Linear Cumulative Damage Law Research Articles

Nonlinear Behavior on Fatigue Life Curves of Super Engineering Plastics for Machines at Elevated Temperature.

The purpose of this study is to investigate the relationship between nonlinear behavior of fatigue life curves and fatigue life for carbon-fiber-reinforced PEEK and PA 66 under two-step loading above Tg (Glass transition temperature) and below Tg. As a results, the fatigue life curves in the case of PEEK/Below Tg, PA 66/Above Tg and PA 66/Below Ty were found linear. Moreover, the fatigue lives were calculated by linear cumulative damage law under two step loading. On the other hand, the fatigue life curves in the case of PEEK/Above Ty was found nonlinear. Moreover, the fatigue lives were not calculated by linear cumulative damage law under two-step loading. It was found that these factors occurred because of 'Transition phenomenon' which fatigue fracture mechanisms transferred in the range between two fatigue life curves.

周巻き円環を用いた一方向ＣＦＲＰの引張疲労寿命の推定

A prediction method of fatigue strength of polymer composites for an arbitrary frequency, stress ratio, and temperature has been already proposed. The method is based upon the four hypotheses, (A) failure mechanism for CSR (constant strain-rate), creep, and fatigue failure is the same, (B) the same time-temperature superposition principle is valid for all failure strengths, (C) linear cumulative damage law is applicable for specimen failure under monotonic loading, and (D) fatigue strength shows linear dependence on stress ratio. In this paper, tensile CSR, creep, and fatigue strengths in the longitudinal direction of unidirectional CFRP at various loading rates and temperatures were measured by the NOL ring tests. The validity of hypotheses B, C, D, and the applicability of this prediction method were confirmed by creep tests and fatigue tests of different conditions of loading rate and temperature. It was also confirmed that the hypothesis A is not always necessarily for this prediction method through discussions.

Prediction of tensile fatigue life under temperature environment for unidirectional CFRP

A method for prediction of fatigue strength under temperature environment was proposed for polymer composites and its validity was confirmed for the flexural fatigue strength of satin-woven CFRP laminates and others. This method is based upon the four hypotheses: (A) same failure process under constant strain-rate (CSR), creep, and fatigue loadings, (B) same time-temperature superposition principle for all failure strengths, (C) linear cumulative damage law for a nondecreasing stress process, and (D) linear dependence of fatigue strength upon stress ratio. Data are provided for tensile CSR, creep, and fatigue tests at various loading rates, frequencies, and temperatures in the longitudinal direction of unidirectional CFRP. In this paper, experimental verification of the prediction method is discussed for the tensile fatigue strength of unidirectional CFRP.

Role of Bubble Collapse Pressure in Cavitation Erosion.

A quantitative relation(F-N curve)was obtained betweent the constant impact load due to cavitation bubble collapse and the number of cycles to the incubation period termination. The relation was derived from the linear cumulative damage law, in which all impact loads including those of very low intensity(0.3 N)are assumed to cause damage. The slope of the F-N curve corresponds well with that of the S-N curve for a smooth specimen obtained from a standard fatigue test, provided that the contact area is obtained by the Hertz theory. The incubation period can be evaluated regardless of cavitation test conditions from the cumulative cycle ratio Σ(ni/Ni), using both the number ni of impact loads and Ni from an extrapolated F-N curve(modified Miner's law)for the corresponding impact load Fi. Similarly, the F-N' curve was obtained for the steady-state period, where N' was defined as the number of cycles required to achieve a mean depth of penetration(MDP) of 1 micron. The slope of the curve coincides well with that of the S-N curve for a slightly notched specimen. The Σ(ni/N'i)has a linear relation with the MDP in the steady-state period. Since N'i is proportional to 1/F2i from the F-N' curve, the cumulative cycle ratio was reduced to Σ F2i·ni, which is consistent with the impact energy from the authors' previous report. It is concluded that the ratios Σ(ni/Ni)and Σ(ni/N'i)are suitable parameters for evaluation of the cavitation damage in the incubation and steady-state periods, respectively.

