Mixed mode crack growth in curved beams with radial edge crack

Mixed mode crack growth in curved beams with radial edge crack is predicted by the prominent S-theory. An improved simple engineering method for obtaining approximate stress intensity factors of curved cracked beams is also used. It takes into account the elastic crack tip stress singularity while using the elementary beam theory. The results are in reasonable agreement with the more accurate calculations in literature.     

Experimental study on crack curving propagation in bending beams under impulsive load

Dynamic fracture behaviour of crack curving in bent beams has been investigated. In order to understand the propagation mechanism of such cracks under impact, an experimental method is used that combines dynamic photoelasticity with dynamic caustics to study the interaction of the flexural waves and the crack. From the state change of the transient stresses in polymer specimen, the curving fracture in the impulsively loaded beams is analyzed. The dynamic responses of crack tips are evaluated by the stress intensity factors for the cracks running in varying curvature paths under bending stress wave. The project supported by the National Natural Science Foundation of China and the Scientific Commission of Yunnan Province of China     

Strain energy density prediction of crack initiation and direction in cracked T-beams and pipes

In this paper, the S-theory is applied to determine crack initiation and direction for cracked T-beams and circumferentially cracked pipes. It makes use of a parameter called strain energy density factor, S, which is a function of the stress intensity factors. The strain energy density theory provides a more general treatment of fracture mechanics problems by virtue of its ability in describing the multiscale feature of material damage and in dealing with mixed mode crack propagation problem. A simple method for obtaining approximate stress intensity factors is also applied. It takes into account the elastic crack tip stress singularity while using the elementary beam theory. Some basic loading conditions in beams and pipes are studied.     

A reexamination of plasticity-induced crack closure in fatigue crack propagation

The crack closure concept is often used to consider the R-ratio and overload effects on fatigue crack growth. The presumption is that when the crack is closed, the external load produces negligible fatigue damage in the cracked component. The current investigation provides a reassessment of the frequently used concept with an emphasis on the plasticity-induced crack closure. A center cracked specimen made of 1070 steel was investigated. The specimen was subjected to plane-stress mode I loading. An elastic–plastic stress analysis was conducted for the cracked specimens using the finite element method. By applying the commonly used one-node-per-cycle debonding scheme for the crack closure simulations, it was shown that the predicted crack opening load did not stabilize when the extended crack was less than four times of the plastic zone size. The predicted opening load was strongly influenced by the plasticity model used. When the elastic–perfectly plastic (EPP) stress–strain relationship was used together with the kinematic hardening plasticity theory, the predicted crack opening load was found to be critically dependent on the element size of the finite element mesh model. For R = 0, the predicted crack opening load was greatly reduced when the finite element size became very fine. The kinematic hardening rule with the bilinear (BL) stress–strain relationship predicted crack closure with less dependence on the element size. When a recently developed cyclic plasticity model was used, the element size effect on the predicted crack opening level was insignificant. While crack closure may occur, it was demonstrated that cyclic plasticity persisted in the material near the crack tip. The cyclic plasticity was reduced but not negligible when the crack was closed. The traditional approaches may have overestimated the effect of crack closure in fatigue crack growth predictions.     

Computational crack path prediction

A computer program has been developed for the numerical prediction of curved crack growth paths under proportional loading conditions. The numerical prediction is performed by the step-by-step method in cooperation with the stress analysis ahead of the crack tip and the determination of the curved increment of the crack growth. The stress analysis is performed by the method of superposition of analytical and finite-element solutions, and the results are then utilized to determine the coefficients of the analytical expression of the curved crack path obtained by the first order perturbation method.The first numerical example is given for the crack path prediction in DCB-type specimen, where we often observe abrupt crack curving. Computational prediction is performed by introducing slight and small initial branching at the original crack tip. Within few steps of numerical calculations unstable crack curving is obtained, and the predicted path shows extremely good agreement with the experimentally measured path. The second numerical prediction is made for an edge crack approaching a circular hole, which may be considered as a crack arrester. In the present case the effect of the initially introduced slight kink diminishes with increasing crack length. The crack turns back to the original direction, resulting arrest at the hole.     

Analytical solution for a Mode III crack in a 3D beam lattice

The brittle fracture behavior of an open cell foam is considered. The foam is modeled by an infinite lattice composed of elastic straight-line beam elements (struts) having uniform cross-sections and rigidly connected at the nodal points. The beams are parallel to the three mutually orthogonal lattice vectors thus forming a microstructure with rectangular parallelepiped cells.A semi-infinite Mode III crack is embedded in the lattice and, for the considered antiplane deformation, each node has three degrees of freedom, namely, the displacement parallel to the crack front and two rotations about the axes perpendicular to this direction. The analysis method hinges on the discrete Fourier transform, which allows to formulate the crack problem by means of the Wiener–Hopf equation. Its solution yields closed-form analytical expressions for the forces and the displacements at any cross-section, and, in particular, at the crack plane. An eigensolution for the traction-free crack faces and K-field remote loading is derived from the solution for the loaded crack using a limiting procedure. An analytical expression for the fracture toughness is derived from the eigensolution by comparing the remote stress field and the stresses in the near-tip struts. The obtained expression is found to be consistent with the known analytical and experimental results for Mode I deformation. It appears, that the dependence of the fracture toughness upon shape anisotropy ratio of the lattice material is non-monotonic. The optimal value of this parameter, which provides the maximum crack arresting ability is determined.     

