Interlaminar Crack Propagation Analysis of ENF Specimens Based on the Cohesive Zone Model北大核心CSCD

Based on the classical laminated plate theory and the cohesive zone model, a theoretical model for general delamination cracked laminates was established for crack propagation of pure mode Ⅱ ENF specimens. Compared with the conventional beam theory, the proposed model fully considered the softening process of the cohesive zone and introduced the nonlinear behavior of ENF specimens before failure. The predicted failure load is smaller than that under the beam theory and closer to the experimental data in literatures. Compared with the beam theory with only fracture toughness considered, the proposed model can simultaneously analyze the influences of the interface strength, the fracture toughness and the initial interface stiffness on the load-displacement curves in ENF tests. The results show that, the interface strength mainly affects the mechanical behavior of specimens before failure, but has no influence on crack propagation. The fracture toughness is the main parameter affecting crack propagation, and the initial interface stiffness only affects the linear elastic loading stage. The cohesive zone length increases with the fracture toughness and decreases with the interface strength. The effect of the interface strength on the cohesive zone length is more obvious than that of the fracture toughness. When the adhesive zone tip reaches the half length of the specimen, the adhesive zone length will decrease to a certain extent. Copyright ©2022 Applied Mathematics and Mechanics. All rights reserved.     

Structural Crack Identification Based on the Variational Mode Decomposition北大核心CSCD

In order to enrich the bridge damage detection method and further improve the accuracy of bridge damage identification, a detection method for simply supported beams with cracks under dynamic loads was proposed not based on the complete finite element model. Under the premise of not blocking traffic, the method only needs to analyze and deal with the acceleration responses of the simply supported beam span, which reduces the mounting, dismounting and maintenance of sensors in practical engineering. At the same time, based on the model, an analytical formula of the acceleration at the midspan of the simply supported cracked beam was derived. Based on the theoretical derivation, the instantaneous energy and the mean energy difference were constructed through the variational mode decomposition and the Hilbert transform, and these 2 crack identification indexes were used to effectively identify small cracks with a crack depth ratio of only 5%. Then the influences of different wheel loads, environmental noises and damage degrees on detection results were studied. The results show that: ① the instantaneous frequency has a better recognition effect for crack positions; ② the mean energy difference is sensitive to crack depth ratio δ and the wheel load magnitude; ③ this method has strong noise robustness. © 2022 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

Stress intensity factors for a finite plate with an inclined crack by boundary collocation

In this paper, we combine the Muskhelishvili＇s complex variable method and boundary collocation method, and choose a set of new stress function based on the stress boundary condition of crack surface, the higher precision and less computation are reached. This method is applied to calculating the stress intensity factor for a finite plate with an inclined crack. The influence of θ （the obliquity of crack） on the stress intensity factors, as well as the number of summation terms on the stress intensity factor are studied and graphically represented.     

Three-Level Safety Evaluation of Suspended Sections of Underwater Buried Pipelines北大核心CSCD

The uneven riverbed, and the impact and scour actions by water flow, make the underwater buried pipeline vulnerable to exposure and suspension, and endanger the pipeline operation safety. To investigate the mechanical properties and failure behaviors of the suspended pipeline section under water impact, according to the failure mechanism of the pipeline, the statics and dynamics analyses of the pipeline were carried out, and the graded safety evaluation technique for the buried pipeline with suspended sections was presented. First, a “static strength safety evaluation under static loads” (level 1) was conducted according to the mechanical features and stress states of the pipeline’s suspended section. Second, a “resonance safety evaluation under dynamic loads” (level 2) was conducted based on the correlation between the natural vibration frequencies of the suspended pipeline and the vortex emission frequencies of water flow. Finally, the periodical change process of the pipeline’s alternating stress was studied to solve the fatigue damage and fatigue life of the pipeline, and the “fatigue strength safety evaluation under dynamic loads” (level 3) was performed. Thus, a 3-level safety assessment procedure for pipelines with suspended sections was proposed. The stabilizing measures for pipelines of poor safety were suggested, and through an example, a specific calculation process was provided. The work serves as a theoretical guide for the safety evaluation of the suspended sections of underwater buried pipelines. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

Dynamic response of planar interface crack between viscoelastic bodies

IntroductionThe dynamic stress intensity factor (SIF) plays an important role in dynamic fracture underboth harmonic and transient loads. It predicts whether or not the fracture toughness of thematerial will be exceeded and catastrophic crack propagation will follow. The dynamic SIFof interfaCe cracks between two dissimilar elastic materials has been studied widely. Kundull]studied the dynamic SIF of interface crack under transient loading with the method based onBetti's reciprocal theore…     

