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.     

Observation of fatigue damage in structural steel by scanning atomic force microscopy

Fatigue slip bands and plastic deformation around fatigue microcracks were observed by scanning atomic force microscopy. In fatigue slip bands, extrusions were observed but intrusions were not detected. Large extrusions were found in slip bands whose traces at specimen surface were almost perpendicular to the loading axis. Microcracks propagated under mixed mode condition of Mode I, Mode II, and Mode III.     

On the relationship between fatigue limit,threshold and microstructure of a low-carbon Cr-Ni steel

The relationship between the fatigue limit stress range, Δσ_w, the threshold stress intensity factor, ΔK_th, and microstructure of low-carbon 12CrNi3A steel has been investigated. Non-propagating microcracks were observed on the surface of smooth specimens which has been subjected to at least 5 × 10⁶ cycles at the fatigue limit stress. The size of the cracks depended on the characteristic sizes of the microstructure of the material. Scanning electron microscopy showed that the fractographic characteristics in the near-threshold region of fatigue macrocrack growth were similar to those in the fatigue microcrack initiation region. This implies that the fatigue limit and fatigue threshold of the material have a similar physical meaning, both signifying the resistance of the material to the propagation of fatigue cracks. The relationship ΔK_th = 1.12Δσ_W √πα was shown to be valid, where a is a material parameter relating to microstructure, rather than to the length of a macrocrack. The results also showed that the value of a depends on the material and microstructure, and that both Δσ_W and ΔK_th will change if the microstructural characteristics of the material change.     

Non-propagating crack behaviour at giga-cycle fretting fatigue limit

Fretting fatigue fracture of industrial machines is sometimes experienced after a long period of operation. It has been a question whether the fatigue limit which means infinite life really exists in fretting fatigue or not. Fretting fatigue tests in ultra high cycle region up to 10⁹ cycles were performed. Test results showed that the S‐N curve had a knee point around 2 × 10⁷ cycles and a clear fatigue limit was observed in the giga‐cycle regime for partial slip conditions. An electropotential drop technique was applied to detect the crack growth behaviour under the contact pad. The real‐time measurement of crack depth during the fretting fatigue test at the fatigue limit showed that a crack initiated at an early stage and then ceased to grow after 2 × 10⁷ cycles and the crack became a non‐propagating crack. These results indicated that the fatigue limit exists in fretting fatigue and infinite endurance is achieved by the mechanism of forming a non‐propagating crack.     

Fretting fatigue under variable loading below fretting fatigue limit

The fatigue limit diagram provides the critical condition of non‐failure against fatigue under constant amplitude loading. The fatigue limit diagram is usually considered to give the allowable stress if every stress component is kept within the fatigue limit diagram. In the case of variable amplitude fretting fatigue, however, this study showed that fatigue failure could occur even when all stresses were within the fatigue limit diagram. An example of such a condition is a repeated two‐step loading such as when the first step stress is R=?1 and the second step stress has a high mean value. The reason why such a phenomenon occurs was investigated. A non‐propagating crack was formed by the first step stress even when well below the fatigue limit. The resultant non‐propagating crack functioned as a pre‐crack for the second step stress with a high mean value. Consequently, fatigue failure occurred even when every stress was within the fatigue limit diagram of constant amplitude loading. The fatigue limit diagram obtained in constant amplitude fatigue test does not necessarily guarantee safety in the case of variable amplitude loading in fretting fatigue.     

Relation between fatigue threshold and fatigue limit for surface-rolled specimens

After cylinder notch fatigue specimens of 40 CrNiMo steel were rolled, their fatigue limit increased by 41%. The rolled specimens did not fracture, even though they had been loaded for 10⁷ cycles under fatigue limit stress, but a non-propagating fatigue crack was generated. Thus the value of the fatigue limit depends on the fatigue threshold value ΔK_th of the metal of the rolled layer. Plastic deformation increased ΔK_th in these experiments. It can be inferred that ΔK_th of the rolled layer increases from the occurrence of plastic deformation and microvoids on the layer. Calculation of the effect of residual stress in the crack wake on the stress intensity factor ΔK indicates that residual compression stress decreases ΔK by 21.5 MPa √M. It was calculated that rolling induced both the length of the non-propagating crack and the increase of fatigue limit. The calculated values are in accord with experiment. Analysis and calculations indicate that the non-propagating crack is generated on the rolled layer. Thus the fatigue limit is improved because rolling produces residual compression stress in the layer (which decreases the stress intensity factor), and increases ΔK_th of the layer.     

