Uniaxial Cyclic Stress Research Articles

Evolution of stress-resultant loading and ultimate strength surfaces in cyclic plasticity of steel wide-flange cross-sections

Abstract The evolution of the shape of limit surfaces during plastic excursions is a key component of the inelastic response of structural members. However, stress-resultant-based computational plasticity formulations rarely account for any change in shape of the loading or ultimate strength surfaces. This research documents the evolution of the shape, size, and position of the loading and ultimate strength surfaces in stress-resultant space for wide-flange steel shapes subjected to cyclic proportional and nonproportional loading having a combination of axial force and either strong- or weak-axis flexure. The evolution is based on numerical integration of the cross-section stresses assuming a cyclic uniaxial stress–strain curve with a trilinear backbone that accounts for the Bauschinger effect. Surface evolution is investigated both with and without residual stresses. The results indicate that the evolution in shape of the loading surface, while relatively path-independent, is substantial, particularly at high levels of plastic excursion, where the loading surface essentially vanishes. The evolution in shape of the ultimate strength surface, in contrast, is mild. The research also documents the relative magnitudes of the components of cyclic plastic deformation. Recommendations are provided for the estimation of the direction of cyclic plastic flow through the calculation of gradients to the limit surfaces within the assumption of using an associated flow rule in stress-resultant space.

A study of small crack growth in aluminum alloy 7075-T6

Previous studies of the growth of small fatigue cracks in aluminum alloy 7075-T6 are reviewed to compare observed behavior and explanations for that behavior. The results of small crack growth tests conducted in this work are then reported. Crack growth was monitored periodically between initial crack sizes of approximately 10 μm to final sizes of approximately 0.5 mm in rotating bending and plate specimens subjected to fully-reversed cycling. Both longitudinal and transverse stress components were present in the central region of the plate specimens, while rotating bending specimens experienced nearly uniaxial cyclic stress. Specimens were taken from rolled 7075-T651 with a pancake microstructure. Tests were conducted at a number of different strain amplitudes. Small cracks grew faster than large cracks for the same stress intensity range ΔK, as expected from previous research by others. When compared on the basis of ΔK, growth rates in the plate specimens varied from being little different than those in rotating bending specimens to approximately four times higher, depending on strain amplitude. The growth rates of cracks at different locations around the circumference of the rotating bending specimens varied little, in spite of the different microstructural orientations of the different locations. In both plate and rotating bending tests, some cracks exhibited marked decelerations and accelerations in growth rate, while others did not. For those cracks that did not exhibit such oscillations in growth rate plus those cracks that had grown large enough for such oscillations to have subsided, growth rates were found to be proportional to crack size and to amplitude of maximum shear strain to a power of approximately 4.5. Growth rate data from both rotating bending and plate specimens were well correlated by that strain parameter.

Uniaxial cyclic ratcheting and plastic flow properties of SS304 stainless steel at room and elevated temperatures

An experimental study was carried out for the uniaxial ratcheting of SS304 stainless steel subjected to cyclic stress at room and elevated temperatures. The effects of stress amplitude, mean stress and their histories on the ratcheting of SS304 stainless steel were analyzed at room and elevated temperatures. The interaction of uniaxial strain cycling and stress cycling was also discussed at variable temperatures. On the basis of the experimental data under uniaxial strain and stress cycling, the plastic flow properties of the material were analyzed. The evolution rules of plastic modulus vs. accumulated plastic strain during cyclic loading were investigated under the condition of variable loading processes. The discussion was focused on the relation of uniaxial ratcheting rate and such plastic flow properties as plastic modulus and accumulated plastic strain. It is shown that the uniaxial cyclic properties of the material depend not only on the current loading case and temperature, but also greatly on the previous loading history. The plastic flow properties of strain cycling are apparently different from those of asymmetrical stress cycling; the ratcheting of asymmetrical stress cycling at room and elevated temperature is greatly influenced by the evolution of plastic modulus and accumulated plastic strain. These conclusions are very useful to the development of constitutive model for ratcheting.

Anisotropy and Nonlinear Viscoelastic Behavior of Saturated Rocks

AbstractLow‐frequency uniaxial stress cycling experiments were conducted on sandstone and marble in different saturation states to investigate the possible anisotropic and nonlinear behavior. The results indicate that under the yield point the attenuation, Young's modulus, Poisson's ratio and velocities of saturated rocks all display obvious anisotropy and rather obvious strain amplitude effect and frequency effect. As strain amplitude increases attenuation increases linearly while Young's moduli and Poisson's ratios decrease approximately linearly. In the frequency range 0.005–4 Hz attenuation shows no strong frequency dependence while Young's moduli, Poisson's ratios and velocities obviously depend on frequency. When the frequency range is enlarged to 15 Hz all the four parameters show rather strong frequency dependence. Attenuation, Yong's moduli, Poisson's ratios and velocities of saturated rocks increase as viscosity coefficient of the saturant increases.