Analytic Study of Magnetohydrodynamic Flow and Boundary Layer Control Over a Wedge

A genuine variational principle developed by Gyarmati, in the field of thermodynamics of irreversible processes unifying the theoretical requirements of technical, environmental and biological sciences is employed to study the effects of uniform suction and injection on MHD flow adjacent to an isothermal wedge with pressure gradient in the presence of a transverse magnetic field. The velocity distribution inside the boundary layer has been considered as a simple polynomial function and the variational principle is formulated. The Euler-Lagrange equation is reduced to a simple polynomial equation in terms of momentum boundary layer thickness. The velocity profiles, displacement thickness and the coefficient of skin friction are calculated for various values of wedge angle parameter m, magnetic parameter ξ and suction/injection parameter H. The present results are compared with known available results and the comparison is found to be satisfactory. The present study establishes high accuracy of results obtained by this variational technique.     

Elastic Analysis of Anisotropic Rotating Sandwich Circular Ring With a Functionally Graded Transition Region北大核心CSCD

The elastic analysis of anisotropic rotating sandwich ring with a functionally graded transition region was carried out. Like the shell sandwich structure in nature, the ring is composed of 3 well⁃bonded regions, of which the inner and outer regions are made of homogeneous anisotropic materials, and the intermediate transi⁃ tion region is made of a material with arbitrary⁃gradient properties along the radial direction. Based on the boundary conditions and the continuity conditions at the interface, the 2nd Fredholm integral equation for the radial stress was obtained with the integral equation method, then the stress and displacement fields of the sandwich ring structure were obtained through numerical solution. The distributions of the stress and displace⁃ ment fields in the sandwich ring structure were given. Different gradient changes encountered in engineering practice can be solved only through substitution of the corresponding function model. The effectiveness and ac⁃ curacy of the integral equation method were verified through comparison of the numerical solutions with the ex⁃ act ones for a special power function gradient variation form. The more general Voigt function model was adopt⁃ ed for the intermediate transition region, and the influences of the anisotropy degree, the gradient parameter, and the thickness on the stress and displacement fields were analyzed. The proposed Fredholm integral equation method provides a powerful tool for the optimal design of anisotropic functionally graded materials and sand⁃ wich ring structures. The numerical results make a theoretical guidance for the safety design of anisotropic functionally graded sandwich ring structures. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

Experimental Study on the Flexural Ductility of BFRP Bar Concrete Beams With Bamboo Fiber and Steel Wire Mesh北大核心CSCD

To study the effects of bamboo fiber and steel wire mesh on the flexural ductility of basalt fiber reinforced polymer（BFRP）bar concrete beams, 7 BFRP bar concrete beams with bamboo fiber and steel wire mesh were tested with different bamboo fiber lengths (0 mm, 30 mm and 45 mm) and different steel wire mesh layout ranges (0, 1/2 maximum bending moment point layout and full beam length layout). The flexural failure tests of the 7 beams were carried out, and the initial crack loads, the crack developments, the ultimate loads and the deformations were detected. The effects of the fiber length and the wire mesh layout range on the crack resistance and the deformation resistance of the specimens were analyzed based on the test data. With the function model, the equivalent yield points of the 7 test beams were obtained, and their ductility coefficients were calculated. The results show that, the addition of bamboo fiber and steel wire mesh increases the cracking loads of BFRP bar concrete beams by 12%~68%, decreases the crack spacings and the crack length development speed, reduces the test beam deformation under the same load, and increases the ductility coefficient by 1.58%~31.75%. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

COPLANAR CRACKS IN A FINITE TRANSVERSELY ISOTROPIC ELASTIC SLAB UNDER ANTIPLANE SHEARL STRESSES

An antiplane crack problem concerning a pair of coplanar cracks in a finite transversely isotropic elastic slab is considered. Using Fourier integral transform together with singular integral equation which can be solvel numerically by suing a collocation technique. Once the integral equation is solved, the relevant crack energy and stress intensity factors of the problem are given. The analysis present can be easily extended to include cases where there are two or more pairs of coplanar cracks in the slab.     

