Constant Mean Stress Research Articles

Analysis of the internal crazes in notched SAN

AbstractCrazing in styrene–acrylonitrile copolymer (SAN) under a triaxial stress state was examined. The damage zone that formed ahead of a semicircular notch under slow tensile loading consisted of two kinds of crazes: internal notch crazes that grew out from the notch root and discontinuous surface crazes. Examination of the damage zone in the optical and scanning electron microscopes revealed that the internal notch crazes sometimes extended through most of the thickness but never penetrated the free surfaces, whereas the surface crazes penetrated about 10–50 μm inward from the surface. Initially, the internal craze tips defined a crescent‐shaped zone. The plane strain elastic stress distribution at the zone boundary satisfied a constant mean stress condition, and the critical mean stress for craze tip growth was determined to be about 35 MPa. This value varied slightly for different resins but was independent of thickness. Propagation of the internal notch crazes occurred in a straight line parallel to the minor principal stress vector at the point of origin on the notch surface, whereas the surface crazes followed the minor principal stress trajectories. The presence of the internal notch crazes resulted in significant stress redistribution, the stress redistribution was described quantitatively using both the deviation of the craze trajectory from the minor principal stress trajectory, and the deviation of the zone shape from the critical elastic mean stress condition.

Low Cycle Fatigue and Cycle Dependent Creep with Continuum Damage Mechanics

A continuum damage mechanics (CDM) model for low cycle fatigue cou pled with cycle dependent creep is presented. The cycle-creep and damage behavior of hot rolled type RS50 steel is analysed by the damage model and compared with those mea sured in satisfactory agreement. The model can describe the gradual acceleration of creep rate under constant stress amplitude and mean stress in low cycle fatigue, a phenomenon which can never be explained by conventional mechanics. The model also results in a con venient experimental method for the measurement of damage values.

The stress-whitened damage zone of PVC blends

The stress-whitened damage zone that formed ahead of a semicircular notch during slow tensile loading has been measured from optical micrographs of translucent blends of poly(vinyl chloride) (PVC) with experimental chlorinated polyethylene (CPE) resins. When the zone was small, the plane strain condition applied and from the elastic stress distribution a constant mean stress condition was found at the boundary of the crescent-shaped zone. The critical mean stress did not depend on the chlorine content or the chlorine distribution of the experimental CPE resin used in the blend. While the critical mean stress decreased as the amount of CPE in the blend was increased, the critical volume strain, calculated from the bulk modulus, was independent of composition and was thought to be the controlling parameter for stress-whitening. When the zone was larger, the shape was qualitatively described by concepts of stress redistribution in the presence of a plastic zone ahead of the notch. Macroscopic flow and necking were only detected near the maximum in the stress-displacement curve.

Fatigue Gauge Utilizing Slip Deformation of Aluminum Foil. 5th Report. Controlling Parameter of Surface Roughening under Variable Stress.

The surface roughening phenomenon of aluminum foil is examined under variable stress, and the controlling parameter that dominates the roughness is clarified. It is found that constant mean stress does not affect surface roughness. When mean stress varies, however, mean stress causes surface roughening. In such a case, the range-pair counting method is appropriate, and the equivalent stress represented by (Σσ^iNi/ΣNi)1/α dominates surface roughness, where σi and Ni are stress amplitude and the number of stress cycles counted by the range-pair method, and a is a material factor. It is concluded that the fatigue gauge made of aluminum foil can evaluate the equivalent stress with high accuracy.

Damage zone development in PVC under a multiaxial tensile stress state

The irreversible deformation mechanisms of poly(vinyl chloride) with a semicircular notch under slow tensile loading have been studied as a function of sheet thickness. Initially, core yielding was observed in the optical microscope as two families of slip lines growing from the notch surface in the centre of the specimen. The size and shape of the core yielding zone could be described by plasticity analysis. A stress-whitened zone subsequently initiated near the tip of the slip line zone. The stress whitening was caused by 1 μm voids that were visible in the scanning electron microscope. The mean stress for stress whitening was calculated to be 43.0±1.5 MPa by a plastic stress analysis of a pressure-dependent yield material. By assuming a constant mean stress along the boundary of the stress-whitened zone, the one-dimensional shift of the elastic stress distribution was obtained. At higher stresses, hinge shear and intersecting shear were observed for thick and thin sheet, respectively.

