Cyclic Stress Range Research Articles

Cyclic response of calcareous soil from the North-West Shelf of Australia

This Paper reports the results from 23 cyclic CIU and CAU triaxial tests on undisturbed samples of calcareous soil. The samples, which include both uncemented and cemented material, have heen subjected to a range of mean and cyclic shear stresses. Results from the tests on the uncemented soil display many of the characteristics of the cyclic response of other cohesionless soils. The more cemented soils sustained higher cyclic stresses and, depending on the load level, showed either elastic behaviour with no pore pressure build-up, eventual stabilization after some pore pressure build-up, or steady state pore pressure build-up and eventual failure. The effect of frequency on the response in the range 0·1 to 10 Hz has heen studied. Since no dramatic differences in performance could he detected, no firm conclusions could be drawn regarding the effect of testing rate. L'article préente les réultats obtenus à partir de 23 essais triaxiaux cycliques de type CIU et CAU effectués sur des échantillons de sol calcaire non-remaniés. Les écbantillons, qui comportent de la matière cimentée et non-cimentée, ont éte soumis à uue gamme de contraintes de cisaillement moyennes et cycliques. Les résultats des essais effectués sur le sol non-cimenté montrent beaucoup des caractéistiques de la réponse cyclique d'autres sols sans cohésion. Les sols cimentés à un degré élevé supportaient des contraintes cycliques plus élevées et selon le niveau de cbargement montraient un comportement élastique sans accroissement de pression interstitielle, une stabilisation finale après quelque augmentation de pression interstitielle, ou bien une accroissement de pression interstitielle stationnaire suivie de la rupture finale. On a étudié I'influence exercée par la fréquence sur la réponse dans une game de 0·1 a 10 Hz. Comme on n'a trouvé aucune diffěrence marquée entre les performances, il était impossible de tirer des conclusions définitives concernant I'influence exercée par la fréquence des essais.

ポリカーボネートの回転曲げ疲労試験片におけるき裂の発生と進展

Fatigue fracture behavior of the smooth specimens of polycarbonate was investigated in the range of low cyclic stress. In such fatigue tests, specimens fail during the process of crack initiation and propagation like metal. An experimental program was set up to examine the process of initiation and growth of a surface crack. This was accomplished by careful observations by using the transmitted light photographs of a surface crack on the smooth specimen of polycarbonate during the rotating bending fatigue test at the speed of 2Hz at room temperature. It was shown that the initiation of the surface crack appeared from a very small inclusion near the surface of specimen at 10-30% of the fatigue life. The experiment showed that the surface crack propagation was hindered by the shear bands formed at the both ends of a crack. The final length of surface crack was discussed in terms of a combination of the stress amplitude and the stress intensity factor at the end of crack. From these results, it became evident that the characteristic behavior of the crack initiation and growth in the smooth specimen of polycarbonate was affected significantly by the mechanical properties and yield behavior of the material.

Two-stage microplastic surface deformation in Al 2219-T851

A theory of the cyclic deformation of a microplastic surface grain is developed that enables the deduction of the mechanical properties of individual grains from certain strain measurements. The measurements are of the hysteresis loop widths measured at zero external stress after a step change in cyclic stress range. To account for the available data, the grain must be presumed to have a lower flow stress corresponding to the onset of measurable plasticity, and an upper flow stress above which flow is nearly perfectly plastic. Only the largest grains, more than twice the average in size, are found to exhibit plasticity. These are, therefore, usually surrounded by an essentially elastic matrix. An application of the model to determine the mechanical properties of two such individual surface grains in an Al 2219-T851 alloy is described.

Propagation of fatigue cracks from notches

AbstractThe traditional design approaches to fatigue at notches, based on stress level–endurance relationships, are briefly reviewed. It is shown, by considering crack propagation from notches and invoking a change in control mode from notch plasticity to crack-tip plasticity, that a critical stress condition can be obtained which must be exceeded if the crack is to propagate to failure. The traditional techniques are then reinterpreted and explained by this propagation method. An example is given of crack growth from a sharp defect at a weld toe. It is shown that the integration of an elastic fracture mechanics growth law can reproduce stress range–cycles to failure data for this situation. There are, however, complexities of stress analysis and crack shape. A simple treatment of residual stresses affecting the threshold and slow–growth regimes, shows some promise as a technique for accounting for residual stresses.MST/70

Evaluation of irreversible fatigue damage for steel 04Kh12N8M by the internal friction method

1. The possibility has been demonstrated of using the internal friction method in order to plot French lines, i. e., in order to determine the number of cycles to the instant of irreversible fatigue-damage occurrence, not as a result of an additional experiment, but in the course of normal fatigue tests. 2. Plotting the fatigue curve and French line by the method developed on one graph makes it possible to determine material test life over a wide cyclic stress range. 3. Since fatigue and irreversible damage curves intersect at a stress level equal to the fatigue limit, this method may be used in order to accelerate determination of the fatigue limit.