Nonlinear viscoelastic behavior of sedimentary rocks, Part II: Hysteresis effects and influence of type of fluid on elastic moduli

Uniaxial stress cycling experiments were conducted on dry, brine saturated and hexadecane saturated Berea sandstone samples to observe in detail the hysteresis in stress‐strain diagrams and to understand the influence of different fluids on the strain amplitude dependence of elastic moduli and attenuation. Cycling experiments were also conducted with sandstone samples saturated with CTAB, a cationic surfactant that renders the mineral surfaces hydrophobic. Hexadecane and CTAB were selected so as to investigate the relative contributions of adhesion hysteresis and stick‐slip sliding on attenuation in sedimentary granular rocks. Young’s moduli and Poisson’s ratios obtained from the cycling tests show a significant dependence on strain amplitude on dry as well as water and hexadecane saturated samples. Bow‐tie‐shaped diagrams are obtained when loading and unloading tangent moduli are plotted against strain. The type of fluid in the pore space and at the grain contacts has a large influence on the hysteresis observed in the stress‐strain diagrams.

Nonlinear viscoelastic behavior of sedimentary rocks, Part I: Effect of frequency and strain amplitude

Sedimentary rocks display nonlinear elastic behavior. This nonlinearity is a strong function of frequency, strain amplitude, and the properties of the saturating fluid. Experimental observations and potential mechanisms that cause these nonlinearities are presented in this and a companion paper. Young’s moduli and Poisson’s ratios obtained from ultrasonic laboratory measurements (50 kHz, 100 kHz, 180kHz and 1 MHz), low‐frequency measurements (1–2000 Hz) and static measurements (0.001–0.05 Hz) show significant differences under identical stress conditions. A comparison of the laboratory‐measured quantities with log‐derived moduli measured at 20 kHz indicates that [Formula: see text]. This shows clearly that a wide variety of sandstones demonstrate frequency‐dependent elastic behavior (viscoelastic behavior) over a range of frequencies. Differences between static (low‐frequency, high‐strain amplitude) velocities and ultrasonic velocities can be explained partially by differences in frequency as predicted by grain contact models. Such models, however, do not explain the strain amplitude dependence observed in our data. A series of uniaxial stress cycling measurements were carried out to investigate the influence of strain amplitude on elastic moduli. These low‐frequency measurements (0.01 Hz) clearly show that the Young’s modulus decreases with strain amplitude for a wide variety of sandstones. Attenuation increases with strain amplitude. The strain amplitude dependence does not change when the rocks are saturated with brine although the rocks soften measureably.

Invariant formulation of a gradient dependent multiaxial high-cycle fatigue criterion

Experimental evidence has shown that the fatigue limit of metallic cylindrical specimens in fully reversed bending is significantly higher than the respective limit in fully reversed tension-compression. The higher values of the bending fatigue limits observed have to be attributed to the benign influence of the gradient of the bending normal stress on the fatigue strength of the metal. Although many approaches for modelling the gradient effect under uniaxial normal cyclic stress have already been tried, attempts to model the very same problem under multiaxial cyclic stress systems are scarce. The present paper starts re-analyzing existing experimental results under cyclic normal stress (i.e. bending, tension-compression) and under cyclic shear stress (i.e. torsion). This closer examination shows that although the fatigue endurance is strongly affected by the gradient of the normal stress in bending tests, it remains insensitive to variations of the gradient of the shear stress in torsion tests. Based on these observations, a gradient dependent multiaxial high-cycle fatigue criterion function of the stress invariants is formulated.

Effect of cyclic stress on Terfenol-D

A rod of grain oriented Terfenol-D has been subjected to cyclic uniaxial stress of /spl plusmn/100 MPa about a mean preload of /spl sim/120 MPa applied along the grain growth axis. The magnetostrictive strain and d-coefficient measured under uniaxial preload and quasi static magnetic fields are shown to increase after the initial 10/sup 6/ cycles of stress. The characterisation of the magnetomechanical behaviour from resonance analyses indicates a slight hardening of the material after /spl sim/6/spl times/10/sup 7/ cycles and that to regain optimum magnetomechanical coupling, the bias preload and DC bias fields require adjustment in keeping with the effects of the stress cycling. These initial results indicate that magnetostrictive devices constructed from Terfenol-D offer a significant advantage compared with ceramic (PZT) actuators when applied in load bearing situations.

