An analysis of crack propagation velocity in delayed failure under repeating load using an internal friction model

Frequency and temperature dependency of crack propagation velocity in delayed failure under superposed repeating load was analyzed using an internal friction model which assumes the interaction between hydrogen atoms and the cyclic moving of the position with tri-axial tensile stress at crack tip.

The decrease of crack propagation velocity (da/dt)_R by the superposition of repeating load, the appearance of minimum value in (da/dt)_R at a certain frequency ƒ₀, and the shift of ƒ₀ by the change of temperature, are well explained by the internal friction model. Another reason for the decrease of (da/dt)_R by the superposition of repeating load appears to be the decrease of effective stress intensity at crack tip, though this cannot explain the appearance of minimum value of (da/dt)_R.     

Effect of specimen thickness on the crack propagation and crack branching in delayed failure

The crack propagation and crack branching behaviors in delayed failure have been investigated on the specimens with various thickness ($\text{B = 1.5–10}\text{mm}$).The crack propagation velocity reveals a maximum value at a medium specimen thickness ($\text{B = 5}\text{mm}$). This fact can be understood by assuming the compound effect of two factors that the triaxiality of stress at crack tip as a driving force for hydrogen diffusion increases with increase of specimen thickness $\text{B}$, and that the invasion of hydrogen atoms from specimen surface increases with decrease of $\text{B}$.The stress intensity factor at crack branching, $\text{K}{}_{\mathrm{IB}}$, increases with decrease of specimen thickness $\text{B}$, and when B is 1.5 mm, the specimen fractures without showing the crack branching. The latter fact can be explained by connecting the necessary and sufficient conditions for crack branching with the decrease in height of plastic region at the crack tip in thin specimens.     

Effect of temperature on the frequency dependency of crack propagation velocity in delayed failure under cyclic load

The crack propagation velocity and the incubation time in delayed failure under repeating load were examined at various frequency ƒ(0–800 cpm) and temperature T(5–80°C) using the pre-cracked specimen of JIS SNCM8 quenched and tempered. The crack propagation velocity under repeating load (da/dt)_R decreased with increase of frequency ƒ and revealed a minimum value (da/dt)_minat a certain ƒ. The activation energy obtained from the Arrhenius plot of (da/dt)_min vs 1/T was about 10,000 cal/mol, which was a little larger than 8100 cal/mol obtained from the relation between the crack propagation velocity under static load and 1/T. The reason for the existence of the minimum value in the crack propagation velocity was explained by assuming the interaction between hydrogen atoms invaded from crack tip and the cyclic change of the position with tri-axial tensile stress. The incubation time under repeating load did not seem to be controlled by the diffusion or concentration process of hydrogen atoms.     

The effect of load level on the mechanism of fatigue crack propagation in ABS

The fatigue crack propagation (FCP) mechanism of an ABS was examined under tension-tension loading as a function of load level. The crack was always preceded by a damage zone consisting of assemblies of stress-whitened lines. Crack growth was predominantly through the root damage line, with occasional jumps into neighbouring lines. These jumps occurred most frequently in the medium load level test. Transmission electron microscopy (TEM) analyses showed the damage within the stress-whitened lines to consist of elongated, and occasionally ruptured, rubbery domains at the specimen surface, with the appearance of extensive crazes bridging their interstices toward the mid-thickness. The craze intensity (size and number) increased with decreasing load level. The crazes manifested themselves on the fracture surface as a patch morphology, which was increasingly pervasive with decreasing load level. In the rougher region that followed, ductile tearing of the matrix is believed to be promoted by rubber cavitation and the merging of crazes. Normal fatigue striations indicate crack advance by greater fractions of the damage zone length at higher load levels.     

Cold expansion effect on the initiation and the propagation of the fatigue crack

In this study, an experimental and numerical investigation was carried out to quantify the effect of the cold expansion on the initiation and the propagation of the fatigue crack.The fatigue life improvement of the damaged structures after the cold expansion process was investigated with the single edge pre-cracked specimens of aluminium alloy which are used in land transport components.Three radii and three degrees of cold expansion were performed at the crack tip. The number of cycles to obtain a new crack initiation (life time), are analysed from the different cases.A numerical investigation with a numerical code (FEM ANSYS code) is conducted to determine the residual stress field and the size of the plastic zone generated by the cold expansion and to establish the influence of the degree of cold expansion (DCE) on the different parameters.Three radii and six degrees of cold expansion were performed in this numerical investigation. It has been shown that the DCE has an influence on the size of the zone of compressive residual stresses (ZCRS) and on the size of the zone of plastic deformation (ZPD), but it appears that the DCE has no influence on the level of the maximum residual stresses in our case.     

