In this paper, the effects of the open crack on the static and dynamic pull-in volt- ages of an electrostatically actuated fixed-fixed and cantilever micro-beam are investigated. By presenting a mathematical modeling,...In this paper, the effects of the open crack on the static and dynamic pull-in volt- ages of an electrostatically actuated fixed-fixed and cantilever micro-beam are investigated. By presenting a mathematical modeling, the governing static and dynamic equations are solved by SSLM and Galerkin-based Reduced Order Model, respectively. Then, each single-side open crack in the micro-beam is modeled by a massless rotational spring and the cracked mode shapes and corresponding natural frequencies are calculated by considering the boundary and patching con- ditions and using transfer matrix methods. Finally, the effects of the crack depth ratio, crack position and crack number on the pull-in voltage of the micro-beams are studied. It is shown that beside the residual stresses created in the machining process, the crack（s） can be initiated, growth and consequently change the pull-in voltage of the system by decreasing the natural frequencies. The results show that the crack position is effective beside the crack depth ratio in decreasing the pull-in voltage. Also it is shown that in the fixed-fixed micro-beam there are several points for the crack location in which, the pull-in voltage is extremum.展开更多
The commonly used method for estimating crack opening displacement(COD)is based on analytical models derived from strain transferring.However,when large background noise exists in distributed fiber optic sensing(DFOS)...The commonly used method for estimating crack opening displacement(COD)is based on analytical models derived from strain transferring.However,when large background noise exists in distributed fiber optic sensing(DFOS)data,estimating COD through an analytical model is very difficult even if the DFOS data have been denoised.To address this challenge,this study proposes a machine learning(ML)-based methodology to complete rock's COD estimation from establishment of a dataset with one-to-one correspondence between strain sequence and COD to the optimization of ML models.The Bayesian optimization is used via the Hyperopt Python library to determine the appropriate hyper-parameters of four ML models.To ensure that the best hyper-parameters will not be missing,the configuration space in Hyperopt is specified by probability distribution.The four models are trained using DFOS data with minimal noise while being examined on datasets with different noise levels to test their anti-noise robustness.The proposed models are compared each other in terms of goodness of fit and mean squared error.The results show that the Bayesian optimization-based random forest is promising to estimate the COD of rock using noisy DFOS data.展开更多
Accurate determination of crack opening stress is of central importance to fatigue crack growth analysis and life prediction based on the crack-closure model. This paper studies the crack opening behavior for center- ...Accurate determination of crack opening stress is of central importance to fatigue crack growth analysis and life prediction based on the crack-closure model. This paper studies the crack opening behavior for center- and edge-crack tension specimens. It is found that the crack opening stress is affected by the crack tip element. By taking the crack tip element into account, a modified crack opening stress equation is given for the center-crack tension specimen. Crack surface displace- ment equations for an edge crack in a semi-infinite plate under remote uniform tension and partially distributed pressure are derived by using the weight function method. Based on these displacements, a crack opening stress equation for an edge crack in a semi-infinite plate under uniform tension has been developed. The study shows that the crack opening stress is geometry-dependent, and the weight function method provides an effective and reliable tool to deal with such geometry depen- dence.展开更多
This paper presents a numerical analysis of a material test program investigating the crack opening properties of fibre reinforced concrete （FRC） round determinate panels （RDP）. The objective of this research is t...This paper presents a numerical analysis of a material test program investigating the crack opening properties of fibre reinforced concrete （FRC） round determinate panels （RDP）. The objective of this research is to set up a modified RDP test method to improve the current ASTM C1550 test method for FRC and fibre reinforced shotcrete （FRS） composite. By this test method, light small-diameter panels are applied and more crack information can be obtained by a new rotation angle measuring technique. It is shown that this modified test method can be used to effectively evaluate the crack opening resistance of FRC. The finite element analysis was then performed to clarify the crack propaga- tions and failure mode of FRC RDP panels. It helps establish a reasonable theoretical method to predict the structural response of RDP. combining with this modified testing technioue.展开更多
