THE THREE-DIMENSIONAL STRESS INTENSITY FACTOR UNDER MOVING LOADS ON THE CRACK FACES

The dynamic stress intensity factor history for a half plane crack in an otherwise unbounded elastic body,with the crack faces subjected to a traction distribution consisting of two pairs of combined mode point loads that move in a direction perpendicular to the crack edge is considered.The analytic expression for the combined mode stress intensity factors as a function of time for any point along the crack edge is obtained.The method of solution is based on the application of integral transform together with the Wiener-Hopf technique and the Cagniard-de Hoop method. Some features of the solution are discussed and graphical results for various point load speeds are presented.

Cracking Propagation of Hardening Concrete Based on the Extended Finite Element Method

Self-deformation cracking is the cracking caused by thermal deformation, autogenous volume deformation or shrinkage deformation. In this paper, an extended finite element calculation method was deduced for concrete crack propagation under a constant hydration and hardening condition during the construction period, and a corresponding programming code was developed. The experimental investigation shows that initial crack propagation caused by self-deformation loads can be analyzed by this program. This improved algorithm was a preliminary application of the XFEM to the problem of the concrete self-deformation cracking during the hydration and hardening period. However, room for improvement exists for this algorithm in terms of matching calculation programs with mass concrete temperature fields containing cooling pipes and the influence of creep or damage on crack propagation.

Crack propagation mechanism of compression-shear rock under static-dynamic loading and seepage water pressure

To reveal the water inrush mechanics of underground deep rock mass subjected to dynamic disturbance such as blasting, compression-shear rock crack initiation rule and the evolution of crack tip stress intensity factor are analyzed under static-dynamic loading and seepage water pressure on the basis of theoretical deduction and experimental research. It is shown that the major influence factors of the crack tip stress intensity factor are seepage pressure, dynamic load, static stress and crack angle. The existence of seepage water pressure aggravates propagation of branch cracks. With the seepage pressure increasing, the branch crack experiences unstable extension from stable propagation. The dynamic load in the direction of maximum main stress increases type I crack tip stress intensity factor and its influence on type II crack intensity factor is related with crack angle and material property. Crack initiation angle changes with the dynamic load. The initial crack initiation angle of type I dynamic crack fracture is 70.5°. The compression-shear crack initial strength is related to seepage pressure, confining pressure, and dynamic load. Experimental results verify that the initial crack strength increases with the confining pressure increasing, and decreases with the seepage pressure increasing.

Degradation mechanism of rock under impact loadings by integrated investigation on crack and damage development

Failure of rock under impact loadings involves complex micro-fracturing and progressive damage. Strength increase and splitting failure have been observed during dynamic tests of rock materials. However, the failure mechanism still remains unclear. In this work, based on laboratory tests, numerical simulations with the particle flow code(PFC) were carried out to reproduce the micro-fracturing process of granite specimens. Shear and tensile cracks were both recorded to investigate the failure mode of rocks under different loading conditions. At the same time, a dynamic damage model based on the Weibull distribution was established to predict the deformation and degradation behavior of specimens. It is found that micro-cracks play important roles in controlling the dynamic deformation and failure process of rock under impact loadings. The sharp increase in the number of cracks may be the reason for the strength increase of rock under high strain rates. Tensile cracks tend to be the key reason for splitting failure of specimens. Numerical simulation of crack propagation by PFC can give vivid description of the failure process. However, it is not enough for evaluation of material degradation. The dynamic damage model is able to predict the stress-strain relationship of specimens reasonably well, and can be used to explain the degradation of specimens under impact loadings at macro-scale. Crack and damage can describe material degradation at different scales and can be used together to reveal the failure mechanism of rocks.

