Stress singularity for a crack with an arbitrarily curved front

To investigate the possibility of a point of a crack front propagating in a direction not in the normal plane of the crack front, the three-dimensional form of the crack front stress field is obtained. To simplify comparisons of the states of stress at various points lying on a spherical surface centered at a point of the crack front, a local spherical coordinate system is used. It is found that the crack propagation will be from each point of the crack front in a direction lying in the normal plane.The results are used in conjunction with the strain energy density fracture criterion for the problem of an elliptical crack. The plane of the flat elliptical crack makes an arbitrry angle with the field of uniform applied tensile stress. Crack growth directions for various positions along the crack front are determined, and loads required for fracture for various angles are obtained.     

Three-dimensional stress and displacement fields near an elliptical crack front

Local stress and deformation fields for an elliptical crack embedded in an infinite elastic body subjected to normal, shear and mixed loads are considered. Particular emphasis is placed on the direction of propagation of points along the crack border. A confocal curvilinear coordinate system related to a fundamental ellipsoid, and a local spherical coordinate system attached to the crack border are adopted. Using asymptotic analysis, this paper obtains the stress and displacement fields in a plane inclined to the 3D crack front. Results show that the present solutions are independent of the curvature of the ellipse, and different from those given by Sih (1991). Based on two different fracture criteria, crack growth analysis shows that a 3D crack would propagate in the direction of the normal plane along the crack front. As a result, the fracture initiation and propagation of a 3D flat crack can be analyzed in the plane normal to the crack front, and the local fields in the normal plane are the linear superposition of the plane strain mode-I, mode-II, and mode-III crack-tip fields.     

High temperature acidic stress corrosion of glass fibre composites: Part I Effect of fibre type

The stress corrosion characteristics of uniaxial glass fibre reinforced thermosetting resin composites have been examined in hydrochloric acid at 80°C. A simple technique based on linear elastic fracture mechanics (LEFM) is presented for characterizing crack growth in these materials subjected to hostile acidic environments. The environmental stress corrosion cracking is investigated both for different types of resin and different types of glass fibre reinforcements. Two matrices were used: DERAKANE* 411-45 epoxy vinyl ester resin (based on Bisphenol-A epoxy resin) and DERAKANE 470-30 epoxy vinyl ester resin (based on epoxidized novolac resin). Two glass fibre types were employed: standard E-glass fibre and ECRGLAS®, a special type of E-glass with superior acid resistance. Model experiments using a modified double cantilever beam test with static loading have been carried out on unidirectional composite specimens in 1 M hydrochloric acid solution at 80°C. The rate of crack growth in the specimen depends on the applied stress, the temperature and the environment. Consequently, the lifetime of a component or structure made from glass fibre reinforced plastics (GRP) subjected to stress corrosion conditions, could be predicted provided the dependence of crack growth rate on stress intensity at the crack tip is known. Scanning electron microscope studies of the specimen fracture surfaces have identified the characteristic failure mechanisms. The most important finding of this work is that the selection of DERAKANE epoxy vinyl ester resins reinforced with ECRGLAS® fibre exhibited superior resistance to crack growth at 80°C compared to similar E-glass reinforced composites at room temperatures.     

A wedge test for quantifying fully plastic fracture

A test using two wedges splitting a small, doubly grooved specimen allows measurement of stable, fully plastic crack initiation and growth under variable amounts of triaxiality. In wedge tests, 25 mm cubes of 1018 hot rolled steel in three different orientations exceeded the limit load predicted by plastic slip-line fields. The tests gave crack tip initiation displacements of 0.7–0.8 mm, regardless of orientation. Since microscopic examination of the fracture surfaces indicated that the wedges suppress blunting, the presence of non-zero initiation displacements suggests that a fracture process zone of finite thickness must be established before crack growth. During growth, a specimen with rolling direction normal to the crack plane had a crack growth ductility (minimum displacement per unit ligament reduction) of 0.006–0.009, compared to ductilities of 0.016–0.027 for specimens with rolling direction parallel to the crack front or parallel to the growth direction. The lower ductility with the crack normal to the rolling direction appears to be due to a smoother fracture surface without zigzagging between inclusion stringers.