疲れき裂進展に及ぼす圧縮応力成分の影響

It has been considered that the crack propagation rate is controlled by the tensile part of stress range but not by the compressive part. However, according to the experimental results carried out by the present authors for a plane bending stress condition, the compressive part of stress range affected the crack propagation behavior and the accelerated crack propagation rate was observed, causing shorter fatigue life than that without a compressive part.To clarify the effect of the compressive stress range of cyclic amplitude on the crack propagation, push-pull fatigue tests with a constant stress amplitude two step multi-fold stresses were carried out for plane sheet specimens (CCT) of low carbon steel (the ultimate tensile strength is 517MPa). The crack opening stress level was measured by the unloading elastic compliance method. The conclusions obtained are summarized as follows:(1) When the crack propagation rate was high, the compressive part of stress range accelerated the propagation, due to the lower crack opening stress level.(2) When the compressive part of stress range, that is the absolute value of minimum stress in cyclic stress range, increased beyond a certain value, the acceleration of crack propagation rate appeared. The compressive part of stress range larger than this value showed the same acceleration effect on the crack propagation behavior.(3) The acceleration effect of the compressive part of stress range on the crack propagation rate was observed in the tests where the stress ratio R1 in one step was 0 and R2 in another step was -0.33.(4) When the crack propagation rate was low, the comppressive part of cyclic stress range decelerated the crack propagation rate because of the oxide induced crack closure.

An Investigation on Formulation of Cyclic Local Strain Range and Estimation of Fatigue Life in Notched Plate (2nd Report)

In order to evaluate the fatigue life in the stress-concentrated region of structures using the results of strain-controlled fatigue tests, it is necessary to know the cyclic local strain range rather than the monotonous strain behavior. In the present study, a simple method to estimate the local strain range under cyclic loading was investigated.Namely, the elastic-plastic finite element analyses under cyclic tensile load were conducted on the highly stress-concentrated models besides the results in the first report. Then an investigation was made into the effects of applied cyclic stress condition, elastic stress concentration factor and material properties on the shakedown and the behaviors of local stress, strain ranges and their concentration factors.As a result, the formulae to estimate the shakedown limit and the cyclic local strain range were derived. Therefore, when the elastic stress concentration factor and the material properties such as cyclic yield stress, workhardening modulus and parameter of the Bauschinger effect are given, the cyclic local strain range can be estimated for a certain applied cyclic stress range. Then, by substituting the estimated strain range into a relationship between the strain range and the failure life obtained by the strain-controlled fatigue test, the fatigue evaluation can be done reasonably for the structural members.The stress-controlled fatigue test on notched plates and the strain-controlled low cycle fatigue test on small smooth specimens were conducted on 50 kgf/mm2 class steel. Then the estimated local strain range and fatigue life were compared to the experimental results. As a result, the estimated values agreed well with the measured values. In addition, the comparisons were made between the estimated fatigue lives on notched plates and the results so far published. Then it was found that the method proposed in this study can be applied to evaluate well the fatigue lives in the wide range from 5 × 102 to 5 × 106 cycles in the notched plates of 41 to 80 kgf/mm2 strength levels.

Fatigue crack growth along planar slip bands

Fatigue crack propagation along planar slip bands under a mixed mode loading is analyzed based on the micromechanical theory of fatigue crack nucleation proposed previously by the authors. Fatigue damage is systematically accumulated within the slip bands with increasing dislocation dipoles and the resulting strain energy density to be a critical value yields crack growth. The propagation rate is given as the crack growth distance in each step divided by the number of cycles to the formation of a new crack ahead of the old crack. The range of cyclic shear stress in a mixed mode acting on the slip plane directly controls the rate of damage accumulation, and the normal stress component provides an additional strain energy release to accelerate fatigue crack growth. The material parameters involved in the theory are the grain size, the dislocation friction stress, and the specific fracture energy. The theory is applied to Stage I fatigue crack growth observed in high-strength alloys, and it is further extended to the near-threshold growth of a long fatigue crack.

