Fatigue Stress Concentration Factor Research Articles

Nonpropagating incipient cracks from sharp notches under fatigue

Growing incipient cracks from sharp notches can stop completely even when the remote applied stress amplitude remains constant. As the crack lengthens, the crack-tip driving force, the stress intensity factor, should increase for a constant remote applied stress, yet, arrest occurs. For this reason, the fatigue stress concentration factor K f differs from the conventional stress concentration factor K t for sharp notches. The arrest has been attributed to increased crack growth resistance as an incipient crack lengthens. The increased resistance has been related to plasticity-induced crack closure, which builds up with crack-wake plasticity during crack growth. In this paper we present a different concept based on our unified approach that considers the existence of two fatigue thresholds rather than one. It is shown that nonpropagation of incipient crack occurs when the total stress intensity factor falls below the long crack growth threshold value in terms of K max. Total stress intensity results from both the remote applied stress and the local internal stress. Even when the remote applied load is constant, the local internal stress can decrease sharply as the incipient crack grows away from the notch tip. Notch-tip plasticity contributes to the changes in the internal stresses. Using extensive data from the literature, it is shown that it is the decreasing crack-tip driving force with length that causes the crack arrest phenomenon. Crack growth under tension–tension, tension–compression, and compression–compression fatigue are all accounted for on the basis of gradient in the internal stresses.

Fatigue strength and stress concentration factors of CHS-to-RHS T-joints

Abstract The static and fatigue behaviour of eight different hollow section T-joints subjected to both axial and in-plane bending loads were investigated experimentally. The joints had circular brace members and rectangular chords. Hot spot stresses and the stress concentration factors (SCFs) were determined experimentally. Fatigue testing was carried out under constant amplitude loading in air. The test results have been statistically evaluated, and show that the experimental SCF values for circular-to-rectangular (CHS-to-RHS) hollow section joints were found to be between those of circular-to-circular (CHS-to-CHS) and rectangular-to-rectangular (RHS-to-RHS) hollow section joints. The fatigue strength, referred to experimental hot spot stress, was in reasonably good agreement with referred fatigue design codes for tubular joints.

Whole tires/mixed-feedstock gasification for syngas production

The critical distance inverse search procedure, recently proposed by the authors (Santus et al., 2018), was experimentally applied in this work to 42CrMo4+QT steel and 7075-T6 aluminium alloy for fatigue load ratios R = −1 and R = 0.1. The inverse search lengths were in good agreement with the critical distances derived from the crack threshold. The Point Method lengths were higher than the Line Method values since the relatively low stress distribution second derivative. However, this difference is compensated for when the corresponding Method, Point or Line, is then used for the fatigue strength assessment of another specimen or a component. The fatigue predictions and comparisons with the experiments are reported in an accuracy chart, showing that a small radius notched specimen is recommended to determine the critical distance and thus obtain an accurate strength assessment of a blunter specimen. This critical distance determination was then extended to the fatigue finite life, again obtaining accurate predictions, especially for the aluminium alloy. The online version of this paper is provided with MATLAB scripts which contain examples for the critical distance inverse search and the direct problem for the fatigue stress concentration factor calculation.

Surface Texture, Fatigue, and the Reduction in Stiffness of Fiber Reinforced Plastics

Abstract In this study the influence of machined surface texture on the fatigue strength of a Graphite/Bismaleimide (Gr/Bmi) laminate was examined. Rectangular beam specimens were machined to achieve specific surface roughness 0.2⩽Ra⩽10.0 μm and then subjected to fully reversed four-point flexural fatigue. The surface texture resulting from machining was evaluated using contact profilometry and the standard surface roughness parameters were used in estimating the effective stress concentration K¯t and effective fatigue notch K¯f factors for the machined surfaces according to models reported in the open literature. Fully reversed flexural fatigue loading of the laminate was conducted at two separate maximum bend loads corresponding to Tsai-Hill ratios for first ply failure of 0.75 and 0.9. It was found that the reduction in stiffness of the Gr/Bmi laminate at both levels of fatigue loading increased with the magnitude of surface roughness. The apparent fatigue stress concentration factors Kf of the machined surfaces determined from experimental results ranged from 1.0 to 1.2. The effective fatigue notch factors estimated using the Arola-Ramulu model for the machined specimens were within 10% of the corresponding Kf determined from experiments.

