Variable Amplitude Stress Research Articles

組合せ繰返し荷重下の切欠き材における分布微小き裂のモデル化に基づいた余寿命評価

A procedure to evaluate residual life under cyclic combined loadings was established for a given initial state of distributed small cracks. Distributed cracks at the initial stage were modeled as straight-line cracks by using an image-processing technique. The algorithm for the analysis of the crack growth after the initial stage was constructed by taking account of both modes of the propagation as a single crack and the coalescence between propagating cracks. Fatigue tests under combined axialtorsional loadings with constant and variable amplitudes were also conducted using cyclindrical specimens of pure copper with circumferential blunt notches. The fatigue life was correlated with the equivalent plastic strain range. When Compared for the same value of the parameter, the fatigue life became longer with increasing shear component in the stress state at the notch root, while no significant difference was observed between two loading modes of constant and variable stress amplitudes. The fatigue life defined by the formation of crack with a specific length was evaluated based on the proposed procedure. The predicted life almost coincided with the experimental data. Cracking morphology was also simulated by using the present model to show good correspondence with experimental observations.

Prediction of fatigue damage and fatigue life under random loading

The objective of the present paper is to find the fatigue damage and fatigue life of a structural component when subjected to variable-amplitude stress loading modeled as a wide-band or narrow-band Gaussian random process. In addition to the well-known Palmgren-Miner's linear damage rule, a nonlinear plastic work interaction damage rule is used as a basis for the accumulation of fatigue damage which gives us a more conservative fatigue life estimation as compared to the Palmgren-Miner rule. Numerical examples are performed and comparison is made for the fatigue damage and fatigue life evaluated under various random loading conditions and based on different damage rules. Several conclusions are drawn at the end of the paper which give us simpler rules to be used in the analysis and design of fatigue structures when subjected to random loading conditions.

アルミニウム薄膜の疲労すべり線発生密度を利用した変動振幅応力の計測

In order to evaluate the stress of a machine part subjected to variable stress amplitude, the density of fatigue slip bands produced on aluminum foil is proposed as a measure for this purpose. The fundamental characteristics of slip band formation were examined under both constant and variable amplitude stresses. It was found that the density of slip bands was dependent on both the stress amplitude and the number of stress cycles. The variation of stress amplitude hardly affected the increase of the slip bands in successive stress cycles, irrespectively of the variable mode of stress. The density of slip bands under variable loading, fs was well correlated with the equivalent stress, σeq=(ΣσαiNi/ΣNi)1/α, where σi, Ni and α are stress amplitude, the number of stress cycles at σi, and a material constant determined from an aluminum foil used, respectively. It is concluded that the equivalent stress can be evaluated by the density of slip bands produced on aluminum foil, using the relationship between fs and applied stress amplitude obtained under constant loading. The accuracy of measuring the equivalent stress was within 3%.

A Basic Study on Fatigue Gauge Made of Copper Electroplating. 3rd Report. Evaluation of Equivalent Stress from the Density of Recrystallized Grains under the Variable Stress Condition.

The possibility of measuring the magnitude and number of stress cycles of the machine parts subjected to service loading was examined by the fatigue gauge, made of electroplated copper. It is found that the recrystallized grains formed by cyclic stresses in the foil can be utilized as a measure for stress determination under both constant and variable amplitude stresses. This method is shown enough accurate to evaluate constant stress amplitude. In case of variable stress amplitude, the fatigue damage is correlated with that of the constant stress amplitude in terms of a equivalent stress. This equivalent stress is expressed by (Σ σαiNi/Σ Ni)1/α, where σi, Ni. and α are the stress amplitude, the number of stress cycles of σi and the material constant of the gauge, respectively.

ＧＦＲＰの層間せん断疲労強度

The purpose of this research was to study the fatigue behaviour and the test method for S2 glass fibre reinforced plastic under an interlaminar shear fracture mode. Fatigue tests were carried out under the short beam shear (SBS) condition of three point bending. The main results obtained are as follows. 1) Interlaminar shear fatigue fracture was realised for SBS specimens with the span ratio of L/t = 4 and 3.5. 2) Fatigue crack propagation was detected during interlaminar shear tests by using scanning acoustic tomography. 3) In interlaminar shear fatigue tests under the condition of varying stress amplitude, the cumulative fatigue damage calculated by Miner's law was approximately unity when the scattering of fatigue data was taken into consideration.