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Résumé L'essai consistant à séparer par deux coins une petite éprouvette à double entaille permet de mesurer l'amorçage stable et totalement plastique d'une fissure et sa croissance sous divers états de triaxialité. On a constaté lors d'essais de ce type que des cubes de 25 mm de côté en acier 1018 brut de laminage présentaient, dans les trois directions caractéristiques, une charge limite en excès par rapport aux prédictions fournies par les champs de bandes de glissement plastique. Les essais produisaient des déplacements de l'extrémité de la fissure à l'amorçage de quelque 0.7–0.8 mm, quelle que soit l'orientation. Un examen microscopique des surfaces de la rupture a révélé que les coins suppriment la formation de cupules; dès lors, la présence de déplacements non nuls à l'amorçage suggère que le processus de rupture à dû se déclencher dans une zone d'épaisseur finie avant que ne croisse la fissure. Au cours de cette croissance, on a constaté qu'une éprouvette dont le sens de laminage était normal par rapport au plan de la fissure présentait une ductilité à la croissance de la fissure de 0.006–0.009, comparée aux valeurs de 0.016–0.027 qu'exhibent des éprouvettes dont le sens de laminage est parallèle au front de fissure ou à la direction de sa croissance (on définit la ductilité à la croissance d'une fissure par le déplacement minimum par une unité de réduction du ligament). La ductilité plus faible constatée pour une fissure normale par rapport à la direction de laminage parait due à une surface de rupture plus lisse, dépourvue de portions en zig-zag entre les inclusions.

     

Hydrogen permeability of niobium during cathodic polarization in hydrochloric acid

Conclusions For high-strength chilled steel, the limit value of the stress intensity factor K^IIIp attained in antiplane strain during short-period fracture by shear is a characteristic that is not sensitive to the effect of an ambient medium such as water and aqueous solutions of sulfuric acid. The possible reduction of short-period bearing capacity of specimens with a crack during loading by mode III takes place only as a consequence of reorientation of the crack into the plane in which the maximum normal stresses act and is associated with reduction in fracture toughness during tear (K_1c) because of the effect of the medium.During long-term corrosion tests in antiplane strain of specimens with a crack, the final act of fracture is almost always completed by tear. In addition, preceding spontaneous fracture, subcritical crack growth is possible by both tear and shear. For certain structural states of steel and ambient media, the latter mechanism and the corresponding high rate of subcritical crack growth may become dominant at low levels of K^III0. This explains the anomalous character of curves of long-term crack resistance observed in these cases.Translated from Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 13, No. 1, pp. 42–46, January–February, 1977.     

Ductile fracture before localized necking in a strip under tension

Unexpected cracking with a 22° opening angle grew out of a rough-sheared edge before appreciable necking in an 0.79 by 37 mm mild steel strip, which normally fractures after diffuse and then localized oblique necking. From the crack tip, two shear bands formed at 55° to the load direction, consistent with isotropic plane stress characteristics (53° was predicted from anisotropy, but necking in thin strips occurred at 67°). Photomicrographs showed that the 22° crack growth occurred by first tunnelling at mid-thickness, and then spreading along through-thickness shear planes. Springback on unloading caused a 0.038 mm crack closure and local buckling. This form of cracking illustrates a size effect in fracture under macroscopically plane stress. It also gives an example of a local mechanism triggering a fracture mode that can require more total work than an alternative.Analysis of isotropic localized necking shows the equivalent strain at fracture in thin strips to be uniquely related to the Reduction in Squared Thickness (RST). With smooth edges, width and thickness strains before and during necking differed by factors of 1.4 and 1.7; such measures of anisotropy should be routinely found and reported for strips.     

