Cyclic Stress-strain Relationship Research Articles

高温における間欠ひずみ波形下の損傷評価法

In order to establish a life prediction method for gas turbuine blades, fatigue tests using intermittent strain waveforms which simulated the service loading of gas turbine blades were carried out for SUS 316 stainless steel and two Ni-base superalloys (IN 738 LC and Inco. 713 LC) at elevated temperatures. The fatigue behavior and fatigue strength in these tests had been reported in the previous papers by the present authors.In this paper, several methods of damage evaluation using intermittent strain waveforms were examined on the basis of a linear cumulative damage concept, and the following conclusion was obtained;The failure life (Nes) in the intermittent strain cycling can be predicted by the equation below, which takes the acceleration of crack propagation rate due to the superposed small strain cycling into consideration.Nes·(1/Nh+η·n2/N2)=1where Nh and N2 are the fatigue lives observed under trapezoidal and constant strain waves respectively. η is the ratio of crack propagation rate under superposed small strain cycling to that under constant strain amplitude cycling, which is represented by the following equations.R≤0;η=2α/(1-R)α R>0;η=2α·(1+R)/(1-R)where α is the Paris's exponent and R is the stress ratio calculated by using the cyclic stress-strain relationship.

The high temperature low cycle fatigue behavior of the nickel base alloy IN-617

Fully reversed strain controlled LCF tests were performed on 4.5 mm thick sheet specimens IN-617 at 1033 K and 1144 K in air. The strain-life and cyclic stress-strain data were analyzed parametrically. While the inelastic strain amplitude-life relationships are similar at the two temperatures, the softer cyclic stress-strain relationship observed at 1144 K produces inferior fatigue resistance to that at 1033 K when comparisons are based on stress or total strain amplitude. Transmission electron microscope observations suggest that grain boundary sliding was the primary mechanism of deformation at 1144 K while at 1033 K intragranular slip produced a dense dislocation substructure which was stabilized by fine scale precipitation of M23C6. At 1144 K, grain boundary migration occurred within the specimen interiors, producing a cellular precipitation of M23C6 as well as the intragranular M23C6 observed at 1033 K. Cellular precipitation was not observed in the near surface regions. This is attributed to oxygen penetration along grain boundaries. Comparison of the data with mean stress-HCF data indicates that the mean load significantly reduces fatigue resistance at both temperatures.

Some Considerations on Cyclic Stress-Strain Relation and Low cycle Fatigue life

Some Considerations on Cyclic Stress-Strain Relation and Low cycle Fatigue life

Pulsating Tension Fatigue Strength and Cyclic Stress-Strain Response of Wire Ropes

The cyclic stress-strain response and the fatigue property of spiral ropes under constant and variable amplitude axial loadings were investigated. The effects of a construction of wire rope and sea water environment on pulsating tension fatigue strength were also examined.Pulsating tensile load fatigue tests of 1×7 wire ropes of 7 mm in diameter were carried out by changing stress ratio. An analysis of test results showed that the zero-to-tension fatigue strength at 4 x 105 to 2 × 106 cycles is about 30% of breaking load, and that the fatigue strength under any stress ratio can be predicted by an elliptic line drawn through the zero- to-tension fatigue strength on the ordinate of stress amplitude and the ultimate strength on the abscissa of mean stress.Though the cyclic creep phenomena were observed, the axial strain ranges were kept nearly constant in each stress level. Then, the cyclic stress-strain relations were almost independent on both of stress ratio and stress history.Pulsating tensile load fatigue tests were also carried out in air and in sea water environments on a 1 × 37 wire rope of 20 mm in diameter consisting of 37 galvanized steel wires, showing that the fatigue strength in air is lower than that of 1 × 7 wire rope in air. Furthermore, it was shown that the sea water environment operates not only detrimental corrosive effect, but also beneficial effect upon the fatigue life due to decrease in the internal wear among wires.The results of random and p-distribution block loadings fatigue tests in air on 1×7 wire ropes showed a valid applicability of linear cumulative damage hypothesis to the estimation of fatigue life for engineering purpose.