Effects of isofield uniaxial cyclic stress on the magnetization of 2% Mn pipeline steel - behavior on minor hysteresis loops and small major hysteresis loops

The present results show that the sense of the stress-induced irreversible changes in the unstressed magnetization is not always towards the anhysteretic. Examples where the change is away from the anhysteretic are shown, as well as cases where the cyclic uniaxial stress does not cause an irreversible change in the sample's unstressed magnetization when that magnetization does not coincide with a point along the anhysteretic curve. Examination of the magnetization changes with cyclic stress along the upper or lower branches of a minor hysteresis loop suggests that the distance along that branch from the previous turning point is the most important factor in determining the sense of the stress-induced changes in magnetization. Initially the stress-induced changes in the unstressed magnetization occur in the same sense as they would have before the turning point, but the interaction between the domain walls and the pinning sites in the sample as the applied magnetic field changes after the turning point causes this stress-induced change to decrease in value and then reverse in sign. This suggests that the isofield cyclic stress-induced changes in the magnetization should be considered to be towards a local equilibrium condition rather than a global equilibrium condition (the anhysteretic curve).< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Magnetization changes in 2% Mn pipeline steel induced by uniaxial tensile stress cycles of increasing amplitude

The application of cyclic stress to a ferromagnet normally gives irreversible magnetization shifts towards the anhysteretic magnetization. Here experimental measurements are presented that show the irreversible magnetization changes induced by cyclic uniaxial isofield stress applied after magnetization at particular points on minor hysteresis loops. Selecting the (M,H) point and magnetization history, then applying stress cycles of increasing amplitude enables irreversible changes, initially away from and later toward the anhysteretic curve, to be obtained. Examples of a second inversion (i.e., irreversible shifts initially toward, then away and subsequently toward the anhysteretic magnetization) with increasing amplitude cyclic uniaxial stress are also given. Preisach diagrams are used to interpret these results qualitatively in terms of local, more extensive and global anhysteretic states.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Effects of isofield uniaxial cyclic stress on the magnetization of 2% Mn pipeline steel-behavior on near saturation major hysteresis loop

Measurements of the effects of cyclic stress on the magnetization of a sample of 0.08%-C 2%-Mn pipeline steel are presented. The sample was magnetized to a position on the upper branch of the near saturation major hysteresis loop. Cyclic uniaxial tension or compression was then applied to the sample under isofield conditions. Two types of stress cycle were tested, one where the maximum stress applied to the sample increased after every cycle, and one where the maximum stress was held at a constant value for each cycle. Plots of the resulting changes in the magnetization indicated the presence of two types of irreversible behavior produced by the stress cycles-irreversible changes in the unstressed magnetization and stress-magnetization hysteresis. The former behavior was found to fall into three different categories that depended on the magnetization of the sample and the type of applied stress. These categories were analyzed in terms of the expected effects of the different stresses on the different magnetization mechanisms, namely, 180/spl deg/ domain wall motions, 90/spl deg/ domain wall motions, and domain magnetization vector rotations. >

THE DEVELOPMENT OF STRESSES AND THEIR DISTRIBUTION IN TWO‐PHASE ALLOYS DURING CYCLIC LOADING

AbstractA finite element program calculates the cyclic behaviour of the individual component phases of a multiphase material using a master curve observed in uniaxial cyclic stress tests. The fatigue behaviour of the two‐phase alloys was characterized by visualizing the evolution of the phase stress (denoted by an average effective stress and an hydrostatic stress) during cyclic loading. The evolution procedure shows a unique fatigue behaviour of the in situ component phases, which differs from that observed in uniaxial or multiaxial fatigue tests of the single phase material. The fatigue damage on a microstructural scale was identified by the distributions of the plastic strain accumulated during cyclic loading and the stress triaxility in the component phases.

Cyclic plasticity under nonproportional loading. (1st report. A new description of hysteresis loops).

Thin-walled tubes of a carbon steel were subjected to nonproportional cyclic loading. A new expression for describing the cyclic deformation under multiaxial stresses was demonstrated for examining the propriety of the constitutive equation in cyclic plasticity presented in a previous paper, based on the random barriers theory. With this expression, the cyclic deformation, both under the proportional loading and under the nonproportional loading, could be discussed inclusively in the same category. The experimental results proved that the plastic potential function used in the equation and its change characteristics depending on the cyclic history, induced from the experiments on the uniaxial stress cycling, were applicable to the case of the multiaxial stress cycling. Moreover, it was suggested that an effect of anisotropy produced by cyclic deformation might be reflected in the internal structure variable which was one of the fundamental components in the constitutive equation.

