Fatigue Limit Stress Research Articles

フラクトグラフィ ロータ鋼の各種破壊挙動に及ぼす組織異方性の影響

In order to clarify the anisotropy of fractography at fracture initiation site, monotonic tension, bending fatigue and tensile creep fracture tests were carried out at room and elevated temperatures, using three oriented specimens extracted from a Cr-Mo-V steel turbine rotor. In the case of monotonic tension, although the effects of temperature on tensile properties and fractography was prominent, the effects of specimen orientation on those were quite small at room and 839K temperatures. The fatigue limit of L-R oriented specimen was about 380MPa, and 25% higher than those of C-R and C-L oriented specimens. The scattering of fatigue life of C-R oriented specimen at the near fatigue limit stress condition was clearly larger than those of the other oriented specimens. Under bending fatigue, markedly different fractographic patterns were observed at the crack initiation site for all the three oriented specimens. It was found that the orientation of two kinds of inclusions, MnS and Al2O3 particles at the fatigue crack initiation site, influences the fractographic mode strongly. The creep result of L oriented specimen showed the longest life, as compared with those of the other oriented specimens, under nearly the same stress condition. The effect of specimen orientation on the fractographic patterns of creep was quite small.

On the Accuracy of Rolling Bearing Fatigue Life Prediction

Ball and roller bearings are designed to meet endurance requirements basically determined according to the Standard fatigue life calculation method. This method is based on the Lundberg-Palmgren fatigue life theory as modified by reliability, material, and lubrication factors. As application load and spied requirements have increased, the Lundberg-Palmgren method has resulted in bearings of increased size, adding unnecessarily to the size and weight of mechanisms. This is a critical design situation for weight and size-sensitive components such as aircraft gas turbine engines and helicopter power transmissions. The bearing life prediction method developed by Ioannides and Harris recognizes the existence of a fatigue limit stress. If the stresses an operating bearing experiences do not exceed the limit stress, the bearing can achieve infinite life. In any case, the method tends to predict longer lives than the Lundberg-Palmgren method. This paper evaluates the life prediction accuracies of the Lundberg-Palmgren and Ioannides-Harris methods by comparing lives calculated according to these methods and to those actually experienced in 62 different applications. As a result of the investigation, the Ioannides-Harris method is shown to more accurately predict bearing fatigue endurance.

A unified approach to mean stress effect on fatigue threshold conditions

A unified approach to the effect of mean stress (or stress ratio R) on the threshold conditions, i.e. fatigue limit and threshold stress intensity factor range, is presented. The approach is based on the premiss that damage caused by cyclic loading is a function of the strain energy range ΔW, i.e. a function of both stress and strain ranges. The severity of the ΔW depends on the relative measure of the tensile mean stress to alternating stress, σm/σa. A number of previously proposed relations are shown to be particular cases of the present approach. It is shown that the mean stress effect on the threshold conditions can be treated in a unified manner for members with or without crack-like flaws. The predictions of the proposed method are compared with experimental results and the agreement is found to be fairly good.

Concurrent Influence of an Increase in Tensile Strength and Thickness Reduction on Fatigue Strength of Hot Rolled Steel.

Plane bending fatigue tests were conducted on smooth and notched specimens made with combinations of tensile strength and thickness of 440 N/mm2 and 2.6 mm, 590 N/mm2 and 2.3 mm, and 780 N/mm2 and 2.0 mm, respectively. A change in the fatigue limit load (moment) was investigated. In smooth specimens, the fatigue limit moment did not change with the variation of steel. In the notched specimen having an 8 mmφ pierced hole, however, the fatigue limit moment decreased drastically with the increase in tensile strength in combination with the reduction of thickness. An improvement in the fatigue limit stress of the notched specimen was then studied from the point of view of the stamping process. It was found that coining the pierced hole is one effective method.