Effects of fatigue on a soldered base metal alloy.

An in vitro tensile fatigue test produced cyclic loading of joints made in a base metal casting alloy with a low-temperature precious metal solder, and the number of cycles to failure was recorded for a range of cyclic stresses. The majority of the joints survived stresses that should represent normal intra-oral loading.

ON THE TRANSITION FROM NEAR‐THRESHOLD TO INTERMEDIATE GROWTH RATES IN FATIGUE

Abstract— Evidence is presented that the cyclic stress intensity threshold for fatigue crack growth in A1 2219‐T851 is associated with a critical maximum value of stress intensity, Kc. This relationship is discovered by measuring the local value of stress intensity at the crack tip which is less than the applied stress intensity because of fatigue induced compressive residual stresses in the plastic zone. Crack growth rates and values of the crack tip residual stress are measured as functions of load ratio. For local stress intensities greater than Kc, the growth rate follows a power‐law relationship, increasing monotonically with δK. For local stress intensities below Kc, growth rates are also sensitive to the cyclic stress range, δσ. If the stress range is small, a threshold to growth, typical of long cracks, is seen. When the cracks are short and δσ exceeds a critical value, growth rates are a complex function of both δσ and δK. This behavior is attributed to the effect of δσ on the propagation of the crack front past obstacles such as grain boundaries.

Biaxial Fatigue of Fiber-Reinforced Composites at Cryogenic Temperatures. Part I: Fatigue Fracture Life and Mechanisms

A study of biaxial fatigue of glass fiber-reinforced composites subjected to in-phase, cyclic tensile and torsional loading at cryogenic temperatures is presented. Fatigue failure of the composite is investigated in terms of cyclic fracture, stiffness degradation, and energy dissipation. Fatigue fracture lives of the cryogenic composite are obtained for the cases of various combinations of cyclic tensile and torsional stresses. A power-law relationship is established between the range of cyclic octahedral shear stress and the number of cycles to fracture. Influences of hydrostatic mean stress and stress biaxiality ratio on fatigue fracture of the fiber composite are determined. Fracture mechanisms in the material during the cryogenic biaxial fatigue are examined by using optical and scanning electron microscopes.

Inversion of an S-N curve in a superalloy

In this study on elevated temperature fatigue behavior at 1 Hz of Nimonic 115, the test procedure adopted is one in which the maximum stress is held constant and the cyclic stress range is varied by lowering the minimum stress. This mode of testing can represent low cycle fatigue conditions in gas turbines or jet engines. The inversion is consistent with the intrusion of large creep strain accumulation. Intergranular fracture replaces stage II type intragranular cracking. 6 refs.

The effect of water vapor on fatigue crack tip stress and strain range distribution and the energy required for crack propagation in low-carbon steel

The formation of a subgrain structure by the passage of a fatigue crack in low-carbon steel has been detected by backscattered electron imaging in the SEM. The distribution of subgrain sizes has been measured as a function of cyclic stress intensity and environment, and from this data the cyclic stress and strain range distributions have been determined, as has the energy dissipated during propagation of the fatigue crack. These results are compared to theoretical and other experimental findings. The energy equivalent (per unit area of incremental crack advance) of the environment is found to be 106 times the surface energy of iron. In an inert environment, the maximum cyclic stress range developed at the crack tip is found to be approximately 2.3 times the yield stress, independent of cyclic stress intensity. Water vapor effectively lowers this stress range, and causes it to assume a dependence upon cyclic stress intensity.

すみ肉溶接継手の止端の研削及びワイヤピーニングによる疲れ強さ向上(第2報)

Various mechanical methods of improving the fatigue strength were investigated by testing the base plate and cruciform fillet welded joint specimens of 40 kg/mm2-80 kg/mm2 class steels. The results obtained are summarized as follows:1) If a peening condition is suitable to a material, the compressive residual stress induced by peening increases as a yield strength increases. As the ratio of applied cyclic stress range to absolute value of the compressive residual stress decreases, the waste of compressive residual stress by applied cyclic stress decreases and the effect of improving a fatigue life (strength) increases. Therefore, the peening effect can increase with incresaing the yield strength of material.2) It is possible to consider that a suitable condition of peening is to add the compressive residual stress as large as a yield strength of the material used, and that ari over peening ravages a surface, and may rather result in a reverse effect.3) As a result of increasing the yield strength of a weld toe and inducing. the compressive residual stress to a weld toe, by peening., a root failure occurs sometimes in the case of non-load-carrying type cruciform, fillet welded joint similarly in thee case of load-carrying type fillet welded double tee joint. Therefore, it is necessary to consider the critical leg length according to a treating condition of a weld toe, in a joint design.

