Examination of the failure behaviour of wood with a short crack in the tangential-radial system by single-edge-notched bending test

Single-edge-notched tests of a tangential-radial system were conducted on agathis specimens to analyze the failure behaviour of wood with a short crack. The nominal bending strength and mode I critical stress intensity factors of the specimens with various crack lengths were measured, and the influence of the crack length on these properties was examined. The nominal bending strength of the cracked specimens was significantly lower than that of a crack-free specimen, even when the crack was extremely short. This finding suggests that the fracture mechanics theory is essential for analyzing the failure behaviour of wood with a very short crack. However, the mode I critical stress intensity factor still depended on the crack length. When considering the fracture process zone developing at the crack tip, the critical intensity factor could be predicted effectively.     

On the influence of rubbing fracture surfaces on fatigue crack propagation in mode III

Fatigue crack growth has been studied under fully reversed torsional loading (R = ?1) using AISI 4340 steel, quenched and tempered at 200°, 400° and 650°C. Only at high stress intensity ranges and short crack lengths are all specimens characterized by a microscopically flat Mode III (anti-plane shear) fracture surface. At lower stress intensities and larger crack lengths, fracture surfaces show a local hill-and-valley morphology with Mode I, 45° branch cracks. Since such surfaces are in sliding contact, friction, abrasion and mutual support of parts of the surface can occur readily during Mode III crack advance. Without significant axial loads superimposed on the torsional loading to minimize this interference, Mode III crack growth rates cannot be uniquely characterized by driving force parameters, such as ΔK_III and ΔCTD_III, computed from applied loads and crack length values. However, for short crack lengths (?0.4 mm), where such crack surface interference is minimal in this steel, it is found that the crack growth rate per cycle in Mode III is only a factor of four smaller than equivalent behaviour in Mode I, for the 650°C temper at $\text{ΔK}{}_{\mathrm{III}}\text{= 45 MPa m}\text{1}\text{2}$.     

Fracture toughness of unidirectional fibre reinforced composites in MODE II

Experimental investigations have been performed on unidirectional glass fibre reinforced/epoxy composites in Mode II (Forward shear) with the presence of crack parallel to the fibres direction through the use of end-cracked beam. A concentrated load at the Centre of the beam produced bending-induced shear deformation at the crack tip. Calibration factors for Mode II have been obtained. The stress-intensity factor at instability $\text{K}$_IIR(INR) is obtained by experiments on a small end cracked beam through a compliance matching procedure. The crack growth resistance at instability and the corresponding critical strain energy release rate are independent of initial crack in the range of crack length investigated. In composite materials, fibre-matrix interfacial shear stress play an important role in load transfer mechanism: hence Mode II study may be very useful to analyse the interfacial mechanisms and to understand the fracture behaviour of unidirectional fibre reinforced composites in Mode I when load is applied in the direction of the fibres.     

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.     

The effect of crack surface interaction on the stress intensity factor in Mode III crack growth in round shafts

Turbine-generator shafts are often subjected to a complex transient torsional loading. Such transient torques may initiate and propagate a circumferential crack in the shafts. Mode III crack growth in turbo-generator shafts often results in a fracture surface morphology resembling a factory roof. The interaction of the mutual fracture surfaces results in a pressure and a frictional stress field between fracture surfaces when the shaft is subjected to torsion. This interaction reduces the effective Mode III stress intensity factor.The effective stress intensity factor in circumferentially cracked round shafts is evaluated for a wide range of applied torsional loading by considering a pressure distribution between mating fracture surfaces. The pressure between fracture surfaces results from climbing of asperities respect to each other. The pressure profile not only depends on the fracture surface roughness (height and width (wavelength) of the peak and valleys), but also depends on the magnitude of the applied Mode III stress intensity factor. The results show that asperity interactions significantly reduce the effective Mode III stress intensity factor. However, the interactions diminish beyond a critical applied Mode III stress intensity factor. The critical stress intensity factor depends on the asperities height and wavelength. The results of these analyses are used to find the effective stress intensity factor in various Mode III fatigue crack growth experiments. The results show that Mode III crack growth rate is related to the effective stress intensity factor in a form of the Paris law.     

