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.     

Rotation at the crack tip and COD of mode I crack in anisotropic plate

Rigid body rotation is obtained at the points near crack tip of mode I crack in infinite anisotropic plate. Using Lekhnitskii's complex analysis procedure the rotation is expressed in terms of complex potentials and complex parameters of the material. A relation of crack tip rotation is obtained by incorporating the stress intensity factor and complex parameters for the known crack configuration. An equation of crack opening displacement is derived. For the case of plates made of composite materials the features of crack tip rotation and crack edge profile due to mode I loading are described.     

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.

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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.

     

VECTOR CTD CRITERION APPLIED TO MIXED MODE FATIGUE CRACK GROWTH

Abstract— This work is aimed at developing a general parameter based on the deformation intensity at a mixed mode crack tip to predict crack growth behaviour, especially in the near threshold region. Being a mechanisms-related parameter, the vector crack tip displacement (CTD) is defined as a vector summation of CTOD and CTSD_c which act, respectively in the directions of mode I and mode II fatigue crack growth. The basic assumption is that both direction and rate of mixed mode fatigue crack growth are governed by the vector ΔCTD, which represents the resultant of the "driving force"at the crack tip. The analytical predictions obtained by using the vector ΔCTD are in good agreement with the reported experimental results of mixed mode I and II fatigue cracks.     

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.     

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.     

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.     

Mode II wood fracture characterization using the ELS test

This paper describes experimental and numerical studies on the application of the end loaded split test to mode II wood fracture characterization. A new data reduction scheme, based on the specimen compliance and on the equivalent crack concept, is proposed. The method presents three main advantages relatively to the classical methodologies: it does not require crack measurement during propagation; it accounts for the root rotation at the clamping point and includes the effect of the fracture process zone at the crack tip. The new procedure was numerically validated using a two-dimensional finite element analysis including a cohesive damage model, which allows the simulation of crack initiation and growth. The results demonstrated the good performance of the model and the applicability of the end loaded split test for mode II wood fracture characterization.     

A new method for determining mode II R-curve by the End-Notched Flexure test

A new method for obtaining the mode II R-curve in a End-Notched Flexure test is proposed in the present work. New compliance and energy release rate equations have been derived incorporating shear, local deformation and bending rotation effects.Mode II R-curve, which represents energy release rate as a function of crack extension, is obtained without optical determination of crack tip position. Crack length and energy release rate are determined at each point of the test based on experimental compliance until unstable advance occurs. In order to confirm the theoretical models, unidirectional carbon/epoxy specimens have been tested. Experimental data are evaluated by means of two reduction schemes: an existing data method named Corrected Beam Theory with effective crack length and the new method named Beam Theory including Bending Rotation effects. Shear and local deformation effects are included in both reduction schemes.Results concerning the determination of crack length without crack advance and during stable crack propagation are presented. The agreement between experimental values and theoretical results obtained by the new approach is excellent. Based on the accurate crack length determination at each point of the test, energy release rate is determined point to point and therefore R-curve is obtained.     

II型III型动态裂纹尖端断裂过程区近似评估方法

动态裂纹尖端断裂过程区轮廓的确定问题仍然是一个没有得到完全解决的问题。基于弹性动力学的理论和复应力函数方法,提出一种伪应力函数方法,用于近似评估动态裂纹尖端应力场。通过与已知应力场计算结果对比,验证了伪应力函数的正确性。利用此近似方法通过Von Mises强度准则和Tresca强度准则,分别确定了不同强度准则条件下、不同裂纹扩展速度下断裂过程区的轮廓。计算结果表明:II型和III型动态裂纹尖端断裂过程区关于裂纹面对称分布,随着裂纹扩展速度增大而增大。当裂纹传播速度接近瑞利波速时,断裂过程区变化加剧。利用Tresca强度准则计算得到的动态裂纹尖端断裂过程区面积比利用Von Mises强度准则计算得到的断裂过程区的面积大。     

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.     

Estimation of the plastic zone by finite element method under mixed mode (I and II) loading

Material fracture by opening (mode I) is not lonely responsible for fracture propagation. Many industrial examples show the presence of mode II and mixed mode I + II. The present work consists in the elaboration of a code to estimate the size of the plastic zone at the crack tip under mode I, mode II and mixed mode I + II loading. The computations are made according to Von Mises and Tresca criteria. The results obtained are compared to those measured by experiments.     