Estimating the fatigue stress concentration factor of machined surfaces

In this study the effects of surface texture on the fatigue life of a high-strength low-alloy steel were evaluated in terms of the apparent fatigue stress concentration. An abrasive waterjet was used to machine uniaxial dogbone fatigue specimens with specific surface quality from a rolled sheet of AISI 4130 CR steel. The surface texture resulting from machining was characterized using contact profilometry and the surface roughness parameters were used in estimating effective stress concentration factors using the Neuber rule and Arola–Ramulu model. The steel specimens were subjected to tension–tension axial fatigue to failure and changes in the fatigue strength resulting from the surface texture were assessed throughout the stress–life regime (10 3≤ N f≤10 6 cycles). It was found that the fatigue life of AISI 4130 is surface-texture-dependent and that the fatigue strength decreased with an increase in surface roughness. The fatigue stress concentration factor ( K f) of the machined surfaces determined from experiments was found to range from 1.01 to 1.08. Predictions for the effective fatigue stress concentration ( K ̄ f ) using the Arola–Ramulu model were within 2% of the apparent fatigue stress concentration factors estimated from experimental results.

Fatigue process zone at notches

Fatigue macrocrack initiation is considered to be a two-parameter process. It is governed by the local stress range and a certain linear parameter of the material, the process (prefracture) zone size, d*. The value of d* determines the fatigue stress concentration factor, K f, and quantitative criterion, a i =d ∗ , for the micro- to macrocrack transition. The experimental and calculational methods for parameter d* estimation are analyzed. The value of K f for the beam and CT specimens based on the author's approach and calculated by the well-known equations of Neuber and Peterson are compared.

Hot spot and volumetric approaches to the high cycle fatigue of notched components

The high cycle fatigue of notched components traditionally is examined using the so-called hot spot approach. This relatively old approach is based on the concept of the fatigue stress concentration factor and the fatigue sensitivity index. It requires empirical relationships between fatigue sensitivity index and notch radius. The more recent volumetric approach is based on the fact that the fatigue mechanism needs a physical volume. Inside this volume, the average stress or effective stress plays the major role. This effective stress is introduced in the fatigue resistance relationship in order to compute the fatigue life duration.

Stress concentration factors for non-90° X-connections made of square hollow sections

A number of fatigue experiments and stress concentration factor measurements on non-90°, square hollow section X-connections have been carried out. Comparison of the measured stress concentration factors with those derived from existing parametric formulae for 90° T- and X-connections showed a strong influence of the brace angle. A tentative extension of the range of validity of the parametric formulae for 90° T- and X-connections for other brace angles has been derived.Key words: steel structures, connections, fatigue, hollow structural sections, hot spot stress, stress concentration factors.

Inherent Damage Zone Model for Fatigue Strength Evaluation

Inherent damage zone model assumes that the stress at a point which is located at a small distance, γ0 from the crack initiation position governs the fatigue characteristics regardless of the geometric configuration of the specimen. The distance γ0 represents the size of effective damage zone and it is an inherent length of the material. Ishibashi proposed the model to explain the difference between fatigue notch factor and stress concentration factor of notched specimen. This paper shows that the inherent damage zone model can explain several fatigue phenomena near the fatigue limit and the crack growth threshold consistently without restriction of smooth specimen, notched specimen or cracked specimens with short and long crack length. A special feature of the paper is using the exact solution of stress distributions of notched and cracked specimens. Neuber's analytical solution for notched specimen and Westergaard's stress function for cracked specimen are employed for this purpose. Relationship between fatigue limit of smooth specimen and threshold stress of cracked specimen, relationship of fatigue strength between round-shaped flaws and crack, occurrence condition of non-propagating crack at the root of sharp notch, and fatigue notch factor are discussed quantitatively based on the proposed model.