Fatigue Damage in Cross-Ply Titanium Metal Matrix Composites Containing Center Holes

The development of fatigue damage in four [0/90]s SCS-6/Ti-15-3 laminates containing center holes was investigated. A methodology to predict damage initiation based on an effective strain parameter was used to determine the stress levels and the number of cycles required for matrix crack initiation. Damage progression was monitored at various stages of fatigue loading. In general, a saturated state of damage consisting of matrix cracks and fiber-matrix debonding was obtained which reduced the composite modulus. Matrix cracks were bridged by the 0° fibers. The fatigue limit (stress causing catastrophic fracture of the laminates) was also determined. The static and post-fatigue residual strengths were accurately predicted using a three dimensional elastic-plastic finite element analysis. The matrix damage that occurred during fatigue loading significantly reduced the notched strength.

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.

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 ΔKth of the metal of the rolled layer. Plastic deformation increased ΔKth in these experiments. It can be inferred that ΔKth 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 ΔKth of the layer.

A MODIFIED FRACTURE MECHANICS APPROACH TO METAL FATIGUE

The fatigue lives, the fatigue limit stress ranges and fatigue notch factors for metallic specimens can be predicted using a modified fracture mechanics model for short cracks based on the combination of solutions for the non-uniform strains at the surface of a metal and the development of crack closure. The resulting local stress intensity factor exceeds that indicated by linear elastic fracture mechanics at short crack lengths. The model predicts a smooth and continuous variation of the fatigue notch factor with notch size between a lower bound of unity and an upper bound equal to the theoretical notch stress concentration factor. The model is verified using experimental data for a 2024-T351 aluminium alloy for smooth and notched specimens tested at various stress ratios.

Development of fatigue design curves for thick-section 9Cr-1Mo ferritic steel forgings

Strain-controlled low-cycle fatigue (LCF) data have been generated on 9Cr-1Mo thick-section (300 mm) tube plate forgings under simulated postweld heat treatment conditions at 723, 773 and 793 K employing a constant strain rate of 1 × 10 −3 s −1. LCF tests were performed over strain amplitudes in the range ±0.25 to 1.00%. The fatigue life was found to decrease with increasing temperature. The effect of temperature was more pronounced at low strain amplitudes. Within the range of strain amplitudes examined, the experimental data on fatigue life at elevated temperatures were found to match well with the life predicted by the Tomkins crack growth model. Tentative fatigue design curves for elevated temperatures have been formulated for 9Cr-1Mo based on information generated in the laboratory using the philosophy outlined in the ASME code case N-47. A fatigue design curve applicable for the temperature range 300–644 K was computed based on room temperature tensile properties, incorporating the concept of fatigue limit and mean stress.

Simplified Contact Fatigue Life Prediction Model—Part I: Review of Published Models

Part I of this two-part paper reviews eleven published spalling fatigue life models, to identify consensus parameters and relationships and to compare model strengths and limitations, as a basis for the construction of a simplified, readily calculated engineering model encompassing the major life variables, based on explicit assumptions and derivations. Part II of the paper presents the new model. It uses the applied alternating shear stress field to define the critical stress as a function of depth, and computes life as crack propagation time through this field. The model defines surface defects as critical defects. Material fatigue susceptibility, fatigue limit stress and the defect severity distribution are the main endurance parameters. In addition to Hertz pressure, life-modifying variables are: interface traction, surface microgeometry and EHD film. It is shown that the new model is capable of representing the influence of all major consensus parameters on life, by relationships that fall within the bounds of previously published behavior.

Simplified Contact Fatigue Life Prediction Model—Part II: New Model

Part I of this two-part paper reviews eleven published models as a basis for the construction of a simplified, readily calculated engineering model encompassing the major life variables, based on explicit assumptions and derivations. Part II of the paper presents the new model. It uses the applied alternating shear stress field to define the critical stress as a function of depth, and computes life as crack propagation time through this field. The model defines surface defects as critical defects. Material fatigue susceptibility, fatigue limit stress and the defect severity distribution are the main endurance parameters. In addition to Hertz pressure, life-modifying variables are: interface traction, surface microgeometry and EHD film. The influence of the variables in the new model on life distribution and on load/life law are compared to the reviewed models and it is shown that the new model is capable of representing the influence of all major consensus parameters on life, by relationships that fall within the bounds of previously published behavior.