Fine and coarse aggregates play an important role in the fracture of concrete. However, quantitative information available on the effect of the coarse aggregate size on the fracture properties of concrete is still lim...Fine and coarse aggregates play an important role in the fracture of concrete. However, quantitative information available on the effect of the coarse aggregate size on the fracture properties of concrete is still limited. In the present paper, the effect of coarse aggregate size （single grade of 5～10, 10～16, 16～20 and 20～25 mm） on stress-crack opening （σ-w） relation in normal and high strength concretes （compressive strength of 40 and 80 MPa, respectively） was studied. The investigation was based on three-point bending tests implemented by fictitious crack analysis. The result shows that coarse aggregate size and cement matrix strength significantly influence the shape of σ-w curve. For a given total aggregate content, in normal strength concrete, smaller size of aggregate leads to a high tensile strength and a sharp stress drop after the peak stress. The smaller the coarse aggregate, the steeper the σ-w curve. By contrast, in high strength concrete, the effect of aggregate size on σ-w relation almost vanishes. A similar σ-w relation is obtained for the concrete except for the case of 20～25 mm coarse aggregate size. The stress drop after the peak stress is more significant for high strength concrete than that for normal strength concrete. Meanwhile, the smaller the coarse aggregate size, the higher the flexural strength. Fracture energy and characteristic length increase with increasing coarse aggregate size in both normal and high strength concretes.展开更多
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
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
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
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
Key components of large structures in aeronautics industry are required to be made light and have long enough fatigue lives.It is of vital importance to estimate the fatigue life of these structures accurately.Since t...Key components of large structures in aeronautics industry are required to be made light and have long enough fatigue lives.It is of vital importance to estimate the fatigue life of these structures accurately.Since the FCG process is affected by various factors,no universal model exists due to the complexity of the mechanisms.Most of the existing models are obtained by fitting the experimental data and could hardly describe the integrative effect of most existing factors simultaneously.In order to account for the integrative effect of specimen parameters,material property and loading conditions on FCG process,a new model named integrative influence factor model（IIF） is proposed based on the plasticity-induced crack closure theory.Accordingly to the predictions of crack opening ratio（γ） and effective stress intensity factor range ratio（U） with different material under various loading conditions,predictions of γ and U by the IIF model are completely identical to the theoretical results from the plane stress state to the plane strain state when Poisson＇s ratio equals 1/3.When Poisson＇s ratio equals 0.3,predictions of γ and U by the IIF model are larger than the predictions by the existing model,and more close to the theoretical results.In addition,it describes the influence of R ratios on γ and U effectively in the whole region from-1.0 to 1.0.Moreover,several sets of test data of FCG rates in 5 kinds of aluminum alloys with various specimen thicknesses under different loading conditions are used to validate the IIF model,most of the test data are situated on the predicted curves or between the two curves that represent the specimen with different thicknesses under the same stress ratio.Some of the test data slightly departure from the predictions by the IIF model due to the surface roughness and errors in measurement.Besides,based on the analysis of the physical rule of crack opening ratios,a relative thickness of specimen is defined to describe the influence of material property,specimen thickness and so forth on FCG characteristics conveniently.In conclusion,the relative thickness of specimen simplifies the expression of FCG characteristic and provides a general parameter to analyze the fatigue characteristics of different materials with various thicknesses under different loading conditions.The IIF model describes the integrative effect of existing influence factors explicitly and quantitatively,and provides a helpful tool for fatigue property estimation of practical component and experiment design.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
Based on a digital image correlation（DIC）method with the measurements of a high speed crack＇s displacement and strain fields,a technique to accurately and automatically locate its crack tip has been developed.The c...Based on a digital image correlation（DIC）method with the measurements of a high speed crack＇s displacement and strain fields,a technique to accurately and automatically locate its crack tip has been developed.The crack tip is identified by finding the abrupt jump on the opening（or dislocation）curve of a point on the trace of the crack propagation,while the opening is measured through a virtual extensometer technique and the abrupt jump is identified by finding the peak on the curve.The method was verified using a specially designed experiment and applied to measure the critical crack tip opening angle of a rock sample.Because the involvement of analytical models has been avoided and then the good performance could be ensured for low resolution speckle images,this technique is expected to be very useful in the quantitative study of high speed cracks in experiments using high speed cameras.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
