A quadratic viscous fluid law for ice deduced from Steinemann's uni-axial compression and torsion experiments

The response of ice to applied stress on ice-sheet flow timescales is commonly described by a non-linear incompressible viscous fluid, for which the deviatoric stress has a quadratic relation in the strain rate with two response coefficient functions depending on two principal strain-rate invariants I2 and I3. Commonly, a coaxial (linear) relation between the deviatoric stress and strain rate, with dependence on one strain-rate invariant I2 in a stress formulation, equivalently dependence on one deviatoric stress invariant in a strain-rate formulation, is adopted. Glen's uni-axial stress experiments determined such a coaxial law for a strain-rate formulation. The criterion for both uni-axial and shear data to determine the same relation is determined. Here, we apply Steinemann's uni-axial stress and torsion data to determine the two stress response coefficients in a quadratic relation with dependence on a single invariant I2. There is a non-negligible quadratic term for some ranges of I2; that is, a coaxial relation with dependence on one invariant is not valid. The data does not, however, rule out a coaxial relation with dependence on two invariants.

The ephemeral development of C' shear bands

<p>C' shear bands are common structures in ductile shear zones but their development is poorly understood. They occur in rocks with a high mechanical strength contrast so we used numerical models of viscoplastic deformation to study the effect of the proportion of weak phase and the phase strength contrast on C' shear band development. We employed simple shear to a finite strain of 18 in 900 steps and recorded the microstructure, stress and strain distribution at each step. We found that C' shear bands form in models with ≥5% weak phase when there is a moderate or high phase strength contrast, and they occur in all models with weak phase proportions ≥15%. Contrary to previous research, we find that C' shear bands form when layers of weak phase parallel to the shear zone boundary rotate forwards. This occurs due to mechanical instabilities that are a result of heterogeneous distributions of stress and strain rate. C' shear bands form on planes of low strain rate and stress, not in sites of maximum strain rate as has previously been suggested. C' shear bands are ephemeral and they either rotate backwards to the C plane once they are inactive or rotate into the field of shortening and thicken to form X- and triangle- shaped structures.</p>

Effect of Anisotropy, Temperature, Strain Rate on deep drawing using Conical Die

This paper covers the role of anisotropy, temperature, and strain rate on the flow behavior of the material when a conical die is used instead of conventional blank holder. The effect of anisotropy was investigated using Lankford’s coefficient (r) in three directions (0°, 45°, and 90°). The effect of working temperatures (Room temperature, 100°C - 300°C) on drawing stress and strain rate sensitivity on punch pressure were also investigated in detail. ANSYS APDL was used to investigate the effects of temperature, strain rate and anisotropy. The simulation results have confirmed that the strain variation in the direction of r0 and r45 are more than the variation of r90.

Traction and strain-rate at the base of the lithosphere: an insight into cratonic survival

SUMMARY Cratons are the oldest parts of the lithosphere, some of them surviving since Archean. Their long-term survival has sometimes been attributed to high viscosity and low density. In our study, we use a numerical model to examine how shear tractions exerted by mantle convection work to deform cratons by convective shearing. We find that although tractions at the base of the lithosphere increase with increasing lithosphere thickness, the associated strain-rates decrease. This inverse relationship between stress and strain-rate results from lateral viscosity variations along with the model’s free-slip condition imposed at the Earth’s surface, which enables strain to accumulate along weak zones at plate boundaries. Additionally, we show that resistance to lithosphere deformation by means of convective shearing, which we express as an apparent viscosity, scales with the square of lithosphere thickness. This suggests that the enhanced thickness of the cratons protects them from convective shear and allows them to survive as the least deformed areas of the lithosphere. Indeed, we show that the combination of a smaller asthenospheric viscosity drop and a larger cratonic viscosity, together with the excess thickness of cratons compared to the surrounding lithosphere, can explain their survival since Archean time.

Lower-crustal rheology and thermal gradient in the Taiwan orogenic belt illuminated by the 1999 Chi-Chi earthquake

The strength of the lithosphere controls tectonic evolution and seismic cycles, but how rocks deform under stress in their natural settings is usually unclear. We constrain the rheological properties beneath the Taiwan orogenic belt using the stress perturbation following the 1999 Chi-Chi earthquake and fourteen-year postseismic geodetic observations. The evolution of stress and strain rate in the lower crust is best explained by a power-law Burgers rheology with rapid increases in effective viscosities from ~1017to ~1019Pa s within a year. The short-term modulation of the lower-crustal strength during the seismic cycle may alter the energy budget of mountain building. Incorporating the laboratory data and associated uncertainties, inferred thermal gradients suggest an eastward increase from 19.5±2.5°C/km in the Coastal Plain to 32±3°C/km in the Central Range. Geodetic observations may bridge the gap between laboratory and lithospheric scales to investigate crustal rheology and tectonic evolution.