不均質層を有する金属材料の曲げ疲労寿命推定法に関する研究 層状不均質性と残留応力の効果に注目して

It has often been reported that the hardening and compressive residual stress at surface were important factors for increasing fatigue strength of surface hardened materials. However, the effects of these two factors on fatigue lives were not always separated in previous experiments. Also it should be emphasized that no thorough investigation for these factors has been undertaken from a mechanical viewpoint.In the present study, the effects of laminated inhomogeneity and residual stress on bending fatigue lives were examined on the clad plates composed of low and medium carbon steels. On the basis of these experimental results, a method to estimate bending fatigue lives of the laminated inhomogenous metals was discussed. The main results obtained are as follows;(1) Cyclic bending stress-strain relation of the laminated inhomogeneous plates could be calculated approximately by applying the cyclic stress-strain relation of push-pull fatigue tests to the static bending deformation analysis.(2) Bending fatigue lives of the laminated inhomogeneous metals without residual stress could be estimated fairly well from S-N curves of the base metals by choosing the plastic strain amplitude (or strain amplitude) as an equivalent factor controlling the fatigue life. In the case with residual stress, the fatigue lives could be understood by adding an effect of residual stress on fatigue crack propagation lives after the microcrack initiation of fatigue to the estimation method mentioned above.

The Effect of Ion Implantation on the Fatigue Behavior of Metals and Alloys

The effect of ion implantation on the strain and stress controlled fatigue behavior of polycrystalline copper has been investigated. The cyclic stress-strain response, strain-life and stress-life relationships and fatigue crack nucleation behavior have been studied. The results from the non-implanted materials have been compared with those from the implanted materials. Four implant species, one with a positive misfit, one with a negative misfit, one with a zero misfit, and one insoluble under equilibrium conditions have been used. Most of the fatigue tests were performed in laboratory air. Ion implantation changes the surface deformation behavior for both monotonic and cyclic loading with a corresponding change in hardening rate. Larger changes are observed for the cyclic loading. Implantations which lead to a more homogeneous deformation (fine slip) near the surface, improves the resistance to fatigue crack initiation. Surface compressive residual stresses, induced from implanting a positive misfit species, have a major influence on crack initiation in the stress-life regime.

The effect of ion implantation on cyclic stress-strain response of polycrystalline copper

The effect of aluminum and boron ion implantation on strain-controlled (low cycle) and stress-controlled (high cycle) fatigue behavior of polycrystalline copper was investigated. The cyclic stress-strain, strain-life and stress-life relations, cyclic slip and crack nucleation behavior of implanted copper are compared with those of unimplanted copper. Under strain control, ion-implanted samples show a lower degree of cyclic hardening and longer fatigue lives than their non-implanted counterparts. Aluminum implantation has a larger effect than boron implantation. Under stress control the fatigue life and the fatigue limit are observed to increase for the aluminum-implanted samples compared with their non-implanted counterparts. These changes in fatigue behavior are associated with changes in deformation behavior in the surface region and surface residual stresses created by ion implantation.

Normalized Dynamic Undrained Strength of Sands Subjected to Cyclic and Random Loading

Normalized cyclic undrained triaxial stress-strain relationships of undisturbed sandy specimens are discussed in this paper. Cyclic undrained triaxial strengths defined by axial strain amplitudes and developments of excess pore water pressure are analyzed. A simplified equation for evaluating cyclic undrained triaxial strength of sands is derived. Based on the empirical normalized strength equation, a relationship between strength for a uniform cyclic loading and that for a random cyclic loading is obtained. A simplified method for evaluating an equivalent uniform loading strength for a random loading is proposed using a strength curve through uniform cyclic loading tests.

Constitutive equations of single crystals and polycrystalline aggregates under cyclic loading

It is found that the existing dislocation hardening mechanisms can be generally classified into two categories: isotropic and kinematic. This classification leads to the concept of “degree of isotropy” in work hardening. Based on this concept, the cyclic stress-strain relations of single crystals and metals are constructed throughout the entire loading history. The connections between the mechanical behaviour of dislocations and a single crystal, and between those of crystal grains and a polycrystal are explored under monotonic and cyclic loading conditions. These explorations show that the Bauschinger effect of a single crystal is caused by the kinematic hardening mechanisms, and that of a polycrystal is caused by both the kinematic mechanisms and the residual stress in the most favorably-oriented slip system. The cyclic hardening and softening behavior of metals are shown to be intimately related to those of its constituent single crystals. The theory developed is applied to describe the cyclic stress-strain relations of a copper crystal, and to predict the cyclic response of a 2024-T351 aluminum alloy; in both cases the agreement with experiments is considered good.