The determination of the critical stress intensity factor in mode II loading and the shear fracture strength of pharmaceutical powder specimens

The shear fracture strength and the critical stress intensity factor in mode II loading of lactose monohydrate and acetylsalicylic acid powder compacts has been evaluated. The experimental results of the shear fracture strength and the critical stress intensity factor in mode II loading appeared to be in good agreement with powder behaviour such as lamination and capping during compaction. Values for the critical stress intensity factor in mode II loading depended on the depth of the crack and hence, any reference of such values or their use to calculate a fracture toughness ratio (K _IC ^I/K _IC ^II) must refer to the notch depth applied. The results confirmed that the failure of such powder compacts occurs mainly in tension, but that lactose monohydrate has a tendency also to fail in shear. The latter does not apply to acetylsalicylic acid. Hence, lactose monohydrate should only be used cautiously in layer or press-coated tablets.     

Mixed mode fracture energy of sprucewood

The characterization of Mixed Mode (Mode I and Mode II) behaviour of wood was concentrated on concepts of linear fracture mechanics in the past. Using an adopted version of the splitting test it was possible to obtain complete load displacement curves under different Mixed Mode loading cases for crack propagation along the grain. Therefore fracture energy concepts (specific fracture energy) could be used to characterize the material behaviour. Additionally strength parameters were used in order to describe crack initation in two crack propagation systems. The values for specific fracture energies as well as the strength values were compared with pure Mode I fracture tests. Moreover, the size effect under Mixed Mode loading was investigated to guarantee size independent material characterizing values for the specific fracture energies.     

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.     

Non-propagating cracks and high-cycle fatigue failures in sharply notched specimens under in-phase Mode I and II loading

Sharply notched specimens were tested under in-phase Mode I and II loading to study the non-propagating crack behaviour in the presence of complex stress states. The material employed in the present investigation was a commercial low carbon steel. Non-propagating cracks were generated under different ratios between Mode I and Mode II stress components. The direct inspection of the cracked samples showed that the early stage of the crack propagation was mixed Mode governed (Stage 1-like process), whereas the subsequent propagation was seen to be mainly Mode I dominated (Stage 2-like process). Moreover, it was observed that non-propagating crack length tended to increase as the Mode II contribution to fatigue damage increased. In any case, independently of the degree of multiaxiality, their average length was of the order of 2L, where L was the material characteristic length calculated according to the theory of critical distances. Finally, the detected crack paths were used to form some hypotheses on the reason why two methods previously formulated by the authors are successful in predicting the multiaxial high-cycle fatigue strength, even though they make quite different assumptions on the physical mechanisms damaging metallic materials in the high-cycle fatigue regime.     

Comparison of shear and tensile fracture in high strength aluminum alloys

A comparison was made between tensile (mode I) and shear (mode II) fracture characteristics in high strength aluminium alloys (7075-T6 and 6061-T651) using a relatively new mode II fracture specimen to evaluate the critical stress intensity factor. The enlarged plastic zone during mode II fracture required that an increased specimen thickness be used for determining K _Hc under a purely plane strain condition. Plane stress conditions prevailed in the mode II fracture of 7075-T6 with a specimen thickness less than 10 mm, while plane strain controlled mode II fracture at a thickness of 10 mm or greater. Fractographic analysis revealed a distinctive difference in the micromechanisms responsible for crack extension. Small dimples were observed only on the mode II fracture surfaces, resulting from a microvoid nucleation fracture mechanism. The mode I fracture surfaces showed a mixed distribution of dimple sizes resulting from a void growth fracture mechanism. Comparing the critical stress intensity factors, the shear mode of failure exhibited a substantially higher value than the tensile mode, resulting from the effect of the sign and magnitude of the hydrostatic stress state on the microvoid nucleation event. Zero hydrostatic tension in the mode II loading configuration helps delay microvoid nucleation, increasing the apparent toughness. The high hydrostatic tension resulting from a mode I loading configuration enhances microvoid nucleation which promotes crack propagation at relatively lower stress intensity factors.     

