Crack tip rotation and shear strain on crack edge of mode II crack in anisotropic plate

Rigid body rotation is obtained at the points near the tip of a mode II crack in an infinite anisotropic plate. From Lekhnitskii's complex analysis the rotation is derived in terms of complex potentials and the material parameters. A relation of crack tip rotation is proposed by incorporating the mode II stress intensity factor and material constants of an anisotropic plate. The shear strain on the crack edge is calculated on the basis of rotation at the points lying on the crack edge.     

Rigid body rotation surrounding the mode II crack

Using Westergaard function in conventional and also in modified form the rigid body rotation at the crack tip and near the crack edges of mode II cracks are obtained. An attempt is made to explain the deformed configuration of a mode II crack. The rotation at the end of the plastic shear strip ahead of the crack tip is shown to be independent of the stress intensity factor. The rotation field in the vicinity of a crack tip under combined mode I and mode II conditions is obtained.     

Rotation at the crack tip under uniform heat flow in an infinite medium

A complex analysis of rigid body rotation is presented. The crack-tip rotation for a line crack subjected to steady uniform heat flow is obtained in terms of thermal stress intensity factor in shear mode of the crack, the material and thermal parameters and coordinates of points close to the crack tip. The shear strip configuration is analysed on the basis of rotation and displacement at the end of the shear strip.     

Rigid body rotation at the tip of a slant crack in an infinite plate

Using Kolosov-Muskhelishvili relations of stresses the rigid body rotation is obtained in the form of complex potentials. The rotation at a point near the tip of a slant crack is expressed in terms of stress intensity factors and the coordinates (r, ) of the point. The relation of rigid body rotation near the crack tip are used to describe some features of mode I and mode II crack tip plastic zone. The rotation field surrounding the tip of a slant crack in infinite plate is obtained and its properties are discussed.

---

Résumé En utilisant les relations de Kolosov-Muskhelishvili relatives aux contraintes, on obtient la rotation d'un corps rigide sous forme de potentiels complexes. La rotation en un point près de l'extrémité d'une fissure inclinée est exprimée en fonction du facteur d'intensité d'entaille et des coordonnées (r-) do point. On utilise les relations de rotation d'un corps rigide au voisinage de l'extrémité d'une fissure pour décrire certaines caractéristiques de la zone plastique à l'extrémité d'une fissure de mode I et de mode II. Le champ rotationnel autour de l'extrémité d'une fissure inclinée dans une plaque infinie est obtenue et ses propriétés sont discutées.

     

Branch crack development from the flank of a fatigue crack propagating in mode II

The propagation of fatigue cracks in mode II often leads to the development of a branch starting from a crack flank, some distance behind the tip and not to the expected bifurcation at the crack tip. This type of branch is suggested to initiate by decohesion along a secondary slip plane and to grow in mode I due to the tensile component of the mode II stress field. Finite element calculations are performed to evaluate the stress intensity factors for the main crack and the branch as a function of the position of the latter. It is shown that the branch has a substantial shielding effect on the main crack and generates contact forces along its flanks. The simultaneous and competitive growth of the main crack and the branch in fatigue is simulated step by step using kinetic data for mode II and mode I obtained for a maraging steel.     

Stress singularities for crack normal to and terminating at bimaterial interface on orthotropic half-plates

The problem of a crack normal to and terminating at an interface in two joined orthotropic plates is considered and the eigenequation for the asymptotic behavior of stresses at the crack tip on the interface is given in an explicit form. It is found that the singular stress field around the crack tip can be separated into two independent fields, respectively of the mode I and II. Also it is found that for both the mode I and II deformations the effects of elastic constants on the stress singularity order can be respectively expressed by three material parameters, two of which are the same for both the mode I and mode II deformations.     

Effect of cooperative grain boundary sliding and migration on dislocation emitting from a semi-elliptical blunt crack tip in nanocrystalline solids

A theoretical model is established to investigate the interaction between the cooperative grain boundary (GB) sliding and migration and a semi-elliptical blunt crack in deformed nanocrystalline materials. By using the complex variable method, the effect of two disclination dipoles produced by the cooperative GB sliding and migration process on the emission of lattice dislocations from a semi-elliptical blunt crack tip is explored. Closed-form solutions for the stress field and the force acting on the dislocation are obtained in complex form, and the critical stress intensity factors for the first dislocation emission from a blunt crack under mode I and mode II loadings are calculated. Then, the influence of disclination strength, curvature radius of blunt crack tip, crack length, locations and geometry of disclination dipoles, and grain size on the critical stress intensity factors is presented detailedly. It is shown that the cooperative GB sliding and migration and the grain size have significant influence on the dislocation emission from a blunt crack tip.     