修正的拉应力裂纹扩展准则及裂隙\=水压对裂纹扩展的影响

对脆性材料的第一主应力--拉应力裂纹扩展准则进行了补充和修正,修正的裂纹扩展准则能确定裂纹扩展步长.以平面斜置裂纹扩展为例,利用无网格Galerkin方法,对不含裂隙水压的二维裂纹扩展进行数值模拟,计算结果与试验结果一致,表明最大周向拉应力准则的正确性.在不同裂隙水压条件下,研究了二维裂纹初始破裂,并在给定水压下对二维裂纹扩展路径进行了数值模拟跟踪.结果表明裂隙水压对裂纹初始破裂方向、破裂步长、破裂载荷和裂隙岩体破裂强度有显著影响.有水压和无水压的扩展迹线不同,但后续的扩展趋势相同.     

Strain rate effect on crack propagation in concrete

Some aspects of cracking in concrete structural elements are discussed. The flexural behaviour of precracked beams made with materials having different mechanical properties is experimentally evaluated at different deformation rates. The crack propagation in the sample is recorded with time by means of particular electric strain gauges. An interaction between ultimate tensile strength failure and brittle crack propagation is eventually pointed out.     

Stable growth of a central crack

The elastic fracture behavior of a plate subjected to uniform stress surrounding two equal cracks inclined at an angle is investigated. The orientation of the crack plane with applied stress can be varied. Among the cases are: (1) two cracks inclined symmetrically with respect to the vertical and horizontal applied stress, and (2) one crack is horizontal while the other is inclined to the vertical applied stress. The strain energy density criterion is used for determining the combined crack and load arrangement that correspond to the lowest critical load at global instability. The direction of crack initiation is also determined. Quantitative results pertaining to the fracture characteristics are given in graphical forms.     

基于圆弧底试件的动态裂纹扩展及止裂规律研究

为了研究脆性材料的动态裂纹扩展及止裂规律,设计了一种带圆弧形底边的梯形开口边裂纹（trapezoidal opening crack with arc bottom,TOCAB）构型的试件。在落锤冲击设备加载下,对圆心角为0°、60°、90°和120°的TOCAB试件进行了冲击实验,并采用裂纹扩展计(crack propagation gauge,CPG)监测裂纹起裂和扩展时间,从而获得裂纹扩展速度。采用有限差分软件AUTODYN对落锤冲击设备和试件进行数值模拟,研究了裂纹的动态扩展过程及止裂规律。还基于实验和数值方法,计算了裂纹的临界动态应力强度因子。实验和数值结果均表明:3种弧度的TOCAB试件都可以实现运动裂纹止裂,该构型可用于研究动态裂纹止裂问题;数值计算的裂纹扩展路径与实验结果基本一致,验证了数值模型的有效性;裂纹起裂和止裂时刻的临界动态应力强度因子大于裂纹动态扩展过程中的临界动态应力强度因子。     

Dynamic crack tip fields and dynamic crack propagation characteristics of anisotropic material

Based on mechanics of anisotropic material, the dynamic crack propagation problem of I/II mixed mode crack in an infinite anisotropic body is investigated. Expressions of dynamic stress intensity factors for modes I and II crack are obtained. Components of dynamic stress and dynamic displacements around the crack tip are derived. The strain energy density theory is used to predict the dynamic crack extension angle. The critical strain energy density is determined by the strength parameters of anisotropic materials. The obtained dynamic crack tip fields are unified and applicable to the analysis of the crack tip fields of anisotropic material, orthotropic material and isotropic material under dynamic or static load. The obtained results show Crack propagation characteristics are represented by the mechanical properties of anisotropic material, i.e., crack propagation velocity M and fiber direction α. In particular, the fiber direction α and the crack propagation velocity M give greater influence on the variations of the stress fields and displacement fields. Fracture angle is found to depend not only on the crack propagation but also on the anisotropic character of the material.     

Dynamic crack growth under stress wave loading

The crack growth process has been analysed on the basis of a fracture criterion of a dynamic stress intensity factor when a crack in an infinite plate was subjected to a pulse type of stress wave. The crack velocity and the amount of crack extension were related to the constant amplitude and the duration of the stress pulse. The calculated amount of crack extension was well in agreement with the experimental one for the polymer material Acrylite (which is similar to polymethylmethacrylate) found by the authors, thus indicating the validity of the present approach.     