FAILURE MECHANISMS IN IMPACT FATIGUE OF METALS

Abstract Impact fatigue tests were performed with smooth and notched specimens of low carbon steels under various impact loading conditions. The characteristic failure mechanisms in impact fatigue was discriminated by comparison with those in non-impact, ordinary fatigue. The fatigue life of smooth specimens was uniquely related to the range of plastic strain at the middle of the fatigue life in both impact and non-impact fatigue, although the characteristics of micro-structural deformation and cyclic stress-strain relationships were markedly different. The growth rate of a fatigue crack in impact fatigue of notched specimens was higher than that in non-impact fatigue when compared at the same stress intensity factor. Fractographic observations with scanning electron microscopy and the X-ray diffraction technique revealed more abundant cleavage facets and a smaller spread of the plastic zone beneath the fracture surface made by impact fatigue. Both nucleation and propagation lives in notched specimens were much shorter in impact fatigue than in non impact fatigue when compared at the same values of nominal stress and stress concentration factor.

The response of high-strength low alloy steel to cyclic plastic deformation

The low cycle fatigue behavior of a niobium-bearing HSLA steel has been investigated at room temperature at an applied total strain rate of dot ϵ = 10 −2 s −1 . Specimens are examined in the as-hot-rolled condition, the cold-rolled 50% condition, and the annealed condition. It has been shown that cyclic saturation is not always obtained in HSLA steels and further, that this transient portion of the stress response to constant strain amplitude cycling may be represented by a power law. The cyclic hardening rate thus defined is independent of cyclic and shows a smooth variation with strain amplitude. The behavior is substantially different for the three specimen treatments with the exception that each treatment suggests cyclic softening at sufficiently low strain amplitudes. The cyclic stress-strain curves obtained by the incremental step method are presented along with companion specimen cyclic stress-strain curves obtained at 1, 10, and 50 percent of crack initiation life. It is found that the number of cycles to crack initiation does not depend strongly on the specimen condition. The energy associated with crack initiation is examined experimentally for this HSLA steel. The results agree quite well with an empirical derivation of this quantity based on the Coffin-Manson relation and the power law cyclic stress-strain relation. It appears that for broad classes of engineering materials, the hysteretic energy associated with crack initiation rises sharply with decreasing strain amplitude.

Cyclic stress strain relations and strain-controlled fatigue of 4140 steel

The strain controlled low cycle fatigue properties and cyclic stress-strain response of a 4140 steel were investigated as functions of tempering temperature. While as-quenched 4140 steel specimens showed cyclic hardening, tempering at 200°C or higher resulted in cyclic softening which was a maximum for 400°C tempering. The hardening in the quenched steel was attributed to dynamic strain aging. Cyclic softening for the 400 and 550°C tempers resulted in part from rearrangement of the dislocation substructure and reduction of dislocation density as shown by transmission electron microscope. Mechanical removal of the yield point also contributed to cyclic softening and was the dominant mode for specimens tempered at 650°C. Removal of the yield point was attributed to an increase in the number of mobile dislocations. On tempering at 650°C, a failure of the Coffin-Manson relation was observed. Agreement was obtained when the plastic strain amplitude was plotted vs cycles to crack initiation rather than cycles to failure. For tempering at 350°C and higher, it is suggested that the endurance limit is essentially equal to the cyclic yield stress.

