Normal Stress Effects in the Creep of Ice

Abstract

AbstractMost non-linear fluids for which the appropriate measurements have been made exhibit non-zero and unequal normal stress differences in shearing flows. Power-law models such as Glen’s law cannot represent this phenomenon. The simplest constitutive equation that does embody normal stress effects defines the second-order fluid. An exact analytical solution for biaxial creep of such a fluid is fit to data from four tests on polycrystalline ice. The model gives an excellent representation of both primary and secondary creep. The fits provide values for the three material constants. These coefficients indicate positive first and second normal stress differences. One consequence is the prediction that a steady open-channel flow will exhibit a longitudinal free-surface depression of up to several meters for sufficiently thick ice on steep slopes. In addition, the compressive principal stress at the channel margin is decreased and the tensile principal stress is increased in magnitude over those predicted by models without normal stresses. The normal stresses thus favor the formation of crevasses. Furthermore, the angle these crevasses form with the channel margin is decreased.