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
This paper presents a direct traction boundary integral equation method(DTBIEM)for two-dimensional crack problems of materials.The traction boundary integral equation was collocated on both the external boundary and e...This paper presents a direct traction boundary integral equation method(DTBIEM)for two-dimensional crack problems of materials.The traction boundary integral equation was collocated on both the external boundary and either side of the crack surfaces.The displacements and tractions were used as unknowns on the external boundary,while the relative crack opening displacement(RCOD)was chosen as unknowns on either side of crack surfaces to keep the single-domain merit.Only one side of the crack surfaces was concerned and needed to be discretized,thus the proposed method resulted in a smaller system of algebraic equations compared with the dual boundary element method(DBEM).A new set of crack-tip shape functions was constructed to represent the strain field singularity exactly,and the SIFs were evaluated by the extrapolation of the RCOD.Numerical examples for both straight and curved cracks are given to validate the accuracy and efficiency of the presented method.展开更多
Focused on the girth weld of a φ762 x 28.6 mm （X65） offshore UOE pipe, the fracture toughness properties at different weld joint positions were tested. Meanwhile,the largest size of different cracks under service c...Focused on the girth weld of a φ762 x 28.6 mm （X65） offshore UOE pipe, the fracture toughness properties at different weld joint positions were tested. Meanwhile,the largest size of different cracks under service condition was calculated by using CRACKWISE. The service life of the UOE pipe with postulated crack-like flaws was calculated by considering various fatigue factors, such as vibrations caused by ocean current and fluctuations of inner pressure. The assessment process and results can be used to direct the repair of weld flaws laid in pipes or to assess the reliability of in-serving pipes.展开更多
A newly developed approach without crack surface discretization for modeling 2D solids with large number of cracks in linear elastic fracture mechanics is proposed with the eigen crack opening displacement (COD) bound...A newly developed approach without crack surface discretization for modeling 2D solids with large number of cracks in linear elastic fracture mechanics is proposed with the eigen crack opening displacement (COD) boundary integral equations in this paper. The eigen COD is defined as a crack in an infinite domain under fictitious traction acting on the crack surface. Respect to the computational accuracies and efficiencies, the multiple crack problems in finite and infinite plates are solved and compared numerically using three different kinds of boundary integral equations (BIEs): 1) the dual BIEs require crack surface discretization;2) the BIEs with numerical Green’s functions (NGF) without crack surface discretization, but have to solve a complementary matrix;3) the eigen crack opening displacement (COD) BIEs in the present paper. With the concept of eigen COD, the multiple crack problems can be solved by using a conventional displacement discontinuity boundary integral equation in an iterative fashion with a small size of system matrix as that in the NGF approach, but without troubles to determine the complementary matrix. Solution of the stress intensity factors of multiple crack problems is solved and compared in some numerical examples using the above three computational algorithms. Numerical results clearly demonstrate the numerical models of eigen COD BIEs have much higher efficiency, providing a newly numerical technique for multiple crack problems. Not only the accuracy and efficiency of computation can be guaranteed, but also the overall properties and local details can be obtained. In conclusion, the numerical models of eigen COD BIEs realize the simulations for multiple crack problems with large quantity of cracks.展开更多
In the present paper,three dimensional analyses of some general constraint parameters and fracture parameters near the crack tip of Mode I CT specimens in two different thicknesses are carried out by employing ADINA p...In the present paper,three dimensional analyses of some general constraint parameters and fracture parameters near the crack tip of Mode I CT specimens in two different thicknesses are carried out by employing ADINA program.The results reveal that the constraints along the thickness direction are obviously separated into two parts:the keeping similar high constraint field(Z_(1))and rapid reducing constraints one(Z_(2)).The two fields are experimentally confiremed to correspond to the smooth region and the shear lip on the fracture face respectively.So the three dimensional stress structure of Mode I specimens can be derived through discussing the two fields respectively.The distribution of the Crack Tip Opening Displacement(CTOD)along the thickness direction and the three dimensional distribution of the void growth ratio(V_(g))near the crack tip are also obtained.The two fracture parameters are in similar trends along the thickness direction,and both of them can reflect the effect of thickness and that of the loading level to a certain degree.展开更多