Cyclic stress strain relations and strain-controlled fatigue of 4140 steel

Cyclic stress strain relations and strain-controlled fatigue of 4140 steel

硬鋼の繰返し応力‐ひずみ関係およびヒステリシスループ形状に及ぼすひずみ履歴の影響

The effects of strain history both on the cyclic stress-strain relation and on the shape of hysteresis loop have been investigated on annealed S55C by the constant strain amplitude tests with different mean strains and the incremental step tests. The results are summarized as follows:(1) The cyclic stress-strain curves of the constant strain amplitude tests coincide with each other irrespective of the mean strain in the stationary state of fatigue process, or at a half of the fatigue life. They can be written as Δσ=KΔεpn, where K=338 and n=0.254, when Δσ is taken as the true stress range and Δεp as the logarithmic plastic strain range.The cyclic stress-strain relation in the incremental step tests also has a similar trend as above, being represented by the equation Δσ=KΔεpn, K=317 and n=0.232, when the stationary state is considered to be at half of the number of blocks to failure.(2) For the constant strain amplitude tests, the shape of hysteresis loop in the stationary state is represented, regardless of mean strain, as σ*=Kεp*n*, K*=KΔεpn-n* and n*=0.06Δεp-0.193, where σ* and εp* designate the true stress and the logarithmic plastic strain respectively, with the origin of the coordinates being located at one end of the hysteresis loop. On the other hand, for the incremental step tests, it is written as follows, since n* is observed to be nearly constant;σ*/Δσ=(εp*/Δεp)n*, n*=0.114The equational difference of the shape of hysteresis loops in both cases has to be discussed carefully in view of some variations of the data obtained. However it may be considered very useful to adopt the latter equation for the incremental step tests, since the mechanical behavior of the material is fully defined from three constants of K, n and n*, which are easily obtained from one specimen.

Notch Effect in Low-Cycle Fatigue : 2nd Report, Considerations on Notch Effect in Low-Cycle Fatigue with Finite Element Method

The paper describes a supplementary investigation on the authors' former work concerning the notch effect in low-cycle fatigue of metals ( 1st Report on the same subject ), and presents another approach to the subject. The approach is such that an elastic-plastic analysis with the finite element method is made about a notched region of a member on the basis of the cyclic stress-strain relation of the material which is obtained under cyclic loading, and the peak value of strain range thus estimated at the notch is taken good as a measure for predicting the crack initiation life. In order to verify the validity of the proposed method in evaluating the notch effect on the low-cycle fatigue, calculations with the finite element method on several notched members, measurements of notch root strains under monotonic and cyclic loadings and low-cycle fatigue tests on smooth and notched specimens were performed. By the comparison of the calculations and tests, the proposed method for the elastic-plastic analysis and for the evaluation of the notch effect was verified to be valid.

ひずみ振幅変動に伴って生ずる繰返し応力‐ひずみ挙動と疲労寿命

The effects of slip character in metal polycrystals on the cyclic hardening and softening behaviors were investigated under the multiple repeated tests at two strain levels, and the fatigue lives of copper and α-brass in the double repeated fatigue tests were considered.The main results obtained are as follows:(1) The stress range after changing the strain amplitude approaches gradually to the inherent value of the virgin material for S10C and copper which show a wavy slip mode. On the other hand, for α-brass having planar slip character, the stress range approaches to the same value as that of the virgin material as the strain level is increased. However, as the strain level is decreased, the stress range reaches the value larger than the inherent value of the virgin material after the transient increase in the early stage. These results can be explained by considering the slip character of materials and the aging effect in α-brass.(2) For S10C and copper, the stress range for a given plastic strain range just after the change in the strain amplitude corresponds to the state of hardening just before the change. On the other hand, for α-brass the former does not always correspond to the latter. This characteristic property for the cyclically deformed α-brass can be explained by considering both the slip character and the aging effect of this material.(3) The cyclic stress-strain relation for α-brass of planar slipping mode is sensitively affected by its strain history, while for copper of wavy slip character this relation is scarcely dependent on it.(4) The double repeated fatigue tests show that the cumulative cycle ratio does not depend on the stressing sequence for copper, while for α-brass it is larger than one in the High-Low test, but less than one in the Low-High test. These test results correspond well with the cyclic strain hardening and softening behaviors shown in (1) and (2).