A Simple Method to Evaluate Cyclic Fatigue Strength in Ceramics.

A simple method to evaluate cyclic fatigue strength in ceramics was proposed using load range, ΔP-increasing procedure and applied for silicon nitride. The proposed method enabled to obtain statistical property of cyclic fatigue strength by much less number of specimens compared to that required in the conventional procedure of statistical fatigue tests. The ΔP-increasing condition was expressed by initial value of maximum stress, σmax, 1, and increasing rate of maximum stress, dσmax/dN. These parameters influenced the maximum stress at failure, σmax, f, which could be approximated by two-parameter Weibull distribution. P-S-N curve was estimated by two Weibull distributions under different ΔP-increasing conditions based on the assumption of crack growth law and of linear cumulative damage law. The estimated P-S-N curves were independent of the assumptions and agreed with the experimental data obtained under ΔP-constant condition at the higher stress level, while it was conservative under lower stress level.

Effect of Varying Load on the Fatigue Crack Propagation of Pure Aluminum Thin Plate Specimens.

In the case of anisotropic pure aluminum thin plate specimens, a small inclination between the loading direction and the rolling direction affects the crack propagation path, and the fatigue crack propagates in the rolling direction under appropriate conditions. In this report, this phenomenon is investigated for both constant and cyclic varying load conditions. The results are as follows. (1) Under constant loading conditions, the fatigue crack propagates in the rolling direction when the stress intensity factor range settles at 5.0∼7.0MPa√(m). In the case of varying load conditions, the same phenomenon can also be explained using the equivalent stress intensity factor range. (2) Fatigue crack propagation in the rolling direction under cyclic varying load conditions is determined by the damage ratio calculated using the linear cumulative damage law. The lower limit of the damage ratio at which the crack propagates in the rolling direction is very small and is only about 10-3 for this specimen.

Corrosion Fatigue of Ship-Structural Steel with Cathodic Protection under Intermittent Immersion Condition in Seawater at 60°C

It is important to clarify the effect of cathodic protection (CP) on corrosion fatigue properties of shipstructural steels in the actual environment of ballast tank. In this study, corrosion fatigue tests were conducted on notched base material specimens and welded joint specimens of a high strength steel for shipbuilding in a simulated environment of ballast tank under intermittent immersion condition (IIC) in synthetic seawater (SSW) at 60°C with CP. And the results were compared with those under continuous immersion condition.It was revealed that CP improves the corrosion fatigue life of the steel under IIC, and CP of-1.0 V (vs. SCE) in SSW is remarkably effective, especially in a longer fatigue life region. However, the fatigue lives under IIC both in SSW with CP of-0.8 V and in 3.5% NaCl aqueous solution with CP of-1.0 V are shorter than that in SSW with CP of-1.0 V. It is considered that the improvement in fatigue life under IIC in SSW with CP of-1.0 V is mainly caused by the wedge effect of calcareous deposits which have been produced on the crack surface during the periods of immersion and have been remaining there during the periods of exposure to damp atmosphere. Therefore, an application of linear cumulative damage law using S-N curves for continuous immersion of SSW with CP of-1.0 V and free corrosion condition leads to a very conservative estimation of IIC fatigue life, especially in a lower stress range region.

On the use of nickel foil strain gages at varying temperatures

When a strain gage made of nickel foil attached on the surface of a specimen is subjected to repeated loads, the elastic stress is measured by observing slip-bands in the foil resulting from repeated strain. Calibration studies with rotating-bending tests at various temperatures between room temperature and 350°C are performed on round steel bars with nickel foil. The relation between the threshold stress for the first appearance of slip-bands and the number of stress cycles is examined at varying temperatures, which provides the calibration values of the nickel foil tested at varying temperatures. Assuming that the first appearance of slip-bands is based on the linear cumulative damage law, the calibration values at varying temperatures are calculated from those established by the calibration tests at several constant temperatures. It is found that the calculated calibration values agree well with the results obtained by the calibration tests at varying temperatures and that the calculation applying the linear cumulative damage law is a useful method to presume the calibration values at varying temperatures without performing the experiment.