Effect of stress wave shape on the crack propagation velocity in cyclic delayed failure

Crack propagation velocity in delayed failure under superposed repeating load, ($\text{d}\text{a/}\text{d}\text{t)}{}_{\mathrm{R}}$, was compared with that under static load, ($\text{d}\text{a/}\text{d}\text{t)}{}_{\mathrm{S}}$Two peaks appear on the relation between decreasing rate of crack propagation velocity, $\text{1-β = 1 ? (}\text{d}\text{a/}\text{d}\text{t))}{}_{\mathrm{R}}\text{/(}\text{d}\text{a/}\text{d}\text{t)}{}_{\mathrm{S}}$ and frequency, ?, both under sinusoidal and square load. By changing the ratio of holding time at maximum stress intensity factor to that at minimum stress intensity factor in square load, it was deduced that the existence of two peaks on the 1 ? β vs $\text{f}$ curve was caused by an asymmetric interaction between hydrogen atoms and cyclic moving of the position with triaxial tensile stress at crack tip. Moreover, the relation between 1 ? β and $\text{f}$ under the positive or negative saw tooth load could be well explained by the interaction model.     

The effects of environment and load frequency on the crack propagation law for macro fatigue crack growth in aluminium alloys

Data are presented for fatigue crack propagation of two aluminium alloys (2024-T3 Alclad-7075-T6 clad) in different environments and for several loading frequencies. Correlation of the data was attempted by the stress-intensity factor by application of the equation for crack growth proposed by Forman. The result was that the influence of the stress ratio on the crack growth was predicted by the equation in agreement with the test results but that the effects of the environment and the load frequency could not be coped with by changes in the constants of the equation. There may be a threshold level of the stress-intensity factor, strongly dependent on the environment and the alloy, in order to make the crack grow.     

Predicting failure from the initiation stage of slow crack growth in polyethylene

The crack opening displacement against time was measured in linear polyethylene as a function of stress, notch depth, and temperature for three-point bending under plane strain conditions. The experimental conditions were accurately controlled so that the scatter in the rate of damage was within ±20%. Microscopic observations showed that the shape of the damaged zone was triangular for stresses less than one-half the yield point and that the length was predictable from measurements of the crack opening displacement. The initial rate of damage prior to crack growth was constant up to crack opening displacement = 15 to 25Μm. The entire shape of the crack opening displacement-time curve and the time to complete failure could be predicted from the initial damage rate. A theory based on the observed microcrazing is presented which explains the dependence of damage rate on stress intensity and microstructural parameters.     

The effect of temperature and loading rate on the crack initiation and propagation energy in carbon steel charpy specimens

The Charpy impact tests were carried out at different temperatures and loading rates. The temperature dependences of crack initiation and propagation in carbon steels 45 and St. 3 under impact testing were determined from the obtained force variation plots. The effect of the impact velocity in the range from 1 to 4.4 m/s on the fracture toughness temperature dependence is estimated. __________ Translated from Problemy Prochnosti, No. 5, pp. 120–127, September–October, 2006.     

Compressive maximum shear crack initiation and propagation

A maximum shear crack γ (a Mode II shear crack along the maximum shear direction associated with the crack tip shear displacement) was produced successfully in a so-called compressive maximum shear (CMS) specimen. This specimen was specificially designed to produce a compressive maximum shear failure which is one of two mechanisms widely believed to be responsible for limiting bearing fatigue life in rolling contact. The fracture initiation stress (or crack nucleation stress) σ_c and the upward crack propagation rate (toward the loading surface) $\text{dli}\text{dσi}$ per unit cyclic compressive stress increment were determined for the 52100 steel. These parameters were measured at two cleanness levels (DE and CEVM) [DE: basic electric arc furnace melted plus vacuum degassed. CEVM: Consumable electrode vacuum melted] and two tempered hardness levels, RC61 and 51. The possibility of determining K₁₁ for ith cycle was also elucidated. The formation of tail cracks and parallel multiple cracks as fine structure of CMS cracks can be well expounded by the concept of restoring tensile stresses and the residual shear stress relaxation at the CMS crack tip. The fracture mechanism advanced here can explain the formation of similar tail cracks and parallel multiple cracks frequently observed along the inclined shear cracks existing in the subsurface regions of rolling     

The initiation of crack growth in linear polyethylene

The initiation of crack growth was observed in single edge notched tensile specimens under plane strain conditions. The shape of the deformation zone varied from being balloon-like above 12 MPa and nearly planar below but neither shape conformed to that predicted by the conventional shear type yield criteria. The initial damaged zone grew at a constant velocity with a stress dependence ofV=V ₀ ⁿ . The spectrum of damage morphologies that preceed crack growth consists of a leading edge of crack-like pores followed by a region of increasing fibrillation which is terminated by a region of increasing fibril fracture.     

