Prediction of non propagating cracks

An explanation for non propagating fatigue cracks is presented based on the criterion that once the value of a particular strain intensity factor reduces to the threshold value for the material the crack should stop. Predicted lengths of these cracks based on solutions for the intensity factor are in good agreement with the experimental data. Intensity factor trends for cracks in notches are shown to vary from an initial decrease to a minimum value followed by an increase and eventual convergence with the trend for the equivalent long crack for sharp notches to the blunt notch curves that continuously increased during their approach to the long crack trend. The type of trend exhibited by a given notch depends both on notch geometry and notch size. In blunt notches the maximum value of the threshold stress for crack propagation is at initiation. However, for sharp notches the peak value of the threshold stress vs crack length curves shifts to a finite length. Stresses above the initiation level but below this peak stress level result in fatigue cracks which start but do not propagate to failure. Predicted values of the fatigue limit stresses for a variety of sizes in a circular and an elliptical notch are in good agreement with experimental results.     

TEM observations of dislocation emission at crack tips in aluminium

Direct observations were made of the propagation of ductile cracks and associated dislocation behaviour at crack tips in aluminium during tensile deformation in an electron microscope. In the electropolished area, the cracks propagated as a Mode III shear-type by emitting screw dislocations on a plane coplanar to the crack plane. A zone free of dislocations was observed between the crack tip and the plastic zone. As the cracks propagated into thicker areas, the fracture mode changed from Mode III to predominantly Mode I. The crack top of the Mode I cracks was blunted by emitting edge dislocations on planes inclined to the crack plane. The blunted cracks did not propagate until the area ahead of the crack tip was sufficiently thinned by plastic deformation. The cracks then propagated abruptly, apparently without emitting dislocations. The stress intensity factor was measured from the crack tip geometry of Mode III cracks and it was found to be in good agreement with the critical value of the stress intensity factor required for dislocation generation.     

THE INFLUENCE OF NOTCH PLASTICITY ON SHORT FATIGUE CRACK BEHAVIOUR

Abstract— A study has been made of fatigue crack formation and growth at the root of different notch profiles in a structural steel subjected to fully reversed tension-compression loading. The scale of stage I microstructural crack growth at notches decreased with increasing notch root strain and was comparable to the size of stage I cracks in shallow hourglass profile specimens at the same strain. Stage II crack growth rates were faster within the notch plastic field than in the elastic stress field of the bulk material.     

Brittle fracture initiation from a blunting crack

Brittle fracture initiation under increasing load occurs from a blunting crack. The present paper proposes as a criterion for the transition from blunting to fast crack growth that the available elastic energy divided by a volume which depends on the fracture mechanism and the crack tip opening displacement reaches a critical value. This criterion is shown to be applicable for initiation from initially sharp cracks, initially rounded notches and from ductile growing cracks. The model allows a quantitative discussion on the size, temperature and notch root radius requirements for fracture mechanics testing.     

Fracture behavior of notched specimens of TiAl alloys

Fracture behavior of a two-phase TiAl alloy was investigated using notched specimens. Fracture surfaces and metallographic sections of surviving notch in double notched specimens are observed. The fracture process of notched specimens of TiAl alloys was described as that several inter-lamellar cracks initiate and extend directly from the notch root and propagate preferentially along the interfaces between lamellae and stop at various obstacles. With increasing applied load, cracks connect with each other and propagate further by translamellar cracks. The toughening mechanisms, which make the main crack difficult to propagate or cause it to be stopped, could be reducing the driving force for crack propagation. The higher toughness of near fully lamellar microstructure than that of finer duplex microstructure is attributed to the path of crack propagation. On the fracture surfaces of the finer duplex microstructure, more low-energy-spending interlamellar fracture facets are observed, which means that it is easier for crack to bypass a fine duplex lamellar grain with lamellae perpendicular to the main crack and to take a interlamellar path.     