Fatigue and corrosion fatigue of beryllium-copper spring materials

Fine gage, 0.006-in. d(0.15-mm) thick, beryllium-copper (Be-Cu) spring materials with tensile strength in the range of 70 to 145 ksi were subjected to cyclic loading in air and salt water environments. Plain and notched (center hole) hour glass specimens were subjected to sinusoidal loading with R = (minimum/maximum) stress = 0.1 at cyclic frequencies of 50 Hz in air and 1 Hz in salt water. Fatigue life was typically from 10[sup 4] to 10[sup 6] cycles with crack initiation as the dominant fatigue process. The excellence fatigue performance of Be-Cu alloys in salt water is well-known, however, current findings demonstrate 10 to 37% reduction in fatigue strength of unnotched specimens in this environment for a life of 3 x 10[sup 5] cycles. This strength degradation is attributed to the use of a lower cyclic frequency for present than for previous tests, i.e., 1 versus about 20 Hz. There was no effect of salt water on crack initiation in notched specimens. The ratios of the fatigue strengths, namely (cold-rolled/annealed) and (aged/annealed), for plain and notched specimens tested in air, decreased from 2 to about 1.4 as fatigue life increased from 10[sup 4] to 10[sup 6] cycles. This effect is attributed tomore » cyclic hardening of the annealed material. The fatigue stress concentration factor, K[sub f] = (plain/notched) fatigue strength, increased by about 30% as fatigue cycles increased from 10[sup 4] to 10[sup 6]. The ranking of K[sub f] values of the various material conditions from highest to lowest was: cold-rolled, aged, and annealed.« less

Fatigue Strength of Corroded Weld Joints

This paper summarises results of an appraisal of measured corrosion data of a hull structure obtained through periodical surveys, corrosion tests of specimens of various welded joints, fatigue tests and stress analysis of corroded specimens. Statistical analysis of pitting corrosion on the bottom plate of oil tankers was carried out with good results. It was also found that tank cleaning has a considerable effect on the progress of pitting corrosion. Data of plate thickness on the lower part of side frames of bulk carriers was appraised by two parameters, the initiation life and progress rate of corrosion wastage. Results showed that the progress rate of corrosion wastage was larger than conventional numerals. A corrosion test of welded joint specimen was carried out under the cycles of sea water and air. Grooving corrosion had initiated at the weld toe of butt joints. The cause of grooving corrosion was presumed to be due to the difference of corrosion potential between HAZ and base metal/weld metal of the specimen. Tensile fatigue test and stress analysis of corroded specimens was carried out. The results were examined as to the relation of fatigue strength and stress concentration factor. It was confirmed that in butt joints, the stress concentration factor was increased by corrosion and fatigue strength was reduced. In a cruciform joint, the factor was nearly unchanged and the fatigue strength was hardly reduced.

Spalling Life Model With Relaxed Distribution Constraints, for Rough Hertz Line Contacts

A Hertz contact spalling fatigue life model is constructed without the constraints of a two-parameter Weibull life distribution. The model is based on the time of crack propagation following a simple Paris law, through the Hertzian alternating shear stress field, from populations of surface defects with depth (severity) distributed according to the Greenwood-Williamson asperity model, to the depth of the maximum alternating shear stress. The life distribution shows moderate deviations from the Weibull form, with the dispersion strongly dependent on the contact parameters. The 90 percent survival quantile is obtained as a function of: Hertz pressure, EHD film ratio, asperity traction coefficient, asperity height, slope and spectrum width, fatigue limit stress and stress concentration factor. This model provides insights into the interrelationship of life with its parameters, not available from models adhering to the power law constraints required to produce a Weibull life distribution. No unbridgeable contradictions emerge between the present formulation and published engineering models.

