that the proposed model can achieve high-precision estimations of stiffness coefficients.Moreover,the assumption of the weakly anisotropic background results in the consistency between the proposed model and Hudson's published theory for the orthorhombic rock.
基金Project(50438010) supported by the Key Program of the National Natural Science Foundation of ChinaProject(JGZXJJ2006-13) supported by the Research and Application Programs of Key Technologies for Major Constructions in the South-North Water Transfer Project Construction in China
文摘Critical crack tip opening displacement (CTODc) of concrete using experimental and analytical evaluation with seven different compressive strengths ranging from 30 up to 150 MPa was studied based on two types of fracture tests:three-point bending (TPB) and wedge splitting (WS).In the tests,the values of CTODc were experimentally recorded using a novel technique,in which fiber Bragg grating (FBG) sensors were used,and two traditional techniques,in which strain gauges and clip gauges were deployed.The values of CTODc of tested concrete were also predicted using two existing analytical formulae proposed by JENQ & SHAH and XU,respectively.It is found that the values of CTODc obtained by both experimental measurements and analytical formulae exhibit a negligible variation as the compressive strength of concrete increases,and the test geometry adopted has little impact on the value of CTODc.Regarding the experimental measurement of CTODc,the clip gauge method generally leads to a larger value of CTODc and shows a more significant scatter as compared with the other two methods,while the strain gauge method leads to a slightly lower CTODc as compared with the FBG sensor method.The analytical formula proposed by JENQ and SHAH is found to generally lead to an overestimation,while the analytical formula proposed by XU shows a good accuracy.
基金supported by the National Natural Science Foundation of China (Grant No.10972131)the Graduate Innovation Foundation of Shanghai University (Grant No.SHUCX102351)
文摘The concept of eigen crack opening displacement （COD） can be defined as the COD of a crack in infinite plate under the tractions acting on the crack surface. By introducing this concept, the eigen COD formulation of boundary integral equation is proposed in this paper, together with the solution procedures for multiple crack problems in plane elasticity. With the proposed approach, the multiple crack problems can be solved with the conventional displacement discontinuity boundary integral equations in an iterative fashion with a small size of system matrix as that in the numerical Green’s function （NGF） approach but without the trouble to determine the complementary solutions since the standard boundary element discretization on the crack surface is no longer required with the proposed approach. Some numerical examples computing the stress intensity factors are presented and compared with those in literature to show the accuracy and the effectiveness of the proposed approach.
基金Project(51925402) supported by the National Natural Science Foundation for Distinguished Young Scholars of ChinaProject(202303021211060) supported by the Natural Science Research General Program for Shanxi Provincial Basic Research Program,China+1 种基金Project(U22A20169) supported by the Joint Fund Project of National Natural Science Foundation of ChinaProjects(2021SX-TD001, 2021SX-TD002) supported by the Shanxi-Zheda Institute of Advanced Materials and Chemical Engineering,China。
文摘Backfill mining is one of the most important technical means for controlling strata movement and reducing surface subsidence and environmental damage during exploitation of underground coal resources. Ensuring the stability of the backfill bodies is the primary prerequisite for maintaining the safety of the backfilling working face, and the loading characteristics of backfill are closely related to the deformation and subsidence of the roof. Elastic thin plate model was used to explore the non-uniform subsidence law of the roof, and then the non-uniform distribution characteristics of backfill bodies’ load were revealed. Through a self-developed non-uniform loading device combined with acoustic emission (AE) and digital image correlation (DIC) monitoring technology, the synergistic dynamic evolution law of the bearing capacity, apparent crack, and internal fracture of cemented coal gangue backfills (CCGBs) under loads with different degrees of non-uniformity was deeply explored. The results showed that: 1) The uniaxial compressive strength (UCS) of CCGB increased and then decreased with an increase in the degree of non-uniformity of load (DNL). About 40% of DNL was the inflection point of DNL-UCS curve and when DNL exceeded 40%, the strength decreased in a cliff-like manner;2) A positive correlation was observed between the AE ringing count and UCS during the loading process of the specimen, which was manifested by a higher AE ringing count of the high-strength specimen. 3) Shear cracks gradually increased and failure mode of specimens gradually changed from “X” type dominated by tension cracks to inverted “Y” type dominated by shear cracks with an increase in DNL, and the crack opening displacement at the peak stress decreased and then increased. The crack opening displacement at 40% of the DNL was the smallest. This was consistent with the judgment of crack size based on the AE b-value, i. e., it showed the typical characteristics of “small b-value-large crack and large b-value-small crack”. The research results are of significance for preventing the instability and failure of backfill.
文摘An accurate crack surface opening displacement formula for edge cracks in finite bodies has been derived,and was subsequently used to develop wide-range closed-form weight functions for edge cracks. The analytical weight function is general and can be easily used to determine accurate stress intensity factors and crack surface opening displacements for arbitrarily loaded edge cracks with high efficiency.Examples have been given for problems of edge crack(s)with a number of typical load conditions for illustration.
基金ministry of Human Resource Development for the financial support
文摘In this paper, a mathematical strip-saturation model is proposed for a poled transversely isotropic piezoelectric plate weakened by two impermeable unequal-collinear hairline straight cracks. Remotely applied in-plane unidirectional electromechanical loads open the cracks in mode-I such that the saturation zone developed at the interior tips of cracks gets coalesced. The developed saturation zones are arrested by distributing over their rims in-plane normal cohesive electrical displacement. The problem is solved using the Stroh formalism and the complex variable technique. The expressions are derived for the stress intensity factors （SIFs）, the lengths of the saturation zones developed, the crack opening displacement （COD）, and the energy release rate. An illustrative numerical case study is presented for the poled PZT-5H ceramic to investigate the effect of prescribed electromechanical loads on parameters affecting crack arrest. Also, the effect of different lengths of cracks on the SIFs and the local energy release rate （LERR） has been studied. The results obtained are graphically presented and analyzed.
文摘The effect of pearlite interlamellar spacing(d)from 0.31 to 0.77 μm of T8 steel on fatigue crack propagation near threshold has been investigated at different stress ratios(R).The closure stress intensity factor(K_(cl)),the threshold value(ΔK_(th))and crack tip opening dis- placement range(ΔCOD)were measured.The results show that pearlite interlamellar spac- ing in this range has no effect on K_(cl),but has effect on the threshold value in low stress ratio. The threshold value is higher for materials with larger interlamellar spacing.No matter what the stress ratio is,during the propagation near threshold,the propagation rate will be the same,provieded the crack tip opening displacement range is the same. Metallurgical examinations were also carried out to show that the crack propagation path is sensitive to mierostructure.The crack always propagates along either boundary of pearlite colony or ferrite lamellar in pearlite.
基金the National Natural Science Foundation of China (19872076) the Postdoctoral Science Foundation of China (00-2001)the National Natural Science Foundation of China for Out-sanding Young Scientists (19925209)
文摘By using Fourier transformation the boundary problem of periodical interfacial cracks in anisotropic elastoplastic bimaterial was transformed into a set of dual integral equations and then it was further reduced by means of definite integral transformation into a group of singular equations. Closed form of its solution was obtained and three corresponding problems of isotropic bimaterial, of a single anisotropic material and of a bimaterial of isotropy- anisotropy were treated as the specific cases. The plastic zone length of the crack tip and crack openning displacement ( COD) decline as the smaller yield limit of the two bonded materials rises, and they were also determined by crack length and the space between two neighboring cracks . In addition , COD also relates it with moduli of the materials .