Shear fracture tests of concrete

Symmetrically notched beam specimens of concrete and mortar, loaded near the notches by concentrated forces that produce a concentrated shear force zone, are tested to failure. The cracks do not propagate from the notches in the direction normal to the maximum principal stress but in a direction in which shear stresses dominate. Thus, the failure is due essentially to shear fracture (Mode II). The crack propagation direction seems to be governed by maximum energy release rate. Tests of geometrically similar specimens yield maximum loads which agree with the recently established size effect law for blunt fracture, previously verified for tensile fracture (Mode I). This further implies that the energy required for crack growth increases with the crack extension from the notch. The R-curve that describes this increase is determined from the size effect. The size effect also yields the shear fracture energy, which is found to be about 25-times larger than that for Mode I and to agree with the value predicted by the crack band model. The fracture specimen is simple to use but not perfect for shear fracture because the deformation has a symmetric component with a non zero normal stress across the crack plane. Nevertheless, these disturbing effects appear to be unimportant. The results are of interest for certain types of structures subjected to blast, impact, earthquake, and concentrated loads.     

Crack initiation and propagation in torsional fatigue of circumferentially notched steel bars

Circumferentially notched bars of austenitic stainless steel, SUS316L, and carbon steel, SGV410, with three different notch-tip radii were fatigued under cyclic torsion without and with static tension. The torsional fatigue life of SUS316L was found to increase with increasing stress concentration under the same nominal shear stress amplitude. Electrical potential monitoring revealed that the crack initiation life decreased with increasing stress concentration, while the crack propagation life increased. This anomalous notch-strengthening effect was ascribed to the larger retardation of fatigue crack propagation by sliding contacts of fracture surfaces. The superposition of static tension on cyclic torsion causes notch weakening. The notch-strengthening effect in torsional fatigue was not found in carbon steels, SGV410. The difference in the crack path of small cracks near notch root between stainless steel and carbon steel gives rise to the difference in the notch effect in torsional fatigue. The factory-roof shape observed on fracture surfaces of SUS316L became finer with higher stress amplitude and for sharper notches. The superposition of static tension makes the factory-roof shape less evident. Under higher stresses, the fracture surface was smeared to be flat. The fracture surfaces of SGV410 became smoother with increasing stress amplitude and notch acuity. The three-dimensional feature of fracture surfaces clearly showed the difference of the topography of fracture surfaces. The topographic feature was closely related to the amount of retardation of crack propagation due to the sliding contact of fracture surfaces.     

Interfacial debonds of layered anisotropic materials using a quasi-static interface damage model with Coulomb friction

The resistance to mode I failure of rubbers is studied by submitting single edge notch samples to uniaxial tension. Reproducing the seminal work of Rivlin and Thomas (J Polym Sci 10:291–318, 1953), single edge notch tension specimens, presenting notches of various lengths, are stretched until break. A styrene butadiene rubber, unfilled and filled with carbon-black, and an unfilled rubber from the latter mentioned work, were considered. When the notch is smaller than one fifth of the sample width, mode I crack opening is observed, leading to catastrophic failure that creates smooth mirror-like crack surfaces. Nonetheless, the experimental force-elongation responses show that the mode I critical energy release rate cannot be calculated by a classical Griffith elastic failure analysis. When notches are longer, the SENT samples are not submitted to pure uniaxial tension only. Structural bending leads to uncontrolled mixed mode crack propagation. The surfaces created when the long notches propagate are rough and bifurcations are witnessed for the filled rubbers.     

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.     

Short fatigue crack growth from a blunt notch in plate specimens

Short crack growth behavior from a notch including crack closure and load ratio effects was investigated. Experiments and analyses were carried out using four-point bending specimens made of SAE 1045 steel, using a blunt notch keyhole specimen geometry. The lower the load ratio, the more notch effect on short crack growth behavior was observed. Short cracks in the notch affected zone had higher growth rates than long cracks. After the crack grew out of the notch effect field, short crack growth rates merged with the long crack growth rates. Several parameters were used to correlate the short crack growth rates including stress intensity factor range, effective stress intensity factor range, and stress intensity factor range based on notch root stress.     