An Approach to Studying Cavitation Bubble Collapse Pressure and Erosion.

A quantitative relation (F-N curve) was obtained between constant impact load due to cavitation bubble collapse and the number of cycles to the incubation period termination. The relation was derived from the linear cumulative damage law, in which all impact loads including ones of very low intensity (0.3 N) are assumed to cause damage. The slope of the F-N curve corresponds well with that of the S-N curve for a smooth specimen obtained from a standard fatigue test, provided that the contact area is obtained by the Hertz theory. The incubation period can be evaluated regardless of cavitation test conditions from the cumulative cycle ratio Σ(ni/Ni), using both the number ni. of impact loads and Ni from an extrapolated F-N curve (modified Miner's law) for the corresponding impact load Fi. Similarly, the F-N' curve was obtained for the steady-state period, where N' was defined as the number of cycles required to achieve a mean depth of penetration (MDP) of 1 micron. The slope of the curve coincides well with that of the S-N curve for a slightly notched specimen. The Σ(ni/N'i) has a linear relation with the MDP in the steady-state period. Since N'i is proportional to 1/F2i from the F-N' curve, the cumulative cycle ratio was reduced to ΣF2i·ni, which is consistent with the impact energy from the authors' previous report. It is concluded that the ratios Σ(ni/Ni) and Σ(ni/N'i) are suitable parameters for evaluation of the cavitation damage in the incubation and steady-state periods, respectively.

Use of Nickel Foil Strain Gages at Varying Temperatures.

Nickel foil strain gages are attached on the surface of a specimen subjected to repeated loads, and the elastic stresses are measured by observing slip bands in the foil gages resulting from repeated strains. Calibration studies with rotating-bending tests at various temperatures in the range of room temperature to 350°C are performed on round steel bars with nickel foil. The relationship between the threshold stress for the first appearance of slip bands and the number of stress cycles is examined at varying temperatures in a range of about 100°C, which provides the calibration values of the nickel foil tested at varying temperatures. Furthermore, assuming that the first appearance of slip bands is based on the linear cumulative damage law, the calibration values at varying temperatures are calculated from those established by the calibration tests at several constant temperatures. The calculated calibration values are compared with the results obtained by the calibration tests at varying temperatures.

EVALUATION OF FATIGUE CRACK PROPAGATION PROPERTIES UNDER RANDOM LOADING AVOIDING CRACK CLOSURE

Abstract— Fatigue crack propagation rates and the fatigue threshold of HT80 steel were measured by maintaining the maximum load during the whole period of random loading in order to prevent fatigue crack closure. The random loading pattern involved 62 level block loadings in which the waveform was approximated to the Rayleigh distribution of peaks. The fatigue crack propagation rates under random loading were well predicted from those obtained from constant amplitude loading and assuming a linear cumulative damage law. That is, da/dn =C{ΔKmeq−ΔKmth} where the equivalent stress intensity factor, ΔKeq={=niΔKmi/dni}1/m, where ni= 0 for ΔKi≤ΔKth, or ni=ni for ΔKi > ΔKth.

Adaptability of a Strain Gage Made of Nickel Foil to Variable Test Temperatures. In Cases of Directly Rising Temperatures.

When nickel foil strain gages are stuck on the surface of a specimen subjected to repeated loads, the elastic stress is measured by observing slip bands in the foil gages resulting from repeated strains. Calibration studies with rotating-bending tests at temperatures from 100°C to 350°C are performed on round steel bars with nickel foil, and the threshold stresses for the first appearance of slip bands are examined at variable temperatures rising directly. Furthermore, assuming that the first appearance of slip bands is subject to the linear cumulative damage law, the threshold stresses at the variable temperatures are calculated from those obtained by the calibration tests at several definite temperatures. The peak stresses in grooved shafts subjected to bending at the variable temperatures are measured with the nickel foil gages. The results are compared with those obtained previously by various methods.