Numerical analysis of blunting of a crack tip in a ductile material under small-scale yielding and mixed mode loading

The blunting of the tip of a crack in a ductile material is analysed under the conditions of plane strain, small-scale yielding, and mixed mode loading of Modes I and II. The material is assumed to be an elastic-perfectly plastic solid with Poisson's ratio being 1/2. The stress and strain fields for a sharp crack under mixed mode loading are first determined by means of elastic-plastic finite element analysis. It is shown that only one elastic sector exists around the crack tip, in contrast with the possibility of existence of two elastic sectors as discussed by Gao. The results obtained for a sharp crack are used as the boundary conditions for the subsequent numerical analysis of crack tip blunting under mixed mode loading, based on slip line theory. The characteristic shapes of the blunted crack tip are obtained for a wide range of Mode I and Mode II combinations, and found to resemble the tip of Japanese sword. Also the stress field around the blunted crack tip is determined.     

Distribution of dislocations at a mode I crack tip and their shielding effect

Distribution of dislocations at a finite mode I crack tip is formulated. Closed form solutions for the dislocation distribution function, the dislocation-free zone (DFZ), the local stress intensity factor and the crack tip stress field are obtained. The dislocation distribution has similar features to a mode III crack model. Under a given applied stress, there may exist different configurations of plastic zone and DFZ. Crack tip shielding by dislocations depends on both applied stresses and the configuration.     

Mixed mode fatigue crack growth: A literature survey

The applications of fracture mechanics have traditionally concentrated on crack growth problems under an opening or mode I mechanism. However, many service failures occur from growth of cracks subjected to mixed mode loadings. This paper reviews the various criteria and parameters proposed in the literature for predictions of mixed mode crack growth directions and rates. The physical basis and limitations for each criterion are briefly reviewed, and the corresponding experimental supports are discussed. Results from experimental studies using different specimen geometries and loading conditions are presented and discussed. The loading conditions discussed consist of crack growth under mode II, mode III, mixed mode I and II, and mixed mode I and III loads. The effects of important variables such as load magnitudes, material strength, initial crack tip condition, mean stress, load non-proportionality, overloads and crack closure on mixed mode crack growth directions and/or rates are also discussed.     

Numerical and experimental analysis of residual stresses for fatigue crack growth

In this paper computational and experimental results are presented concerning residual stress effects on fatigue crack growth in a Compact Tension Shear (CTS) specimen under cyclic mode I loading. For a crack of constant length it is found that hardly any compressive residual stresses or crack closure effects are generated along the crack surfaces behind the crack tip through the considered cyclic mode I loading with a load ratio of R=0.1. Only if fatigue crack growth is modelled during the simulation of the cyclic loading process these well-known effects are found. On the other hand it is shown that they have hardly any influence on the residual stresses ahead of the crack tip and thus on further fatigue crack growth. For all cases considered the computational finite element results agree well with the experimental findings obtained through X-ray diffraction techniques.     

Investigation of crack tunneling in ductile materials

Crack tunneling has been commonly observed in crack growth experiments on specimens made of ductile materials such as steel and aluminum alloys. The objective of this study is to investigate the crack tunneling phenomenon and study the effects of crack tunneling on the distribution of several mechanics parameters controlling ductile fracture. Three-dimensional (3D) elastic-plastic finite element analyses of stable tearing experiments involving tunneling fracture are carried out. Two model problems based on stable tearing experiments are considered. The first model problem involves a plate specimen containing a stationary, single-edge crack with a straight or tunneled crack front, under remote mode I loading. In the numerical analyses, the crack tip opening displacement, the von Mises effective stress, the mean stress, the stress constraint and the effective plastic strain around straight and tunneled crack fronts are obtained and compared. It is found that crack tunneling produces significant changes in the stress and deformation fields around the crack front. The second model problem involves a specimen containing a stably growing single-edge crack with a straight or tunneled crack front, under remote mode I loading. Crack growth events with a straight or tunneled crack front are simulated using the finite element method, and the effect of crack tunneling on the prediction of the load-crack-extension response based on a CTOD fracture criterion is investigated.     

Large crack tip deformations and plastic crack advance during fatigue

Finite-deformation elastoplastic analysis of a crack subjected to mode I cyclic loading under small scale yielding was performed. The influence of the load range, load ratio and overload on the crack tip deformations is presented. Cyclic crack tip opening displacements agreed with predictions of simpler models, where available. Crack closure was not detected. Plastic crack advance was evidenced. Its rate per cycle reproduced common trends of the fatigue cracking dependence on loading range and overload.     

On a thermo-mechanical effect and criterion of crack propagation

A thermo-mechanical effect from partial conversion of fracture work into heat energy during crack propagation is considered with a simple mathematical model. It is assumed that the heat production zone in the vicinity of the crack tip is very small. Thus, the crack propagation process can be viewed as propagation of the crack in elastic material with a point thermal heat source fixed at the tip of the crack. This thermal heat source generates its own temperature and stress fields around the crack tip. As shown in this paper it also generates a negative stress intensity factor that specifies fracture mode I and has to be accounted for in the energetic fracture criterion. The model developed may help to explain many experimental observations such as the increase in the specific surface energy that accompanies an increase in the crack speed and why fracture mode I has a special role in crack propagation phenomena.     