The Theory of Critical Distances to estimate the static strength of notched samples of Al6082 loaded in combined tension and torsion. Part I: Material cracking behaviour

The present paper is the first of a two-part series reporting an experimental and theoretical study of the fracture of circumferentially notched samples of a commercial aluminium alloy, i.e. Al6082, subjected to tension, torsion and mixed tension/torsion loading. The overall aim of the work was to investigate the use of a particular method of failure prediction, known as the Theory of Critical Distances. This first part reports the experimental data - load-deflection curves and observed material failure modes - and discusses the consequences of these findings for the development of the theory, which is covered in the second part. It was observed that relatively blunt notches loaded in tension failed by a conventional ductile fracture mode similar to plain (unnotched) specimens. However, in tensile specimens containing sharp notches, failure occurred via the initiation, stable propagation and, finally, unstable propagation, of circumferential ring cracks. Under torsional loading, and independent of the notch root radius, static failures of the tested samples always occurred by the formation and stable propagation of ring cracks. Under mixed-mode loading there was a gradual transition between the ductile and brittle modes and between stable and unstable cracking. For all types of loading, it was observed that crack initiation always coincided with peak loading conditions, and that cracks invariably grew on the plane perpendicular to the specimen’s longitudinal axis.     

Propagation of fatigue cracks from notches

Abstract

The traditional design approaches to fatigue at notches, based on stress level–endurance relationships, are briefly reviewed. It is shown, by considering crack propagation from notches and invoking a change in control mode from notch plasticity to crack-tip plasticity, that a critical stress condition can be obtained which must be exceeded if the crack is to propagate to failure. The traditional techniques are then reinterpreted and explained by this propagation method. An example is given of crack growth from a sharp defect at a weld toe. It is shown that the integration of an elastic fracture mechanics growth law can reproduce stress range–cycles to failure data for this situation. There are, however, complexities of stress analysis and crack shape. A simple treatment of residual stresses affecting the threshold and slow–growth regimes, shows some promise as a technique for accounting for residual stresses.

MST/70     

Analysis of endurance limits under very high cycle fatigue using a unified damage approach

A critical evaluation of endurance limits under very high cycle (giga-cycle range) fatigue is presented. The available experimental results are analyzed using the unified damage approach developed earlier by the authors. It is shown that the experimental evidence supports the theory that endurance limits at very high cycle fatigue are related to thresholds for crack propagation of incipient cracks from stress-concentration sites. The crack propagation behavior of the incipient cracks is related to the accumulation of internal stresses that is needed to augment the preexisting stresses. These in turn cause the incipient cracks to initiate at stress concentrations which either grow or arrest depending on the magnitude and gradient of the internal stresses. Micro-deformations at localized stress concentrations, such as inclusions, can further augment the local internal stresses needed for the incipient crack to nucleate and propagate. The presence of trapped hydrogen at inclusions can reduce the resistance to deformation, and hence reduce crack initiation and growth process. Understanding the role of preexisting stress concentrations (such as notches, inclusions, and hard second phases) provides a bridge for understanding the fatigue damage evolution in a smooth specimen compared to that in a cracked specimen. Kitagawa diagram helps provide this necessary bridge. Several critical issues related to fatigue testing method; fracture surface analysis, load history and environment are raised in this paper and briefly discussed in a self-consistent manner based on our unified damage approach.     

Effect of Closure of a Crack Caused by the Roughness of Its Surfaces on Fatigue Fracture under the Conditions of Transverse Shear

We develop a model aimed at the prediction of propagation of mode II fatigue cracks with regard for the interaction of their lips caused by the roughness of the fracture surfaces. In this model, the relationship between normal and shear contact stresses is described by the Amonton's law of friction and the plastic yield of the material in the prefracture zone is taken into account with the help of the model of thin plastic strips. The method of singular integral equations is used to solve the corresponding boundary-value problem for a plate with cracks propagating from two semiinfinite collinear notches. The distribution of contact stresses is determined and the stress intensity factors and displacements of the crack lips are evaluated. The proposed example is used to analyze the basic specific features of the influence of contact of the crack lips on fatigue fracture under the action of shear loads. The obtained results are confirmed by the experimental data on the propagation of mode II fatigue cracks in specimens of HY-130 steel.     