Ductile-brittle behavior at the (1 1 0)[0 0 1] crack in bcc iron crystals loaded in mode I

Fracture experiments performed at room temperature on four test samples made of Fe-3wt.%Si single crystals with an edge crack (1 1 0)[0 0 1] (crack plane, crack front) showed approximately 45° deflections of the crack from the initial crack plane (1 1 0). This behavior appeared to be independent on loading rate. Fractographic analysis confirmed that the cracks were deviated along {1 0 0} planes and the fracture was accompanied by dislocation slip and by twinning. 3D simulations at 300 K by molecular dynamic technique in bcc iron with edge cracks of equivalent orientation indicated that the crack itself could contribute to understanding of this behavior by three processes: twinning on oblique {1 1 2} planes, which hindered growth of the original crack, and by emission of dislocations on oblique {0 1 1} and {1 2 3} planes, which led to separation of the {1 0 0} planes and might cause decohesion and subsequent cleavage fracture along the mentioned planes.     

The influence of porosity on the fatigue crack growth behavior of Ti–6Al–4V laser welds

The effect of porosity––a common welding defect––on the fatigue crack growth rate (FCGR) in Ti–6Al–4V laser welds was investigated. The experimental results reveal that porosity was present in partial penetration welds over a narrow fusion zone (FZ) with martensite structure. The FCGR of the FZ was lower than that of the base plate. The fracture surface morphology of weld metal was much rougher as compared to that of the base plate. Randomly oriented martensite in the FZ led to local cleavage fracture along a preferred plane, thus, altering the crack growth direction significantly out of the primary crack plane. The zigzag crack path in the FZ resulted in a reduced FCGR at a given ΔK compared to the base plate. Besides, the porous weld showed a serration on the crack growth curve, and behaved the similar crack growth characteristics as the defect free one. SEM fractography revealed that the deflection of crack path around porosity together with local notch blunting as the crack tip pierced into porosity, balanced the increased FCGR for the occurrence of instant crack advance as the crack front reached the porosity at a low stress ratio. In contrast, the serration and drop in FCGR occurred sparingly at a high stress ratio as the crack front met the porosity.     

Nucleation and propagation of fatigue cracks in Al-304 stainless steel laminate composite

A study has been made of fatigue crack nucleation and propagation in Al-stainless steel (30 vol%) laminate composites. A Paris type power relationship between the crack growth rate, da/dN, and the alternating stress intensity, K, was obtained over the crack growth rates ranging from 10^–7 to 10^–4 mm/cycle, with an exponentm of 2.7. The cracks nucleated first in Al strips and then in stainless steel strips accompanied by some interface decohesion. The fatigue crack propagated in two stages. In the first stage, where the Al-steel interface was largely intact, the crack propagated in a plane strain mode (flat fracture surface with striations, each striation consisting of a cluster of interstriations). In the second stage, where there occurred extensive Al-steel interface delamination and the concomitant loss of mutual constraint, the crack propagated in the plane stress mode (slant fracture with voids). The crack growth was faster in Al than that in steel since the apparent striation spacing was larger in the former than in the latter. No one to one correspondence existed between the apparent striation spacing and the macroscopic crack growth rate.Thus, although, microscopically, the crack front was not planar; macroscopically, it could be regarded as planar, and a Paris type power relationship did characterize the macroscopic fatigue crack growth in this laminate system over the applied stress amplitude studied. Comparing the fatigue crack growth rates among Al-steel laminate, commercial or pure aluminium and 304 stainless steel, the Al-steel laminate has the lowest crack growth rate. This plus the weight and cost saving benefits make Al-steel laminate quite attractive.     