Simulation of Electroosmotic and Pressure-Driven Mixed Flow of Viscoelastic Fluids in Converging-Diverging Tubes北大核心CSCD

The electroosmotic and pressure⁃driven mixed flow was widely used in various biochemical microflu⁃ idic fields, where the elastic instability of the viscoelastic fluid cannot be ignored. A viscoelastic fluid was used to numerically simulate electroosmotic and pressure⁃driven mixed flow in a 10 ∶ 1 ∶ 10 microchannel converging⁃ diverging tube. The effects of different pressures and different polymer concentrations on the fluid flow were studied, and the superposition principle for the velocity distributions of Newtonian fluids and viscoelastic fluids in converging⁃diverging tubes was analyzed. The results show that, the reverse pressure brings the viscoelastic fluid into higher instability, which makes the inlet vortex larger by 25 μm for every 1 Pa pressure increase. The positive pressure makes the eddy current smaller. For a relatively small reverse pressure, the inlet vortex in⁃ creases with the polymer concentration and tends to be stable gradually. For a relatively large reverse pressure, the vortex size first increases and then decreases with the polymer concentration. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

裂纹间作用机制探讨及微裂纹区对主裂纹的作用效应研究

采用迭加原理和Kachanov提出的简化方法,研究了裂纹间的相互作用机理,分析了不同裂纹布置形式所产生的增强或屏蔽效应,发现当微裂纹沿着或垂直于最大拉应力方向布置时都不产生最大的作用效应,这有别于Ortiz的结论．还探讨了混凝土类材料的微裂纹的产生机制及微裂纹区对主裂纹尖端产生的作用效应,得出微裂纹区对主裂纹是起增强的作用,增强程度随微裂纹密度和微裂纹长度的增大而增大的结论．     

基于裂纹尖端二阶弹性解的断裂过程区尺度

基于Westergaard应力函数裂纹尖端二阶弹性解,推导了裂纹尖端微裂区的轮廓线和特征尺寸的解析表达式;采用幂函数模型描述的拉应变软化模型,确定了在最大拉应力强度理论和最大拉应变强度理论下断裂过程区（FPZ）临界值的解析表达式;将基于Westergaard应力函数一阶弹性解及二阶弹性解、Muskhelishvili应力函数和Duan-Nakagawa模型确定的FPZ临界值进行了比较．结果表明裂纹尖端微裂区和FPZ临界值随着Poisson比的减小而增加并逐渐趋近于应用最大拉应力强度理论确定的结果;二阶弹性解确定的裂纹尖端微裂区和FPZ临界值大于一阶弹性解的值;FPZ临界值随着拉应变软化指数的增加而增加;二阶弹性解确定的FPZ临界值的精度远高于一阶弹性解确定的值.     

Modeling crack micro-branching using finite elements with embedded strong discontinuities

The emphasis of this work lies in the development of a numerical method which is capable of representing the complex physical phenomena arising in the case of crack branching in brittle materials. In particular, the formation of crack micro-branches needs to be accounted for when it comes to the prediction of the propagation pattern of crack macro-branches which will ultimately lead to the failure of the material. This is achieved by numerically modeling the failure zones within the individual finite elements based on the concept of the embedded finite element method, where all the information with regard to the geometry of the failure zone is stored locally on the element level leading to a very efficient methodology capable of discretely resolving the failure zone. The main feature of the current work is the redundancy of the branching criterion based on crack tip velocity and that both, micro- as well as macro-branches can be modeled. Whether a micro-crack develops into a macro-crack solely depends on the local state of the material as it is outlined based on the application of the proposed numerical scheme on a rectangular block with a pre-existing notch set under tension. A comparison of the oscillatory behavior of the obtained crack tip velocity every time a micro-crack develops with experimental results from the literature is provided. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

圆形杂质对裂纹扩展的影响

在单轴拉伸载荷作用下，运用分布位错方法对无限大平面内含有一个裂纹和一个任意方向的杂质问题进行求解，得到了裂纹尖端的应力强度因子、应力场以及应变能密度.利用最小应变能密度因子准则来判断裂纹扩展方向.结果显示:软杂质对裂纹尖端应力强度因子、应变能密度和应力场有增强作用，而硬杂质则具有屏蔽作用.在 -30°<θ<30°范围内，杂质对裂纹扩展方向的影响较小，而在 -90°<θ<-30°或30°<θ<90°范围内，杂质对裂纹扩展方向的影响较大.软杂质对裂纹扩展有吸引作用，而硬杂质具有排斥作用.     