Fatigue life prediction of notched members based on local strain and elastic-plastic fracture mechanics concepts

Fatigue life predictions for notched members are made using local strain and elastic-plastic fracture mechanics concepts. Crack growth from notches is characterized by J-integral estimates made for short and long cracks. The local notch strain field is determined by notch geometry, applied stress level and material properties. Crack initiation is defined as a crack of the same size as the local notch strain field. Crack initiation life is obtained from smooth specimens as the life to initiate a crack equal to the size of cracks in the notched member. Notch plasticity effects are included in analyzing the crack propagation phase. Crack propagation life is determined by integrating the equation that relates crack growth rate to ΔJ from the initiated to final crack size. Total fatigue life estimates are made by combining crack initiation and crack propagation phases. These agree within a factor of 1.5 with measured lives for the two notch geometries.     

Evaluation of fibre bridging stress of short fatigue cracks in SCS-6/Ti-15-3 composite

Single‐edge notched specimens of a unidirectional SiC long fibre reinforced titanium alloy, were fatigued under four point bending. The propagation behaviour of short fatigue cracks from a notch was observed on the basis of the effects of fibre bridging. The branched fatigue cracks were initiated from the notch root. The fatigue cracks propagated only in the matrix and without fibre breakage. The crack propagation rate decreased with crack extension due to the crack bridging by reinforced fibres. After fatigue testing the loading and residual stresses in the reinforced fibres were measured for the arrested cracks by the X‐ray diffraction method. The longitudinal stresses in the reinforced fibres were measured using high spatial resolution synchrotron radiation. A stress map around the fatigue cracks was then successfully constructed. The longitudinal stress decreased linearly with increasing distance from a location adjacent to the wake of the matrix crack. This region of decreasing stress corresponded to the debonding area between the fibre and the matrix. The interfacial frictional stress between the matrix and the fibre could be determined from the fibre stresses. The bridging stress on the crack wake was also measured as a function of a distance from a notch root. The threshold stress intensity factor range, corrected on the basis of the shielding stress, was similar to the propagation behaviour of the monolithic matrix. Hence the main factor influencing the shielding effect in composites is fibre bridging.     

FATIGUE CRACK GROWTH BEHAVIOUR OF FIBRE-METAL LAMINATE GLARE-1 AND METAL LAMINATE 7475 WITH DIFFERENT BLUNT NOTCHES

Abstract— The fatigue crack growth behaviour of the fibre metal laminate "GLARE-1" has been investigated for different blunt notches in Constant Amplitude (CA) tests. In order to investigate the influence of the fibres, the same laminate material but containing no fibres (Laminate 7475) was also tested. The fatigue crack growth properties of GLARE-1 are superior to those of Laminate 7475. GLARE-1 shows lower crack growth velocities at the same K_nom values and in addition the crack growth rates decrease with increasing crack length. The Laminate 7475 shows typical metal behaviour for single crack propagation and accelerating crack growth with increasing crack length. In GLARE-1, multiple crack propagation takes place. The cracks propagate independent of each other and have similar crack growth rates, in part due to closure effects caused by the unbroken fibre layers.
The crack growth rates of specimens having a small root radius are higher in both materials than in specimens with a large notch radius. In GLARE-1, the superiority of a larger notch radius is more pronounced than in the Laminate 7475 and is attributed to a stronger crack closure effect owing to fibre bridging. The reason for the higher bridging capability in specimens containing larger notches is that less fibres are broken or damaged in the notch vicinity.     

Fatigue crack growth in AlCu4Mg1 under nonproportional bending-with-torsion loading

We present the experimental results on fatigue crack growth for AlCu4Mg1 aluminum alloy under proportional and nonproportional bending with torsion obtained at the Opole University of Technology. Specimens with square sections and stress concentrators in the form of external one-sided sharp notches were used. The tests were performed in a high-cycle fatigue mode for the stress ratio R = -1 and the phase shift between the bending and torsion loads equal to ϕ = 0, 45° and 90°. Three loading paths were used: line, ellipse, and circle. The fatigue crack growth was cyclically measured with the use of an optical microscope (with a magnification of 25 diameters), strain gauges, and a computer to record the signals of loading. In the tested specimens, it was possible to observe the growth of cracks conforming with the mixed mode I + III. The crack growth was nonuniform on both sides of the specimen surface. However, the difference between the crack lengths was rather small. In the biaxial tests, the influence of bending was six times greater due to the notches in the bending plane. The experimental results are described by range of the stress intensity factor ΔK.