文摘In this paper, the effects of the open crack on the static and dynamic pull-in volt- ages of an electrostatically actuated fixed-fixed and cantilever micro-beam are investigated. By presenting a mathematical modeling, the governing static and dynamic equations are solved by SSLM and Galerkin-based Reduced Order Model, respectively. Then, each single-side open crack in the micro-beam is modeled by a massless rotational spring and the cracked mode shapes and corresponding natural frequencies are calculated by considering the boundary and patching con- ditions and using transfer matrix methods. Finally, the effects of the crack depth ratio, crack position and crack number on the pull-in voltage of the micro-beams are studied. It is shown that beside the residual stresses created in the machining process, the crack（s） can be initiated, growth and consequently change the pull-in voltage of the system by decreasing the natural frequencies. The results show that the crack position is effective beside the crack depth ratio in decreasing the pull-in voltage. Also it is shown that in the fixed-fixed micro-beam there are several points for the crack location in which, the pull-in voltage is extremum.
基金The Young Scientists Fund of the National Natural Science Foundation of China(Grant No.42407250)the Fund from Research Centre for Resources Engineering towards Carbon Neutrality(RCRE)of The Hong Kong Polytechnic University(Grant No.No.1-BBEM)the Fund from Natural Science Foundation of Jiangsu Province(Grant No.BK20241211)。
文摘The commonly used method for estimating crack opening displacement(COD)is based on analytical models derived from strain transferring.However,when large background noise exists in distributed fiber optic sensing(DFOS)data,estimating COD through an analytical model is very difficult even if the DFOS data have been denoised.To address this challenge,this study proposes a machine learning(ML)-based methodology to complete rock's COD estimation from establishment of a dataset with one-to-one correspondence between strain sequence and COD to the optimization of ML models.The Bayesian optimization is used via the Hyperopt Python library to determine the appropriate hyper-parameters of four ML models.To ensure that the best hyper-parameters will not be missing,the configuration space in Hyperopt is specified by probability distribution.The four models are trained using DFOS data with minimal noise while being examined on datasets with different noise levels to test their anti-noise robustness.The proposed models are compared each other in terms of goodness of fit and mean squared error.The results show that the Bayesian optimization-based random forest is promising to estimate the COD of rock using noisy DFOS data.
文摘Accurate determination of crack opening stress is of central importance to fatigue crack growth analysis and life prediction based on the crack-closure model. This paper studies the crack opening behavior for center- and edge-crack tension specimens. It is found that the crack opening stress is affected by the crack tip element. By taking the crack tip element into account, a modified crack opening stress equation is given for the center-crack tension specimen. Crack surface displace- ment equations for an edge crack in a semi-infinite plate under remote uniform tension and partially distributed pressure are derived by using the weight function method. Based on these displacements, a crack opening stress equation for an edge crack in a semi-infinite plate under uniform tension has been developed. The study shows that the crack opening stress is geometry-dependent, and the weight function method provides an effective and reliable tool to deal with such geometry depen- dence.
基金Supported by the National Natural Science Foundation of China (50708084)Wuhan Chenguang Science and Technology Project for Young Experts (20035002016-30)
文摘This paper presents a numerical analysis of a material test program investigating the crack opening properties of fibre reinforced concrete （FRC） round determinate panels （RDP）. The objective of this research is to set up a modified RDP test method to improve the current ASTM C1550 test method for FRC and fibre reinforced shotcrete （FRS） composite. By this test method, light small-diameter panels are applied and more crack information can be obtained by a new rotation angle measuring technique. It is shown that this modified test method can be used to effectively evaluate the crack opening resistance of FRC. The finite element analysis was then performed to clarify the crack propaga- tions and failure mode of FRC RDP panels. It helps establish a reasonable theoretical method to predict the structural response of RDP. combining with this modified testing technioue.
