Path prediction of I + III mixed mode fatigue crack propagation

In this paper, compact tension specimens with tilted cracks under monotonic fatigue loading were tested to investigate I + III mixed mode fatigue crack propagation in the material of No. 45 steel with the emphasis on the propagation rate expression and the path prediction. It is found that during the mode transformation process, the crack propagation rate is still controlled by the mode I stress intensity factor; and Paris equation also holds for the relationship between and ΔK_I . Crack propagation path can be predicted only when both the crack mode transformation rate and propagation rate are available.     

Strain energy density fracture criterion in elastodynamic mixed mode crack propagation

Sih's fracture criterion based on strain energy density, S, for mixed mode crack extension under static loading is extended to dynamic mixed mode, K_I and K_II, crack propagation. Influence of the second order term, σ_ox, which represents the non-singular constant stress acting parallel to the direction of crack propagation, on the S distribution surrounding the crack tip, is demonstrated. Numerical studies show that positive σ_ox enhances the fracture angle and negative σ_oxreduces the fracture angle irrespective of the sign of K_II/K_I, when S is measured at a critical distance r_c from the crack tip. This fracture criterion is verified by the crack curving results of dynamic photoelastic fracture specimens. Omission of σ_ox term leads to predicted fracture angles which are at variance with experimental data.     

Evaluation of fatigue crack propagation by mode I and mixed mode in 1050 aluminium

The mechanism of mixed‐mode fatigue crack propagation was investigated in pure aluminum. Push‐pull fatigue tests were performed using two types of specimens. One was a round bar specimen having a blind hole, one was a plate specimen having a slit. The slit direction cut in the specimen was perpendicular or inclined 45 degrees relative to the centre of the specimen axis. In both cases, cracks propagated by mode I or by the mixed mode combining mode I and shear mode, depending on the testing conditions. In these cases the crack propagation rate was evaluated with a modified effective stress intensity factor range. Crack propagation retardation was observed in some specimens. However, it was found that the crack propagation rate could also be evaluated by the effective stress intensity factor range independent of the crack propagation mode.     

A proposed maximum ratio criterion applied to mixed mode fatigue crack propagation

In the present paper, the crack initiation and propagation in rectangular magnesium alloy plates containing an inclined through crack are investigated experimentally and theoretically. Based on the complex stress state at the crack tip, a maximum ratio criterion is developed to determine the crack propagation for a given inclination angle by means of an opening mode theory. It is assumed that the crack begins to propagate when the maximum value of ratio approaches its critical value, and the direction of crack propagation coincides with the direction of maximum ratio defined. The experiments for checking the theoretical predictions from the proposed criterion have been conducted. The material properties and fracture characteristics are evaluated during the tests. The results obtained are compared with those obtained using the commonly employed fracture criteria and the experimental data.     

Weld root crack propagation under mixed mode I and III cyclic loading

This study examined fatigue propagation behaviour and fatigue life of weld root cracks under mixed mode I and III loading. Fatigue tests were performed on butt-welded joints with a continuous lack-of-penetration (LOP) inclined at angles of 0°, 15°, 30° or 45° to the normal direction of the uniaxial cyclic load. Branch and/or co-planar crack propagation was observed, depending on the initial mode I stress intensity factor (SIF) range. Co-planar crack propagation predominated when the SIF range was large. The fatigue crack propagation mode affected fatigue life; the life of branch crack propagation was longer than that of co-planar crack propagation. Using an initial equivalent SIF range based on a maximum strain energy release rate criterion, the results obtained from the 0°, 15°, 30°, and 45° specimens indicated almost the same fatigue lives, despite the different inclination angles.     