Fatigue and Corrosion Fatigue of Beryllium-Copper Spring Materials

Abstract Fine gage, 0.006-in. (0.15-mm) thick, beryllium-copper (Be-Cu) spring materials with tensile strength in the range of 70 to 145 ksi (482 to 999 MPa) were subjected to cyclic loading in air and salt water environments. Plain and notched (center hole) “hour glass” specimens were subjected to sinusoidal loading with R = (minimum maximum) stress = 0.1 at cyclic frequencies of 50 Hz in air and 1 Hz in salt water. Fatigue life was typically from 104 to 106 cycles with crack initiation as the dominant fatigue process. The excellence fatigue performance of Be-Cu alloys in salt water is well-known, however, current findings demonstrate 10 to 37% reduction in fatigue strength of unnotched specimens in this environment for a life of 3 × 105 cycles. This strength degradation is attributed to the use of a lower cyclic frequency for present than for previous tests, i.e., 1 versus about 20 Hz. There was no effect of salt water on crack initiation in notched specimens. The ratios of the fatigue strengths, namely (cold-rolled annealed) and (aged/annealed), for plain and notched specimens tested in air, decreased from 2 to about 1.4 as fatigue life increased from 104 to 106 cycles. This effect is attributed to cyclic hardening of the annealed material. The fatigue stress concentration factor, Kt = (plain notched) fatigue strength, increased by about 30% as fatigue cycles increased from 104 to 106. The ranking of Kf values of the various material conditions from highest to lowest was: cold-rolled, aged, and annealed.

Residual strength in notched composite materials

The main objective was to understand the stress concentration factor of fatigue damage for centrally notched composite laminates of various lay-ups in the proportion of 45, −45, 90 and 0 deg plies. The application of fatigue stress concentration factor was used to predict the residual strength. The Whitney-Nuismer (WN) extended point stress fracture criterion and the extended average stress fracture criterion were adopted. The characteristic length is not necessarily a constant; it depends on the shape of the damage zone, the number of applied cycles, the hole radius, etc. The tests were performed at low-frequency tension-tension (T-T) fatigue loading with constant stress amplitude at room temperature. In simple terms, after thousands of cycles, because of the geometric change of a circular hole to the deformed laminate, the stress concentration factor decreases with the increasing number of applied cycles, which is the reason for the increase of residual strength of the notched laminate. The correlation of the residual strength as predicted by the numerical methods and the fatigue stress concentration analysis is found to be satisfactory, in comparison with the experimental data.

Combined Fatigue Stress Concentration Factor Determination

The paper begins with a panoramic view of the state of the art embracing the spectrum of methods employed by different designers to account for all stress concentration effects in calculations for use in the design of machine elements and components subjected to combined/fatigue loadings. Then, on the basis of the widely accepted von Mises-Goodman approach, and the method deemed the best for incorporating combined stress concentration effects, a general expression is derived for the combined fatigue stress concentration factor which is applicable to any machine element or component subjected to any combination of fatigue loadings. Various load combinations are considered not only to illustrate the use of the derived expression, but also to demonstrate other methods which may lead to calculations which are incorrect depending upon the nature and magnitude of the parameters involved. The specific machine component, that of a stepped shaft subjected to combined fatigue loadings, is selected for particular, detailed and further demonstration. Demonstrative tables and a curve plot are also included.

Fatigue Reliability With Notch Effects for AISI 4130 and 1038 Steels

Methodologies for developing distributional theoretical stress concentration factors, fatigue stress concentration factors, and notch sensitivity factors for circumferentially grooved, rotating AISI 4130 and AISI 1038, 3/8-in.-dia rods subjected to reversed bending are developed and the results are presented. The groove radii vary from 0.031 in. to 1.870 in., and the base diameters at the groove vary from 0.0937 in. to 0.2700 in. Two illustrative cases for designing such components to a specified life and reliability are given.

The Relationship Between Fatigue and Stress Concentration

It is well known that notches have a deleterious influence on the fatigue strength of parts. A constant, the sensitivity index, is commonly used to relate the fatigue stress concentration factor to the elastic stress concentration factor. The author outlines a simpler hypothesis, which he claims to be a more reliable guide to fatigue behaviour in notches. Briefly it assumes that the elastic stress concentration factor gives the reduction in the fatigue strength due to the notch, but because of the local nature of the stress concentration, the endurance limit is increased according to a simple law. This increase in the fatigue strength depends on the smallness of the notch.