Subsonic and intersonic mode II crack propagation with a rate-dependent cohesive zone

A recent experimental study has demonstrated the attainability of intersonic shear crack growth along weak planes in otherwise homogeneous, isotropic, linear elastic solids subjected to remote loading conditions (Rosakis et al., Science 284 (5418) (1999) 1337). The relevant experimental observations are summarized briefly here and the conditions governing the attainment of intersonic crack speeds are examined. Motivated by experimental observations, subsonic and intersonic mode II crack propagation with a rate-dependent cohesive zone is subsequently analyzed. A cohesive law is assumed, wherein the cohesive shear traction is either a constant or varies linearly with the local sliding rate. Complete decohesion is assumed to occur when the crack tip sliding displacement reaches a material-specific critical value. Closed form expressions are obtained for the near-tip fields. With a cohesive zone of finite size, it is found that the dynamic energy release rate is finite through out the intersonic regime. Crack tip stability issues are addressed and favorable speed regimes are identified. The influence of shear strength of the crack plane and of a rate parameter on crack propagation behavior is also investigated. The isochromatic fringe patterns predicted by the analytical solution are compared with the experimental observations of Rosakis et al. (1999) and comments are made on the validity of the proposed model.     

Extraction of cohesive-zone laws from elastic far-fields of a cohesive crack tip: a field projection method

A solution method of an inverse problem is developed to extract cohesive-zone laws from elastic far-fields surrounding a crack-tip cohesive zone. The solution method is named the “field projection method (FPM).” In the process of developing the method a general form of cohesive-crack-tip fields is obtained and used for eigenfunction expansions of the plane elastic field in a complex variable representation. The closing tractions and the separation-gradients at the cohesive zone are expressed in terms of orthogonal polynomial series expansions of the general-form complex functions. The series expansion forms a set of cohesive-crack-tip eigenfunctions, which is complete and orthogonal in the sense of the interaction J-integral in the far field as well as at the cohesive-zone faces. The coefficients of the eigenfunctions in the J-orthogonal representation are extracted directly, using interaction J-integrals in the far field between the physical field of interest and auxiliary probing fields. The path-independence of the interaction J-integral enables us to identify the cohesive-zone variables, i.e. tractions and separations, and thus the cohesive-zone constitutive laws uniquely from the far-field data. A set of numerical algorithms is developed for the inversion method and the results from numerical experiments suggest that the proposed algorithms are well suited for extracting cohesive-zone laws from the far-field data. The set includes methods to find the position and size of a cohesive zone. Further included are discussions on error analysis and stability of the inversion scheme.     

Spark-generated bubble collapse near or inside a circular aperture and the ensuing vortex ring and droplet formation

This paper aims to study the oscillation of a sparkgenerated submerged bubble located near or inside a circular aperture made in a flat plate using high-speed visualization technique. In the case of a bubble oscillating near an aperture the initial free surface of the water was set at the bottom surface of the plate. The effects of aperture size and bubblefree surface distance on the bubble behavior as well as on the ensuing droplet dynamics are investigated. It was found that the direction of the bubble reentrant jet was towards the aperture or away from it respectively when the normalized aperture size was smaller or greater than a certain critical value. In addition, a toroidal vortex ring was observed to form, which rotated inwards as it moved away from the aperture. It was also found that if the bubble was incepted at a distance sufficiently away from a supercritical size aperture a single droplet could be produced. In the case of a bub- ble initiated in the middle of a circular aperture submerged just beneath the water free surface, the bubble was found to take the shape of an ellipsoid during its expansion. Then a reentrant jet was initiated and pierced the bubble from its top side.     

Cohesive zone size of microcracks in brittle materials

Consideration of cohesive microcracks in continuum micromechanics is a challenging task since a lot of applications (such as, e.g., estimation of the stiffness of a microcracked solid) require a priori knowledge of the size of the cohesive zone. The latter, however, can be determined analytically only for the special case of Barenblatt–Dugdale cracks, i.e. for cracks with spatially constant cohesive tractions. Herein, we deal with the general case of spatially non-constant cohesive tractions: Generalizing the Barenblatt–Dugdale approach, we consider that each crack is surrounded by a plane annular cohesive zone characterized by a constitutive softening law (introduced as a power law) relating the vector of cohesive tractions to the displacement discontinuity. The size of this cohesive zone is then estimated using the theorem of minimum potential energy, based on a class of kinematically admissible displacement fields.     