Crack growth behavior in an epoxy strip above and below Tg

Crack growth behavior in a viscoelastic epoxy strip above and below the glass temperature T_g is extensively discussed by focusing on (1) the threshold condition of crack growth; (2) subsequent crack growth behavior; and (3) the characteristics of fracture surface. To realize good reproducibility of crack growth behavior that depends strongly on time and temperature, a new technique for introducing an initial crack simulating the mathematical model, i.e., a single plane crack with sharp tip, has been developed. Taking experimental evidence into account, an approach to the M_ID criterion, based on the displacement field around the crack tip for crack growth under monotonically increasing loading, is proposed. Two types of equations predicting crack growth rate are evaluated through the comparison with experimental results. As a measure of the critical condition of crack growth, an extended J-integral derived for linearly viscoelastic material, is discussed. The fracture surface is carefully investigated for morphological features of the submicroscopic structural change related with heterogeneous local deformation around the crack tip. Only stable crack growth of a single main crack is observed above T_g, while below T_g not only both of stable and unstable crack growth, but sometimes branching to multi-cracks is observed. This revised version was published online in July 2006 with corrections to the Cover Date.     

Cyclic fatigue crack growth behaviour in β-(Si–Al–O–N) at ambient and elevated temperatures

Four-point bending fatigue tests on a hot-pressed sintered Sm–-(Si–Al–O–N) ceramic were conducted at room temperature, 900 °C and 1000 °C in air under different load ratios and cyclic frequencies. The growth of indentation cracks was measured during the fatigue tests. The results indicate that the cyclic fatigue crack growth threshold is lower and crack growth rates are higher, for given values of K_max, at 1000 °C than those at room temperature. The cyclic fatigue crack growth behaviour at 900 °C is similar to that at room temperature. It was found that the crack growth retardation due to cyclic fatigue loading is much more pronounced at higher frequencies. An increase in cyclic frequency from 1 to 10 Hz cause a reduction of up to two orders of magnitude in crack propagation rates. High-temperature cyclic fatigue crack growth rates increased and threshold stress intensity factor ranges decreased with increasing load ratio. Possible mechanisms for cyclic crack growth are discussed.     

Cyclic fracture toughness of structural alloys with surface cracks at low temperatures

In the present paper, we study specific features of crack propagation from surface flaws in full-scale sheets used in manufacturing pressure vessels for cryogenic applications. The process of crack propagation consists of several stages and terminates in stages of surface through or central through cracks under conditions of low-frequency repeated tension. The effect of a decrease in temperature from 292 to 77°K on crack growth behavior was studied for sheets with a thickness of 2, 8, and 12mm. We describe a procedure for testing for crack-growth resistance at cryogenic temperatures and construct fatigue crack growth diagrams. It is shown that zones of influence of the front and rear faces of the specimen on the stress and strain fields near the crack front arise in the plane of a semielliptic crack. The shape of the interface of these zones can be approximated by a second-order curve. Variations in the thickness of the specimen and the test temperature affect the slope of the curve, i.e., the interface of the zones of influence. Specific features of the fracture process in the material of the plate with surface cracks manifest themselves most adequately at points of the crack front located on the indicated interface. We suggest a procedure for estimating the cyclic crack growth resistance of highly ductile stainless steels that is based on the use of the cyclic J-integral. We propose to regard the lengthl of the interface of the zones of influence of the front and rear faces of the specimen as a geometric parameter of the crack. It is used to construct kinetic fatigue crack growth diagrams for specimens with semielliptic surface cracks.Published in Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 31, No. 1, pp. 9–19, January – February, 1995.     

Indentation crack initiation in ion-exchanged aluminosilicate glass

The threshold load for crack initiation resulting from Vickers indentation is investigated in chemically tempered aluminosilicate glass. Aluminosilicate glass was ion-exchanged in a potassium nitrate salt bath at temperatures of 380, 400, and 420°C for times ranging from two to sixty minutes. The ion-exchange profiles were investigated using an electron microprobe, and the diffusion coefficients and activation energy for ion-exchange elucidated. Residual stresses were not measured directly, but were estimated using an indentation fracture analysis. A physically-based fracture model is developed to describe the threshold indentation load data. From kinetic and indentation threshold models, predictions of crack initiation thresholds are made over a wide range of ion-exchange conditions.     

