Fatigue Laws Via Functional Equations

In routine industrial design, fatigue life estimation is largely based on S-N curves and ad hoc cycle counting algorithms used with Miner's rule for predicting life under complex loading. However, there are well known deficiencies of the conventional approach. Of the many cumulative damage rules that have been proposed, Manson's Double Linear Damage Rule (DLDR) has been the most successful. Here we follow up, through comparisons with experimental data from many sources, on a new approach to empirical fatigue life estimation (A Constructive Empirical Theory for Metal Fatigue Under Block Cyclic Loading', Proceedings of the Royal Society A, in press). The basic modeling approach is first described: it depends on enforcing mathematical consistency between predictions of simple empirical models that include indeterminate functional forms, and published fatigue data from handbooks. This consistency is enforced through setting up and (with luck) solving a functional equation with three independent variables and six unknown functions. The model, after eliminating or identifying various parameters, retains three fitted parameters; for the experimental data available, one of these may be set to zero. On comparison against data from several different sources, with two fitted parameters, we find that our model works about as well as the DLDR and much better than Miner's rule. We finally discuss some ways in which the model might be used, beyond the scope of the DLDR.

High temperature time-dependent low cycle fatigue behaviour of a type 316L(N) stainless steel

Total strain controlled low cycle fatigue tests on 316L(N) stainless steel have been conducted in air at various strain rates in the temperature range of 773-873 K to identify the operative time-dependent mechanisms and to understand their influence on the cyclic deformation and fracture behaviour of the alloy. The cyclic stress response at all the testing conditions was marked by an initial hardening followed by stress saturation. A negative strain rate stress response is observed under specific testing conditions which is attributed to dynamic strain ageing (DSA). Transmission electron microscopy studies reveal that there is an increase in the dislocation density and enhanced slip planarity in the DSA regime. Fatigue life is found to decrease with a decrease in strain rate. The degradation in fatigue resistance is attributed to the detrimental effects associated with DSA and oxidation. Quantitative measurement of secondary cracks indicate that both transgranular and intergranular cracking are accelerated predominantly under conditions conducive to DSA.

Impedance-fatigue correlated studies on SrBi2Ta2O9

Ceramic samples of SrBi2Ta2O9 (SBT) were prepared by the solid state reaction method with a view to study their electrical properties. Reasons as to why SBT shows better fatigue endurance than conventional perovskites like Pb(Zr, Ti)O-3 are looked into. Complex impedance spectroscopy (CIS) was used as a tool to do so. CIS data was acquired over the temperature range from room temperature to 500 degrees C over a wide range of frequencies. Electrical conductivity data indicates that the conductivity in SBT is essentially due to oxygen vacancies and the activation energy for conduction in the high temperature region was found to be 0.95 eV. CIS was used to separate out the bulk and the interfacial contributions to complex impedance.

Effects of tempered structure on the near threshold fatigue crack growth behavior of a coarse grained high strength steel

Near threshold fatigue crack growth behavior of a high strength steel under different temper levels was investigated. It is found that the observed variations in ΔKth could predominantly be attributed to roughness induced crack closure. The closure-free component of the threshold stress intensity range, ΔKeff,th showed a systematic variation with monotonic yield strength.

Fatigue crack growth rates and fracture toughness in electroslag refined En 52 steel

En 52 steel has been electroslag refined and the resultant effects of refining on its mechanical properties have been assessed. It was found that refining caused a decrease in fatigue crack growth rates and increases in fatigue strength, fracture toughness, Charpy fracture energy and tensile ductility. Fatigue crack growth rates in region I and in region III were found to be considerably lower in the electroslag refined steel: they were unaffected in region II. The fracture toughness values for the electroslag refined steel are nearly twice those estimated for the unrefined steel. Measurements on heat-treated samples have shown that the electroslag refined steel has a better response to heat-treatment. The improvement in the mechanical properties is explained in terms of the removal of nonmetallic inclusions and a reduction in the sulphur content of the steel.