The fracture of brittle and ductile crystals. Force and deformation criteria

The growth and branching of sharp cracks in ideal single crystals are investigated. Neuber-Novozhilov force and deformation criteria are proposed for the branching of sharp cracks; these criteria describe the brittle, quasibrittle, quasiductile and ductile behaviour of materials on fracture. For internal cracks, simple relations are obtained that describe the branching of cracks when the Coulomb-Mohr single-crystal theoretical strength curves are known for a generalized stress state. The possibility of multiple branching of cracks is found, which is linked to the multiplicity of the eigenvalues on loss of stability of the system. It is established that, for ideal single crystals, the principle of local symmetry is satisfied in the vicinity of the crack tip if the axis of symmetry of the crystal coincides with the axis of the crack. When there are asymmetrical disturbances of the atomic lattice in the vicinity of the crack tip, or when the axis of symmetry of the single crystal does not coincide with the crack axis, the principle of local symmetry is not satisfied.     

Two-dimensional extension of polyethylene and polypropylene film

The two-dimensional extension of polyethylene and polypropylene film has been investigated by optical microscopy. It has been established that there is no two-dimensional plastic flow (two-dimensional necking) and that failure is quasi-brittle in character. In a small region near the cracks that develop, uniaxial orientation of the polymer associated with stress concentrations near the crack tip is observed. Measurements show that the ultimate stress in two-dimensional extension is close to the necking stress in uniaxial tension.Mekhanika Polimerov, Vol. 3, No. 1, pp. 41–45, 1967     

双I—型裂纹断裂动力学问题的非局部理论解

研究了非局部理论双中I－型裂纹弹性波散射的力学问题,并利用富里叶变换使本问题的求解转换为三重积分方程的求解,进而采用新方法和利用一维非局部积分核代替二维非局部积分核来确定裂纹尖端的应力状态,这种方法就是Schmidt方法,所得结是比艾林根研究断裂静力学问题的结果准确和更加合理,克服了艾林根研究断裂静力学问题时遇到的数学困难,与经典弹性解相比,裂纹尖端不再出现物理意义下不合理的应力奇异性,并能够解释宏观裂纹与微观裂纹的力学问题。     

Multiscale Modeling for the Simulation of Damage Processes at Refractory Materials under Thermal Shock

Refractory materials, for example ceramic materials, initially contain a multitude of defects such as voids, microcracks, grain boundaries etc. The deformation process and failure mechanisms due to thermal shock at high temperatures above 1000°C are going along with the creation of new micro defects as well as the growth and coalescence of cracks. A material damage model based on the theoretical concept of damage mechanics and the mechanics of microcracks is presented in this paper. Cell models are developed as representative volume elements (RVE) including crack initiation and growth as well as microstructural shielding effects. For simple configurations of the microstructure, the relation between stress, strain and temperature is derived from analytical considerations. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Out-of-plane displacement measurement near the crack tip during a crack propagation: Validation of a 3D formulation for a specimen in PMMA loaded in mode I.

The fundamental aim of this study is the determination zone of the 3D effects and the transient one at the vicinity of the crack tip during a crack propagation in brittle materials ( PMMA ) using an optical method (Michelson interferometer). With the obtained interferograms, we can extract the phase (thus the relief) by using a new numerical approach based on the principle of images correlation between real fringes and virtual fringes. Different dynamic tests are realized by a plate loaded in mode I under a constant loading. We compare the obtained data with the two-dimensional theory of Westergaard (plane stress hypothesis) [1]. With the divergence is established, we propose a new 3D formulation, based on a formulation employed for static crack, which takes into account 3D and transient effects. For the static cracks, the 3D effects relate to a presence of the state of three-dimensional stresses. However in dynamics, the transient effects appear and are related to the crack propagation velocity. The 3D effects and transient effects lead to results equivalent to experimental ones in terms of displacement but are completely different to results given by the two-dimensional theory near the crack tip. It is possible to quantify the zone when the plane stress hypothesis is not valid according to the crack propagation speed V. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Non-local theory solution of two collinear mode-I cracks in piezoelectric materials

In this paper, the basic solution of two collinear cracks in a piezoelectric material plane subjected to a uniform tension loading is investigated by means of the non-local theory. Through the Fourier transform, the problem is solved with the help of two pairs of integral equations, in which the unknown variables are the jumps of displacements across the crack surfaces. To solve the integral equations, the jumps of displacements across the crack surfaces are directly expanded in a series of Jacobi polynomials. Numerical examples are provided to show the effects of the interaction of two cracks, the materials constants and the lattice parameter on the stress field and the electric displacement field near crack tips. Unlike the classical elasticity solution, it is found that no stress and electric displacement singularities are present at crack tips. The non-local elastic solutions yield a finite hoop stress at the crack tip, thus allowing us to using the maximum stress as a fracture criterion in piezoelectric materials.