Interpretation of effects at the static fatigue limit of soda-lime-silicate glass

Crack growth in soda-lime-silicate glass near the static fatigue limit is rationalized by a fracture mechanics model of the crack tip, in which a stressed layer is built up on the crack surface as a consequence of ion exchange at the crack tip. This model extends the one presented earlier by Bunker and Michalske. Ion exchange, between hydronium (H₃O⁺) ions in the solution and sodium (Na⁺) ions in the glass, gives rise to compressive stresses at the tips of cracks in soda-lime-silicate glasses. These compressive stresses are responsible for (1) the occurrence of a fatigue limit in glass, (2) for the fact that crack tips remain sharp at the fatigue limit even though the walls of the crack are corroded by the basic solutions that form as a consequence of ion exchange, (3) for the crack tip bifurcation often observed when cracks are held at the fatigue limit for a while and then restarted at higher loads, and (4) for the fact that a delay time to restart the crack is often observed after the crack is held under load at the static fatigue limit. Most of the predictions are in quantitative agreement with experimental observations on crack growth and crack tip structure for soda-lime-silicate glass. The prediction of the time required to restart the crack is, however, only qualitatively correct, as experimental data report a sharp peak centered at the fatigue limit in the plot of restart time versus hold stress intensity factor, whereas the model gives a broad maximum on such a plot. Clearly, further development of the model will be needed for a better representation of the experimental data.     

FATIGUE LIMIT MODEL FOR HARDENED STEELS

A fracture mechanics-based model is developed for the fatigue limit of hardened steels. In such steels, non-metallic inclusions are known to initiate fatigue cracks. In this work, these inclusions are modelled as spherical voids and, as the fatigue process continues, fatigue cracks are thought to develop from these sites. The growth or arrest of these cracks is analysed in terms of the effective stress intensity range and the corresponding effective threshold for crack propagation. Elasto-plastic crack closure is evaluated by finite element calculations. The fatigue limit of a sample is defined in terms of crack arrest at all inclusions. Simple equations of the model are presented and compared to experimental data from the literature as well as to an earlier model by Murakami.     

A MICRO-MECHANICS MODEL OF CORROSION-FATIGUE CRACK GROWTH IN STEELS

Principles of Microstructural Fracture Mechanics (MFM) are used to develop a model for the characterization of environment-assisted short fatigue crack growth. Fatigue cracks are invariably initiated at corrosion pits formed at inclusions, hence the analysis includes stress concentration effects at pits that lead to the propagation of fatigue cracks the rates of which are considered to be proportional to the crack tip plastic displacement. This plasticity is constrained by microstructural barriers which are overcome in a non-aggressive environment at critical crack lengths only when the applied stress is higher than the fatigue limit. However, the superposition of an aggressive environment assists fatigue damage via crack tip dissolution, enhancement of crack tip plastic deformation, the introduction of stress concentrations at pits and a reduction of the strength of the microstructural barrier. These environment effects are manifested in a drastic reduction of the fatigue limit and higher crack propagation rates. The model is compared with fatigue crack propagation data of a BS251A58 steel tested in reversed torsion when submerged in a 0.6M NaCl solution.     

Behaviour of small cracks during their propagation from Vickers indentations in coarse-grain steel: An experimental investigation

In this investigation we look at the influence of the local residual stresses caused by Vickers-pyramid indenting on the initiation and early propagation of small cracks from indentations in coarse-grain martensitic steel. The size of these indentations is comparable to the grain size. Specimens with and without a local residual stress field were tested on a rotary bending machine. A focused ion beam and a scanning electron microscope were used to reveal the influence of those stresses on the location of the cracks’ initiation and the mechanism of the small-crack propagation. The existing local residual stresses assist in the initiation of two cracks at a level lower than the fatigue limit. The early small-crack propagation is gradually obstructed by the residual stress-field configuration until the cracks become non-propagating cracks. At levels higher than the fatigue limit, both cracks succeed in breaking through the compressive stressed domain and link together. From that moment the crack begins to behave as a long crack, penetrating outside the indentation into the tensile-stressed domains.     