Prediction of short fatigue crack growth of Ti‐6Al‐4V

It is observed that the short fatigue cracks grow faster than long fatigue cracks at the same nominal driving force and even grow at stress intensity factor range below the threshold value for long cracks in titanium alloy materials. The anomalous behaviours of short cracks have a great influence on the accurate fatigue life prediction of submersible pressure hulls. Based on the unified fatigue life prediction method developed in the authors' group, a modified model for short crack propagation is proposed in this paper. The elastic–plastic behaviour of short cracks in the vicinity of crack tips is considered in the modified model. The model shows that the rate of crack propagation for very short cracks is determined by the range of cyclic stress rather than the range of the stress intensity factor controlling the long crack propagation and the threshold stress intensity factor range of short fatigue cracks is a function of crack length. The proposed model is used to calculate short crack propagation rate of different titanium alloys. The short crack propagation rates of Ti‐6Al‐4V and its corresponding fatigue lives are predicted under different stress ratios and different stress levels. The model is validated by comparing model prediction results with the experimental data.     

The preferred fatigue crack propagation mode in a M250 maraging steel loaded in shear

Macroscopic torsional fatigue cracks are shown to propagate in shear, in plain tubular specimens, in the M250 maraging steel, for stress ranges from 90% down to 40% of the yield stress. This cannot be explained in terms of microcrack coalescence for the smallest stress range, for which microcracks are scarce. The kinetics and mechanisms of mode II fatigue crack growth are thus investigated, using precracked CTS or tubular specimens. For a high Δ K _II , slowly decelerating mode II propagation takes place for a distance that increases with Δ K _II before branching occurs. Friction stresses along the crack flanks shield the applied load and explain this deceleration. An inverse analytical procedure is used to derive the effective stress intensity factor, allowance being made for friction effects, from displacement profiles measured from microgrids using a scanning electron microscope. The measured crack growth rates correlate much better with the effective stress intensity factor than with the nominal Δ K _II value. The crack paths observed in torsion are discussed in terms of maximum crack velocity.     

Creep Crack Growth in Polyethylene Under Combined Mode I and Mode II Loading

Creep crack growth characteristics under various combined mode I and mode II loadings were studied using the compact tension shear (CTS) specimens of polyethylene. Creep crack growth rates da/dtunder combined mode I and mode II loading can be correlated with a single effective stress intensity factor K _Ieffderived from the combined — mode fracture toughness envelope. The steady state or constant crack growth rates which occupy the significant part of creep failure life increase with the increasing initial effective stress intensity factor.     

Fracture of austenitic steel subject to a wide range of stress triaxiality ratios and crack deformation modes

The stress triaxiality ratio (hydrostatic pressure divided by von Mises equivalent stress) strongly affects the fracture behaviour of materials. Various fracture criteria take this effect into consideration in their effort to predict failure. The dependency of the fracture locus on the stress triaxiality ratio has to be investigated in order to evaluate these criteria and improve the understanding of ductile fracture.This was done by comparing the experimental results of austenitic steel specimens with a strong variation in their stress triaxiality ratios. The specimens had cracks with varying depths and crack tip deformation modes; tension, in-plane shear, and out-of-plane shear. The crack growth in fracture mechanics specimens was compared with the failure of standard testing specimens for tension, upsetting and torsion. By associating the experimental results with finite element simulations it was possible to compare the critical plastic equivalent strain and stress triaxiality ratio values at fracture. In the investigated triaxiality regime an exponential dependency of the fracture locus on the stress triaxiality ratio was found.     

Ductile-to-brittle transition in tensile failure due to shear-affected zone with a stress-concentration source: a comparative study on punched-plate tensile-failure characteristics of precipitation-hardened and dual-phase steels

The effect of shear-affected zone (SAZ), with a stress-concentration source induced by the punching process, on tensile properties was investigated. Tests using honed specimens (which have the same shapes and stress-concentration without any SAZ) and smooth specimens were conducted to compare the effect with that of the punched specimens. Dual-phase steel, which has a high work-hardening ability and low yield strength, and precipitation-hardened steel, which has a low work-hardening ability and high yield strength, were used in the tests. Materials with two tensile strength grades were prepared from both types of steel. Only the precipitation-hardened steel with higher strength grade punched specimen showed a brittle fracture with extremely short fracture-elongation, whereas the other specimens showed a ductile fracture. The fracture surface analysis revealed that cracks initiated in the maximum shear stress plane of the SAZ under tensile loading at first. We call the crack “shear crack.” The steel which showed brittle fracture used in this study easily exhibited plastic-strain localization compared with the other steels. If the shear crack is sharp, then the transition from ductile to brittle failure tends to occur. Furthermore, the strength characteristics of the punched specimen depend on the crack length dependency of the strength resistance and the failure phenomenon of the original material.     