An analysis of a fracture specimen for rough crack in shear

In this paper, a BEM formulation predicting the reduced mode II and the enhanced mode I stress intensity factors of the mode II test specimen caused by fracture surface roughness is presented. The dilatant boundary conditions (DBC) are based on the assumptions of idealized uniform sawtooth crack surfaces and an effective Coulomb sliding law. They are obtained by relating the crack opening displacement and crack sliding displacement through the assumption of rigid body asperity sliding as in Young (1999). Three different types of crack, i.e. (1) non-interfering flat closed crack; (2) DBC with elastic crack tip; and (3) DBC with plastic crack tip are discussed. The results show a good approximation of the present BEM model. This study also shows the potential application of the present method determining the effect of crack face roughness in a realistic experimental specimen.     

Effect of crack closure on non-linear crack tip parameters

Crack closure concept has been widely used to explain different issues of fatigue crack propagation. However, some authors have questioned the relevance of crack closure and have proposed alternative concepts. The main objective here is to check the effectiveness of crack closure concept by linking the contact of crack flanks with non-linear crack tip parameters. Accordingly, 3D-FE numerical models with and without contact were developed for a wide range of loading scenarios and the crack tip parameters usually linked to fatigue crack growth, namely range of cyclic plastic strain, crack tip opening displacement, size of reversed plastic zone and total plastic dissipation per cycle were investigated. It was demonstrated that: (i) LEFM concepts are applicable to the problem under study; (ii) the crack closure phenomenon has a great influence on crack tip parameters decreasing their values; (iii) the ΔK_eff concept is able to explain the variations of crack tip parameters produced by the contact of crack flanks; and (iv) the analysis of remote compliance is the best numerical parameter to quantify the crack opening level. Therefore the crack closure concept seems to be valid. Additionally, the curves of crack tip parameters against stress intensity factor range obtained without contact may be seen as master curves.     

On the effect of the residual stresses on the crack opening displacement in a cracked sheet

The residual stress and displacement fields caused by localized plastic flow near a mode I crack tip in a sheet under plane stress conditions are investigated. The present study founds on the classical Dugdale scheme of the plastic flow localization. The residual stress field is considered to be induced by reversed plastic flow near the crack tip caused by an unloading. As it is found the residual stresses around the crack compress the crack tip, while the residual tensile stresses in a distant from the crack tip zone occur. It is shown the maximum residual tensile stresses can reach the significant value of the one third of the yield limit. The length of the compressed plastic zone and the residual displacement distributions are obtained. The exact formula for the residual crack opening displacement to estimate the crack closure is found. Then the next loading of the cracked plate is considered. It is shown that the second loading causes the origin of two plastic zones localized near the crack tip and at the point, where the maximum residual tensile stresses are concentrated. Again, according to the Dugdale scheme of the plastic localization, both the plastic flow zones are modelled as narrow stripes on the line extending the crack. To determine three non-dimensional parameters, characterizing the position of the segment-like plastic flow zones, a non-linear system of equations is obtained and analyzed. The exact formula for the crack opening displacement after a loading–unloading cycle is obtained. An asymptotic analysis (as the linear dimension of the distant plastic flow zone compared with the actual crack length is small) is given. It shows that the effect of the distant plastic flow zone appears as some complementary crack closure.     

Unsteady growth of mode III crack in elastic perfectly-plastic material

In this paper the assembly of the near-tip fields given by J. R. Rice is completed for the mode III crack growing quasi-statically and unsteadily in elastic perfectly-plastic material. The obtained results provide a particular example for the general theoretical relations between the steady state and unsteady state crack growth. Further, the general expression of the rate of crack opening displacement is obtained, which is similar to one by J.R. Rice and co-workers for mode I crack growing in elastic perfectly-plastic material. The fracture criterion of the critical opening displacement at a prescribed distance behind the crack tip is discussed. As a result, the theoretical J-resistance curves are given.     

Analysis of the stress intensity factor dependence with the crack velocity using a lattice model

In this work, the influence of crack propagation velocity in the stress intensity factor has been studied. The analysis is performed with a lattice method and a linear elastic constitutive model. Numerous researchers determined the relationship between the dynamic stress intensity factor and crack propagation velocity with experimental and analytical results. They showed that toughness increases asymptotically when the crack tip velocity is near to a critical. However, these methods are very complex and computationally expensive; furthermore, the model requires the use of several parameters that are not easily obtained. Moreover, its practical implementation is not always feasible. Hence, it is usually omitted. This paper aims to capture the physics of this complex problem with a simple fracture criterion. The selected criterion is based on the maximum principal strain implemented in a lattice model. The method used to calculate the stress intensity factor is validated with other numerical methods. The selected example is a finite 2D notched under mode I fracture and different loads rates. Results show that the proposed model captures the asymptotic behaviour of the SIF in function of crack speed, as reported in the aforementioned models.