MULTI-SCALE AGGREGATION OF PARTICLES IN GAS-SOLIDS FLUIDIZED BEDS

The multi-scale characteristics of clusters in a fast fluidized bed and of agglomerates in a fluidized bed of cohesive particles are discussed on the basis of large amounts of experiments.The cluster size and concentration are dominated by the local voidage of the bed.A cluster consists of many sub-clusters with different sizes and discrete par-ticles,and the sub-cluster size probability density distribution appears as a negative exponential function.The agglom-erates in a fluidized bed of cohesive particles also possess the multi-scale nature.The large agglomerates form a fixed bed at the bottom,the medium agglomerates are fluidized in the middle,and the small agglomerates and discrete parti-cles become the dilute-phase region in the upper part of the bed.The agglomerate size is mainly affected by cohesive forces and gas velocity.The present models for prediction the size of clusters and agglomerates can not tackle the in-trinsic mechanism of the multi-scale aggregation,and a challenging problem for establishing mechanistic model is put forward.     

“Frictionless” and “frictional” ThermoElastic Dynamic Instability (TEDI) of sliding contacts

Recently, we found that a new form of coupled instability, named ThermoElastic Dynamic Instability (TEDI), can occur by interaction between frictional heating and the natural dynamic modes of sliding bodies. This is distinct from the classical dynamic instabilities (DI) which is produced by an interaction between the frictional forces at the sliding interface and the natural modes of vibration of the bodies if the friction coefficient is sufficiently high, and also from ThermoElastic Instability (TEI), which is due to the interaction of frictional heating and thermal expansion, leading for example to low pitched brake noise above some critical speed. This result was relative to an highly idealized system, comprising an elastic layer sliding over a rigid plane including both dynamic and thermoelastic effects, but neglecting shear waves at the interface due to frictional tractions (from which the denomination “frictionless TEDI”). We demonstrate here that including these shear waves destabilizes both the shear and dilatational vibration modes of the system at arbitrarily small friction coefficients and speeds, where DI and TEI are predicted to be stable. A detailed study of the new modes and transient simulations show that for low pressures and high speed, the system tends towards the results of the previous model (“frictionless TEDI”), i.e. the tendency to a state in which the layer bounces over the plane, with alternating periods of sliding contact and separation. In the case of low speeds and high pressures, viceversa, the system is dominated by the modes near the resonance of the shear and dilatational modes, with a resulting complex behaviour, but generally leading to stick-slip regimes, reducing the jumping mode of “frictionless TEDI”, because stick reduces or stops frictional heating production.     

Delamination mechanism maps for a strong elastic coating on an elastic–plastic substrate subjected to contact loading

Hard wear resistant coatings that are subjected to contact loading sometimes fail because the coating delaminates from the substrate. In this report, systematic finite element computations are used to model coating delamination under contact loading. The coating and substrate are idealized as elastic and elastic–plastic solids, respectively. The interface between coating and substrate is represented using a cohesive zone law, which can be characterized by its strength and fracture toughness. The system is loaded by an axisymmetric, frictionless spherical indenter. We observe two failure modes: shear cracks may nucleate just outside the contact area if the indentation depth or load exceeds a critical value; in addition, tensile cracks may nucleate at the center of the contact when the indenter is subsequently removed from the surface. Delamination mechanism maps are constructed which show the critical indentation depth and force required to initiate both shear and tensile cracks, as functions of relevant material properties. The fictitious viscosity technique for avoiding convergence problems in finite element simulations of crack nucleation and growth on cohesive interfaces allows us to explore a wider parametric space that a conventional cohesive model cannot handle. Numerical results have also been compared to analytical analyses of asymptotic limits using plate bending and membrane stretching theories, thus providing guidelines for interpreting the simulation results.     

数学网格和物理网格分离的有限单元法(II):粘聚裂纹扩展问题中的应用

强化有限单元法将物理网格与数学网格分离开来,可以方便地描述非连续变形;粘聚区域模型是模拟断裂过程区作用最简单有效的方法,且可以避免裂纹尖端的应力奇异性.本文以平面问题为例,将强化有限单元法与粘聚区域模型相结合,利用富集数学节点描述任意粘聚裂纹扩展过程中的非连续变形问题,提出了裂纹扩展过程中数学节点富集和数学单元定义的方法.本文还导出了与平面4～8节点平面等参单元对应的8～16节点粘聚裂纹单元列武.最后,通过三点弯梁的裂纹扩展过程模拟验证了本文提出的粘聚裂纹扩展模拟方法的有效性.     