Effect of electroslag refining on the fracture toughness and fatigue crack propagation rates in heat treated AISI 4340 steel

The AISI 4340 steel has been electroslag refined and the improvement in mechanical properties has been assessed. Electroslag refining (ESR) has improved tensile ductility, plane strain fracture toughness, Charpy fracture energy, and has decreased fatigue crack growth rates. The KIC values for the ESR steel are nearly twice those estimated in the unrefined steel and higher than those obtained in the vacuum arc remelted steel. Fatigue crack growth rates in region I and in region III are found to be decreased considerably in the ESR steel, while they are unaffected in region II. Measurements on heat treated samples have shown that the ESR steel has a better response to heat treatment. Both the suggested heat treatments namely austenitizing at 1140–1470 K as well as the conventional heat treatment of austenitizing at 1140 K have been followed. The improvement in the mechanical properties of ESR steel has been explained on the basis of removal of nonmetallic inclusions and reduction in sulfur content in the steel.

Some Considerations on the Occurrence of Intergranular Fracture during Fatigue Crack growth in Steels

The occurrence of a maximum in the percentage of intergranular fracture on the fracture surface during the transition from intermediate to low fatigue crack growth rates has been observed for a high strength steel. It is suggested that transgranular planar slip leading to slip localization is essential in promoting intergranular fracture when the cyclic plastic zone size becomes equal to the prior austenite grain size.

The effect of crack closure on the grain size dependence of fatigue crack growth threshold

Recent studies (I-7) clearly indicate a strong dependence of fatigue threshold parameter, A K on grain size in several alloy systems. Attempts to explain these observations on the basis of crat~tortuosity (1,8), fracture surface roughness (5,9) and crack closure (6) appear to present a fairly clear picture of the mechanisms that cause a reduction in crack growth rates at threshold. In general, it has been shown that coarse grained microstructures exhibit higher fatigue threshold in low carbon steels (1,5) aluminium alloys (7) and titanium alloys (6). In spite of these observations, there exists (10-1#) considerable uncertainity about the manner in which the AK~L depends on prior austenitic grain size in quenched and tempered steels. Studies in quenched and tempered steels demonstrating both an increase (3,12,14) as well as a decrease (11,12) in AKth with an increase in prior austenitic grain size can be sought to illustrate this point. Occasionally , the absence of any sensitivity of AKth to the variations in prior austenitJc grain size has also been reported (11,13). While a few investigators (5-7) comfortably rationalised the grain size effects on AK~L on the basis of crack closure by a comparison in terms of the closure-free component of the thresho~Ifc~, AK -f such an approach has yet to be extended to high strength steels, An attempt has been made in t~et ,pthrg sent study to explai. n the effect of pri, or austeniti.c grain size on &Kth on the basis of crack closure measurements in a high strength steel.

Low cycle fatigue behaviour of a low interstitial Ni-base superalloy

The low cycle fatigue behaviour of precipitation strengthened nickel-base superalloy 720Li containing a low concentration of interstitial carbon and boron was studied at 25, 400 and 650 degrees C. Cyclic stress response at all temperatures was stable under fully reversed constant total strain amplitude (Delta epsilon/2) when Delta epsilon/2 <= 0.6%. At Delta epsilon/2 > 0.6%, cyclic hardening was followed by softening, until fracture at 25 and 650 degrees C. At 400 degrees C, however, cyclic stress plateaued after initial hardening. Dislocation-dislocation interactions and precipitate shearing were the micromechanisms responsible for the cyclic hardening and softening, respectively. The number of reversals to failure vs. plastic strain amplitude plot exhibits a bilinear Coffin-Manson relation. Transmission electron microscopy substructures revealed that planar slip was the major deformation mode under the conditions examined. However, differences in its distribution were observed to be the cause for the bilinearity in fatigue lives. The presence of fine deformation twins at low Delta epsilon/2 at 650 degrees C suggests the role of twinning in homogenization of cyclic deformation.