ランダム荷重下における溶接継手の疲労き裂伝ぱ

Fatigue crack propagation properties of welded joints under random loading were investigated in air and synthetic sea water. The fatigue crack closure did not occur for whole excursion of loading, because the stress ratio around crack tip became high due to the tensile residual stresses around crack tips. That is, the applied range of stress intensity factor coincided with the effective range of stress intensity factor. The fatigue threshold in synthetic sea water was about a half of that in air. The fatigue crack propagation rates under random loading could be well estimated by the results obtained from constant amplitude tests assuming a linear cumulative damage law.

下限値近傍におけるランダム荷重下の溶接継手の疲れき裂伝ぱ

62 level block fatigue loadings in which waveform were approximating to the Rayleigh distribution of peak (distribution factor=0.25, 0.5 and 1) were applied on center cracked transverse butt welded joints in which tensile residual stresses were always induced at the crack tip. It was revealed that the fatigue crack propagation rate, da/dn*, could be estimated by the result obtained at constant amplitude tests assuming linear cumulative damage law. That is, da/dn*=C(ΔK*eqm-ΔKmth)whereΔK*eq={(ΣΔKmi ·ni)/ni}1/m, ni=0 at ΔKi≤ΔKth or ni=ni at ΔKi>ΔKth.

On the adaptability of the nickel electroplating method of stress analysis to variable test temperatures.

The adaptability of the electroplating method of stress analysis to variable test temperatures is examined by using nickel plating foil of 5 μm in thickness. The test temperatures vary gradually or stepwise in the range from 100°C to 200°C. The relations between the proper stress σp of the nickel plating foil and the number of stress cycles N, namely, the σp-N curves at variable test temperatures are obtained by the calibration tests in rotating bending in which N=(0.54.5)×106 cycles are designated. It is found that the σp-values at variable test temperatures can be estimated by using the formulas of the σp-N curves at constant temperatures, which is based on the assumption that the appearance of slip-bands in the nickel plating foil owing to cyclic straining is subject to the linear cumulative damage law.

Local crack-tip strain approach to fatigue crack propagation

A progressive crack-tip strain approach to fatigue crack propagation is presented. Localstrain damage accumulation curve for crack initiation is used as a “cyclic damage accumulation” and “fracture criterion” in the heavily deformed region, R h , just adjacent to the crack-tip. The changes of cyclic strain ahead of the crack-tip is experimentally measured by the real-time finegrid-method. Using the average strain range in R h and linear cumulative damage law of local strain, the number of cycles N ∗ necessary for the material failure over the distance, R h is calculated from local-strain damage accumulation curve. The average crack propagation rate, da/dN, in R h is estimated as the ratio R h/N ∗ . As a result, very good agreements between the measured and predicted da/dN are obtained in cases of two kinds of steels, MANTEN and RQC-100. This fact suggests the possibility that we can estimate the fatigue crack propagation rate by combining the cyclic strain ahead of the crack-tip with local-strain damage accumulation curve, and that, we can unify the two fatigue stages, crack initiation and propagation, from the view point of the local crack-tip strain.