Some issues in the application of cohesive zone models for metal–ceramic interfaces

Cohesive zone models (CZMs) are being increasingly used to simulate discrete fracture processes in a number of homogeneous and inhomogeneous material systems. The models are typically expressed as a function of normal and tangential tractions in terms of separation distances. The forms of the functions and parameters vary from model to model. In this work, two different forms of CZMs (exponential and bilinear) are used to evaluate the response of interfaces in titanium matrix composites reinforced by silicon carbide (SCS-6) fibers. The computational results are then compared to thin slice push-out experimental data. It is observed that the bilinear CZM reproduces the macroscopic mechanical response and the failure process while the exponential form fails to do so. From the numerical simulations, the parameters that describe the bilinear CZM are determined. The sensitivity of the various cohesive zone parameters in predicting the overall interfacial mechanical response (as observed in the thin-slice push out test) is carefully examined. Many researchers have suggested that two independent parameters (the cohesive energy, and either of the cohesive strength or the separation displacement) are sufficient to model cohesive zones implying that the form (shape) of the traction–separation equations is unimportant. However, it is shown in this work that in addition to the two independent parameters, the form of the traction–separation equations for CZMs plays a very critical role in determining the macroscopic mechanical response of the composite system.     

Mechanics of advancing pin-loaded contacts with friction

This paper considers finite friction contact problems involving an elastic pin and an infinite elastic plate with a circular hole. Using a suitable class of Green's functions, the singular integral equations governing a very general class of conforming contact problems are formulated. In particular, remote plate stresses, pin loads, moments and distributed loading of the pin by conservative body forces are considered. Numerical solutions are presented for different partial slip load cases. In monotonic loading, the dependence of the tractions on the coefficient of friction is strongest when the contact is highly conforming. For less conforming contacts, the tractions are insensitive to an increase in the value of the friction coefficient above a certain threshold. The contact size and peak pressure in monotonic loading are only weakly dependent on the pin load distribution, with center loads leading to slightly higher peak pressure and lower peak shear than distributed loads. In contrast to half-plane cylinder fretting contacts, fretting behavior is quite different depending on whether or not the pin is allowed to rotate freely. If pin rotation is disallowed, the fretting tractions resemble half-plane fretting tractions in the weakly conforming regime but the contact resists sliding in the strongly conforming regime. If pin rotation is allowed, the shear traction behavior resembles planar rolling contacts in that one slip zone is dominant and the peak shear occurs at its edge. In this case, the effects of material dissimilarity in the strongly conforming regime are only secondary and the contact never goes into sliding. Fretting tractions in the forward and reversed load states show shape asymmetry, which persists with continued load cycling. Finally, the governing integro-differential equation for full sliding is derived; in the limiting case of no friction, the same equation governs contacts with center loading and uniform body force loading, resulting in identical pressures when their resultants are equal.     

Separation work analysis of cohesive law and consistently coupled cohesive law

An appropriate coupled cohesive law for predicting the mixed mode failure is established by combining normal separation and tangential separation of surfaces in the cohesive zone model(CZM) and the cohesive element method.The Xu-Needleman exponential cohesive law with the fully shear failure mechanism is one of the most popular models.Based on the proposed consistently coupled rule/principle,the Xu-Needleman law with the fully shear failure mechanism is proved to be a non-consistently coupled cohesive la...     

Dislocation shielding of a cohesive crack

Dislocation interaction with a cohesive crack is of increasing importance to computational modelling of crack nucleation/growth and related toughening mechanisms in confined structures and under cyclic fatigue conditions. Here, dislocation shielding of a Dugdale cohesive crack described by a rectangular traction-separation law is studied. The shielding is completely characterized by three non-dimensional parameters representing the effective fracture toughness, the cohesive strength, and the distance between the dislocations and the crack tip. A closed form analytical solution shows that, while the classical singular crack model predicts that a dislocation can shield or anti-shield a crack depending on the sign of its Burgers vector, at low cohesive strengths a dislocation always shields the cohesive crack irrespective of the Burgers vector. A numerical study shows the transition in shielding from the classical solution of Lin and Thomson (1986) in the high strength limit to the solution in the low strength limit. An asymptotic analysis yields an approximate analytical model for the shielding over the full range of cohesive strengths. A discrete dislocation (DD) simulation of a large (>10³) number of edge dislocations interacting with a cohesive crack described by a trapezoidal traction-separation law confirms the transition in shielding, showing that the cohesive crack does behave like a singular crack at very high cohesive strengths (∼7 GPa), but that significant deviations in shielding between singular and cohesive crack predictions arise at cohesive strengths around 1GPa, consistent with the analytic models. Both analytical and numerical studies indicate that an appropriate crack tip model is essential for accurately quantifying dislocation shielding for cohesive strengths in the GPa range.     