An experimental and numerical study of the factors governing crack growth under cyclic compression

Cyclic compressive fatigue tests were performed on double-edge-notched specimens of a medium carbon low alloy steel for different stress amplitude under constant mean stress and different mean stress under constant stress amplitude. The crack growth rate, the length of the arrested crack and the shape of the crack front were examined, based on the characteristics of the tensile stress field obtained from finite element analysis. A plot to show the characteristics of the tensile field are proposed and the influence of some key factors, such as stress state, stress ratio and the compressive plastic zone (i.e. minimum compressive stress) on the behavior of the cyclic compressive fatigue were discussed.

Fatigue Life under Random Loading Condition (5 th Report)

In the previous paper, a method for estimating fatigue strength under random loading condition was proposed, a method that combined fatigue tests with calculations. The loading condition is limited to the case where the mean stress level, or the stress ratio of the minimum stress to the maximum stress, is constant. However, in the actual service loading condition, both mean stress and stress amplitude generally vary from cycle to cycle. Therefore, a random fatigue test with a constant mean stress or stress ratio is not enough to clarify fatigue behavior under actual service loading conditions.In this paper, a random test procedure similar to the method shown in the previous paper is proposed. However, the new-procedure both mean stress and stress ratio are able to change according to the service loading condition.To check the applicability and accuracy of this new procedure, axial load controlled random loading tests, with an exponential distribution of the peak to peak-stress, were carried out for plane mild steel specimens. Fatigue behavior patterns are then examined.

Computer simulated deformation of compact granular assemblies

The paper is concerned with the mechanics of granular material under quasi-equilibrium conditions. The characterisation of the microstructure of granular material is discussed and the relationship between the microstructure and the stress tensor is examined. Results from computer simulated experiments on a large, initially random, dense assembly of different sized discs are used to investigate the evolution of both stress and structure. Two tests are reported: one a constant mean stress test and the other a constant volume test. It is shown that, although the two tests were subjected to different strain histories the degree of induced structural anisotropy evolved in an identical manner. The computer simulated tests show that there also exists a statical anisotropy due to the biased distribution of contact forces within an assembly. This also evolves in the same way for both tests reported. Consequently, the evolution of the angle of internal shearing resistance with strain is found to be unique.

Crack growth properties of nuclear graphite under cyclic loading conditions

Crack growth properties of four kinds of nuclear graphites under cyclic loading conditions were investigated at room temperature, 373, 673 and 975 K, using double cantilever beam (DCB) specimens. The crack growth rates can be expressed as a function of the stress intensity factor range at the constant mean stress intensity factor ( K mean ) and the constant minimum stress intensity factor ( K min ): that is, da/ dN = CΔK 1 n , where the constants C and n depend upon the kind of graphite and its coke grain size. The crack growth rate at the constant K mean becomes smaller than that at the constant K min . For the fine-grained graphite tested at higher temperatures, the crack growth rate increases with increasing temperature. Also cracks in the coarse grained coke graphites extend at a higher rate than that in the fine-grained high strength graphites. It seems that cracks in graphites run mostly along the coke grain boundaries.

Apparatus for Cyclic Stress Path Testing

Abstract A simple change in the conventional cyclic triaxial cell was made to carry out constant mean stress tests on dry Ottawa sand. Test results show that stress-strain characteristics under cyclic loading conditions are significantly affected by the imposed stress path.