変動ひずみ条件下における高温疲労 ＩＩ Ｃｒ‐Ｍｏ‐Ｖ鋼の変動ひずみ条件下の高温疲労特性に及ぼす介在物の影響

The effect of service loading on the fatigue behavior of a steam turbine rotor steel with large inclusions (1Cr-1Mo-1/4V steel with non-metallic inclusions of about 0.5mm in diameter) was investigated at 550°C. The service loading was simulated by a multiple two-step straining (MTSS). Under the MTSS tests, the life of the defect-free materials was reduced remarkably (1/10-1/100) as previously reported by the authors, and the reduction was even larger for a material containing large inclusions. However, the inclusions had little effect in reducing the life as far as a constant strain range was applied. Therefore the effect of inclusions was effectively evaluated through variable strain testing, not by conventional low cycle fatigue tests. An estimation of fatigue life was carried out based on the assumption of linear cumulative fatigue damage law in terms of the measured plastic strain range. This method tended to overestimate the life by a factor of two for the defected material under programed loading, though it effectively predicted the life for the defect-free ones. This was attributed to the crack initiation period reduced by inclusions. In the case of low cycle fatigue tests the crack initiation life was relatively short (-20%) even for the defect-free materials and therefore little effect of inclusions on the total life was noticed. For a conservative designing of a turbine rotor which might contain defects, it would be of significance to apply a fracture mechanics approach on an assumption that the total life is predominated by the crack growth period.

Fatigue crack initiation from notch root (local-strain damage accumulation process on crack initiation)

Local deformation (i.e. local-strain behavior) at the notch root in a crack initiation process in annealed 0.48% carbon steel was investigated by the real-time fine-grid method. The fatigue crack initiation cycle was controlled by local-strain damage accumulation. For a quantitative expression of cumulative fatigue damage, we propose a new parameter, the “average local-strain accumulation value,” Δ \\ ̄ ge 1 , which is defined by the integration of local-strain histories until crack initiation. The relationship between average local-strain accumulation range, Δ \\ ̄ ge 1 , and crack initiation cycles, N c , showed a line whose slope was nearly −0.5 on a log-log coordinate graph. This line we term the “local-strain damage accumulation curve.” The mean stress effect in cases of R = −1, 0 on this line ( Δ \\ ̄ ge 1 vs N c ) was very small or negligible. From the results of variable-loading tests, the linear cumulative damage law based on the local-strain value was also confirmed.

変動ひずみ条件下におけるタービンロータ材の高温疲労特性とその評価法

The effect of service loading on the fatigue behavior of steam turbine rotor steel (1Cr-1Mo-1/4V steel) was studied at 550°C. The service loading was simulated by a multiple two-step straining. Under the programed fatigue tests the life was reduced remarkably (1/10-1/100), as compared to the estimated values based on the conventional methods using a linear cumulative law in terms of fatigue and creep damages. This decrease in fatigue life was largely attributed to the accumulation of increased plastic strain range corresponding to the small strain cycles after large strains. For the programed fatigue tests, the fatigue life was estimated under the assumption of linear cumulative fatigue damage law in terms of the measured plastic strain range. The results of this estimation were in agreement with those of the constant strain range tests. The plastic strain range which increased after a large strain cycle could be expressed as a relatively simple function of strain con-ditions. This was indicative of a possible system for monitoring fatigue life of turbine rotors by using the above-mentioned linear cumulative damage law. The fatigue curve could be modified with the data above so as to estimate fatigue life under variable strains for use in designing. It was shown, however, that the curves were affected largely by the number of cycles of small strains (n2) and tended to increase in life with n2. The significance of further examinations on the effects of service loadings was indicated.

The Cyclic Plastic Strain and Cumulative Fatigue Damage

It is well known that the stress amplitudes below the fatigue limit can damage the materials under the programmed fatigue tests or in service loadings. But its proper estimation has not yet so far been established. The authors have found that the linear cumulative fatigue damage law in terms of the plastic strain range-pair gave good estimation of the fatigue lives in low and high cycle fatigue nearly up to the fatigue limit with the low or medium carbon steels. From such a view point, the push-pull type programmed fatigue tests having the stress amplitude below the fatigue limit with intermittent high level stress were carried out with unnotched specimens of the normalized medium carbon steel S35C, and the behavior of the plastic strain was investigated.In the constant stress amplitude test, it is observed that there is fatigue limit to the plastic strain as there is to the stress. In the programmed tests the plastic strain range corresponding to the stress below the fatigue limit is found to be larger than that of the constant stress amplitude, due to the influence of intermittent high level stress. Moreover, it is found that the fatigue limit in terms of the plastic strain has disappeared, and that the fatigue damage caused by the plastic strain range below it is linearly accumulated.