Effect of Notch Shapes on Crack Intiation Life

In order to investigate the effect of notch shapes on fatigue crack initiation, the axial load controlled fatigue tests were carried out employing the double edge notched plate specimens. Materials used in this study were SM 50 B, SM 58, HT 80 steel plates and A 5083 aluminium alloy.SM 50 B butt welded joints were also tested in order to investigate the relation with the notched plates and were discussed from a viewpoint of the fatigue crack propagation and initiation.It was found from these test results that Nc depended on mainly the local maximum cyclic stress range of notch root as same as that proposed by Topper et. al.. Also, in the case of the notched plates, a good correlation of the normalized stress intensity parameter, ΔK0/σyc√πρ, with Nc was obtained in the high cycle region and, from that, the crack initiation threshold level, ΔKth, ρ, proposed by Barsom et. al. was obtained. After that, the correlation of ΔKth, ρ with the crack propagation threshold level, ΔKth, was investigated and was discussed in relation with the notch shapes. And it was found that in the region of ρ that was larger than ρth, ΔKth, ρ had larger values than ΔKth and so that the parameter, ΔKth, ρ, was a useful for the design of structures.Moreover, the definition for the fatigue crack initiation was discussed by the way of investigating the fatigue crack propagation from notch root and was applied for the case of the test results of this study. And the difference of the crack initiation life was discussed for several crack lengths that had physically a meaning from a viewpoint of the fatigue crack propagation.

Measurement of Surface Fatigue Damage by Using Photostimulated Exoelectron Emission

Commercial aluminum (purity 99.5 %) specimens are fatigued in the vacuum of 1×10-5 Torr and the distribution of the photostimulated exoelectron emission (PSEE) on the specimen surface is measured by scanning the surface with a small light spot. In the range of cyclic stress and strain amplitudes examined in the present investigation, the PSEE increases up to approximately 10 % and 30–52 % of fatigue life in the load-controlled mode and the straincontrolled mode, respectively saturates or decreases slowly with additional cycling and finally increases drastically at the failure of the specimen. The relation between the PSEE and fatigue properties in vacuum is discussed.

Closed-Form Expressions for Determining the Fatigue Damage of Structures Due to Ocean Waves

Abstract Closed-form mathematical expressions are derived for the fatigue damage of structures because of ocean waves. The expressions incorporate relationships between wave height and stress range, between stress range and number of cycles to failure (i.e., a fatigue curve), and the probability distribution for the occurrence of wave heights. The expressions can be used to predict the fatigue damage resulting from a single sea state, from a storm, or during the service life of a structure. Also, the fatigue life of a structural element can be determined directly from the stress range resulting from the design wave, or conversely, an "allowable stress range" can be determined for the design wave that will insure a specified fatigue life. Example applications are given for areas having wave climates similar to the North Sea and the Gulf of Mexico. Introduction Ocean waves encountering a structure cause the stress in each structural element to cycle. The accumulated effect of the stress cycles can cause element of an improperly designed structure to fail because of fatigue. In general, from the standpoint of fatigue damage, there are two categories of structures:structures with a response to ocean waves that are significantly affected by dynamic amplification andstructures without significant dynamic amplification. This paper will be restricted to the last category of structures for which dynamic amplification can be neglected for fatigue analyses. The current state-of-practice for the fatigue analysis of ocean structures is summarized by Marshall. The analysis of the fatigue life of a structure requires a lengthy numerical calculation procedure which utilizes: procedure which utilizes:The appropriate curve for the structural element being considered. The curve relates the number of cycles to failure (N) for a cyclic stress range (), having a constant amplitude (see Fig. 1).The Palmgren-Miner rule that predicts the cumulative effect of stress cycles having different amplitudes.An empirical relationship between the wave height encountering the structure and the stress range induced in the structural element for all wave heights that the structure will encounter.A statistical description of the occurrence rates for wave heights that the structure will encounter during its life. The numerical analysis consists of breaking the range of wave heights into discrete bands and determining the number of waves that will occur in each height band. For each height band, the stress range corresponding to the mid-band height is determined for the structural element. Then, the curve is used to determine the fatigue damage for the element because of the stress range associated with each height band. The final step is to accumulate the damage for all height bands using the Palmgren-Miner rule. This procedure can be undertaken manually in a straightforward, time-consuming manner or can be programmed for a digital computer. As a result of the time required to undertake the procedure for each fatigue-prone element, a fatigue procedure for each fatigue-prone element, a fatigue analysis rarely is undertaken during the initial design phase of a structure. Instead, during the initial design, members are sized only on the basis of ultimate loading and a fatigue analysis is performed after the initial design. If the analysis performed after the initial design. If the analysis indicates potential fatigue problems, the design procedure is recycled. procedure is recycled. In this paper, closed-form expressions are derived that permit a fatigue analysis to be performed quickly, compared with the equivalent performed quickly, compared with the equivalent numerical procedure outlined above. The expressions can be applied manually or as part of a stress analysis computer program. As a result, fatigue considerations can be integrated into the initial phase of the design along with ultimate stress phase of the design along with ultimate stress considerations. The closed-form equations yield results that are no better nor worse, but equal to a careful numerical analysis. The sufficiency of such a procedure depends on the situation and must be decided on a case-to-case basis. SPEJ P. 431

