Multiaxial stress loading

In a recent study, Saintier et al. ° investigated the multiaxial effects on fatigue crack nucleation and growth in natural mbber. They found that the same mechanisms of decohesion and cavitation of inclusions that cause crack nucleation and crack growth in uniaxial experiments were responsible for the crack behavior in multiaxial experiments. They studied crack orientations for nonproportional multiaxial fatigue loadings and found them to be related to the direction of the maximum first principal stress of a cycle when material plane rotations are taken into account. This method accounts for material rotations in the analysis due to the displacement of planes associated with large strain conditions. 

Although the uniaxial test has traditionally received the most attention, such tests alone may be insufficient to characterize adequately the mechanical capability of solid propellants. This is especially true for ultimate property determinations where a change in load application from one axis to several at once may strongly affect the relative ranking of propellants according to their breaking strains. Since the conditions usually encountered in solid rocket motors lead to the development of multiaxial stress fields, tests which attempt to simulate these stress fields may be expected to represent more closely the true capability of the material. 

The 1-D concentric cylinder models described above have been extended to fiber-reinforced ceramics by Kervadec and Chermant,28,29 Adami,30 and Wu and Holmes 31 these analyses are similar in basic concept to the previous modeling efforts for metal matrix composites, but they incorporate the time-dependent nature of both fiber and matrix creep and, in some cases, interface creep. Further extension of the 1-D model to multiaxial stress states was made by Meyer et a/.,32-34 Wang et al.,35 and Wang and Chou.36 In the work by Meyer et al., 1-D fiber-composites under off-axis loading (with the loading direction at an angle to fiber axis) were analyzed with the... 

By definition, ESC is influenced by the level of the applied multiaxial stress, ft is expected that below an assigned value of stress in a specific medium ESC will not occur. Fatigue crack growth experiments at various constant levels of A K can be applied to study the influence of the crack-tip loading on the ESC behavior in a systematic way. As an example, cast CT specimens of PMMA (Mn = 4.6 x 105) were tested in air and IPA at different levels of AK (0.6, 0.7, 0.8, 0.9 MPa -v/m). The tests were performed as described earlier, with the application of the medium after a certain time of cyclic loading in air. From the plots of the crack length ratio vs. number of cycles, the following observations can be made (Fig. 23) ... 

At this point it can be concluded that core-shell nodules can toughen PET when loading conditions induce multiaxial stress fields (i.e., notched samples or dart tests). Precise physical phenomena involved have to be identified. This is done combining several techniques ... 

The stress tensor for each point of the grain can be represented by one point in principal stress space. In that space, there exists a volume where the propellant is made worthless by significant damage, even possibly a crack. A major difficulty of such a representation is the fact that the failure properties of propellant depend strongly on loading conditions (temperature and strain rate). So in this paper, for each loading condition (one strain rate and one temperature), we construct a failure surface based on experimental data for several multiaxial stress states. 

It is important to note that the uniaxial loading of an off-axis plate generates a local (inherent) multiaxial stress state. It is therefore worth mentioning the investigations by Kawai and coworkers for the description of the off-axis fatigue behavior of UD and woven reinforced laminates [61,71,72] and their fatigue damage mechanics model [61]. The model is based on the nondimensional effective stress concept, which is the square root of the Tsai—Hill polynomial. 

It would be certainly highly desirable to increase twinning suppression in quartz X-plate in the application for sensors. Another possible way is to increase the load limit below which no twinning takes place. Thermodynamics offers basically two possibilities for that. Either the radial pre-stress in suitable direction tends to AG > 0 for negative T values, or the jaw material is chosen in order to minimize the unwanted multiaxial stresses. Both methods were not realized practically up to now. 

Meggiolaro, M.A., de Castro J.T.P., de Olivera Miranda, A.C. Evaluation of multiaxial stress-strain models and fatigue life prediction methods under proportional loadings. In da Costa, M., Alves, M. (Eds.) Mechanics of solids in Brazil. Brazilian Soc. of Mech. Sci. Engn. (2009)... 

To determine the mechanical behavior of plastics under compressive load, it is possible to carry out the compressive test described in DIN ISO 604 for the testing of plastics [9]. By contrast to tensile tests, cylindrical, solid-material specimens are compressed between two plane-parallel plates and the compressive stress/compression behavior is recorded. One problematical aspect of these tests is that the friction that occurs between the plane-parallel clamping surfaces and the specimen inhibit the lateral extension of the test specimen and hence leads to a convex barrel shape, which is the manifestation of a multiaxial stress state inside the specimen. 

Figure 16 illustrates several test specimens which have been used (46) in the multiaxial characterization of solid propellants. The arrows indicate the direction of load application. The strip tension or strip biaxial test has been used extensively in failure studies. It can be seen that the propellant is constrained by the long bonded edge so that lateral contraction is prevented and tension is produced in two axes simultaneously. The sample is free to contract normal to these axes. The ratio of the two principal tensile stresses may be varied from 0 to 0.5 by varying the bonded length of incompressible materials. 

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