Fatigue Gauge Utilizing Slip Deformation of Aluminum Foil. 4th Report. Surface Roughening under Variable Amplitude Stress.

The surface roughening phenomenon of aluminum foil under variable amplitude stress is examined in order to use the foil as the fatigue gauge to detect the total amount of cyclic stress. It is found that the effect of load history on the surface roughening phenomenon can be observed when the stress amplitude varies simply as in two-level single block loading. However, it is negligible small when the stress amplitude varies many times as in two-level multiple loading. In such a case, the stress evaluated from the surface roughness using the aluminum foil fatigue gauge is represented by (ΣσαiNi/ΣNi)1/α with sufficient accuracy, where σi, Ni, and a are the stress amplitude, the number of stress cycles of σi and the material factor, respectively.

A Basic Study on Fatigue Gauge Made of Electroplated Copper Foil : Effects of Understress

Fundamental investigations are made regarding the phenomena of slip band initiation and grown grain initiation in an electroplated copper foil under variable amplitude stress which consists of overstress and understress. It is found that the modified Miner's rule does not hold for the slip band and grown grain initiation under two-level single block loading and two-level multiple loading composed of overstress and understress

Prediction of Fatigue Life With and Without Hold Times Using the Chaboche Viscoplastic Constitutive Theory

The titanium alloy Ti-6Al-4V is known to exhibit creep behavior at temperatures as low as room temperature. Consequently, for cyclic loading with hold times it is possible that the rate dependent behavior of Ti-6Al-4V can have negative bearing upon the low cycle fatigue life. If this effect is shown to be present at room temperatures, then it will certainly be magnified and, therefore, very important at elevated temperatures. In order to account for the effects of strain rate dependent deformation in fatigue life prediction methodology, it was considered necessary to incorporate a viscoplastic constitutive equation into the fatigue life calculational algorithm. After critical evaluation of a score of recently proposed viscoplastic constitutive theories, the Chaboche theory, which employs a yield condition, was considered to offer the most promise for description of a wide range of inelastic material behavior characteristics. The six viscoplastic material parameters that are required for nonelevated temperature applications were determined from data of uniaxial tests, conducted elsewhere and made avialable to this study. The fatigue life testing of smooth round bar specimens included load cycles with load hold times. Fatigue life predictions were performed using the equivalent fully reversed symmetric cycle, and the Smith-Watson-Topper parameter, for load cycles having varying stress amplitudes and varying hold times. The predicted fatigue life results indicate that: (i) For a given stress level above the initial yield stress, shorter load hold time periods result in longer fatigue lives. (ii) The higher the stress level (above the initial yield stress) the more pronounced becomes the effect of the load hold time on the fatigue life prediction. (iii) The rate of loading also has an effect on fatigue life. Analysis indicates that the slower the rate of loading, the higher the rate dependent (primary creep) deformation, and consequently, the lower the resulting fatigue life.

A basic study on fatigue gauge made of copper electroplating. 2nd Report. Effects of understress on initiation of grown grain.

Fundamental investigations were made as to grain growth phenomenon in copper electroplating foil under a variable amplitude stress which consists of overstress and understress. The applicability of the foil to fatigue gauge that detects fatigue damage was discussed. It was found that the modified Miner's rule does not hold for the initiation of grown grains under such conditons as mentioned above. The cumulative cycle ratio is dependent on load histories. It was also found that fatigue damage under two-level multiple loading increases as the cycle ratio of overstress to understress increases. This indicates that fatigue damage during understress applied after overstress is greater in the early period of the cycles. Furthermore, it was found that the density of grown grains initiated under variable stress is dependent on the equivalent stress. This enables the evaluation of the equivalent stress based on the density of grown grains.

A basic study on fatigue gauge made of copper electroplating. 1st report. Effects of understress on slip initiation.