Effect of Grain Size on Cyclic Stress-Strain Relation and Fatigue Strength of Copper and α-Brass

Many studies have been carried out in regard to the grain size dependence of fatigue strength of metals. And it has been made clear that fatigue strength of f. c. c. metals greatly depends on the stacking fault energy γ, and the effect of γ on the crack propagation process is different from that on the crack initiation process. In this work, the grain size dependence of the fatigue strength was mainly examined under the rotating bending fatigue test, and the cyclic work hardening behavior under the push-pull fatigue test. Furthermore, the surface structure due to fatigue deformation was observed by means of optical and electron microscopes. From the viewpoints of both microscopic structure and dynamical behavior of the materials, the grain size dependence of fatigue strength was investigated in copper and α-brass.The results obtained are summarized as follows:(1) The grain size dependence in the crack initiation process in α-brass is very remarkable at 200°C as well as at room temperature. This result suggests that the effect of grain size on fatigue strength must be considered from both viewpoints of the configuration of slip line and ageing effect.(2) The grain size dependence in crack propagation process in α-brass is very small at R.T, but it increases at 200°C.(3) The cyclic work hardening in α-brass is larger in fine grains than in coarse grains. On the other hand, in copper almost opposite result was obtained. From these results the difference in grain size dependence under constant stress fatigue test can be explained.

Analysis of the Cyclic Stress-Strain Behavior by a Distributed Element Model

The distributed-element model is applied to the analysis of the cyclic stress-strain relation. The model regards a material as the aggregate consisting of a number of elastic-plastic elements with different yield strains. The values of the rate of hardening are the same for all of the elements, but they vary only with the number of cycles. The stress-strain behavior of a material can be obtained from summing statistically the strss-strain responses of all the elements. In order to examine the suitability of the model, the cyclic bending test was performed on plate specimens under a constant strain amplitude. From the comparison between the experiment and the theory, it is clear that the behavior of a material under cyclic stress can be predicted well by the present distributed-element model. Furthermore, this analysis is found to be useful to estimate fatigue life.

Investigation of Stress State at Fatigue Crack Tip by Means of X-Ray Microbeam

The stress-strain relation at the vicinity of fatigue crack tip is one of the most demanded points in the study of fatigue crack propagation. Recently, the oscillating crystal X-ray microbeam diffraction technique which enables to measure the stress in such a minute domain as the vicinity of fatigue crack tip has been devised by K. Honda and T. Konaga.In the present study, the stress condition at the crack tip was studied by this technique. An alternating tension-compression load was applied to the annealed and recovered plate specimens of 0.05%C low carbon steel with notches at the both sides. The stresses at the vicinity of fatigue crack tip in the area of 180μ in diameter were measured under several loading conditions. The results obtained are summarized as follows;(1) The stress concentration factor, which is the ratio of the stress at the maximum load or the minimum load to the applied nominal stress, is approximately the same for both annealed and recovered specimens: it's value is nearly unit for compression load, nearly 2.5 for tension load in the case of annealed specimens and nearly 2.2 in the case of recovered specimens.(2) The mean value of cyclic stress at the vicinity of fatigue crack tip is an almost zero as a consequence of compressive residual stress when the applied mean stress is zero.(3) No remarkable distribution of residual stress is measured in the vicinity of crack tip.(4) The result mentioned in (1) suggests that the cyclic stress-strain relation at the tip of crack having a relatively low propagation rate is similar to the relation obtainable after the saturation of cyclic hardening or softening.(5) The residual stress at the crack tip tends to change in reverse direction to the applied mean stress so that the cyclic stress at crack tip is almost in a fully reversed stress condition almost irrespective of the mean applied stress.

Cyclic stress-strain relations from bending and push-pull tests

Cyclic plastic-straining tests have been conducted in push-pull on cylindrical specimens and in uniform bending on rectangular-section bars of mild steel (B.S. 1501–161 Grade 28A) and of stainless steel (En 58J). The mild-steel specimens were tested at room temperature and 350°C, the stainless-steel specimens at room temperature and 650°C. It is found that there is good correspondence between cyclic stress-strain relations (the cyclic semi-range of strain and the corresponding cyclic semi-range of stress) derived from bending tests, when an expression analogous to that developed by Nadai for monotonic straining is used, and those obtained more directly from push-pull tests.