Fatigue crack growth retardation under constant amplitude and variable mean stress

Fatigue crack growth retardation under stress spectra with constant amplitude and variable mean stress, respectively, was studied. Flat specimens with a central through crack were tested under tension-tension load. The specimens were made with low alloy steel 4 mm thick, with yield strength of 625 Mpa and ultimate tensile strength of 784 MPa. Overload affected crack length increments Δa ∗ were studied. The best correlation was obtained between monotonic plane stress plastic zone size 2r y and Δa ∗. The cyclic plastic zone size 2r pc correlated with crack length increment of minimum crack growth rate after overload. Forman's equation and Willenborg's model of fatigue crack growth retardation were used for theoretical prediction of fatigue crack propagation life. The best agreement between theoretical and experimental results was also obtained using monotonic plastic zone size instead of monotonic plastic zone radius or cyclic plastic zone size. The agreement is reasonably good, even though in the case of one spectrum, cracks were arrested for several thousand cycles.

Mechanical behavior of New Mexico rock salt in triaxial compression up to 200°C

Experiments were conducted to determine the ‘quasi‐static’ mechanical behavior of rock salt in support of the structural design of a waste isolation pilot plant. The salt studied was from the Salado formation in the Delaware Basin, southeastern New Mexico. Three groups of tests are discussed to identify the relative and site‐specific importance of deviator stress, confining pressure (mean stress), temperature, time (loading rate), and stress path. The three groups of experiments consist of (1) hydrostatic loading, (2) triaxial compression tests (σ1 > σ2 = σ3 = const), and (3) variable stress path tests including experiments at approximately constant σ1 and at constant mean stress. The range of parameters considered was 0 ≤p (hydrostatic pressure) ≤ 34.5 MPa, 0 ≤ σ 2 = σ3 ≤ 20.7 MPa, 0 ≤ (σ1 − σ3) ≤ 62 MPa, 23 ≤ T (temperature) ≤ 200°C, and 1.7 ≤ d(σ1 − σ3)/dt ≤ 3.5 kPa/s. All data were generated on 100‐mm‐diameter specimens. The rock salt exhibited nonlinear response under all loading coditions, a low initial elastic limit (σ1 − σ3) ≤ 0.7 MPa, and an apparent inseparability of permanent deformations into time‐independent and time‐dependent components. Pressure and temperature did not alter the elastic constants over the range 29.6 ≤ E ≤ 36.5 GPa and 0.17 ≤ v ≤ 0.26, depending on core lithology. Pressure and temperature affected the principal strain ratio, the ratio of volumetric to shear strain, rock salt ductility, and the ultimate stress. In particular, low pressure and temperature permitted pronounced dilatancy and loss in load bearing ability. Under such conditions the volumetric strains reached sizeable fractions of the shear strains, ∣∈/(∈1 − ∈3)∣ ≥ 0.2. Pressure remained important even at 200°C temperature because it influenced the rate of shearing at constant loading rates. Load path and stress history may be significant under deviatoric loading conditions and for large variations in pressure.

岩質材料の変形特性に関する実験的研究

The deformation characteristics of rock-like materials with different porosities have been studied experimentally using the specimens of cement mortar and tuff under triaxial compression states. The stress and strain are dealt with respectively by dividing into their isostatic and deviatoric components, and the experimental results are considered from a point of view of continuum mechanics. The results are as follows:(1) The deformation characteristics of the porous rock-like materials depend essentially upon the variation of form of microscopic structure with the stress history.(2) The stress-strain relationships of these materials under the isostatic stress are represented approximately by a bi-linear curve and its bending point may be considered as the yield point for the hydrostatic pressure.(3) In the state of normal compression, the amount of recoverable shearing strain γoct varies in proportion to τoct up to the yield point and its rate of variation does not depend on the mean stress σm.(4) In the state of normal compression, the contractancy arises with the increase of shearing strain under the constant mean stress and its magnitude increases with the mean stress.(5) In the state of over compression, the slope of τoct-γoct curve up to the yield point is steeper than one in the state of normal compression, and the slope does not depend upon the normal stress.(6) In the state of over compression, the contactancy is smaller than one in the normal compression and the dilatancy arises when the mean stress is relatively small.The deformation characteristics of rock-like materials mentioned above may be explained reasonably by assuming the end cap-shaped yield surface in hardening for the yield condition of materials.