Evaluation of the elastic-plastic mixity parameters on the base of different crack propagation criteria. Part 1. Preliminary analysis

In order to evaluate the mechanical behavior around small-scale yielding crack tip for both plane strain and plane stress, the asymptotic governing equations and their boundary conditions by considering fracture mechanisms are formulated. A total deformation theory of plasticity with a power-law hardening is used. The analysis of the near-tip fields is carried out for both the maximum tensile and shear stress crack growth direction criteria, as well as for the complete range of mixity parameters and various strain-hardening levels. The new scheme of mixed-mode problem solution is proposed. Realationships between elastic and plastic mixity parameters are given as functions of the crack growth direction criterion and the strain-hardening exponent.Translated from Problemy Prochnosti, No. 1, pp. 60–75, January–February, 2005     

取向玻璃纤维增强塑料的应力腐蚀开裂研究

应用断裂力学的理论和方法对±30°、±45°、±60°三种取向玻璃纤维增强塑料的应力腐蚀开裂行为进行了研究,并与单向玻璃纤维增强塑料的应力腐蚀开裂行为进行了比较。结果表明,纤维取向对玻璃纤维增强塑料的应力腐蚀行为有很大影响。三种取向玻璃纤维增强塑料的耐应力腐蚀性能强弱顺序为:±30°、±45°、±60°玻璃纤维增强塑料。与单向玻璃纤维增强塑料相比,三种取向玻璃纤维增强塑料有更高的应力腐蚀临界载荷值,低于该载荷,可以认为在可接受的时间范围内不会发生应力腐蚀。进一步的讨论证实纤维/基体界面在取向玻璃纤维增强塑料的应力腐蚀中起着重要作用。随外加载荷的变化,取向玻璃纤维增强塑料与单向玻璃纤维增强塑料的应力腐蚀裂纹扩展机理不同。      

Study of slant fracture in ductile materials

Slant fracture is widely observed during crack growth in thin sheet specimens made of ductile materials, providing a good case for investigating three-dimensional criteria for mixed-mode ductile fracture. To gain an understanding of slant fracture events and to provide insight for establishing a slant fracture criterion, stable tearing fracture experiments on combined tension-torsion (nominal mixed-mode I/III) specimens and nominal Mode I Arcan specimens made of Al 2024-T3 are analyzed using the finite element method under three-dimensional conditions. Two types of finite element models are considered for the study of slant fracture: (a) combined tension-torsion specimens containing stationary, flat and slant cracks subject to loads corresponding to the onset of crack growth, and (b) stable tearing crack growth with slanting in a nominal Mode I Arcan specimen. Analysis results reveal that there exists a strong correlation between certain features of the crack-front effective plastic strain field and the orientation of the slant fracture surface. In particular, it is observed that (a) at the onset of crack growth in the combined tension-torsion experiments, the angular position of the maximum effective plastic strain around the crack front serves as a good indicator for the slant fracture surface orientation during subsequent crack growth; and (b) during stable tearing crack growth in the Mode I Arcan specimen, which experiences a flat-to-slant fracture surface transition, the crack growth path on each section plane through the thickness of the specimen coincides with the angular position of the maximum effective plastic strain around the crack front.     

Significance of the deviations of the crack front into the plane perpendicular to the crack propagation direction - I. Crack-front dislocation generation

