Multiaxial testing

Due to the plane-specific namre of crack nucleation under multiaxial tests. Mars and Fatemi proposed the cracking energy density as an equivalence parameter that represents the portion of strain energy density available to be released as crack growth on a specific material plane. The form of the cracking energy density Wc is... 

Some efforts have been undertaken to study propellant dilatation in multiaxial stress fields and even in small motor configurations. Farris (25) has conducted limited investigations along this line and has made approximate correlations between uniaxial and multiaxial tests. 

Multiaxial test geometries and test conditions may be analyzed with reference to three orthogonal principal stresses as shown in Figure 15. 

A unique and considerably more elaborate multiaxial test employs a thick-walled hollow sphere test specimen which may be pressurized internally or externally with a nearly incompressible liquid. Figure 20 illustrates the essential features of the test device as described by Bennet and Anderson (5). The specimen is prepared by casting propellant in a mold fitted with a sand-poly (vinyl alcohol) mandrel inside the sphere which may be removed easily after curing. A constant displacement rate instrument drives the piston to pressurize the chamber and apply large deformations. The piston s total displacement volume is transferred to... 

Further work will be focusing on lifetime prediction methods for gas turbine materials (superalloys) and experiments on fracture mechanics in superalloys as well as finite element calculations of multiaxial loaded tubes and validation of multiaxial tests (tension, torsion, internal pressure). 

To evaluate the performance of different constitutive models, it is important to perform multiaxial tests in addition to uniaxial tension and compression experiments. The multiaxial tests are necessary for material model validation studies because it is knovm that some constitutive models... 

For criterion in mode I, we had no multiaxial test results, but we had different traction/compression results associated to given orientations. 

G. P. Sendecky), A Brief Survey of Empirical Multiaxial Strength Criteria for Composites, In Composite Materials Testing and Design (Second Conference), H. T. Corten (Chairman), Anaheim, Caiifomia, 20-22 April 1971, ASTM STP 497, American Society for Testing and Materials, 1972, pp. 41-51. 

Two-in. multiaxial (axial/torsional/intemal pressure) composite tube test method [43]... 

This discussion applies to various test configurations whether uniaxial or multiaxial and is related, in general, to commercially available testing machines with controlled jaw displacement rates. The characteri-... 

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. 

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. 

In a recent attempt to bring an engineering approach to multiaxial failure in solid propellants, Siron and Duerr (92) tested two composite double-base formulations under nine distinct states of stress. The tests included triaxial poker chip, biaxial strip, uniaxial extension, shear, diametral compression, uniaxial compression, and pressurized uniaxial extension at several temperatures and strain rates. The data were reduced in terms of an empirically defined constraint parameter which ranged from —1.0 (hydrostatic compression) to +1.0 (hydrostatic tension). The parameter () is defined in terms of principal stresses and indicates the tensile or compressive nature of the stress field at any point in a structure —i.e.,... 

On the other hand, San Miguel and Duran (Ref 125) showed that the mechanical properties of polyurethane solid proplnt were degraded significantly by gamma irradiation dosages greater than 106 R. The tests used to determine the effects were by swelling, torsion, uniaxial tension and multiaxial tension... 

ISO 4600 details a ball or pin impression method for determining the ESCR. In this procedure, a hole of specified diameter is drilled in the plastic. An oversized ball or pin is inserted into the hole, and the polymer is exposed to a stress cracking agent. The applied deformation, given by the diameter of the ball or pin, is constant. The test is multiaxial, relatively easy to perform, and with not very well-defined specimens, and the influence of the surface is limited. Drawbacks are the small testing surface and the undefined stress state. After exposure, tensile or flexural tests may be performed on the specimens. This leads to the determination of either the residual tensile strength or the residual deformation at break. 

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) ... 

In practice, however, the multiaxial stress applied in a falling dart test without a preferred direction, has to be expected. This is addressed by the Gardner test of ASTM, in which a falling dart strikes centrally on a flat surface (e.g. a circular disk). The results of both test methods are important polymer design considerations. 

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 ... 

Hyperelastic finite element analysis Accommodates complex geometries. Can handle nonlinearity in material behavior and large strains. Rapid analysis possible. Standard material models available. Does not include rate-dependent behavior. Cannot predict permanent deformation. Does not handle hysteresis. Some material testing may be required. Can produce errors in multiaxial stress states. 

Finally, to examine the multiaxial behavior of the glass-filled PTFE material, a set of small punch ex-perimentst l were performed. In these tests, a cylindrical specimen with a diameter of 6 mm and a thickness of 0.5 mm was indented by a spherical punch head (Fig. 11.17). 

ISO 6603-2, Determination of multiaxial impact behaviour of rigid plastics Part 2 Instrumented puncture test, 1989. 

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