Fundamental investigations were made as to slip initiation phenomenon in copper electroplating foil under variable amplitude stress which consists of overstress and understress. The applicability of the foil to the fatigue gauge which detects fatigue damage was discussed. It was found that the modified Miner's rule does not hold for the slip initiation under two-level single block loading composed of overstress and understress. The cumulative cycle ratio in this case is dependent on load histories. Namely, fatigue damage of high-low loading is greater than that of low-high loading and that of two-level multiple loading is the greatest. It was also found that fatigue damage under two-level multiple loading increases as the cycle ratio of overstress to understress increases. This indicates that fatigue damage during understress applied after overstress is greater in the early period of the cycles. The deviation from modified Miner's rule, however, can be said to be small.

LONG LIFE FATIGUE BEHAVIOR OF FILLET WELDED JOINTS UNDER COMPUTER SIMULATED HIGHWAY AND RAILROAD LOADING

Fatigue behavior of fillet welded joints with a scallop under highway and railroad loading was studied. Variable amplitude stress fluctuations were generated by computer simulations of highway and railroad live loads. Fatigue failure occurred even if the equivalent stress range was less than the constant amplitude fatigue limit. Therefore, fatigue life evaluation assuming that stress ranges below the fatigue limit did no damage was unconservative. It was verified that the fatigue life under variable amplitude loading could be estimated accurately by applying the fracture mechanics approach with the linear damage rule.

A fundamental study on the fatigue gage utilizing the copper electroplating method. Characteristics of slip band initiation in the copper plating under variable stress amplitude and variable mean stress.

Fundamental experiments are carried out to examine the parameter that dominates slip band initiation in copper electroplating under the condition where the mean stress as well as the stress amplitude varies. It is found that, in the case of constant amplitudes stressing, the relation between the proper stress σp for slip band initiation and the number of cycles N is well represented by σαp·N=C. This mean that slip bands appear when the total hysterisis energy applied to the copper plating attains a critical value. when the mean stress varies stepwise or sinusoidally, the range pair of the stress mainly dominates the occurrence of slip bands, and Miner's rule holds for the accumulation of fatigue damage. Accordingly, the parameter (√σαi)1/α, where σi is the range pair and α is the exponent of the σp-N relation, is equivalent to the proper stress under constant amplitude stressing. Based on these results, the applicability of the copper plating to the fatigue gage that accumulates and indicates a load experience is discussed.

鋼道路橋の疲労設計曲線に関するパラメトリック解析

Fatigue design curves of steel highway bridges were analyzed parametrically under computer simulated variable amplitude stresses. Crack propagation life of 4 types of welded joints was estimated by applying the constant amplitude da/dN-ΔK relationship and the liner cumulative damage rule. The configuration of fatigue life curves under variable amplitude stresses varied with the traffic constitution and the beam span particularly in the longer life region. The fatigue limit under variable amplitude stresses for each joint could be defined by using estimated fatigue life curves and Miner's rule.

Plastic Work Interaction Damage Rule Applied to Narrow-Band Gaussian Random Stress Situations

Fatigue life estimates that use a structural material’s constant amplitude stress life data values and a linear cumulative damage rule are always nonconservative for stress histories containing numerous subcycles and only a few large-amplitude cycles. Conservative fatigue life estimates were previously achieved by others with a plastic work interaction damage rule using the material’s overstrain fatigue life parameter values. Verification fatigue tests were run on laboratory specimens of 1020 steel using four selected variable amplitude stress wave form profiles. This paper extends the application of the plastic work interaction damage rule to narrowband Gaussian random stress situations. The derived stress life mathematical expression is of a power law form. The predicted fatigue life is more accurate than that predicted using a conventional linear damage rule.

Fatigue behavior of ceramic materials under variable stress amplitude

Most of the previous investigations on fatigue of ceramic materials have been conducted experimentally as well as theoretically under constant stress amplitude conditions. However, both a theoretical approach and experimental data for variable stress amplitude loadings will be necessary to improve the reliability in the fatigue design of ceramic components. In this study, the formulation of fatigue life under variable stress amplitude was discussed on the basis of an analysis on the stable crack growth from a dominant inherent flaw. The formulated results were applied to evaluate the probabilistic distribution of fatigue life for the random variable of the initial size of flaw to be a fracture origin. Fatigue tests of two ceramic materials were carried out under repeated two-step loading conditions. The experimental results verified the applicability of the present analytical procedure to the prediction of life distribution.