Analysis of Fatigue-Crack Growth in a High-Strength Steel—Part I: Stress Level and Stress Ratio Effects at Constant Amplitude

High-strength pressure vessel steel surface flaw or part-through crack (PTC) specimens were selected for studies of fatigue crack growth rate (da/dN) under constant amplitude cycling to assess the effects of varied stress ratio R (minimum nominal stress/maximum nominal stress, σmin/σmax) and stress level (maximum nominal stress/yield stress, σmax/σys). Analyzed within the framework of linear elastic fracture mechanics, these studies warrant the following conclusions regarding fatigue-crack growth in this material: • Crack growth does not appear to be influenced by stress level, per se, even for stress levels approaching net section yield. • It is moderately influenced by both positive (tension-tension) and negative (tension-compression) stress ratios. • It is principally related to the tensile range of cyclic stress as expressed by the fracture mechanics stress-intensity range parameter, ΔK. Utilizing the results of this investigation, a normalizing relationship expressing da/dN as a function of both ΔK and R, which is applicable to both positive and negative values, is discussed. It is concluded that the stress-intensity range ΔK provides a viable analytical approach to fatigue crack-growth analyses relevant to high-strength pressure vessels.

Some fatigue characteristics of thermoplastics

Uniaxial and rotating bending fatigue tests were carried out on polypropylene, polycarbonate, poly(methyl methacrylate) (PMMA), poly(tetramethylene terephthalate) (PTMT) and glass filled PTMT to establish the general régimes of thermal softening and fatigue types of failure observed in earlier tests on acetal copolymer. In the uniaxial testing PMMA exhibited both types of behaviour whereas polypropylene and PTMT were particularly prone to the thermal type of failure over a wide range of cyclic frequency and stress and fatigue failure could not be achieved for endurances up to 10 7 cycles. However, for PC and filled PTMT only the cracking type of fatigue failure was obtained as there was only a slight temperature rise which stabilized and hence did not lead to thermal softening. It was evident that the two types of failure were related to the magnitude of the loss tangent value for the material. Under uniaxial loading the effect of a sharp notch in each material was to reduce the thermal effect so that, for example, fatigue failures were produced in polypropylene and PTMT under stresses which would only produce thermal failures in plain material. In general fatigue endurances were reduced owing to the presence of the notch. Rotating bar fatigue tests using the same specimen as in the uniaxial tests exhibited both thermal softening and fatigue type failures, but at higher stress amplitudes and frequencies compared with the uniaxial tests since only the outer surface was subjected to the maximum stress. The results of constant strain rate and creep rupture tests on these materials have also been included for comparison.

Fatigue Tests of Beams with Rectangular Web Holes

Fatigue tests on ASTM A36 steel wide-flange beams with rectangular web holes demonstrated the effect of stress concentrations at the hole corners on the fatigue strength of the beams. Under combined cyclic bending and shear forces at the hole, fatigue lives greater than 2,000,000 cycles were achieved without corner cracks when the corner radii were sufficiently large so that the cyclic stress range of the maximum elasticity boundary stress did not exceed 24 ksi. Good quality machine-burned hole surfaces were found to be sufficiently smooth to achieve lives of 2,000,000 cycles with no cracks at the boundary. Although additional work is required before detailed design provisions can be suggested, the tests indicated that for fatigue lives of 2,000,000 cycles, the corner radii of rectangular web holes in A36 steel beams should not be less than about 1 inch.