Weak field control of remanent magnetization changes produced by uniaxial stress cycling

The effect of weak fields (∼0.01 mT.) upon the remanent magnetization of basalts, granodiorites and polycrystalline magnetite during uniaxial compression has been investigated. Samples carrying NRM and AF demagnetized NRM were used. The demagnetized samples showed the largest effects. In the low stress range of less than 100 bars, the influence of stress was demagnetization. In the absence of an applied field, the magnetization rotated away from the compression axis, as is commonly observed. However, with the application of a field of between .01 to .02 mT., the magnetization rotated into alignment with the field as stress was increased. AF demagnetization after the application of 1 kbar of load produced large and repeatable magnetization increases confined to a very narrow coercivity band. AF demagnetization to 10 mT. removed most of the stress induced remanence. These observations are explained in terms of enhanced remanence acquisition in the presence of stress. This reversible effect unblocks soft domain wall sections which can respond to weak applied fields, or to internal demagnetizing fields.

Calculations for Uniaxial Stress and Strain Cycling in Plasticity

Within the framework of an existing purely mechanical, rate-type theory of plasticity, detailed calculations are presented for certain types of material response during stress and strain cycling in a uniaxial homogeneous deformation. These features pertain specifically to material response in stress cycling between fixed values of stress in tension and compression (not necessarily equal in magnitude) resulting in ratcheting of strain, and a type of saturation hardening caused by strain cycling between any two fixed values of strain when the mean value of stress (in tension and compression) tends to zero.

Viscoelastic solid relations for the deformation of ice

A frame indifferent differential operator law relating stress, stress-rate, strain, and strain-rate is constructed to describe the qualitative features of both constant load and constant displacement rate response in uni-axial stress experiments. No lower order differential relation can describe both responses, but the two responses are not sufficient to determine the response coefficients of the relation. The jump relation is determined for a stress discontinuity applied in a general configuration. A simple initially isotropic model is proposed to investigate the effects of loading history and the anisotropy induced in a configuration following a loading-unloading cycle. Both uni-axial stress and shear cycles are treated, followed by uni-axial stress loading in different directions. The respective deformation histories are determined in the small strain approximation, and demonstrate a significant influence of the initial load cycle on response from the unloaded configuration.

Effect of uniaxial stress upon remanent magnetization: Stress cycling and domain state dependence.

Polycrystalline magnetite and rock samples have been subjected to uniaxial compression and stress cycling at room temperature. The changes in the components of remanent magnetization were recorded continuously as a function of stress, and the changes in direction and total intensity of magnetization were inferred. Different types of response were recognized, according to the type of magnetization the sample was carrying, i. e., high field or weak field remanence. The anomalous increase of weak field remanence previously reported, appears partly reversible under stress cycling. However, the changes in the lowest stress range are irreversible and reduce the zero stress magnetization from cycle to cycle. Reversible rotations of the magnetization vector of as much as 180° were observed during each half cycle and were primarily due to changes in the sign of the component of magnetization parallel to compression. An andesite whose magnetic phases are single domain according to hysteresis criteria showed a much smaller effect regardless of the type of magnetization it carried. These results again draw attention to the variety of stress responses and the importance of three component observations in field attempts to detect seismomagnetic precursors.

A Theoretical Investigation on the Thermal Ratcheting

A method to estimate the deformation due to thermal ratcheting under multiaxial stress was presented from the viewpoint of thermoplasticity by employing the general yield function associated with the kinematic hardening rule. The analysis developed here indicates that the ratchet strain of a sufficiently work-hardened material under varying stress and temperature can be predicted from the data of the progressive strain under uniaxial cyclic stress at constant temperatures.Also the comparison was made with the experimental results of low carbon steel subjected to uniaxial cyclic thermal stress combined with mechanical steady stress.

Experimental Study of Dilatational vs Distortional Straining Action in Material-Damping Production

Experimental test setups for measuring material damping in structural metals have invariably been limited to producing states of strain wherein the distortional component is dominant. In the case of flexural vibrations of plates and shells, however, this condition is often reversed, sometimes with the elastic energy associated with dilatational straining action exceeding the corresponding distortional component by an order of magnitude. It has, therefore, been conjectured that effects due to dilatational straining, small enough to be masked by experimental scatter in the aforementioned tests, might become significant under conditions of pronounced dilatational straining, viz., plate vibrations. For this purpose, a test machine was designed to measure material damping in thin-walled, cylindrical specimens subject to combined internal pressure and axial cyclic loading. Tests were carried out on a number of manganese-copper alloy specimens for which prior studies, already published, had established damping properties under uniaxial cyclic stress. The new tests extended the ratio of dilatational to distortional strain energies from a fraction up to a factor of 2, the latter limit being determined by possible onset of stress-history effects, which were avoided. The results display a small but definite influence of dilatational straining action in producing additional material damping to that arising from distortional straining action. As a consequence, a modified formula is suggested for the treatment of material damping in plate vibrations.