Griffith's criterion for mixed mode crack propagation

The fracture criterion of mixed mode crack has been investigated extensively by many people on the basis of Griffith's theory. In this paper, the energy release rate of crack propagation along an arbitrary direction is obtained by the use of Griffith's theory. Then the general expression of the energy release rate criterion has been derived. The results have been compared with the measured data of the fracture testing under combined Mode II–III and Mode I–II–III loading.     

A strain energy criterion for mixed mode crack propagation

The strain energy criterion for crack propagation proposed in the paper is based on the principle that the direction of crack propagation takes place along the direction where the distance from the crack tip to a certain contour line of constant distortional strain energy density is minimum, and the crack will begin to propagate when the total strain energy in the region surrounded by the contour line reaches a critical value. In the paper, predicted was compared with the measured results.     

Fatigue crack propagation under non-proportional mixed mode loading

Under non-proportional mixed I+II loading, two kinds of stable crack propagation may be distinguished. An existing precrack will either kink, mode I controlled (tensile mode), or will propagate, coplanarly mode II controlled (shear mode). Shear mode growth will occur if the effective mode II range exceeds the material-specific threshold ΔK_{II th sm} and in addition to that, the ΔK_II-value on the starter crack is larger than the ΔK¹_I (Δϕ)-range on the infinitesimally short additional crack. Examination under the scanning electron microscope showed that flaws are not the reason for the mode II controlled crack propagation and support the criteria introduced. If the crack opening is large enough, the crack propagation rate is higher for shear-stress controlled crack growth than for normal-stress controlled crack extension, the deviation angle of which is well predictable via the MTS criterion due to Erdogan and Sih [On the crack extension in plates under plane loading and transverse shear. J Basic Engng 1963;85:519–25].     

Mechanisms of mixed mode fatigue crack propagation at rail butt-welds

In the present paper, the fatigue crack propagation of longitudinal flaws starting in butt-welded joints of rails is analysed. Firstly Finite Element simulations are carried out, in order to determine the actual stress intensity factor histories caused by the passage of the wheel over the rail. Simulations show that fatigue crack growth is dominated by an out-of-phase Mode I–Mode II mechanism with an overlapping of about 180 degrees. Then, mixed-mode fatigue test experiments have been designed in order to reproduce in-service conditions at laboratory test level. For this purpose, tubular specimens have been subjected to mixed-mode loading (reversal torsion combined with axial tension/compression). The crack growth propagation dominated by the shear has been confirmed. At the end of the paper, the conditions to obtain the shear mode crack propagation are discussed and the kinetics data are presented.     

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.     

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.     

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.     

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.     

Fully automated mixed mode crack propagation analyses based on tetrahedral finite element and VCCM (virtual crack closure-integral method)

The authors have been developing a crack propagation analysis system that can deal with arbitrary shaped cracks in three-dimensional solids. The system is consisting of mesh generation software, a large-scale finite element analysis program and a fracture mechanics module. To evaluate the stress intensity factors, virtual crack closure-integral method (VCCM) for the quadratic tetrahedral finite element is adopted and is included in the fracture mechanics module. The rate and direction of crack propagation are predicted by using appropriate formulae based on the stress intensity factors. In this paper, the crack propagation system is briefly described and some numerical results are presented.     

A mixed mode fatigue crack closure model

Fatigue crack closure conditions leading to mixed mode crack-tip stress states are discussed. A closure model based on contact between impinging fracture surface asperities is introduced. Asperity angle, magnitude of mode II interference, friction between contacting surfaces and distance of the contact surfaces from the crack-tip are features included in the model. The magnitudes of mode I and mode II stress intensity factors due to closure contact are found to vary substantially with asperity angle. Also, because of a reversal of friction force direction during cycle loading, the stress intensity factors exhibit a complex behavior. During the closure phase of the loading cycle, the mode II contribution is found to be quite significant. For loading through an entire cycle, which includes both the closure and crack open phases, nonproportional stress states are developed. Also, it is concluded that the mixed mode states developed could provide the conditions required for crack branching.