Considerations of probability-based fatigue design for marine structures

Fatigue is a major failure modelin marine structures which respond dynamically to random wave and wind loading. Oscillatory stresses produce fatigue at points of stress concentration, typically the welded joints. Because all fatigue design factors are subject to significant uncertainty, a reliability approach to management of such uncertainty seems appropriate. This article summarizes some studies in fatigue reliability research and demonstrates how reliability methods can be effectively utilized by designers to avoid fatigue in marine structural components. Included are (1) a description of fatigue damage under variable amplitude stresses employing the characteristics S-N and fracture mechanics models, (2) models for reliability assessment relative to fatigue and the use of these models to derive design criteria, and (3) an elementary application of system fatigue reliability analysis to establish component design criteria.

The effect of overstress on the non-propagating crack formed in a specimen with a small hole.

In the present study the effect of overstress on a non-propagating crak is investigated on the specimens with a small hole (dia. : 100μm, depth : 100μm). The effect of overstress on the behavior of the non-propagating crack under the first stress level is larger in this type of specimen than in the plain specimen. This phenomenon is closely related to the length of a non-propagating crack formed under the first stress level. This experimental result suggests that the existence of defects is more dangerous under varying stress amplitude than under constant stress amplitude. Moreover, the crack closure behaviors before and after overstress were measured by the S shaped unloading curve method in order to explain the effect of overstress.

The fatigue damage mechanics of a carbon fibre composite laminate: II—life prediction

The equations of fatigue damage mechanics for a carbon fibre composite laminate, developed in Part I of this paper, are applied to life prediction under constant and varying stress amplitudes. The S-N curves predicted for constant stress amplitude at various mean stresses are in good agreement with experiments. Life prediction for various block and random loadings are less satisfactory: there is an acceleration in damage growth caused by load-block interaction which is not, at present, well modelled, but can be included empirically. However, the predictions are far better than those of Miner's Rule, which is seriously non-conservative.

Stress-Strain Response and Fatigue Damage of Mild Steel Plate under Variable Stress Amplitude

In this study, seven types of load controlled fatigue tests were carried out under variable stress amplitude in order to clarify the stress-strain response and the fatigue strength of SS 41 and STPY 41 plate specimens. The tests were conducted in constant stress amplitude loading, step stress amplitude loading, repeated high-to-low and low-to-high block loading, two types of block-random loading and random loading with exponential distribution. In each test, stress-strain loops were recorded with X-Y plotter from the start of cycling to visual crack initiation by using the strain gauges put them on the test piece.As a result, the following conclusions were obtained.(1) Sa-εpa (stress amplitude-plastic strain amplitude) curves are different with each variable loading patterns.(2) Cyclic softening for random loading is greater than that for constant stress amplitude in the conditions of Sa≥σy and Sa≤Saw, while the relation is contrary to above in the conditions of Saw<Sa<σy, where Saw is a fatigue limit and σy is a static yield stress of the material.(3) Sa-εpa curve for random loading with exponential distribution can be obtained approximately by the step stress amplitude loading.(4) Fatigue life estimations by Miner's rule and Modified Miner's rule make over estimation compared with experimental results for block, block-random and random loadings.(5) Fatigue life estimations by Manson-Coffin's law do not coincide with the experimental results for block-random loading and random loading with exponential distribution included the large repeated number of stress amplitudes below fatigue limit.(6) Fatigue life estimations by Corten-Dolan's method fairly coincide with experimental results for various kind of variable stress amplitude loading.

ＳＣＭ４３５丸棒の応力変動時の疲れき裂進展挙動

The constant and variable stress amplitude fatigue tests were carried out on smooth and pinholed specimens of SCM 435 steel under rotating bending conditions.In the constant stress amplitude tests, the fatigue crack propagation rate was not affected by the stress level and it was represented well by ΔK.The crack initiated by the over-stress σa1 cycles was retarded by the under-stress σa2 cycles, when the difference between σa1 and σa2 was large. In the case of non-propagating cracks, their length was shorter than that in plain carbon steels. The condition of crack retardation under σa1 repetition following σa2 application was elucidated.The crack propagation behavior of pin-holed specimens in two step multi-fold tests was similar to that in two step two-or three-fold tests. The discussion was made on the shift from unity in cumulative cycle ratio for smooth specimens, based on the results of crack propagation behavior of pin-holed specimens.