Effects of fractal crack

Experimental results indicate that propagation paths of cracks in geomaterials are often irregular, producing rough fracture surfaces which are fractal. In this paper, crack tip motion along a fractal crack trace is discussed. A fractal kinking model of the crack extension path is established to describe irregular crack growth. The length, velocity and kinking effects of the fractal crack are analysed. A formula is derived to describe the effects of fractal crack propagation on the dynamic stress intensity factor and on crack velocity. Finally, expressions of stress and displacement fields near the fractal crack tip are given.     

Elastic-plastic analysis of antiplane crack near crack surface region

The elastic-plastic stress distribution and the elastic-plastic boundary con- figuration near a crack surface region are significant but hard to obtain by means of the conventional analysis. A crack line analysis method is developed in this paper by consid- ering the crack surface as an extension of the crack line. The stresses in the plastic zone, the length, and the unit normal vector of the elastic-plastic boundary near a crack surface region are obtained for an antiplane crack in an elastic-perfectly plastic solid. The usual small scale yielding assumptions are not needed in the analysis.     

Transient crack growth under creep conditions

Transient crack growth in an elastic/power-law creeping material is investigated under antiplane shear loading and small-scale-yielding conditions. At time t = 0 the solid is suddenly loaded far from the crack by tractions that correspond to the elastic crack-tip stress distribution. At that time the crack begins to propagate at a constant velocity. The stress fields evolve in a complex manner as the crack propagates due to the competing effects of stress relaxation due to constrained creep and stress elevation due to the instantaneous elastic material response to crack growth. From detailed finite element calculations it is shown that these fields can be approximated by a simple matching of three asymptotic singular crack-tip solutions. A characteristic stress, distance and time are defined for this problem which provide a normalization that accounts for any crack velocity, loading and all material properties for a given creep exponent n. Results are presented for crack-tip stresses, strains, crack opening displacements and creep zones.     

Stress-strain field near crack tip and calculation of critical stress of crack propagation in a pure bending beam of rectangular section with one-sided mode i crack

This paper studies the stress-strain field near crack tip in a pure bending beam of rectangular section with one-sided mode I crack by the analytic method of Ref. [1], then it gives the stress and strain components at the crack tip when the crack propagates and further it obtains the formulas of calculating the elastic deformed area width, the deformed intensity area width and the equation groups of calculating the critical stress of crack propagation, last the equation group of calculating critical stress of crack propagation is verified by calculating instance. The maximum error is 0.18%. First Received May 7, 1994.     

Finite element analysis of a bimaterial interface crack

In this investigation, the enriched element method developed by Benzley was extended to treat the stress analysis problem involving a bimaterial interface crack. Unlike crack problems in isotropic elasticity, where the stress singularity at the crack tip is of the inverse square root type, the interface crack contains an additional oscillatory singularity. Although the effect of this oscillatory characteristic is confined to a region very close to the crak tip, it nevertheless requires proper treatment in order to obtain accurate predictions on the stress intensity factors. Using appropriate crack tip stress and displacement expressions, the enriched element method can model the stress singularity for an interface crack exactly. The finite element implementation of this method has been made on the code APES. Stress intensity factor results predicted by the modified APES program compare favorably with those available in the literature. This indicates tha the enriched element technique provides an accurate and efficient numerical tool for the analysis of bimaterial interface crack problems.     

A simple model of the double cantilever beam crack propagation specimen

A very simple model of the double cantilever beam (dcb) dynamic crack propagation specimen is studied. The main assumption on which the model is based is that the arms of the dcb specimen deform as shear beams. The particular problem studied is the dynamic growth of a sharp crack from a blunt pre-crack with the ends of the specimen arms held at a fixed separation distance. It is demonstrated that this simple model predicts crack motion which is qualitatively consistent with the results of more detailed numerical analyses of the problem and with experimental results. The analysis employs an energy balance crack propagation criterion and both constant specific fracture energy and a class of crack speed dependent fracture energies are considered. Among the features exhibited by the model is that, for constant specific fracture energy, the crack tip speed is constant from initiation up to arrest. On the other hand, for the same geometry and loading conditions, but a strongly crack speed dependent specific fracture energy, the crack speed decreases gradually between fracture initiation and crack arrest.     

A two dimensional asymmetrical crack problem

The distribution of stress in the neighborhood of a Griffith crack located asymmetrically in an infinitely long elastic strip is considered. It is assumed that the edges of the strip are stress free and that the crack is opened by an internal pressure varying along its length. Expressions are derived up to the order of δ^?8, where 2δ denotes the thickness of the strip, for the stress intensity factor, the shape of the deformed crack, and the crack energy.