Triaxial stress state

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

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 ... 

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). 

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). 

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). 

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.

Figure 18. Effect of interparticle distance, A, on plastic deformation of matrix strands between particles (a) definitions of the size parameters D = particle diameter, vP = particle volume content, aQ = applied stress, and aK = stress concentration (b) with a small interparticle distance, a uniaxial stress state is dominant between the particles and microvoids after cracking of the particles, and plastic yielding can be obtained and (c) with a large interparticle distance, thick matrix strands favor a triaxial stress state between the particles and microvoids, and plastic yielding is hindered.

The effect necessary for stress transformation from a triaxial stress state into a more uniaxial stress state requires relatively small interparticle distances because the stress state must be changed in the whole polymeric material between particles. This fact may explain the experimental results for critical in-... 

Case c stress-induced formation of shear deformation. The stress concentration of the modifier particles, usually too small, is increased by the formation of cavities inside the particles. By these cavities, and if A is small enough, the originally triaxial stress state between particles is transformed into a more uniaxial stress state. Then the matrix strands between particles can be plastically deformed where the necessary volume increase, which arises from the cavitated particles, appears. 

Figure 7.41a shows the sample-based coordinate system used to deduce the basic equations for stress measurements. The lattice deformations cL(p measured close to the surface obtained according to Eq. (7.8) in the directions q>, yr are taken as the deformations i.ql expected from the theory of elasticity. The angle cp is the azimuthal angle to the x-axis, and the angle y/ is the distance angle to the z-axis, that is the surface normal N of the sample. For a triaxial stress state oq, av [Pg.361]

Both AS ME Code, Section 1I1, Division 2 and AS ME Code, Section III, utilize the maximum shear stress criterion. This theor) closely approximates experimental results and is also easy to use. This theory also applies to triaxial states of stress. In a triaxial stress state, this theory predicts that yielding will occur whenever one-half the algebraic difference betu een the maximum and minimum stress is equal to one-half the yield stress. Where 0 > a i> 0.3. the maximum shear stress is (oi —03)72. 

Total energy actually absorbed by rock samples under triaxial stress state ... 

If purely elastic behaviour is considered, elastic response of the adhesive may be obtained by attaching extensometers to the adherend either side of the bondline, making a suitable correction for adherend strain. Beyond the elastic limit, yield of the adhesive may be suppressed by the triaxial stress state, occurring at a stress higher than that in uniaxial tension. On the other hand, brittle adhesives which fracture before they yield will probably indicate a low failing stress because of stress concentrations. 

Plane strain defines a triaxial stress state at the crack tip, which is, for example, the case for a thick block of material. Plane stress is typical for thin samples where there is no stress acting normal to the plane of the sample. 

For an isotropic material, the creep functions B t) and C(r) are determined using the same procedure. For an axisymmetric triaxial stress state, let cti be the axial stress, CT3(< o) (with >2 = 0 ) the confining pressure, i the measured axial strain and 3 the measured lateral strain. Then setting... 

In this Section we present an outline of the Cam clay model. Note that we assume a conventional triaxial stress state ox = aj), and the following variables for stress and strain are introduced ... 

Loading of the material in a triaxial stress state that keeps Mohr s circle small and shifts it to the right in the direction of the cleavage strength. Such a stress state can be found in the notched bar impact bending test [42]. In components, changes in cross section and notches cause such... 

The maximum external force during the test is larger in the notched than in the un-notched case. This is again due to the triaxial stress state and can be explained in the same way as for the onset of yielding above. It has to be kept in mind that the diameter of the un-notched specimen is the same as that of the notched specimen at the notch position. Thus, it should not be assumed that a specimen can be made stronger by notching it. 

---