文摘Fine and coarse aggregates play an important role in the fracture of concrete. However, quantitative information available on the effect of the coarse aggregate size on the fracture properties of concrete is still limited. In the present paper, the effect of coarse aggregate size （single grade of 5～10, 10～16, 16～20 and 20～25 mm） on stress-crack opening （σ-w） relation in normal and high strength concretes （compressive strength of 40 and 80 MPa, respectively） was studied. The investigation was based on three-point bending tests implemented by fictitious crack analysis. The result shows that coarse aggregate size and cement matrix strength significantly influence the shape of σ-w curve. For a given total aggregate content, in normal strength concrete, smaller size of aggregate leads to a high tensile strength and a sharp stress drop after the peak stress. The smaller the coarse aggregate, the steeper the σ-w curve. By contrast, in high strength concrete, the effect of aggregate size on σ-w relation almost vanishes. A similar σ-w relation is obtained for the concrete except for the case of 20～25 mm coarse aggregate size. The stress drop after the peak stress is more significant for high strength concrete than that for normal strength concrete. Meanwhile, the smaller the coarse aggregate size, the higher the flexural strength. Fracture energy and characteristic length increase with increasing coarse aggregate size in both normal and high strength concretes.
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.
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supported by Military Pre-study Project of General Armament Department of China (Grant No. YG060101C)
文摘Key components of large structures in aeronautics industry are required to be made light and have long enough fatigue lives.It is of vital importance to estimate the fatigue life of these structures accurately.Since the FCG process is affected by various factors,no universal model exists due to the complexity of the mechanisms.Most of the existing models are obtained by fitting the experimental data and could hardly describe the integrative effect of most existing factors simultaneously.In order to account for the integrative effect of specimen parameters,material property and loading conditions on FCG process,a new model named integrative influence factor model（IIF） is proposed based on the plasticity-induced crack closure theory.Accordingly to the predictions of crack opening ratio（γ） and effective stress intensity factor range ratio（U） with different material under various loading conditions,predictions of γ and U by the IIF model are completely identical to the theoretical results from the plane stress state to the plane strain state when Poisson＇s ratio equals 1/3.When Poisson＇s ratio equals 0.3,predictions of γ and U by the IIF model are larger than the predictions by the existing model,and more close to the theoretical results.In addition,it describes the influence of R ratios on γ and U effectively in the whole region from-1.0 to 1.0.Moreover,several sets of test data of FCG rates in 5 kinds of aluminum alloys with various specimen thicknesses under different loading conditions are used to validate the IIF model,most of the test data are situated on the predicted curves or between the two curves that represent the specimen with different thicknesses under the same stress ratio.Some of the test data slightly departure from the predictions by the IIF model due to the surface roughness and errors in measurement.Besides,based on the analysis of the physical rule of crack opening ratios,a relative thickness of specimen is defined to describe the influence of material property,specimen thickness and so forth on FCG characteristics conveniently.In conclusion,the relative thickness of specimen simplifies the expression of FCG characteristic and provides a general parameter to analyze the fatigue characteristics of different materials with various thicknesses under different loading conditions.The IIF model describes the integrative effect of existing influence factors explicitly and quantitatively,and provides a helpful tool for fatigue property estimation of practical component and experiment design.
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.
基金Supported by the National Natural Science Foundation of China(11172039,11402023)the Fundamental Research Funding of BIT(20120142021)the State Key Laboratory of Earthquake Dynamics(LED2011B03)
文摘Based on a digital image correlation（DIC）method with the measurements of a high speed crack＇s displacement and strain fields,a technique to accurately and automatically locate its crack tip has been developed.The crack tip is identified by finding the abrupt jump on the opening（or dislocation）curve of a point on the trace of the crack propagation,while the opening is measured through a virtual extensometer technique and the abrupt jump is identified by finding the peak on the curve.The method was verified using a specially designed experiment and applied to measure the critical crack tip opening angle of a rock sample.Because the involvement of analytical models has been avoided and then the good performance could be ensured for low resolution speckle images,this technique is expected to be very useful in the quantitative study of high speed cracks in experiments using high speed cameras.