Interaction between tensile strength failure and mixed mode crack propagation in concrete

Crack size and structure size transitions are illustrated which connect the two limit-cases of ultimate tensile strength failure (small cracks and small structures) and mixed-mode crack propagation (large cracks and large structures). The problem of mixed-mode crack propagation in concrete is then faced. By increasing the size-scale of the element the influences of heterogeneity and cohesive crack tip forces disappear and crack branching is governed only by the linear elastic stress-singularity in the crack tip region. It is proved in this way that the fracture toughness of the material is measured by a unique parameter (G_IF, G_IC or K_IC) even for the mixed-mode condition. The ratio of the sliding or Mode II fracture toughness (G_IIF, G_IIC or K_IIC) to the opening or Mode I fracture toughness depends only on the crack branching criterion adopted and not on the material features. Eventually, very controversial experimental results recently obtained on the shear fracture of concrete are explained on the basis of the above-mentioned size-scale transition.     

Experimental study of I + III mixed mode fatigue crack transformation propagation

In this paper, compact tension specimens with tilted cracks under monotonic fatigue loading were tested to investigate I + III mixed mode fatigue crack propagation in the material of No. 45 steel with the emphasis on the mode transformation process. It is found that with the crack growth, I + III mixed mode changes to Mode I. Crack mode transformation is governed by the Mode III component and the transformation rate is a function of the relative magnitude of the Mode III stress intensity factor. However, even in the process of the crack mode transformation the fatigue crack propagation is controlled by the Mode I deformation.     

Nodal grafting for crack propagation studies

A simple, efficient method for propagating cracks through a finite element mesh is presented: nodes, borrowed from other points in the mesh, are ‘grafted’ along the advancing crack front. The method requires neither an increase in bandwidth nor a mesh regeneration. It can be easily implemented in any existing program using iso(sub)parametric elements of at least quadratic order.     

Influence of effective stress intensity factor range on mixed mode fatigue crack propagation

ABSTRACT The behaviour of fatigue crack propagation of rectangular spheroidal graphite cast iron plates, each consisting of an inclined semi‐elliptical crack, subjected to axial loading was investigated both experimentally and theoretically. The inclined angle of the crack with respect to the axis of loading varied between 0° and 90°. In the present investigation, the growth of the fatigue crack was monitored using the AC potential drop technique, and a series of modification factors, which allow accurate sizing of such defects, is recommended. The rate of fatigue crack propagation db/dN is postulated to be a function of the effective strain energy density factor range, ΔS_eff. Subsequently, this concept is applied to predict crack growth due to fatigue loads. The mixed mode crack growth criterion is discussed by comparing the experimental results with those obtained using the maximum stress and minimum strain energy density criteria. The threshold condition for nongrowth of the initial crack is established based on the experimental data.     

Combined mode fatigue crack propagation predictions using mode one data

A method of estimating the combined-mode growth rate of a crack in an engineering component is described. The main advantage of the technique is that only Mode I data, which are generally available, are needed. Also, both stages I and II growth can be assessed, as can the most probable propagation direction.     

A mixed mode crack tip finite element

A special finite element for plane analysis of elastic structures with through the thickness cracks is presented. Generalized displacements are used in developing the element, and it contains the proper singularities. The opening (K _I), in plane shearing (K _II), and combined (K _I+K _II) modes of deformation are present. The stiffness matrix is given explicitly and its eigenvalues are shown. Numerical results are presented and compared with other solutions.

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Résumé On présente un système spécial d'éléments finis pour l'analyse en état plan de structures élastiques comportant des fissures traversant l'épaisseur du produit. Les déplacements généralisés sont utilisés pour le développement de ces éléments, ceux-ci comportant leurs propres singularités. On présente l'ouverture (K _I) en cisaillement plan (K _II) et en modes combinés de déformation (K _I+K _II). La matrice de rigidité est donnée explicitement et on montre qu'elle correspond à eigenvalues. Les résultats numériques sont présentés et comparés avec d'autres solutions existantes.

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This work was sponsored by Martin-Marietta's Independent Research and Development Program.     

Cohesive crack model for mixed mode fracture of brick masonry

This paper presents a numerical procedure for mixed mode fracture of brickwork masonry. The model is an extension of the cohesive model prepared by the authors for concrete, and takes into account the anisotropy of the material. After the crack path is obtained, an interface finite element (using the cohesive fracture model) is incorporated into the trajectory. Such a model is then implemented into a commercial code by means of a user subroutine, consequently being contrasted with experimental results. Fracture properties of masonry are independently measured for two directions on the composed masonry, and then input in the numerical model. This numerical procedure accurately predicts the experimental mixed mode fracture records for different orientations of the brick layers and two homothetic sizes on masonry panels.     

