Multiaxial extension

Failure Criterion. In the design of a propellant structure, the output of the calculation is a tensor quantity in terms of either stress or strain, which must be compared with some experimentally available failure properties. These properties are generally obtained from uniaxial and multiaxial extension... 

The generation of a practical propellant failure criterion has been the object of extensive study for several years. No completely general analytical criterion seems to be forthcoming, but significant advances in the experimental characterization of ultimate properties in multiaxial stress fields promise more reasonable empirical guidelines. 

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.,... 

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... 

PS or copolymers are used extensively in injection blow molding. Tough and craze-resistant PS containers have been made by multiaxially oriented injection-molded parisons (238). This process permits the design of blow-molded objects with a high degree of controlled orientation, independent of blow ratio or shape. 

However, several papers have been published on the development of polynomial criteria for fatigue failure or dealing with the extension of existing static criteria to life prediction for local as well as global multiaxial cyclic loadings. Examples are reported in Refs [10,19,20,23,24,26,34,35,37,58—67] and some of them are briefly discussed below. 

The present section deals with the review and extension of Schapery s single integral constitutive law to two dimensions. First, a stress operator that defines uniaxial strain as a function of current and past stress is developed. Extension to multiaxial stress state is accomplished by incorporating Poisson s effects, resulting in a constitutive matrix that consists of instantaneous compliance, Poisson s ratio, and a vector of hereditary strains. The constitutive equations thus obtained are suitable for nonlinear viscoelastic finite-element analysis. 

Various arrangements of rotating clamps (/fC, ) for multiaxial elongation, (a) Equi-biaxial S = sample C,- = one of eight pairs of scissors transducers 7) (T-L of Figure 7.4.2) record the forces, (b) Planar clamps A-F rotate with constant speed, while G and H remain stationary, recording only force. L = 158 mm. If only G and H rotate and A-F are removed, we have uniaxial extension of a strip, (c) Multiaxial with m = 0.5 (eq. 7.1.4) ellipse axes a = 268 mm, b = 380 mm. From Meissner et al. (1982) and Demarmels and Meissner (1985). 

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. 

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