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 .
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This work was supported by The National Key R&D Program of China(Grant No.2017YFC0804601)the National Natural Science Foundation of China(No.51741410)Open Research Fund of State Key Laboratory of Geomechanics and Geotechnical Engineering,Institute of Rock and Soil Mechanics,Chinese Academy of Sciences(Grant No.Z017017).
文摘This paper presents a direct traction boundary integral equation method(DTBIEM)for two-dimensional crack problems of materials.The traction boundary integral equation was collocated on both the external boundary and either side of the crack surfaces.The displacements and tractions were used as unknowns on the external boundary,while the relative crack opening displacement(RCOD)was chosen as unknowns on either side of crack surfaces to keep the single-domain merit.Only one side of the crack surfaces was concerned and needed to be discretized,thus the proposed method resulted in a smaller system of algebraic equations compared with the dual boundary element method(DBEM).A new set of crack-tip shape functions was constructed to represent the strain field singularity exactly,and the SIFs were evaluated by the extrapolation of the RCOD.Numerical examples for both straight and curved cracks are given to validate the accuracy and efficiency of the presented method.
文摘Focused on the girth weld of a φ762 x 28.6 mm （X65） offshore UOE pipe, the fracture toughness properties at different weld joint positions were tested. Meanwhile,the largest size of different cracks under service condition was calculated by using CRACKWISE. The service life of the UOE pipe with postulated crack-like flaws was calculated by considering various fatigue factors, such as vibrations caused by ocean current and fluctuations of inner pressure. The assessment process and results can be used to direct the repair of weld flaws laid in pipes or to assess the reliability of in-serving pipes.
文摘A newly developed approach without crack surface discretization for modeling 2D solids with large number of cracks in linear elastic fracture mechanics is proposed with the eigen crack opening displacement (COD) boundary integral equations in this paper. The eigen COD is defined as a crack in an infinite domain under fictitious traction acting on the crack surface. Respect to the computational accuracies and efficiencies, the multiple crack problems in finite and infinite plates are solved and compared numerically using three different kinds of boundary integral equations (BIEs): 1) the dual BIEs require crack surface discretization;2) the BIEs with numerical Green’s functions (NGF) without crack surface discretization, but have to solve a complementary matrix;3) the eigen crack opening displacement (COD) BIEs in the present paper. With the concept of eigen COD, the multiple crack problems can be solved by using a conventional displacement discontinuity boundary integral equation in an iterative fashion with a small size of system matrix as that in the NGF approach, but without troubles to determine the complementary matrix. Solution of the stress intensity factors of multiple crack problems is solved and compared in some numerical examples using the above three computational algorithms. Numerical results clearly demonstrate the numerical models of eigen COD BIEs have much higher efficiency, providing a newly numerical technique for multiple crack problems. Not only the accuracy and efficiency of computation can be guaranteed, but also the overall properties and local details can be obtained. In conclusion, the numerical models of eigen COD BIEs realize the simulations for multiple crack problems with large quantity of cracks.
文摘In the present paper,three dimensional analyses of some general constraint parameters and fracture parameters near the crack tip of Mode I CT specimens in two different thicknesses are carried out by employing ADINA program.The results reveal that the constraints along the thickness direction are obviously separated into two parts:the keeping similar high constraint field(Z_(1))and rapid reducing constraints one(Z_(2)).The two fields are experimentally confiremed to correspond to the smooth region and the shear lip on the fracture face respectively.So the three dimensional stress structure of Mode I specimens can be derived through discussing the two fields respectively.The distribution of the Crack Tip Opening Displacement(CTOD)along the thickness direction and the three dimensional distribution of the void growth ratio(V_(g))near the crack tip are also obtained.The two fracture parameters are in similar trends along the thickness direction,and both of them can reflect the effect of thickness and that of the loading level to a certain degree.