Threshold and growth mechanism of fatigue cracks under mode II and III loadings

ABSTRACT The fatigue crack growth behaviour of 0.47% carbon steel was studied under mode II and III loadings. Mode II fatigue crack growth tests were carried out using specially designed double cantilever (DC) type specimens in order to measure the mode II threshold stress intensity factor range, ΔK_IIth. The relationship ΔK_IIth > ΔK_Ith caused crack branching from mode II to I after a crack reached the mode II threshold. Torsion fatigue tests on circumferentially cracked specimens were carried out to study the mechanisms of both mode III crack growth and of the formation of the factory‐roof crack surface morphology. A change in microstructure occurred at a crack tip during crack growth in both mode II and mode III shear cracks. It is presumed that the crack growth mechanisms in mode II and in mode III are essentially the same. Detailed fractographic investigation showed that factory‐roofs were formed by crack branching into mode I. Crack branching started from small semi‐elliptical cracks nucleated by shear at the tip of the original circumferential crack.     

Delamination in elastic shear deformable circular layers

This work extends the analytical solution of an interface crack in straight layered structures to circular layered structures. A small segment at the vicinity of an interface crack tip in a circular laminated beam is analyzed by a novel shear deformable bi-layered circular beam theory. Two concentrated forces are found existing at the crack tip due to the requirement of the equilibrium condition. Closed-form solution of the total energy release rate of the interface crack is obtained as the half of the product of the concentrated forces and the corresponding displacement gradient discontinuities at the crack tip. Closed-form expressions of the mode I and II components of the energy release rate are also obtained by global and local methods. Numerical verifications are conducted by analyzing the interlaminar delamination of a circular beam with an edged crack and comparing with the baseline results obtained through finite element analysis. Excellent agreements between the present method and finite element analysis on the predictions of total energy release rate and mode partition verify the accuracy and efficiency of the present solution.     

The effect of T‐stress on crack‐tip plastic zones under mixed‐mode loading conditions

In this paper, the influence of T‐stress on crack‐tip plastic zones under mixed‐mode I and II loading conditions is examined. The crack‐tip stress field is defined in terms of the mixed‐mode stress intensity factors and the T‐stress using William's series expansion. The crack‐tip stress field is incorporated into the Von Mises yield criteria to develop an expression that determines the crack‐tip plastic zone. Using the resultant expression, the plastic zone is plotted for various combinations of mode II to mode I stress intensity factor ratios and levels of T‐stress. The properties of the plastic zone affected by T‐stress and mixed‐mode phase angle are discussed. The observations obtained on plastic zones variations are important for further fatigue and fracture analyses for defects in engineering structures under mixed‐mode loading conditions.     

ANALYSIS OF CRACK TIP HYDROGEN DISTRIBUTION UNDER I/II MIXED MODE LOADS

Abstract— The distribution of hydrogen in the vicinity of a crack tip was studied using SIMS (Secondary Ion Mass Spectrometry) under different ratios of I/II mixed mode loads. Modified WOL specimens with kinked slits were employed in the course of the experimental work. Spectrographic measurements show that under I/II mixed mode loading, both in the HIC and in the r ^max_p directions, there are two hydrogen accumulation peaks ahead of the crack tip, corresponding to the location of the maximum hydrostatic stress and maximum equivalent plastic strain, respectively. Based on results obtained over a range of loading conditions from mode I to a high K_II/ K_I, ratio, it is shown that the mode II component has a clear influence on both peaks. The conditions for hydrogen redistribution are discussed in terms of crack tip stress-strain fields.     

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.     

The Stress Intensity Factor of an Edge Dislocation Near an Elliptically Blunted Crack Tip

The stress field around the tip of an elliptically blunted crack induced by an edge dislocation has been obtained in closed form, from which the mode I and mode II stress intensity factors induced by the edge dislocation are obtained. The solutions apply to the edge dislocation either emitted from crack-tip surface or originated elsewhere, and for the dislocation located anywhere around the crack tip. The effects of the crack length, the crack-tip bluntness, the origination and position of the dislocation on the stress intensity factors are examined.     

A geometric model for fatigue crack closure induced by fracture surface roughness under mode I displacements

A geometric model dealing with the roughness-induced fatigue crack closure under mode I displacements is proposed. It is shown that roughness-induced crack closure can also be acquired without mode II and III displacements at the crack tip. In this mechanism, the severe contact region is near the crack tip. The average crack closure ratio is the result of discrete asperities which come into contact.     

Evaluating mixed-mode stress intensity factors from full-field displacement fields obtained by optical methods

A method for evaluating mode I, mode II and mixed-mode stress intensity factors from in-plane displacement fields using the method of nonlinear least-squares is proposed in this paper. Along with stress intensity factors, crack tip location and rigid body displacement components are determined simultaneously from both displacement components obtained using full-field optical methods or numerical methods. The effectiveness is validated by applying the proposed method to mixed-mode displacement fields obtained through digital image correlation, displacement fields obtained by analysis using elasto-plastic finite element method, and displacement fields around a fatigue crack obtained by electronic speckle pattern interferometry. Results show that the proposed method can extract stress intensity factors from the displacement fields both accurately and easily. Furthermore, they can be determined even if the material at a crack tip exhibits small-scale yielding. It is expected that the proposed method is applicable to various fracture problems during experimental and numerical evaluation of structural components.