THE SHORT CRACK PROBLEM

Abstract— The problem associated with short crack growth, defined as situations in which the intensity of the crack tip field is underestimated by linear elastic fracture mechanics analyses, is briefly reviewed.
Two cases are identified, cracks growing in plastically strained materials, such as occurs in high strain fatigue studies and at notch roots, and small cracks growing in single grains as occurs close to the fatigue limit in plain specimens.
Important mechanical and metallurgical features of short cracks are discussed with particular reference to the upper and lower bound definition of a short crack.     

Short fatigue cracks in austempered ductile cast iron (ADI)

The growth of short fatigue cracks was investigated in an austempered ductile cast iron (wt% 3.6C, 2.5Si, 0.6Mn, 0.15Mo, 0.3Cu), austenitized at 870 °C and then austempered at 375 °C for 2 h. At stress amplitudes close to the fatigue limit endurance limit of 10⁷ cycles, subcritical crack nuclei initiated at graphite nodules. The crack nucleus decelerated and arrested after propagating a short distance. The position of an arrested crack tip was characterized using an electron backscatter diffraction technique, demonstrating that short fatigue cracks in austempered ductile cast iron (ADI) can be arrested by boundaries such as those between ausferrite sheaves or packets and prior austenite grains. Refinement of the prior austenite grain size decreased the size of subcritical crack nuclei. It is proposed that the arrest and retardation of short crack nuclei are controlled by the austenite grain size and graphite nodule size. This determines the fatigue endurance limit.     

Microstructural effects on crack closure and propagation thresholds of small fatigue cracks

The crack closure behaviour of microstructurally small fatigue cracks was numerically simulated by combining the crack-tip slip band model with the plasticity-induced crack closure model. A Stage II crack started to propagate from an initiated Stage I crack. When the plastic zone was constrained by the grain boundary or the adjacent grain with higher yield stresses, the crack opening stress increased with crack extension, and the effective component of the stress range decreased. The crack-tip opening displacement range (Δ CTOD ), first decreased with crack extension due to the development of the residual stretch, then increased until the tip of the plastic zone reached the neighbouring grain boundary. When the plastic zone was blocked by the grain boundary, Δ CTOD began to decrease. The arrest condition of cracks was given by the threshold value of Δ CTOD . At the fatigue limit, the arrest of small cracks takes place just after the Stage II crack crosses the grain boundary when the grain boundary does not act as a barrier. Only when the grain boundary has a blocking strength and the yield stress of adjacent grains is not so high, the arrest of Stage II cracks takes place before the crack reaches the grain boundary. The fatigue limit decreases with the mean stress. The predicted relation between the fatigue limit and the mean stress is close to the modified Goodman relation.     

TORSIONAL FATIGUE OF A MEDIUM CARBON STEEL CONTAINING AN INITIAL SMALL SURFACE CRACK INTRODUCED BY TENSION–COMPRESSION FATIGUE: CRACK BRANCHING,NON-PROPAGATION AND FATIGUE LIMIT

In order to examine the threshold condition for the fatigue limit of materials containing a small crack under cyclic torsion, reversed torsional fatigue tests were carried out on 0.47% C steel specimens containing an initial small crack. Initial small semi-elliptical cracks ranging from 200 to 1000 μm in length were introduced by the preliminary tension–compression fatigue tests using specimens containing holes of 40 μm diameter. The threshold condition for the fatigue limit of the specimens containing artificial small defects under rotating bending and cyclic torsion are also reviewed. Crack growth behaviour from an initial crack was investigated. The torsional fatigue limit for a semi-elliptical small crack is determined by the threshold condition for non-propagation of Mode I branched cracks. The torsional fatigue limit of specimens containing an initial small crack can be successfully predicted by the extended application of the √area parameter model in combination with the σ_θmax criterion.     

Einfluß einer Laseroberflächenhärtung auf die Dauerlestigkeit von glatten Proben mit kurzem Riß aus dem Stahl C70W2

The influence of laser transformation hardening on fatigue limit of smooth C70W2 steel specimens with small crack Laser transformation hardening as a local heat treatment technology can be used to restore the fatigue strength of crack-damaged components. The investigations have been carried out on smooth steel specimens containing small surface cracks. The obtained 80% fatigue limit improvement of the laser hardened specimens in relation to the crack-damaged initial condition is explained by the fatigue crack growth threshold increase due to martensitic transformation hardening, the action of residual stresses on the crack front and possible crack tip blunting.     

