Cyclic stress-strain curve

FIGURE 28.9 Idealized cyclic stress-strain curve, showing the fuU viscoelastic curve together with its elastic component. (Redrawn from Andrew, C., Introduction to Rubber Technology, Knovel e-book publishers, 1999.)... 

Cyclic stresses/strains, 13 481-483 Cyclic stress-strain curves, 13 491 Cyclic structures, nonaromatic, 15 5 Cyclic thermomechanical characterization, of shape-memory polymers, 22 358-362 Cyclic trimer ketone peroxides, 14 292 Cyclic trioxides, 18 448 Cyclic voltammetry, 9 580 Cyclitols, 4 710 Cyclization(s)... 

Fig. 6.5 Cyclic stress-strain behavior observed during the room temperature fatigue of unidirectional SiQ/LAS-II at a maximum stress below the 105 fatigue limit (loading frequency = 10 Hz, crmin/crmax = 0.1). The cyclic stress-strain curves show very limited, if any, hysteresis. Note that the strength and strain capability is retained after cyclic loading below the proportional limit stress. After Prewo.42...

Figure 7.12 Typical compressive cyclic stress-strain curves, (a) Fine-grained and coarse-grained Ti3SiC2. The dotted line is a linear elastic response expected forTi3SiC2 had kinking not occurred. Also included are the results on AI2O3 and Al for comparison [5] ...

Cyclic hardening/softening was deduced and cyclic stress-strain curves over wide ranges of plastic strain amplitudes were published in [1.178, 179] for Mo, in [1.172,180,181] for Ta, and in [1.182] for Nb and... 

Low-Cycle Fatigue Properties. Results of low-cycle fatigue experiments under strain control on as-worked W plate material at 815 °C are shown in Fig. 3.1-172. Low-cycle fatigue tests of pure W were performed in the temperature range between 1650 °C and 3300 C [1.184]. A relationship Afaiiure = exp(—aT) was found to be valid up to test temperatures of 2700 °C [1.185]. In all cases the failure mode was intercrystalline. Similar results were also obtained at a test temperature of 1232 °C [ 1.186]. The deformation behavior of Nb and Nb IZr under plastic-strain control at room temperature was investigated and cyclic stress-strain curves published [1.182]. 

To determine the local strain range, the cyclic stress strain curve is used, since under the influence of cyclic loads, the material will soon approach the stable cyclic condition. The cyclic stress-strain curve is computed as... 

Petrequin, Roche and Tortel derived a plastic strain magnification factor (similar to the ASME Code Kg factor) for notches using Neuber s rule and cyclic stress-strain curves.This factor is calculated as a function of elastic strain range. 

In Figure 11.4, the ASME and MITI Code fCg factors have been compared with the computed values for a structural alloy (Alloy 600) using the cyclic stress-strain curve and using Sp/Sn = 2.0 and 5.0. The computed values of the Ke factors obtained by Chattopadhyay appear to follow the same trend as the ones specified in the MITI Code for the material investigated. ... 

The cyclic stress-strain curve is frequently approximated by the Ram-berg-Osgood law, equation (3.15), using modified parameters K and n ... 

To reduce the experimental efforts in measuring cyclic stress-strain curves, the incremental-step test can be used. In this test, the strain amphtude is varied block-wise between zero and a maximal value as sketched in figure 10.30. After the block has been repeated several times, the material behaviour does not change an5rmore and a stationary state is arrived at. If the stress is measured at each of the strain maxima, the... 

The cyclic stress-strain curve can be used, for example, to perform finite element simulations of cyclic loadings. To simulate the complete experiment in the computer, it would be necessary to obtain information on the hardening of the material (isotropic and kinematic hardening) and to determine a material model that correctly describes it. This would be an extremely comphcated procedure. Furthermore, the entire number of cycles would have to be calculated, which would require an immense amount of computing time. Instead, the flow curve, taken by the finite element software to be monotonous, can be replaced by the cyclic stress-strain curve. A single, monotonous loading of the component is then simulated. Stresses and strains calculated in this way correspond well with those in the cyclically loaded component. 