CRACK PROPAGATION IN POLYCRYSTALLINE ELASTIC-VISCOPLASTIC MATERIALS USING COHESIVE ZONE MODELS

Cohesive zone model was used to simulate two-dimensional plane strain crack propagation at the grain level model including grain boundary zones. Simulated results show that the original crack-tip may not be separated firstly in an elastic-viscoplastic polycrystals. The grain interior's material properties (e.g. strain rate sensitivity) characterize the competitions between plastic and cohesive energy dissipation mechanisms. The higher the strain rate sensitivity is, the larger amount of the external work is transformed into plastic dissipation energy than into cohesive energy, which delays the cohesive zone rupturing. With the strain rate sensitivity decreased, the material property tends to approach the elastic-plastic responses. In this case, the plastic dissipation energy decreases and the cohesive dissipation energy increases which accelerates the cohesive zones debonding. Increasing the cohesive strength or the critical separation displacement will reduce the stress triaxiality at grain interiors and grain boundaries. Enhancing the cohesive zones ductility can improve the matrix materials resistance to void damage.     

THE BNARD CONVECTION IN A LAYER OF FLUID WITH A TIME-DEPENDENT MEAN TEMPERATURE

The onset of Bénard convection, or the critical Rayleigh number in a layer of fluid with a time-dependent mean temperature has been investigated theoretically. The critical Rayleigh number is regarded as a function of time and is expanded in series of a small parameter. Up to second approximation a simple expression of critical Rayleigh number is obtained for the time region for away from the point of zero.     

临近边坡的基础的极限承载力

本文推导了了靠近边坡的基础的极限承载力计算公式,它由地基内摩擦角,粘聚力,土壤比生,以及几何参数：基础宽,坡顶距和坡角等完全决定。     

THE INTERACTIONS BETWEEN WAVE AND COHESIVE SEDIMENT

淤泥质海岸泥沙运动活跃,泥沙淤积问题严重,直接关系到岸滩演变和海岸防护. 该文主要综合国内外有关研究成果,对淤泥质海岸黏性泥沙的流变特性,波浪与底泥之间的相互作用,波浪衰减以及波浪作用下的底泥质量输移作简要总结,供进一步研究参考.     

Characterization of strongly interacted multiple cracks in an infinite plate

Based on the Kachanov method and the alternating iteration technique, a new method is proposed to deal with the problem of the strongly interacted multiple cracks in an infinite plate. Unlike the Kachanov method which neglects the interaction of the tractions of the non-uniform components, the tractions of the non-uniform components on the surfaces of cracks are considered through the alternating technique. The accuracy and efficiency of present method are validated by comparing the results of two collinear and two parallel overlapped open the cracks obtained by the present method with those of the exact solutions, the results of the Kachanov method and the alternating iteration technique. Applications of present method in solving sliding close crack problems and evaluating the plastic zones demonstrate the versatility of present method.     

内聚力模型的形状对胶接结构断裂过程的影响

内聚力模型被广泛应用于粘接结构的断裂数值模拟过程中,为深入分析不同形状内聚力模型与胶黏剂性质和粘接结构断裂之间的关系,本文分别采用脆性和延展性两种类型胶黏剂,对其粘接的对接试件进行了单轴拉伸、剪切实验,以及其粘接的双臂梁试件进行了断裂实验.3种类型的内聚力模型(抛物线型、双线型和三线型)分别模拟了以上粘接结构的断裂过程,并与实验结果进行对比.结果发现:双线型的内聚力模型适用计算脆性胶黏剂的拉伸与剪切的断裂过程;指数型内聚力模型较适合计算延展性胶黏剂的拉伸和剪切的断裂过程,临界应力、断裂能和模型的形状参数是分析拉伸和剪切的重要参数;双臂梁试件的断裂过程模拟结果发现,断裂曲线与胶黏剂性质有关,内聚力模型形状参数也有影响.通过实验与计算结果分析,双线型内聚力模型更适合脆性胶黏剂粘接的双臂梁断裂计算,而三线型更适合计算延展性胶黏剂粘接的双臂梁断裂过程,此研究结果对胶黏剂的使用和粘接结构的断裂分析有很重要意义.     

Stability of free convection in a rotating porous layer distant from the axis of rotation

The stability and onset of convection in a rotating fluid saturated porous layer subject to a centrifugal body force and placed at an offset distance from the center of rotation is investigated analytically. The marginal stability criterion is established in terms of a critical centrifugal Rayleigh number and a critical wave number for different values of the parameter representing the dimensionless offset distance from the center of rotation. At the limit of an infinite distance from the center of rotation the results are identical to the convection resulting from heating a porous layer from below subject to the gravitational body force. At the other limit, when the parameter controlling the offset distance approaches zero, the results converge to previously found solutions for the convection in a porous layer adjacent to the axis of rotation. The results provide the stability map for all positive values of the parameter controlling the offset distance from the center of rotation, hence bridging the gap between the two extreme limit cases.