EFFECT OF SURFACE TEXTURE ON FATIGUE LIFE IN A SQUEEZE-CAST 6082 ALUMINIUM ALLOY

The effect of surface texture on fatigue life in a squeeze-cast Al-Mg-Si alloy has been investigated in terms of initiation and subsequent propagation of small fatigue cracks. Small cracks nucleated from defects on both as-cast and polished surfaces. However, the large (∼90μm in diameter) surface defects found on as-cast surfaces caused an approximate 20% reduction in fatigue life when compared to polished surfaces where cracks initiated from smaller (∼ 12 μm in diameter) microporosity. Integration of averaged small fatigue crack growth data enables the fatigue lives of both types of specimen to be predicted at stresses above the fatigue limit, showing that the difference in fatigue behaviour is principally due to the extra period of crack growth in the polished surfaces.     

Fatigue damage of low amplitude cycles in low carbon steel

The influences of low load cycles on fatigue damage in 0.15% C steel (C15E, No. 1.1141) are investigated in the very high cycle fatigue regime using ultrasonic fatigue testing equipment. Constant amplitude (CA) endurance limits at limiting lifetime of 10⁹ cycles are determined in cyclic tension–compression and cyclic torsion tests. Non-propagating fatigue cracks are found in specimens subjected to cyclic torsion loading at the endurance limit. The endurance limit is considered as maximum stress amplitude where possibly initiated fatigue cracks do not propagate to failure. Two-step variable amplitude (VA) tension–compression endurance tests are performed with repeat sequences consisting of high stress amplitudes above the endurance limit and far greater number of cycles below. The measured lifetimes are compared with linear damage accumulation calculations (Miner calculations). If the high stress amplitude is more than approximately 13% above the CA endurance limit, detrimental influences of low load cycles and failures at low damage sums are found. If the high stress is less than 13% above the CA endurance limit, numerous low load cycles cause prolonged fatigue lifetimes and specimens can sustain large damage sums without failure. Two-step VA fatigue crack growth investigations show that load cycles below the threshold stress intensity accelerate crack growth, if the high stress intensity is 18% or more above the CA threshold stress intensity. In repeat sequences with high stress intensities 14% above threshold stress intensity, low load cycles decelerated and stopped fatigue crack growth. Low load cycles can reduce or prolong fatigue lifetimes of low carbon steel and one reason is the accelerated or retarded fatigue crack growth due to numerous low amplitudes, and the maximum load amplitude of a VA load sequence determines whether detrimental or beneficial effects prevail.     

Propagation of physically short cracks in a bainitic high strength bearing steel due to fatigue load

Physically short cracks in a bainitic high strength bearing steel were fatigue loaded. The rapid propagation rate of early open short cracks agreed with that of long closure free cracks. After some rapid growth, the short cracks entered a transition period to the rate of growth limited long cracks. Potential drop showed that the short cracks were open to the tip throughout the growth sequence, which excluded crack face closure in the wake as the growth limiting mechanism in this material. Instead the short crack effect was related to residual stresses and other mechanisms at the crack tip. Crack manufacturing procedures were determined for straight long and short start cracks in the present material. LEFM with effective material parameters and limit compensation predicted the short crack lives.     

THE NUCLEATION AND GROWTH OF SHORT FATIGUE CRACKS BOTH AT PLAIN SURFACES AND NOTCHES

Abstract— The problem of the nucleation and growth of short fatigue cracks is addressed from an energetic point of view. It is explained that vanishingly small cracks can only nucleate and grow at the expense of the release of some locally stored energy during the fatigue deformation. This is necessary because an external loading system alone cannot provide a positive driving force for the growth of a crack whose length is below a critical value. The concept of the local driving force is used to explain the nucleation and growth of short fatigue cracks both at plain surfaces and at notches. With this approach a meaningful definition can be given of a "short fatigue crack" and a sound physical interpretation of the Kitagawa-Takahashi plots is provided. The conditions for the existence of non-propagating cracks are clearly established and the relationship between the stress concentration factor at the root of notches and the fatigue limit is explained. The paper sets up a physical framework for the sound understanding and treatment of short fatigue cracks and the microstructural parameters which control their growth.     