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.     

Computation of the stress intensity factors for repaired cracks with bonded composite patch in mode I and mixed mode

In this study, the finite element method is used to analyse the behaviour of repaired cracks with bonded composite patches in mode I and mixed mode by computing the stress intensity factors at the crack tip. The effects of the patch size and the adhesive properties on the stress intensity factors variation were highlighted. The plot of the stress intensity factors according to the crack length in mode I, shows that the stress intensity factor exhibits an asymptotic behaviour as the crack length increases. In mixed mode, the obtained results show that the Mode I stress intensity factor is more affected by the presence of the patch than that of mode II.     

The application of fracture mechanics to the testing of wood

The problem of a mode I fracture toughness of wood is considered. After a short discussion of relevant literature the test results concerning mode I fracture on three types of wood and the obtained values of stress intensity factor, K _Ic, are discussed. The compressive and tensile strength of the wood fibres and flexural strength are also presented. A considerable variation of the stress intensity factor, K _Ic, has been found to depend on the wood species and the direction of taking specimens for tests. The character of a failure process and the obtained values of the stress intensity factor, K _Ic, were determined by interrelations of cohesion forces existing between particular components of the wood structure, and by anisotropy of the wood. Both the compressive and tensile strength tests performed along the fibres and the bending strength tests crosswise to the fibres have not confirmed the tendencies observed in the fracture toughness tests. The investigations performed show the usefulness of fracture mechanics for evaluation of the strength properties of wood. It is concluded that materials science must consider wood as a valuable and rewarding material upon which to focus research efforts.     

The fatigue crack direction and threshold behaviour of mild steel under mixed mode I and III loading

As part of a programme to investigate the mixed mode fatigue crack growth threshold behaviour of mild steel, tests were carried out on three-point bend specimens with spark machined initial slits inclined to give mixed Mode I and III displacements. Overall the expected tendency to Mode I crack growth showed as an initial directional discontinuity followed by a smooth rotation of the crack front until it was almost perpendicular to the specimen sides. At a smaller scale, initial crack growth was by the formation of Mode I branch cracks which developed into a ‘twist’ fracture surface consisting of narrow Mode I facets separated by cliffs. The facets eventually grew out and the fracture surface became smooth. The result in the initiation it was necessary to distinguish between the threshold conditions which result in the initiation of crack growth, specimen failure and crack arrest. An envelope based on Mode I branch crack growth provides a reasonable lower bound to the results for crack initiation and specimen failure. The crack arrest threshold results and some of the crack growth threshold results could not be analysed in detail because of lack of appropriate stress intensity factors.     

Mode II fracture testing method for highly orthotropic materials like wood

In this paper a mode II fracture testing method has been developed for wood from analytical, experimental and numerical investigations. Analytical results obtained by other researchers showed that the specimen geometry and loading type used for the proposed mode II testing method results in only mode II stress intensity and no mode I stress intensity at the crack tip. Experiments have been carried out to determine mode II fracture toughness K _IIC and fracture energy G _IIF from the test data collected from both spruce (pice abies) and poplar (populus nigra) specimens. It was found that there existed a very good relation between fracture toughness K_IIC and fracture energy G _IIF when the influence of orthotropic stiffness E _II ^* in mode II was taken into account. It verified that for this mode II testing method the formula of LEFM can be employed for calculating mode II fracture toughness even for highly orthotropic materials like wood. In the numerical studies for the tested spruce specimen, the crack propagation process, stress and strain fields in front of crack tips and the stress distributions along the ligament have been investigated in detail. It can be seen that the simulated crack propagating process along the ligament is a typical shear cracking pattern and the development of cracks along the ligament is due to shear stress concentrations at the crack tips of the specimen. It has been shown that this mode II fracture testing method is suitable for measuring mode II fracture toughness K _IIC for highly orthotropic materials like wood.