Automated estimation of fatigue crack length and closure/opening stress

An experimental technique is proposed for the estimation of crack length as well as crack closure/opening stress during fatigue crack growth. A specially designed, single cantilever, crack opening displacement gauge is used to monitor these variables during fatigue crack propagation testing. The technique was experimentally validated through electronfractography.

The formation of carbon nanostructures by in situ TEM mechanical nanoscale fatigue and fracture of carbon thin films

A technique to quantify in real time the microstructural changes occurring during mechanical nanoscale fatigue of ultrathin surface coatings has been developed. Cyclic nanoscale loading, with amplitudes less than 100 nm, is achieved with a mechanical probe miniaturized to fit inside a transmission electron microscope (TEM). The TEM tribological probe can be used for nanofriction and nanofatigue testing, with 3D control of the loading direction and simultaneous TEM imaging of the nano-objects. It is demonstrated that fracture of 10-20 nm thick amorphous carbon films on sharp gold asperities, by a single nanoscale shear impact, results in the formation of < 10 nm diameter amorphous carbon filaments. Failure of the same carbon films after cyclic nanofatigue, however, results in the formation of carbon nanostructures with a significant degree of graphitic ordering, including a carbon onion.

Assessment of the residual fatigue strength in RC beams

In conventional analysis and design procedures of reinforced concrete structures, the ability of concrete to resist tension is neglected. Under cyclic loading, the tension-softening behavior of concrete influences its residual strength and subsequent crack propagation. The stability and the residual strength of a cracked reinforced concrete member under fatigue loading, depends on a number of factors such as, reinforcement ratio, specimen size, grade of concrete, and the fracture properties, and also on the tension-softening behavior of concrete. In the present work, a method is proposed to assess the residual strength of a reinforced concrete member subjected to cyclic loading. The crack extension resistance based approach is used for determining the condition for unstable crack propagation. Three different idealization of tension softening models are considered to study the effect of post-peak response of concrete. The effect of reinforcement is modeled as a closing force counteracting the effect of crack opening produced by the external moment. The effect of reinforcement percentage and specimen size on the failure of reinforced beams is studied. Finally, the residual strength of the beams are computed by including the softening behavior of concrete.

Near-threshold fatigue crack growth in bulk metallic glass composites

A major drawback in using bulk metallic glasses (BMGs) as structural materials is their extremely poor fatigue performance. One way to alleviate this problem is through the composite route, in which second phases are introduced into the glass to arrest crack growth. In this paper, the fatigue crack growth behavior of in situ reinforced BMGs with crystalline dendrites, which are tailored to impart significant ductility and toughness to the BMG, was investigated. Three composites, all with equal volume fraction of dendrite phases, were examined to assess the influence of chemical composition on the near-threshold fatigue crack growth characteristics. While the ductility is enhanced at the cost of yield strength vis-a-vis that of the fully amorphous BMG, the threshold stress intensity factor range for fatigue crack initiation in composites was found to be enhanced by more than 100%. Crack blunting and trapping by the dendritic phases and constraining of the shear bands within the interdendritic regions are the micromechanisms responsible for this enhanced fatigue crack growth resistance.

Prediction of fatigue strength in plain and reinforced concrete beams

A fatigue crack propagation model for concrete is proposed based on the concepts of fracture mechanics. This model takes into account the loading history, frequency of applied load, and size, effect parameters. Using this model, a method is described based on linear elastic fracture mechanics to assess the residual strength of cracked plain and reinforced concrete (RC) beams. This could be used to predict the residual strength (load carrying capacity) of cracked or damaged plain and reinforced concrete beams at a given level of damage. It has been seen that the fatigue crack propagation rate increases as. the size of plain concrete, beam increases indicating an increase in brittleness. In reinforced concrete (RC) beams, the fracture process becomes stable only when the beam is sufficiently reinforced.