The fretting fatigue limit based on local stress at the contact edge

It is well known that fretting fatigue is affected by various factors such as contact pressure, relative slip, contact length, specimen size, loading type and so on. In this study, the reason why these factors affect fretting fatigue was investigated on the basis of the stress distribution near the contact edge. The local stress distribution near the contact edge was experimentally measured using a small multi-element stress concentration gauge. It was shown that the magnitude of the stress concentration at the contact edge varied significantly depending on these factors. It was found that the S – N curve was expressed uniquely on the basis of the local stress amplitude at the contact edge     

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.     

The nature of initiation and propagation S-N curves at and below the fatigue limit

The traditional stress-life method of life prediction relies on an S – N curve of stress versus total life. However, the total life of a sample can be divided into two phases—an initiation phase and a propagation phase that leads to ultimate failure. Although this break-up of total life into two phases has been recognized in theory, there has been no experimental method to generate initiation and propagation S – N curves. In this paper a methodology to generate initiation and propagation S – N curves is presented. Acoustic emission technology is used to detect the transition from the initiation phase to the propagation phase. The phenomenon of fatigue limits is also explored and it is shown that the fatigue limit of the traditional S – N curve corresponds to the fatigue limit of the initiation phase and that initiated cracks continue to propagate at stress levels below the initiation endurance limit. It is also shown that no damage is accrued at stress levels below the fatigue limit. A method to extend the propagation life curve below the initiation endurance limit is also presented. The proposed two-phase S – N curve will greatly extend the life-predicting capability of the stress-life method and can explain some of the contradictions observed in experiments.     

The effect of material hardness and mean stress on the fatigue limit of steels containing small defects

Fatigue tests on material containing small defects were performed under a wide range of mean stress for three grades of steels with different hardness. The ΔK_th of small defects had a peculiar dependency on material hardness and mean stress, which was quite different from those of long cracks or plain specimens. The crack closure of short cracks was measured. It was shown that the formation of the crack closure was affected by the material hardness and mean stress. This behaviour of crack closure resulted in characteristic fatigue limit properties of materials containing small defects.     

Effect of small notch and absorbed hydrogen on the fatigue fracture in two-step stress test within fatigue limit diagram

It is usually regarded as a common understanding that fatigue failure would not occur if all stresses were kept within fatigue limit diagram. However, it was shown that fatigue failure occurred in some special cases of variable amplitude loading condition even when all stresses were kept within fatigue limit diagram in the case of small-notched specimen. The cause of such a phenomenon was examined using two-step stress pattern for low alloy steel SCM440H. In the case of constant stress amplitude loading, non-propagating crack was formed only at low mean stress and not formed at high mean stress. However, in the case of two-step stress pattern in which the first step stress was chosen as  R  =−1 and the second step stress was with high mean stress, a non-propagating crack was formed by the first step stress. This crack functioned as a pre-crack for the second step stress with high mean stress. Consequently, fatigue failure occurred by the stresses within fatigue limit diagram. In this study, the effect of notch size and shape were examined. The effect of absorbed hydrogen was also investigated. Absorption of 0.3 ppm hydrogen caused more reduction of fatigue limit.     

Nanoscopic fatigue and stress corrosion crack growth behaviour in a high-strength stainless steel visualized in situ by atomic force microscopy

In situ atomic force microscope (AFM) imaging of the fatigue and stress corrosion (SC) crack in a high‐strength stainless steel was performed, under both static and dynamic loading. The AFM systems used were (1) a newly developed AFM‐based system for analysing the nanoscopic topographies of environmentally induced damage under dynamic loads in a controlled environment and (2) an AFM system having a large sample stage together with a static in‐plane loading device. By using these systems, in situ serial clear AFM images of an environmentally induced crack under loading could be obtained in a controlled environment, such as in dry air for the fatigue and in an aqueous solution for the stress corrosion cracking (SCC). The intergranular static SC crack at the free corrosion had a sharp crack tip when it grew straight along a grain boundary. The in situ AFM observations showed that the fatigue crack grew in a steady manner on the order of sub‐micrometre. The same result was obtained for the static SC crack under the free corrosion, growing straight along a grain boundary. In these cases, the crack tip opening displacement (CTOD) remained constant. However, as the static SC crack was approaching a triple grain junction, the growth rate became smaller, the CTOD value increased and the hollow ahead of the crack tip became larger. After the crack passed through the triple grain junction, it grew faster with a lower CTOD value; the changes in the CTOD value agreed with those of the crack growth rate. At the cathodic potential, the static SC crack grew in a zigzag path and in an unsteady manner, showing crack growth acceleration and retardation. This unsteady crack growth was considered to be due to the changes in the local hydrogen content near the crack tip. The changes in the CTOD value also agreed with those of the crack growth rate. The CTOD value in the corrosive environment was influenced by the microstructure of the material and the local hydrogen content, showing a larger scatter band, whereas the CTOD value of the fatigue crack in dry air was determined by the applied stress intensity factor, with a smaller scatter band. In addition, the CTOD value in the corrosive environment under both static and dynamic loading was smaller than that of the fatigue crack; the environmentally induced crack had a sharper crack tip than the fatigue crack in dry air.     