DYNAMIC STRESS INTENSITY FACTORS AROUND TWO CRACKS NEAR AN INTERFACE OF TWO DISSIMILAR ELASTIC HALF－PLANES UNDER IN－PLANE SHEAR IMPACT LOAD

Transient stresses around two collinear cracks which lie in parallel with theinterface of the two dissimilar half-planes are studied in this article.The surfaces ofthe cracks are sheared suddenly. Application of the Fourier and Laplace transforms technique reduces the problem to that of solving dual integrai equations.To solvethese,the differences of.the crack surface displacements are expanded in a series offunctions which are automatically zero outside of the cracks. The unknown coefficients accompanied in the series are determined by the Schmidt method. The stress intensity .factors are defined in the Laplace transform domain and these are inverted numerically in the physical space .As an example ,the dynamic stress intensity factors around two cracks in a ceramic and steel bonded composite are numerically calculated.

Crack spacing threshold of double cracks propagation for large-module rack

Large-module rack of the Three Gorges shiplift is manufactured by casting and machining, which is unable to avoid slag inclusions and surface cracks. To ensure its safety in the future service, studying on crack propagation rule and the residual life estimation method of large-module rack is of great significance. The possible crack distribution forms of the rack in the Three Gorges shiplift were studied. By applying moving load on the model in FRANC3 D and ANSYS, quantitative analyses of interference effects on double cracks in both collinear and offset conditions were conducted. The variation rule of the stress intensity factor(SIF) influence factor, RK, of double collinear cracks changing with crack spacing ratio, RS, was researched. The horizontal and vertical crack spacing threshold of double cracks within the design life of the shiplift were obtained, which are 24 and 4 times as large as half of initial crack length, c0, respectively. The crack growth rates along the length and depth directions in the process of coalescence on double collinear cracks were also studied.

Crack Propagation Path in Two-Directionally Graded Composites Subjected to Mixed-Mode Ⅰ+Ⅱ Loading

Crack propagation path in two-directionally graded composites was investigated by the finite element method.A graded extended finite element method(XFEM)was employed to calculate displacement and stress fields in cracked graded structures.And a post-processing subroutine of interaction energy integral was implemented to extract the mixed-mode stress intensity factors(SIFs).The maximum hoop stress(MHS)criterion was adopted to predict crack growth direction based on the assumption of local homogenization of asymptotic crack-tip fields in graded materials.Effects of material nonhomogeneous parameters on crack propagation paths were also discussed in detail.It is shown that the present method can provide relatively accurate predictions of crack paths in two-directionally graded composites.Crack propagates in the decreasing direction of effective Young′s modulus.The shape and steepness of property gradient perpendicular to the crack surface have great influences on crack paths.Through redesigning material property reasonably,crack growth in graded material can be changed to improve mechanical behaviours of cracked structures.

Numerical study on static and dynamic fracture evolution around rock cavities

In this paper,a numerical code,RFPA2D（rock failure process analysis）,was used to simulate the initiation and propagation of fractures around a pre-existing single cavity and multiple cavities in brittle rocks.Both static and dynamic loads were applied to the rock specimens to investigate the mechanism of fracture evolution around the cavities for different lateral pressure coefficients.In addition,characteristics of acoustic emission（AE） associated with fracture evolution were simulated.Finally,the evolution and interaction of fractures between multiple cavities were investigated with consideration of stress redistribution and transference in compressive and tensile stress fields.The numerically simulated results reproduced primary tensile,remote,and shear crack fractures,which are in agreement with the experimental results.Moreover,numerical results suggested that both compressive and tensile waves could influence the propagation of tensile cracks;in particular,the reflected tensile wave accelerated the propagation of tensile cracks.

DAMAGE TOLERANCE ANALYSIS ON HOLLOW AXLES OF HIGH SPEED MOTOR TRAINS

According to the rules of UIC515-3, the service loads of the axles are defined, which include some different loads cases as follows： the static loads; the impact loads resulted from running through the rail joints and unevenness rails; the loads through curves and from braking. Through the calculating and analysis, the stress distribution of the hollow axles is obtained for 200 km/h high speed motor trains used in China. At the same time, the fatigue crack growth of hollow axles is studied, and the initial surface cracks of 2 mm depth caused by hard objects strike or the other causes are discussed. On the basis of the linear elastic fracture mechanics theory, the stress intensity factor of the crack of the geometry transition outside the wheel seat is also studied. Associated with fatigue crack propagation equation and the corresponding crack propagation threshold, the crack propagation characteristics under different shapes are calculated. Then the running distances are educed with different shapes propagating to the critical length, and the estimation of the residual lives about hollow axles which are the reference values of examine and repair limit of the hollow axle is given.