ねじの締付力と疲労強度

The theoretical expression for the calculation of the optimum clamping force of the boltconnection with the clamping force extended plastic region under constant external mean stress was inducted with the following three assumptions : (1) The bolt carries only the axial stress.(2) The material of the bolt is elastic-lineally plastic solid.(3) There is no plastic deformation in the fastened body. Also, the effect of pre-stressing by clamping was investigated theoretically and experimentally. The results are as follows : (1) With the optimum clamping force, the endurance limit increased about 170% against the conventional value, at mean stress σm= 31.5 kg/mm2.(2) The theoretical value in the optimum clamping force nearly fitted to the experimental value.(3) The endurance limit was more improved when the optimum clamping force was given after the pre-stressing.

平均応力が変動する条件下における等価両振り応力に関する一考察

The fatigue test of 7075 T6 aluminum alloy under constant mean stress σm in the range of 0.20 ≤A≤∞(A=σa/σm) was carried out by use of a testing machine of Schenck type. Also, the fatigue test under cyclic varying mean stress σm' was performed by a newly constructed cyclic creep testing machine. From these tests, the following results were obtained:(1) From the results of fatigue test under constant mean stress, the equivalent alternating stress σae was determined. The curve for the relation between σae/σa and A was found to be represented nearly by two linear lines with a junction point at A=0.5∼0.7. It was also found that the fatigue life curve in the range of A>0.5∼0.7 was nearly parallel to that under fully reversed stressing (A =∞) but in the range of A<0.5∼0.7 it was not parallel.(2) From the results of fatigue test under cyclic varying mean stress with secondary stress superimposed, the equivalent alternating stress σae was also determined and the curve for the relation between σae/σa and the stress ratio of σa to σm, A', was represented by two curved lines with a junction point at A'=0.5∼0.6. In the range of A'<0.5∼0.6 the curve was nearly a straight line, in the range of 0.5∼0.6<A'<0.8 it showed a convex toward the upper direction and in the range of A'>0.8 it was again nearly a straight line.(3) From the results of fatigue test under cyclic varying mean stress without secondary stress, the equivalent alternating mean stress Ye and the varying mean stress, Y=1/√2(σm'-σm), were determined. It was found that the relation between Ye/Y and the stress ratio A'(=Y/X) was represented by a similar curve given in (1) and (2).

動クリープおよび高温疲労の寿命に関する一考察

For prediction of the rupture life of metals subjected to reversed stressing of stress amplitude σa under a constant mean stress σm at elevated temperatures, the linear damage rule was adapted and its rupture life was analized by partitioning of parameter A, or the stress ratio σa/σm. In the range of 0≤A≤1, an equivalent static stress σme for rupture life was determined by use of A and slope αt of rupture life curves based on σm. If rupture life curves of static creep are given, it is possible to predict approximately the rupture life curve of dynamic creep by calculation. In the range of 1≤A≤∞, an equivalent alternating stress σae for fatigue life was determined by using A and slope αt of completely reversed life curves based on σa. Therefore, a fatigue life curve for any mean stress will be predicted analytically from the completely reversed fatigue life curves.

ＳＭ５８鋼溶接継手の疲れ強さにおよぼす平均応力変動の影響

Many informations on the effect of the constant mean stress have been reported by Munse and other investigators. But in the case that the mean stress is fluctuating in a long period, it is considered that we can not estimate simply from the result of fatigue test with constant mean stress.In this report, the relation between the crack propagation rate and the mean stress was studied using the single notched specimens and that result was examined using the concept of effective stress in the vicinity of crack apex due to Erdogan and et. al.. After those studies, the effect of programmed mean stress on the fatigue strength and the relation between the crack propagation rate and the fatigue life about the both of the welded joint and the base metal were investigated by the analysis of fracture mechanics. The material used in this study was 14 mm thick plates of a steel for welded structure SM58. Fatigue tests were carried out from the high cycle region to the low cycle region in the axial loading condition with constant R-value or programmed R-value.Firstly in the fatigue test with constant R-value, it was found that in the high cycle region, the fatigue test result of base metal was well agreed with the equation of aeff⋅Nαf=C used the effective stress, but that of the welded joint was not because of the scatter of the welded reinforcement. In the low cycle region, though the elasto-plastic DM model could not be adopted and so the effective stress was not used, formally we could seem to use the assumption with m=0 in the high mean stress condition.The fatigue test with programmed R-value were carried out in the very small cycle ratio and it was found that the modified Miner's rule was coincided with the test result of the base metal, and we could estimate the fatigue life with programmed R-value from the result of that with R=0 using the effective stress. But in the case of the welded joint, the observed values had larger fatigue life than the estimated values from the modified Miner's rule. According to the crack propagation rule, the estimations of fatigue life were carried out on the fatigue test with programmed R-value, and it was found that considering the invalid cyclic portion in the vicinity of the threshold of crack propagation, we could have the more exact estimation of fatigue life with programmed R-value.

