Quadrant Of Principal Stress Space Research Articles

Stability of the Viscous-Plastic Sea Ice Rheology

The large-scale two-dimensional rheology of a sea ice pack arises from the local contact forces between adjacent does in convergence. It is conventionally modeled by a viscous-plastic constitutive relation to reflect the low or zero stress in a divergent flow field and the rate-independent ridging process in convergence. The authors demonstrate how, for a simple one-dimensional configuration, the elliptical yield curve results in tensile in-plane stresses in divergence that cause a short wave length linear instability. As the ice pack diverges, the ice strength, which is the root cause of the instability, is rapidly reduced, and so, although the model is linearly unstable, it is nonlinearly stable. The practical significance is that the model does not blow up, but systematic grid size-dependent errors associated with the linear instability are introduced throughout the pack. Artificial diffusion terms can be used to prevent the growth of the linear instability. Numerical models must almost always possess artificial diffusion to permit them to run. Here, however, the diffusion is necessary to overcome physical inaccuracies in the model. Diffusion alone is not even a total cure. Generally, diffusive coefficients shrink as a power of the grid size, so as model resolution becomes finer, a previously stable algorithm will become unstable. The problem can be properly posed by constraining the yield curve to lie within the third quadrant of principal stress space.

On criteria for craze initiation in glassy polymers

The previous published data on biaxial critical stresses for craze initiation on the surface of cylindrical specimen of glassy polymers have been reexamined. A new interpretation is presented for the trend of crazing stress near pure shear state in the second quadrant of principal stress space which was observed in air at elevated temperatures. That is, an increase in the tensile stress for crazing with an increase in the magnitude of the compressive stress is interpreted not to be followed by a decrease in the dilatational stress but by development of shear yielding. On the basis of this interpretation, a new empirical criterion for craze initiation is proposed by considering the stress concentration due to surface scratch. The theoretical crazing locus accorded with the previous experimental results, except for the data near the shear yield locus in the second quadrant, which were considered to be affected by shear yielding. It was also indicated in the calculation that the shape and direction of surface scratch exert a considerable influence on the trend of biaxial crazing stress.

Fracture of A12O3 in Combined Tension/Torsion: I, Experiments

Combined tension/torsion tests were performed on solid A12O3 rods at principal stress ratios σ2/σ1 of 0 (pure tension), ‐0.17, ‐0.38, ‐0.78, and ‐1.0 (pure torsion). The tensile principal stress at fracture σ1 increased with increasing compressive principal stress σ2, resulting in a higher strength in torsion than uniaxial tension. The ratio σ1 (torsion)σ1 (tension) was 1.31 for A12O3, in general agreement with limited torsional data for brittle materials in the literature. Brittle fracture data in the tension‐compression quadrant of principal stress space show an interesting dichotomy since strengthening is observed in torsional investigations, whereas weakening is observed for pressurized‐tube studies. This difference may be either a pressurized‐tube test artifact or a real effect due to the presence of stress gradients.

Yielding of glassy polymers in the second quadrant of principal stress space

Abstract Second quadrant crazing and shear yielding studies were performed on glassy poly(methyl methacrylate) by means of combined torsion-tension loading. The results are in quantitative agreement with the shear and normal stress yielding criteria proposed by Sternstein and Ongchin. It is shown that four distinct regions of material response exist in the second quadrant and, depending on the stress state, 1) no crazing and no shear yielding, 2) crazing alone, 3) shear yielding alone, or 4) crazing and shear yielding can occur. An analysis of stress field induced brittle-ductile transitions is presented which is in agreement with other studies of high-pressure yielding.