Crack movement in layered composites under electric field affect

The variation principle is applied for defining a crack in the solid body. The methods proposed in [G. Sih, C. Chen, Non-self-similar crack growth in elastic–plastic finite thickness plate, Theoretical and Applied Fracture Mechanics 3 (1985) 125–139] extend to presence of electromagnetic fields in material. Crack propagation in non-homogeneous media has been considered. It is shown that electromagnetic fields in the material are essentially affecting the trajectory. The crack trajectory stability has been studied as function of fracture energy, phase portraits of the trajectory in different media have been built, and various attractor types have been revealed. Different crack morphologies from single straight and oscillating crack propagation to straight double crack propagation were theoretically founded. In compliance with the experimental data of [R. Niefanger, V.-B. Pham, G. Schneider, H.-A. Bahr, H. Balke, U. Bahr, Quasi-static straight and oscillatory crack propagation in ferroelectric ceramics due to moving electric field: experiments and theory, Acta Materialia 52 (1) (2004) 117–127], it has been demonstrated that periodic electromagnetic field results in trajectory stochastization. This can be used for switching the crack over from the mode of mainline propagation into the mode of development of the field of diffused microcracks.     

Energy approach to crack growth in a fiber-reinforced brittle material modeled by an inclusion

Brittle materials randomly reinforced with a low volume fraction of strong, stiff and ductile fibers are considered, with specific reference to fiber-reinforced cements and concrete. Visible cracks in such materials are accompanied by a surrounding damage zone – together these constitute a very complex “crack system”. Enormous effort has been put into trying to understand the micromechanics of such systems. Almost all of these efforts do not deal with the “crack system” propagation behavior as a whole. The propagation process of such a “crack system” includes propagation of the visible crack and the growth of the damage zone. Propagation may take place by lengthening of the visible crack together with the concomitant lengthening of the surrounding damage zone, or simply by broadening of the damage zone while the visible crack length remains unchanged – or simultaneously by growth of both types. A phenomenological completely theoretical model (for an ideal material) is here proposed which can serve to examine the propagation process by means of energy principles, without recourse to the microscopic details of the process. An application of this theoretical approach is presented for the case of a damage zone evolving with a rectangular shape. This shape is chosen because it is expected that it will illustrate the nature of damage evolution and because the computational procedure necessary to follow the growth is the most straightforward.     

Assessing the effect of residual stresses on the fatigue behavior of integrally stiffened structures

Residual stresses emerge quite often in real structures due to the various manufacturing processes such as, welding, forming, cutting, milling, etc. In such cases, development of cracks at regions influenced by manufacturing operations demand additional attention. In the present work a numerical methodology has been developed, based on three-dimensional Finite Element Analysis, for the calculation of Stress Intensity Factors at cracks in welded components. The residual stress fields, which are used in SIF calculations, have been computed by the numerical simulation of the thermo-mechanical process. A numerical algorithm based on interpolation principles is developed, in order to introduce the three-dimensional field in the computational model of the cracked structure. The SIF calculation methodology is initially validated for the case of a welded plate by comparison of numerical results with existing analytical solutions. A cracked stiffened panel is analysed afterwards and the calculated fatigue crack propagation results are compared to experimentally measured data. Finally, the numerical procedure is applied to study the effect of more complicated residual stress fields on SIF values developing at cracks located in stiffened panels.     

A numerical study of crack tip constraint in ductile single crystals

In this work, the effect of crack tip constraint on near-tip stress and deformation fields in a ductile FCC single crystal is studied under mode I, plane strain conditions. To this end, modified boundary layer simulations within crystal plasticity framework are performed, neglecting elastic anisotropy. The first and second terms of the isotropic elastic crack tip field, which are governed by the stress intensity factor K and T-stress, are prescribed as remote boundary conditions and solutions pertaining to different levels of T-stress are generated. It is found that the near-tip deformation field, especially, the development of kink or slip shear bands, is sensitive to the constraint level. The stress distribution and the size and shape of the plastic zone near the crack tip are also strongly influenced by the level of T-stress, with progressive loss of crack tip constraint occurring as T-stress becomes more negative. A family of near-tip fields is obtained which are characterized by two terms (such as K and T or J and a constraint parameter Q) as in isotropic plastic solids.     