金属材料に平均応力の変動する繰返し応力を負荷した場合の疲れ強さと強度線図に関する一考察

Fatigue tests of 7075 T6 aluminum alloy under constant mean stress σm in the range of 0.20≤A ≤∞(A=σa/σm) were carried out by use of a testing machine of Schenck type. Also, fatigue tests under cyclic varying mean stress σm' were performed by using a new type of cyclic creep testing machine. The results obtained are as follows:(1) The strength diagram σa-σm of stress cycle number N2 by use of fatigue test results under a constant mean stress σm, is shown nearly by a straight line. In the same way, the strength diagram of cycle number N2, by using fatigue test results under a cyclic varying mean stress σm', is shown nearly by a straight line. On the other hand, the strength diagram σm'-σm of cycle number N2, which was counted from summation tr of upper hold time in the test results of fatigue under only cyclic varying mean stress σm', is shown nearly by an ellipse.(2) Using the above three strength diagrams of same cycle number N2, the strength diagram of σm-σm'-σa is represented by an elliptic-cone.

Stress-induced diffusion during folding

The application of thermodynamics to folding shows that mechanical disequilibria also correspond to chemical disequilibria and that they can be adjusted by the diffusion of elements down the free-energy gradient. Mechanical disequilibria in the form of heterogeneous stress distribution for the two-dimensional, large-amplitude folding of competent layers in a less competent matrix have been determined by a series of finite-element analyses. Folds with high viscosity contrast ( 100 1 ) have a gradient of the mean stress (pressure) in the competent layer which is directed perpendicularly to the layer. The incompetent layers in a folded multi-layer sequence show a mean stress gradient directed parallel with the layer, and the pressure minima are located at the hinge zone. Folds with low viscosity contrast have the isopachs (lines of constant mean stress) oriented almost parallel to the direction of compression and a minimum mean stress on the outer arc. The variations of mean stress in experimentally produced folds are in qualitative agreement with the variation in: 1. (1) the mineral composition; 2. (2) the bulk chemical composition; 3. (3) the chemical composition of a mineral; and 4. (4) the grain-size variation of natural folds.

Fatigue Strength of Metals under Service Load

As one of the investigations of fatigue strength of metals under service load, the fatigue tests have been carried out in the case where mean stresses fluctuated sinusoidally. In these cases, the fatigue age and endurance limits are reduced as compared with those in the case of constant mean stress, but they do not depend on the fluctuating speed, in spite of the difference in the rates of the speed from 5 to 420cpm.We have been able to estimate the fatigue age and endurance limits in these cases by means of the criterion on the fatigue damage and the calculating method, which were proposed by the authors. These stress patterns are analyzed in the same way as in the case of varying stress amplitudes, and the fatigue strength in this case is possible of being estimated with the results of fatigue tests of constant mean stresses. It has been confirmed that both the results of the experiments and estimations exactly agree with each other.If σ=H(n)is the equation of the cumulative frequency of repeated stresses, the formula of estimation of fatigue age Nt is as follows.Nt=-n0/m∫n00H(n)dnloge{1-m∫n00H(n)dn/∫n00exp[A·H(n)+D]dn}where the constants, A, D and m are obtained from the results of fatigue tests in the case of constant mean stress, the n0 is the cumulative number of stress cycles in one of the periods of the fluctuating mean stresses.