A probabilistic approach for thermal shock fatigue life of glass

This paper presents a probabilistic approach for predicting fatigue life of glass subjected to near‐ΔT_C (critical temperature difference) thermal shock which exhibits little subcritical crack extension. First, thermal shock fatigue life N_f was derived as a function of temperature difference ΔT, fracture probability F and Biot's modulus β from the slow crack growth concept in conjunction with the Weibull distribution model. Next, thermal shock fatigue tests as well as flexural tests were performed for borosilicate glass to measure ΔT_C and N_f versus ΔT. The parameters associated with slow crack growth were then determined from the experimental results while the heat transfer coefficient h or β was obtained with the aid of finite element analysis. Thirdly, the thermal shock fatigue diagram (ΔT?N_f curves) was depicted for various values of β. Finally, crack length was simulated on the basis of the present approach.     

Fatigue strength of small-notched specimens under variable amplitude loading within the fatigue limit diagram

Although the fatigue limit diagram is defined in principle for constant stress amplitude, it is often considered that fatigue failure would not occur, even in varying loading, if applied stresses were kept within the fatigue limit diagram. However, it was shown in the case of small‐notched specimens that fatigue failure occurred in some special cases of variable amplitude loading, even when all stress amplitudes were kept within the fatigue limit diagram. The cause of this phenomenon was examined using two‐step stress and repeated two‐step stress patterns in which the first step stress was chosen to be equal to the fatigue limit with zero mean stress and a mean stress was superposed on the second step stress. A non‐propagating crack was formed by the first step stress. This crack functioned as a pre‐crack for the second step stress with high mean stress. Consequently, fatigue failure occurred even when all stress amplitudes were kept within the fatigue limit diagram. It was an unexpected fracture caused by the interference effect of a non‐propagating crack and a mean stress change.     

莫来石陶瓷的室温应力腐蚀开裂行为

分别在空气、蒸馏水和碱性溶液中测定了莫来石陶瓷材料在不同外加应力水平下的室温断裂寿命,探讨了应力腐蚀裂纹缓慢扩展机理．研究表明,在高载荷下,吸附效应为裂纹扩展的主导机理,而在低载荷下,裂纹尖端钝化效应为主导机理．此外,在蒸馏水和碱性溶液两种介质中裂纹扩展指数N值有所不同,反映了介质对水合层的不同溶解能力．     

Prediction of stable crack growth geometry in residually stressed glass

Processing procedures have been developed that produce stress distributions in glass with a maximum compressive stress below the surface. These glasses can exhibit rising apparent fracture toughness behavior and reduced strength variability associated with the stable growth of surface cracks under applied tensile stress. A weight function approach was used to determine stress intensity factors as a function of crack geometry for surface cracks under the effects of stress distributions similar to those found in these glasses. These calculations were then used to predict the growth behavior of surface cracks as a function of the applied and residual stress fields.     

Modelling the effects of surface finish on fatigue limit in austenitic stainless steels

Existing short fatigue crack models have been reviewed to determine the most suitable fatigue model to analyse the effect of the surface finish on the fatigue limit of Type 304 austenitic stainless steels. A mechanistic model firstly proposed by Navarro and Rios (N‐R model) was selected as the most suitable generic model, because the model can include the effects of surface finishing parameters such as surface roughness and residual stress depth profile on the fatigue limit. The N‐R model has been implemented for fatigue specimens with various surface finishing conditions, and the effect of the surface finish on the fatigue limit was simulated. The material/surface properties required for the implementation were fully characterized by experiments. The applicability of the model to this study was also discussed. It is concluded that a development of the model would be required for proper prediction of the surface effects on fatigue in austenitic stainless steels.     

The influence of hammer peening on fatigue in high-strength steel

An investigation of the influence of hammer peening on fatigue crack initiation and propagation in high-strength steel has been performed using edge notch specimens. The crack initiation time was found to decrease after peening; however, the fatigue crack growth stage remained unchanged or decreased depending upon the peening parameters. The results have been used to develop an analytical model to predict the fatigue crack growth rate in peened materials, based upon the compressive residual stress effect.