利用岩石声发射凯塞效应测定岩体地应力

将砂岩在整个变形阶段的声发射信号特征可划分为加载初期、压密阶段、裂纹稳定扩展阶段、裂纹非稳定扩展阶段、砂岩破坏阶段5部分。利用岩样声发射信号的特征,确定出岩石的凯塞效应点与其裂纹稳定扩展阶段的起始点相对应,并进一步得出岩石凯塞效应点的上限为裂纹稳定扩展阶段的终点,裂纹非稳定扩展阶段的起始点。凯塞效应点受岩样两端面的平行度、压机加载速率等有关,岩样端面不平整,在加载初期会有强烈的声发射信号;压机加载速率过大,声发射信号可能显示不出来或被后续更强的声发射信号所掩盖。计算出深度为670m处巷道周围天然应力3个主应力的大小和方向,与在现场用应力解除法和水压致裂法测得的天然应力相比,其数值基本一致,但方向存在一定的偏差。     

Mode III effects on interface delamination

For crack growth along an interface between dissimilar materials the effect of combined modes I, II and III at the crack-tip is investigated. First, in order to highlight situations where crack growth is affected by a mode III contribution, examples of material configurations are discussed where mode III has an effect. Subsequently, the focus is on crack growth along an interface between an elastic-plastic solid and an elastic substrate. The analyses are carried out for conditions of small-scale yielding, with the fracture process at the interface represented by a cohesive zone model. Due to the mismatch of elastic properties across the interface the corresponding elastic solution has an oscillating stress singularity, and this solution is applied as boundary conditions on the outer edge of the region analyzed. For several combinations of modes I, II and III crack growth resistance curves are calculated numerically in order to determine the steady-state fracture toughness. For given values of K_I and K_II the minimum fracture toughness corresponds to K_III=0 in most of the range analyzed, but there is a range where the minimum occurs for a nonzero value of K_III.     

Refined Dugdale plastic zones of an external circular crack

The refined Dugdale-type plastic zones ahead of an external circular crack, subjected to a uniform displacement at infinity, are evaluated both analytically and numerically. The analytical method utilizes potential theory in classical linear elasticity with emphasis on the contrast from the internal crack problem. A closed-form solution to the mixed boundary problem is obtained to predict the length of the plastic zone for a Tresca yield condition. The analytical solution is also used to benchmark the results obtained from the numerical method, which show good agreement. Through an iterative scheme, the numerical technique is able to estimate the size of crack tip plasticity zone, which is governed by the non-linear von Mises criterion. The relationships between the applied displacement and the length of the plastic zone are compared for the different yielding conditions. Computational modeling has demonstrated that the plastic constraint effect based on the true yield condition can significantly influence the load-bearing capacity. It is also discovered from the comparative study that the stress components predicted by the three different yield conditions may differ notably; however, the stress triaxiality in the ligament region has only small deviations. The proposed study may find applications in predicting the plastic flow in a circumferentially notched round bars under tension.     

Understanding crack growth in fuselage lap joints

The problem of multi-site damage and multiple interacting cracks is one experienced by many aircraft manufacturers and operators. This paper focuses on understanding the phenomena, and on developing a predictive capability that can form the engineering framework for maintaining continued airworthiness. To this end the present paper uses a simple formulation based on the Frost–Dugdale crack growth law to study the problem of cracking at fastener holes in fuselage lap joints and shows that the predicted crack growth history is in good agreement with both experimental results and with fleet data.     

Modified boundary layer analysis of an electrode in an electrostrictive material

A thin electrode embedded in an electrostrictive material under electric loading is investigated. In order to obtain an asymptotic form of electric fields and elastic fields near the electrode edge, we consider a modified boundary layer problem of an electrode in an electrostrictive material under the small scale saturation condition. The exact electric solution for the electrode is obtained by using the complex function theory. It is found that the shape of the electric displacement saturation zone is sensitive to the transverse electric displacement. A perturbation solution of stress fields induced by incompatible electrostrictive strains for the small value of the transverse electric displacement is obtained. The influence of transverse electric displacement on a microcrack initiation from the electrode edge is also discussed.     

Deflection criterion of a crack approaching a bi-material interface obliquely

Deflection criterion for oblique cracks terminating at a bi-material interface was established numerically based on a remote loading condition where the crack deflection event took place well within the K-dominant stress field. The criterion was described in terms of the ratio of the energy release rate of a deflected crack (G _d) to the maximum energy release rate of a penetrated crack (). The criterion was markedly more conservative than the existing solution based on wedge loading which did not converge with respect to limited number of a/L ratios in the literature (a is the size of the putative crack; L is the loading distance). Further, the criterion established herein for the cracks slightly oblique from the normal direction to the interface was more conservative than the crack normal to the interface.