Stress triaxial

Triaxial stress states - high tensile stresses in eomparison to shear stresses... 

When a craze occurs around a rubber droplet the droplet is stressed not only in a direction parallel to the applied stress but also in the plane of the craze perpendicular to the applied stress (see Figure 3.9). Such a triaxial stress leading to dilation of the particle would be resisted by the high bulk modulus of the rubber, which would thus become load bearing. The fracture initiation stress of a polyblend should not therefore be substantially different from that of a glass. 

Figure 3.9. Rubber particle straddling craze perpendicular to stress is subjected to triaxial stresses and because of its high bulk modulus becomes load bearing. (After Bucknall )...

The foregoing are but examples of the types of mechanics of materials approaches that can be used. Other assumptions of physical behavior lead to different expressions for the four elastic moduli for a unidirectionally reinforced lamina. For example, Ekvall [3-2] obtained a modification of the rule-of-mixtures expression for and of the expression for E2 in which the triaxial stress state in the matrix due to fiber restraint is accounted for ... 

Figure 4.9 Schematic of a triaxial stress testing cell [12]...

The second noteworthy morphological feature is presented in Fig. 12b. This micrograph depicts the pre-crack front of 15-1500-70F, which had a value significantly above that of the control, as shown in Fig. 11 a. The holes may be examples of the dilatation effect observed in CTBN-modified epoxies l9,22> in which rubber particles dilate in mutually perpendicular directions under the application of a triaxial stress and then collapse into spherical cavities following fracture. Dilatation requires a mismatch in coefficients of thermal expansion of resin and rubber 11. This effect will therefore be most striking when the elastomeric phase is homogeneous, as is apparently the case here. 

The sequence of events arising during croid formation is summarized in Fig. 13.9. At the crack tip, due to a high triaxial stress field, internal... 

Crazes usually form under tensile stress when a critical strain is surpassed they do not occur under compressive stress applying hydrostatic pressure during tensile deformation can even inhibit their development. Crazes always nucleate preferentially at points of triaxial stress concentration. It is the dilatational strain which initiates crazes and cracks. 

In Charpy-like tests, a severe triaxial stress state prevails at the sample crack tip. Softer modes of loading can be of interest for specific applications. Biaxial tests like impact falling weight are therefore often used. Plaques of defined dimensions are impacted with a hemispherically tipped dart of given diameter at selected test speed(s) (often 3 ms-1 and more). 

Since crazing represents a cavitational form of plasticity, it is clear that crazes play an important role in the fracture of polymers. Crazing is, generally, involved when PC fails under plane strain conditions, e.g. in fracture mechanics tests on thick samples with sharp notches where high triaxial stresses are built... 

This early rubber cavitation is not necessary for an efficient toughening of amorphous PET because of its lower sensitivity to triaxial stress states (compared to semi-crystalline PET). 

In a bar subject to pure tension the normal stress acts only in a single direction. But in general there will be stress components in two or three directions at right angles to one another, forming so-called biaxial or triaxial stress systems. However, the stress at right angles to a free surface is always zero at that surface, so that at the surface of a body, which is the only place where we can measure stress, we... 

R. A. Winholtz and J. B. Cohen, Generalized Least-squares Determination of Triaxial Stress States by X-Rays Diffraction and the Associated Errors, A sr. J. Phys., 41 189-99 (1988). 

Stress Distributions in Rubber-Toughened Epoxy. The toughening mechanisms described in the introduction of this chapter are observed ahead of a crack, in a triaxial stress field. The simplest triaxial stress field that can be applied to the spherical cell is a pure hydrostatic stress. This stress field can be directly imposed by the application of stress, without prior knowledge of the material properties of the overall material. The shape of the deformed grid is automatically spherical, and this is the correct deformed shape. Pure hydrostatic stress was used for the detailed investigation of the stress distributions and the effect of rubber properties. 

Figure 10. Propagation scheme of the craze and of the triaxial stress state in front of the craze tip, which is necessary to transform the matrix material into crazes.

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