Fretting fatigue limit as a short crack problem at the edge of contact

This paper proposes a local stress concept to evaluate the fretting fatigue limit for contact edge cracks. A unique S–N curve based on the local stress could be obtained for a contact edge crack irrespective of mechanical factors such as contact pressure, relative slip, contact length, specimen size and loading type. The analytical background for the local stress concept was studied using FEM analysis. It was shown that the local stress uniquely determined the ΔK change due to crack growth as well as the stress distribution near the contact edge. The condition that determined the fretting fatigue limit was predicted by combining the ΔK change due to crack growth and the ΔK_th for a short crack. The formation of a non‐propagating crack at the fatigue limit was predicted by the model and it was experimentally confirmed by a long‐life fretting fatigue test.     

Fatigue propagation threshold of short cracks under constant amplitude loading

In this study a threshold for fatigue crack propagation as a function of crack length is defined from a depth given by the position d of the strongest microstructural barrier to crack propagation, which defines the plain fatigue limit. The material threshold is estimated from the plain fatigue limit Δσ_eR, the position d of the strongest microstructural barrier and the threshold for long cracks, ΔK_thR. The threshold for eight different materials for which experimental results can be obtained from the literature was estimated. Good agreement was observed in all cases. Some quantitative analyses of the fatigue propagation behavior of short cracks are carried out and discussed.     

On the application of laser shock peening for retardation of surface fatigue cracks in laser beam‐welded AA6056

The present study aims to investigate the extent to which the fatigue behaviour of laser beam‐welded AA6056‐T6 butt joints with an already existing crack can be improved through the application of laser shock peening. Ultrasonic testing was utilized for in situ (nondestructive) measurement of fatigue crack growth during the fatigue test. This procedure allowed the preparation of welded specimens with surface fatigue cracks with a depth of approximately 1.2 mm. The precracked specimens showed a 20% reduction in the fatigue limit compared with specimens without cracks in the as‐welded condition. Through the application of laser shock peening on the surfaces of the precracked specimens, it was possible to recover the fatigue life to the level of the specimens tested in the as‐welded condition. The results of this study show that laser shock peening is a very promising technique to recover the fatigue life of welded joints with surface cracks, which can be detected by nondestructive testing.     

Fracture mechanics and scale effects in the fatigue of railway axles

Fatigue of railway axles is one of the basic problems of fatigue. However, in spite of the criticality of this component, modern approaches have not been used for addressing a critical revision of traditional design. The scope of this paper is to study the scale effects in fatigue limit and in crack growth rate for a high strength steel used for high speed railway axles.Fatigue limit tests on micro-notched specimens led to the determination of fatigue thresholds for small cracks of the examined steel. This allowed us to successfully analyse the `scale effect' and the fatigue strength of full-scale axles in terms of threshold stress for short cracks emanating from small non-metallic inclusions.A series of crack propagation tests on small scale specimens lead to the definition of an EPFM crack propagation model which has been successfully compared with propagation data on full-scale components. These results support the application of the crack propagation model for the determination of axle inspection intervals.     

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.     

Predicting the total fatigue life in metals

When a metal specimen is subjected to cyclic loading, a large number of initiated cracks will initiate in its volume. The specimen forms a sample of initial cracks: the larger specimen, the larger is the sample. In previous work of the author it was shown that the fatigue limit can be predicted by estimating the largest expectable crack depth with the help of statistics of extremes. In this paper it is shown that the fatigue crack initiation time above the fatigue limit can be predicted in an analogous manner. Instead of estimating the largest crack size with the distribution of maxima, prediction of the shortest expectable initiation time is obtained using the distribution of minima. Good agreement with extensive set of experimental data was obtained.The presented method offers a new way for estimating the total fatigue life of a component. When estimates of the crack initiation life and the critical crack size are obtained, the stable crack growth can be computed using Paris law. The estimate of the total fatigue life is obtained as the sum of initiation and crack growth lives. A method for constructing design curves for finding the crack initiation life for any material is presented.