The effect of mean stress on delay in fatigue crack growth under load stepdown

The effect of mean stress together with decreasing stress range on fatigue crack propagation behaviour in mild steel is investigated. The delay period between crack arrest and reprogation is found to be a function of the maximum stress intensity factor stepdown ration, K_2max/K_1max. Delay only occurs when this ratio is less than unity. For specimen thicknesses of 1.6 to 6.4 mm, non-propagating cracks, where the affected delay cycles are 500 000 cycles or greater, appear to occur when K_2max/K_1max has a value of approximately 0.7 and the stepdown plastic zone size is about half the initial load plastic zone size, which is approximately equal to the affected crack length.     

Prediction of crack initiation and propagation of adhesive lap joints using an energy failure criterion

In a previous paper, the present authors have pointed out limitations of some fracture mechanics parameters and shown that the vectorial J-integral can be applied to adhesive joints. Here, problems concerning the practical application of the vectorial J-integral are discussed and a more suitable failure criterion has been proposed, based on a specific strain energy criterion. The specific energy is not so sensitive to the size of the integration zone since it is ‘averaged’ over the volume of the zone. This criterion has been used to model the crack initiation and propagation in single lap joints with a brittle adhesive and a ductile adhesive. The effect of the shrinkage thermal stresses, adhesive fillet, surface preparation and type of adherends (aluminium and steel) were studied. The predicted failure loads and crack patterns are in very good agreement with the experimental results. One of the major conclusions is that the predictions can explain well the experimental scatter band that is always present in single lap joints due to the difficulty of controlling the adhesive fillet.     

The effect of load ratio on fatigue life and crack propagation behavior of an extruded magnesium alloy

Fatigue experiments were carried out in laboratory air using an extruded magnesium alloy, AZ31, to investigate the effect of load ratio on the fatigue life and crack propagation behavior. The crack propagation behavior was analyzed using a modified linear elastic fracture mechanics parameter, M. The relation crack propagation rate vs. M parameter was found to be useful in predicting fatigue lives at different R ratios. Good agreement between the estimated and the experimental results at each stress ratio was obtained.     

Predicting the effect of asymmetry of load cycles on crack growth rate

Translated from Fiziko-khimicheskaya Mekhanika Materialov, Vol. 27, No. 3, pp. 61–65, May–June, 1991.     

Modeling of crack initiation, propagation and coalescence in rocks

One of the most successful criteria proposed so far to describe the initiation and propagation of cracks under quasi-static loading in rock-like materials is a stress-based criterion developed by Bobet (Fracture coalescence in rock materials: experimental observations and numerical predictions. Sc. D, Thesis, Massachusetts Institute of Technology, 1997) which is embedded in FROCK, a Displacement Discontinuity code that was developed by the rock mechanics group at MIT. Even though the predictions obtained with this criterion generally correspond to the experimental results, there are cases in which the quasi-static crack propagation results obtained with FROCK are not satisfactory. For this reason, a qualitative study using the Finite Element code, ABAQUS, was conducted to analyze stress-, strain- and energy-based criteria used for modeling crack development. Based on the ABAQUS relative quantitative analysis, it was found that the strain- and stress-based criteria may be more appropriate than the energy-based criterion to model quasi-static crack development. Thus, a strain-based and a normal stress-dependent criterion were implemented in FROCK. The cracking patterns obtained with these proposed criteria were compared with those obtained using Bobet’s original stress-based criterion and with experimental observations made in molded gypsum specimens. The proposed strain-based criterion implemented in FROCK appeared to yield better results than Bobet’s stress-based criterion. The influence of the friction angle ( $\upvarphi $ φ ) on the cracking patterns was studied with the proposed normal stress-dependent criterion and showed that friction angles closer to $0^{\circ }$ 0 ° yielded the best results, which may indicate that, at least for the microscale, the critical shear stress at which rock fails does not depend upon the normal stresses applied.     

Molecular dynamics simulation of crack initiation and propagation in bcc iron under load within spur gear tooth root

Spur gears are widely used in practice, and one of their typical failures is tooth breakage. In general, the tooth breakage occurs at tooth root, and the amount of crack growth during a meshing cycle is in atomistic scale. This work aims at identifying the mechanisms of crack initiation and propagation at tooth root by using molecular dynamics simulation. The results prove that there are phase transition regions and edge dislocations at crack tips. According to the distribution characteristic of the atomic potential, its concentration can be observed obviously by visualization software. In these concentration regions, microvoids come into being and expand gradually, which results in the subcrack initiation. Additionally, the microvoids and subcracks propagate along the high potential direction and then come together to accelerate the crack growth. Through carrying out a comparative simulation, the effects of heavy load at single meshing area on crack initiation and propagation are addressed.