Effect of potential on the corrosion fatigue crack growth rate of FeAlMn alloy in 3.5% NaCl solution: Duh, J.-B., Tsai, W.-T., Lee, J.- T. and Chang, H. Corrosion Dec. 1990 46, (12), 983–988

Strain-controlled low-cycle fatigue (LCF) data have been generated on 9Cr-1Mo thick-section (300 mm) tube plate forgings under simulated postweld heat treatment conditions at 723, 773 and 793 K employing a constant strain rate of 1 × 10−3 s−1. LCF tests were performed over strain amplitudes in the range ±0.25 to 1.00%. The fatigue life was found to decrease with increasing temperature. The effect of temperature was more pronounced at low strain amplitudes. Within the range of strain amplitudes examined, the experimental data on fatigue life at elevated temperatures were found to match well with the life predicted by the Tomkins crack growth model. Tentative fatigue design curves for elevated temperatures have been formulated for 9Cr-1Mo based on information generated in the laboratory using the philosophy outlined in the ASME code case N-47. A fatigue design curve applicable for the temperature range 300–644 K was computed based on room temperature tensile properties, incorporating the concept of fatigue limit and mean stress.

The fatigue behaviour of HSLA non-load-carrying spot-welded joints: Hamel, F.G. and Masounave, J. Can. Metall. Quart. Oct.⇌ec. 1990 29, (4), 313–318

Strain-controlled low-cycle fatigue (LCF) data have been generated on 9Cr-1Mo thick-section (300 mm) tube plate forgings under simulated postweld heat treatment conditions at 723, 773 and 793 K employing a constant strain rate of 1 × 10−3 s−1. LCF tests were performed over strain amplitudes in the range ±0.25 to 1.00%. The fatigue life was found to decrease with increasing temperature. The effect of temperature was more pronounced at low strain amplitudes. Within the range of strain amplitudes examined, the experimental data on fatigue life at elevated temperatures were found to match well with the life predicted by the Tomkins crack growth model. Tentative fatigue design curves for elevated temperatures have been formulated for 9Cr-1Mo based on information generated in the laboratory using the philosophy outlined in the ASME code case N-47. A fatigue design curve applicable for the temperature range 300–644 K was computed based on room temperature tensile properties, incorporating the concept of fatigue limit and mean stress.

Fatigue crack propagation and cryogenic fracture toughness behaviour in powder metallurgy aluminium-lithium alloys: Rao, K.T.V. and Ritchie, R.O. Metall. Trans. A Jan. 1991 22A (1), 191–202

Strain-controlled low-cycle fatigue (LCF) data have been generated on 9Cr-1Mo thick-section (300 mm) tube plate forgings under simulated postweld heat treatment conditions at 723, 773 and 793 K employing a constant strain rate of 1 × 10−3 s−1. LCF tests were performed over strain amplitudes in the range ±0.25 to 1.00%. The fatigue life was found to decrease with increasing temperature. The effect of temperature was more pronounced at low strain amplitudes. Within the range of strain amplitudes examined, the experimental data on fatigue life at elevated temperatures were found to match well with the life predicted by the Tomkins crack growth model. Tentative fatigue design curves for elevated temperatures have been formulated for 9Cr-1Mo based on information generated in the laboratory using the philosophy outlined in the ASME code case N-47. A fatigue design curve applicable for the temperature range 300–644 K was computed based on room temperature tensile properties, incorporating the concept of fatigue limit and mean stress.

アルミナ短繊維強化ＡＣ８Ａアルミニウム合金複合材料の疲労挙動

Cyclic bending fatigue tests were performed on alumina short fiber reinforced AC8A aluminum alloys in order to examine the effects of volume fraction of fibers and nonfibrous inclusions (shots) on S-N curves. Fatigue limit stress increased with increasing volume fraction of fibers. The effect of shots on S-N curves was very little when shot content was less than 0.1%. Cyclic fatigue crack propagation rate was also measured on the composites. The crack propagation rate increased with increasing volume fraction of fibers when it was compared at the same stress intensity range.