Characterization of mixed mode crack opening in concrete

In real concrete structures cracks often open in mixed mode after their initiation. To capture the direct material behavior of a mixed mode crack opening a stiff biaxial testing machine, capable of imposing both normal and shear loads on a given crack area, has been applied. The opening and sliding components of the mixed mode displacement are measured using a custom made orthogonal gauge, and the measurements are used directly as the closed loop control signals. A double notch, concrete specimen is used for the crack investigation. The tests are divided into two steps, a pure Mode I opening step, where a macro crack is initiated in the specimen followed by the mixed mode opening step. The high stiffness of the set-up together with the closed control loop ensures a stable crack initiation followed by a controllable mixed mode opening. The deep notches result in a plane crack, only influenced by material aspects such as the aggregate size and concrete strength. Despite the occurrence of a few, local, secondary cracks during the mixed mode crack opening, the results can be treated as the mixed mode material point behavior of a crack in concrete. Results are reported for a range of mixed mode angles and for varying initial Mode I openings of the crack.     

Strain-energy-density factor applied to mixed mode crack problems

This paper deals with the general problem of crack extension in a combined stress field where a crack can grow in any arbitrary direction with reference to its original position. In a situation, when both of the stress-intensity factors,k ₁,k ₂ are present along the crack front, the crack may spread in any direction in a plane normal to the crack edge depending on the loading conditions. Preliminary results indicate that the direction of crack growth and fracture toughness for the mixed problem of Mode I and Mode II are governed by the critical value of the strain-energy-density factor,S _cr. The basic assumption is that crack initiation occurs when the interior minimum ofS reaches a critical value designatedS _cr. The strain-energy-density factorS represents the strength of the elastic energy field in the vicinity of the crack tip which is singular of the order of 1/r where the radial distancer is measured from the crack front. In the special case of Mode I crack extensionS _cr is related tok _1c alone asS _cr = (κ ? 1)k ₁ ² /8μ. In general,S takes the quadratic forma _{1 1} k ₁ + 2a _{1 2} k ₁ k ₂ +a _{2 2} k ₂ whose critical value is assumed to be a material constant. The analytical predictions are in good agreement with experimental data on the problem of an inclined crack in plexiglass and aluminum alloy specimens. The result of this investigation provides a convenient procedure for determining the critical crack size that a structure will tolerate under mixed mode conditions for a given applied stress.     

About the Dugdale crack under mixed mode loading

The plane problem of a Dugdale crack under mixed mode loading is investigated. An exact closed form solution is given and the corresponding crack displacements are discussed.

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Résumé On étudie le problème plan d'une fissure de Dugdale soumise à une sollicitation selcn un mode mixte. Une solution exacte de forme fermée est fournie et les déplacementsde fissure correspondants sont discutés.

     

Dislocation emission criterion for a wedge crack under mixed mode loading

Dislocation emission criterion for a wedge crack under mixed mode loading was investigated using Airy stress function. The order of singularity at the wedge crack tip due to remote loading was found to vary with the loading mode. The plastic zones for plane stress and plane strain were studied based on von Mises' and Tresca criteria. The dislocation emission criterion was examined for both loading modes. The mechanism of crack propagation was believed to be controlled by dislocation emission. Under an action of Mode I loading, the wedge tip movement occurred when a pair of edge dislocations of Burgers vectors be ⁱ and –be ^–i were emitted from the wedge tip where b and were the magnitude of Burgers vector and the angle between the positive x axis and the line connecting from the tip to dislocation. Similarly, under an action of Mode II loading, the wedge crack tip moved as soon as either an edge dislocation of Burgers vector along the x direction was emitted from its tip or a pair of edge dislocations of Burgers vectors be ⁱ and be ^–i were emitted from the wedge tip. The conventional mechanism of crack propagation based on the energy release rate was not expected to occur. The calculated results for a few special cases were presented and compared with those reported in the literature.