A static crack front deviates more and more from straight line in a solid as I. the number of dislocations generated from the crack front increases and/or II. the temperature increases. The significance of these deviations into the plane perpendicular to the crack propagation direction is the subject of the present study, which we divide into two parts. In this paper (Part I), the influence of dislocation generation on the shape of a static crack front and on the conditions for crack motion are investigated. We have considered an elastic-plastic crack model in which, due to dislocation generation during mode I loading, the initially straight crack front deviates in the sinusoidal form in a plane perpendicular to both the average crack plane and the direction of fracture propagation. No crack opening displacement is allowed. The dislocations generated form a plastic zone separated from the crack by a dislocation free zone. Both the crack and the plastic zone are described in terms of continuous distributions of dislocations that are sinusoidal and straight edges, respectively. Expressions for the dislocation distributions, the relative displacement of the faces of the crack, the number of dislocations in the plastic region, and the crack opening force G per unit length of the crack front are evaluated. The similarities with isolated cracks (planar and wavy) are emphasized. It is shown that the stress at the front of the sinusoidal crack is unbounded in the mean fracture plane but bounded outside. Consequently, only the crack front sites located on the average crack plane are possible sites for the initiation of crack motion. G differs from that of the planar crack by a geometrical factor that depends on a new parameter, the crack front inclination angle θ. This is an acute angle, measured in the plane perpendicular to the crack propagation direction, between the crack front and the average fracture plane. As θ increases with the number of dislocations generated, G decreases and is ultimately zero for a critical value θ_c=tan ^?1(1/sqrtν) where ν is the Poisson ratio. This is a new condition for crack arrest in solids. Applying the theory to a steel, it is found that this condition could be achieved under localized plastic yielding at crack tips.     

Delayed failure of a commercial vitreous bonded alumina

The static fatigue resistance of a commercial low-cost alumina is evaluated. Flexural stress rupture results are compared to fracture mechanics crack growth testing. The original goal of this work was to develop satisfactory experimental procedures for the two test methods prior to more extensive testing on high-performance ceramics such as silicon nitride. The static fatigue trends measured by the two methods are comparable at 1000° C. The results are consistent with a model of static fatigue involving microcrack growth, coalescence and fracture due to stress corrosion. Creep deformations are very small, suggesting that creep fracture is not the mechanism of failure. A refined method for double torsion testing is presented.     

Sustained Mode I and Mode II fatigue crack growth in flat plates

This study was conducted to contribute to the understanding of fatigue crack growth under mixed mode loading. This was accomplished by developing and analyzing a flat plate specimen capable of maintaining crack growth on a plane oblique to the direction of the applied load. Several specimens were built and exposed to controlled fatigue loading in the laboratory. These specimens were then modeled using finite elements to determine the stress intensity factors (SIF). For the “Mode I/Mode II” specimens developed, the crack was forced to grow in a direction other than perpendicular to the load. The resulting crack front did not remain straight and flat, but stabilized into a curved or warped shape. Based on finite element analyses of these curved specimen cracks, it is concluded that the SIR were predominantly Mode I, with the Mode II and III SIR being negligible.     

Multiaxial small fatigue crack growth in metals

Observations related to the formation and growth of small cracks ranging from subgrain dimension up to the order of 1 mm are summarized for amplitudes ranging from low cycle fatigue (LCF) to high cycle fatigue (HCF) conditions for polycrystalline metals. Further efforts to improve the accuracy of life estimation which address LCF, HCF and LCF–HCF interactions must consider various factors that are not presently addressed by conventional elastic–plastic fracture mechanics (EPFM) or linear elastic fracture mechanics (LEFM) approaches based on long, self-similar cracks in homogeneous, isotropic materials, nor by conventional HCF design tools such as the ε–N curve, the S–N curve, modified Goodman diagram and fatigue limit.Development of microstructure-sensitive fatigue crack propagation relations relies on deeper understanding of small crack behavior, including (a) interactions with microstructure and lack of constraint for microstructurally small cracks, (b) heterogeneity and anisotropy of cyclic slip processes associated with the orientation distribution of grains, and (c) local mode mixity effects on small crack growth. The basic technology is not yet sufficiently advanced in these areas to implement robust damage tolerant design for HCF. This paper introduces an engineering model which approximates the results of slip transfer calculations related to crack blockage by microstructure barriers; the model is consistent with critical plane concepts for Stage I growth of small cracks, standard cyclic stress–strain and strain–life equations above threshold, and the Kitagawa diagram for HCF threshold behaviors. It is able to correlate the most relevant trends of small crack growth behavior, including crack arrest at the fatigue limit, load sequence effects, and stress state effects.