Flexural behavior of textile reinforced mortar-autoclaved lightweight aerated concrete composite panels

To improve the deficiencies of prefabricated autoclaved lightweight aerated concrete(ALC)panel such as susceptibility to cracking and low load-bearing capacity,a textile-reinforced mortar-autoclaved lightweight aerated concrete(TRM-ALC)composite panel was developed in this study.One group of reference ALC panels and five groups of TRM-ALC panels were fabricated and subjected to four-point flexural tests.TRM was applied on the tensile side of the ALC panels to create TRM-ALC.The variable parameters were the plies of textile(one or two),type of textile(basalt or carbon),and whether the matrix(without textile)was applied on the compression side of panel.The results showed that a bonding only 8-mm-thick TRM layer on the surface of the ALC panel could increase the cracking load by 180%−520%.The flexural capacity of the TRM-ALC panel increased as the number of textile layers increased.Additional reinforcement of the matrix on the compressive side could further enhance the stiffness and ultimate loadbearing capacity of the TRM-ALC panel.Such panels with basalt textile failed in flexural mode,with the rupture of fabric mesh.Those with carbon textile failed in shear mode due to the ultra-high tensile strength of carbon.In addition,analytical models related to the different failure modes were presented to estimate the ultimate load-carrying capacity of the TRM-ALC panels.

Propane catalytic cracking on pretreated La-ZSM-5 zeolite during calcination for light olefins production

The purpose of this study was to increase light olefins yield and selectivity in catalytic cracking of propane. Pretreatment of ZSM-5 zeolite was performed during calcination. First, lanthanum was loaded on the catalyst by wet impregnation method and then the effect of parameters, such as temperature（400–800 oC）, time（120–480 min） and type of stream, on La-ZSM-5 zeolite was examined during calcination using central composite design（CCD） method. Based on the proposed models, the optimized condition for maximizing selectivity of light olefins for air stream was 680 oC and 310 min and for the nitrogen stream was 735 oC and 173 min that under these conditions, selectivity amount increased 24% for nitrogen stream and 19% for air stream as compared with H-ZSM-5 catalyst. The synthesized catalysts were characterized by X-ray diffraction（XRD） and temperature-programmed desorption（TPD） techniques. According to the results of NH3-TPD, as the temperature increased, the number of strong acid sites（specially Bronsted acid sites） reduced and resulted in increased production of light olefins as well as catalyst stability. Accordingly, stability of the samples calcined with nitrogen stream was higher than the samples calcined with the air stream.

Assessment of Elasticity,Plasticity and Resistance to Machining-induced Damage of Porous Pre-sintered Zirconia Using Nanoindentation Techniques

Porous pre-sintered zirconia is subject to white machining during which its elasticity, plasticity and resistance to machining-induced damage determine its machinability and final quality. This study used nanoindentation techniques and the Sakai＇s series elastic and plastic deformation model to extract the resistance to plastic deformation from the plane strain modulus and the contact hardness for presintered zirconia. The modulus and the resistance to plasticity were used to calculate the relative amount of elasticity and plasticity. The fracture energy and the normalized indentation absorbed energy were used to deconvolute the resistance to machining-induced cracking based on the Sakai-Nowak model. All properties were extracted at a 10 mN peak load and loading rates of 0.1-2 mN/s to determine the loading rate effects on these properties. We found that the resistance to plasticity and the resistance to machining-induced cracking were independent of the loading rate （ANOVA, p 〉 0.05）. The elastic and plastic displacements depended on the loading rate through power laws. This loading rate-dependent deformation behaviour was explained by the maximum shear stress generated underneath the indenter and the indentation energy. The plastic deformation components and the indentation absorbed energy at all loading rates were higher than the elastic deformation components and the elastic strain energy, respectively. Finally, we established the linkage among the pore structure, indentation behaviour and machinability of pre-sintered zirconia.