Fig. 1.24 Cyclic stress-strain curve (solid line) obtained by connecting tips of stabilized hysteresis loops [30]. The monotonic stress-strain curve is also shown for comparison (dashed...

Fig. 1.26 Cyclic stress-strain curve obtained on Cr-Mo-V steel of 660 MPa yielding strength and 820 MPa ultimate with the incremental step test [32]...

Fig. 6.3 According to Masing s hypothesis, all stabilized cycles, such as 1, 2 and 3, moved to have their points of load inversion F, E and D in the origin 0 describe a curve that can be mathematically expressed as the factor two expansion of the cyclic stress-strain curve...

Once the elastic-plastic response is known, Fig. 6.16c, using Eqs. (6.6) and (6.7) and the memory effect each hysteresis loop of Fig. 6.16d can be separately analyzed. In using Eqs. (6.6) and (6.7) it must be recalled what has been said in Sect. 6.2 about the Masing hypothesis and the factor of two that must be applied to handle the case as if the hysteresis loop traces were equivalent to a cyclic stress-strain curve. Therefore, Eqs. (6.6) and (6.7) becomes... 

Equation (6.32) shall be used with the material cyclic stress-strain curve given by Eq. (6.3) instead of the monotonic one, so that for the initial loading ramp of the cycle Eq. (6.32) becomes... 

Equation (6.33) may be solved using an iteration technique that yields the coordinates ea and nominal stress stress value a 2, as shown in Eig. 6.22. This results in a change of the notch root strain As and stress Ac. The new intersection between the unloading ramp and the Neuber s hyperbola must be found, as shown in Fig. 6.22 by point B, using the hysteresis loop curve, instead of the cyclic stress-strain curve, as done before for the loading ramp. The origin of the axes is now at point A. The new equations to be used are Eq. (6.32) with A[Pg.333]

Still linear while kfis, applied when strains are well into the plastic domain. Walker [42] using aluminum specimens with lateral groves to maintain triaxiaUty also on the external surface, found that when notch root stresses remain elastic an analysis based on the theoretical stress concentration factor Iq with a triaxial cyclic stress-strain curve yields the same results as with the kf notch factor and an uniaxial stress-strain cyclic curve, as schematized in Fig. 6.29. 

The second evaluation is obtained from the interpolation of experimental cyclic stress-strain curve Ca — Sp shown in Fig. 6.33. The procedure yields... 

Fig. 6.35 Monotonic and cyclic stress-strain curves for the steel considered in the sample problem...

Tests have been run to derive the cyclic stress-strain curve both at 25 °C and at the operating temperature of 288 °C. Results are shown in Fig. 6.43. It is possible to recognize that at 288 °C the material is undergoing a dynamic strain aging process that makes the steel behave much better than at room temperature. The Ramberg-Osgood Eq. (6.3) of the cyclic curve at 288 °C is... 

Fig. 6.43 Cyclic stress-strain curves obtained with A 106 B carbon steel specimens at room temperature and 288 °C. Also shown are the Neuber s hyperbolas for six different loading conditions...

The cyclic stress-strain curve is different from the initial behavior that is measured in a traditional tensile test. A power function (Eq. (1.19)) may be fit to this curve to obtain three material properties ... 

In the calculation, plasticity is taken into account. The membrane stress am is obtained using the cyclic stress-strain curve and a parameter qgp as shown in Fig. 1(a). For the bending stress,... 

In the stress relaxation process, JNC assumes a strain hardening rule for the calculation of the creep strain rate.The loading conditions, the geometry of the plates and the dimensions of the initial notches are given in Table 1. The membrane stress Gm and the bending stress Gb can be calculated elastically. The material properties are given in Table 2. The cyclic stress-strain curve at 650°C is expressed as follows [5]. 

The temperature dependant mechanical properties and the cyclic stress-strain curve of the type 304 stainless steel material constituting the specimen are given in Table 3. The fatigue... 

Temperature dependant cyclic stress-strain curve... 

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