Process zone size fracture criterion for ceramics.

Ceramics are typically brittle materials. However, fracture toughness of ceramics is variable with flaw size and also notch root radius. Generally, a process zone is formed ahead of the crack or notch tip. Numerous microcracks or phase transformations are formed in the process zone. The following are the main results obtained in this paper. Formation stress of process zone is equal to fracture stress or static fatigue limit stress of plain specimen. A new failure criterion based on process zone size is proposed. Based on the process zone size failure criterion, calculated failure stress as a function of crack size or notch root radius shows a very good agreement with experimented failure stress. Calculated process zone size is about 5 times the average grain diameter.

Effect of grain size on the high cycle fatigue behaviour of polycrystalline copper

The effect of grain size on the cyclic stress-strain response and on the fatigue life including the plastic strain fatigue limit was determined for a large number of specimens. No plateau was found in the cyclic stress-strain curves of polycrystalline copper. The saturation stress exhibits an untypical grain size effect, namely a higher stress for a coarser grain size. The total strain fatigue limit and the stress fatigue limit are almost grain size independent, while the plastic strain fatigue limit depends strongly on the grain size. Fine-grained material obeys the Coffin-Manson law; coarse-grained material does not. The observed phenomena are discussed on the basis of types of dislocation structure and behaviour of both short and long cracks.

Effect of Yield Stress and Grain Size on Threshold and Fatigue Limit

Experimental investigations have been carried out to study the effects of grain size and yield stress on fatigue limit and threshold stress intensity range. The relations between fatigue limit and grain size and yield stress and those between threshold stress intensity range and grain size and yield stress which were predicted according to the model proposed in the previous paper agreed quite well with the experimental data. The difference in the dependence of fatigue limit and threshold stress intensity range on yield stress was discussed based on the analytical relations between them.

Unified rolling contact life model with fatigue limit

A generalization of the present author's “unified model for rolling contact life prediction” is presented, allowing for non-zero fatigue limit stress. The model is based on a crack growth rate relationship with local plastic strain and ductility, in which plastic strain sets in only for local stress in excess of a non-zero limit. The description of defect populations below and at the contact surfaces and of the effects of matrix strength, defect severity, surface traction, contact geometry and asperity interactions is retained from the previous model. Effects of the non-zero fatigue limit are identified for subsurface- and surface-origin spalling. They include excess life which increases as a percentage of classically predicted life for longer lives and higher fatigue limit. Asymptotic conditions are defined where fatigue life becomes unlimited. The load-life law changes from an inverse power law to one with asymptotic loads at which failures cease for given life quantiles. For surface-originated failures, the new model predicts that macrocracks originated by surface distress stop propagating when the fatigue limit is high and the traction is low. A survey of published experimental results produces indications of deviation from the classic Weibull life distribution and the load-life law of the order predicted by the model.

アルミナ粒子分散エポキシ樹脂の疲労強度

Fatigue tests of notched and smooth specimens of alumina particulate filled epoxide composites were conducted and the effects of alumina dispersion on the fatigue strength, the fatigue limit, the fatigue fracture process, the final fracture condition in fatigue and the inherent flaw size were studied. The alumina volume fractions Vf used in this experiment were 13% and 37%. As a basis of comparison epoxy resin with no filler was also tested.The results obtained are summarized as follows.(1) Alumina dispersion had both (a) reinforcement effect and (b) flaw dispersion effect from the viewpoint of fatigue strength. The fatigue strength of the smooth specimens with 13% Vf reduced from the level of epoxy resin, and the strength recovered when Vf increased to 37%.(2) The fatigue strength of the notched specimens was improved as alumina Vf was increased.(3) The inherent flaw size became longer by the alumina dispersion and the composite became less sensitive to surface flaws than the epoxy resin.(4) The fatigue limit of the composites seems to be determined by the condition that microdebond of particle/matrix interface in surface layer does not propagate. A model of fatigue limit was proposed based on the observation and the fatigue limit stress level vs. Vf relation was satisfactory explained.