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.

Ductile fracture in plane stress

A micromechanics-based ductile fracture initiation theory is developed for high-throughput assessment of ductile failure in plane stress. A key concept is that of inhomogeneous yielding such that microscopic failure occurs in bands with the driving force being a combination of band-resolved normal and shear tractions. The new criterion is similar to the much popularized Mohr—Coulomb model, but the sensitivity of fracture initiation to the third stress invariant constitutes an emergent outcome of the formulation. Salient features of a fracture locus in plane stress are parametrically analyzed. In particular, it is shown that a finite shear ductility cannot be rationalized based on an isotropic theory that proceeds from first principles. Thus, the isotropic formulation is supplemented with an anisotropic model accounting for void rotation and shape change in order to complete the prediction of a fracture locus and compare with experiments. A wide body of experimental data from the literature is explored and a simple procedure for calibrating the theory is outlined. Comparisons with experiments are discussed in some detail.

A multiaxial prediction equation of low/medium/high cycle fatigue life of metallic materials for plain and notch components

In this paper, it is important to illustrate that, for the LCF of metallic materials, a “stress quantity” calculated based on the linear-elastic analysis of the studied component is taken to be a mechanical quantity, S, to establish a relation of the mechanical quantity, S, to the fatigue life, N, is practicable. Based on the practicability, a prediction equation, for a low/medium/high cycle fatigue life assessment of metallic materials, is proposed. The prediction equation is a stress invariant based one, in which the computation of stress invariant is on the basis of the linear-elastic analysis of the studied component. Using experimental data of plain specimens reported in literature, it is proved that the prediction equation is both accurate and high efficient. In addition, the prediction equation in conjunction with the Theory of Critical Distances and linear-elastic notch mechanics are combined to establish the fatigue life estimation equation of the notched components. Finally, using experimental data of the fatigue life of 16MnR steel, validation verification of the notch fatigue life prediction equation is given.

A hyperelastic model for soils with stress-induced and inherent anisotropy

In this paper, modelling of the superposition of stress-induced and inherent anisotropy of soil small strain stiffness is presented in the framework of hyperelasticity. A simple hyperelastic model, capable of reproducing variable stress-induced anisotropy of stiffness, is extended by replacement of the stress invariant with mixed stress–microstructure invariant to introduce constant inherent cross-anisotropic component. A convenient feature of the new model is low number of material constants directly related to the parameters commonly used in the literature. The proposed description can be incorporated as a small strain elastic core in the development of some more sophisticated hyperelastic-plastic models of overconsolidated soils. It can also be used as an independent model in analyses involving small strain problems, such as dynamic simulations of the elastic wave propagation. Various options and features of the proposed anisotropic hyperelastic model are investigated. The directional model response is compared with experimental data available in the literature.

An Extended Drucker Yield Criterion to Consider Tension–Compression Asymmetry and Anisotropy on Metallic Materials: Modeling and Verification

Pressure sensitive asymmetric Drucker yield criterion is developed to deal with pressure dependent sheet metals for instance steels and aluminum alloys. The sensitivity to pressure is conserved by introducing three-dimensional anisotropic parameters in the first stress invariant; while the third deviatoric stress invariant is remained in odd function form to consider the strength differential effect (SDE). To describe the flow stress directionalities of metallic materials, the Drucker yield function is extended using two transformation matrix consisting of anisotropic parameters. The proposed Drucker yield criterion is utilized to predict the anisotropic yield and plastic deformation of aluminum alloys with weak SDE: AA 2090-T3 with face-centered cubic (FCC) crystal systems and AA 2008-T4 with body-centered cubic (BCC) crystal systems as well as metals with strong SDE: Zirconium clock-rolled plate with hexagonal close packing (HCP) crystal systems. The comparison between the predicted anisotropic behavior and experimental results reveals that the extended anisotropic Drucker yield criterion can precisely model the anisotropy for FCC, BCC and HCP metals. The proposed function is implemented into ABAQUS VUMAT subroutines to describe the four-point bending test which is used to consider the effect of various yield functions and material orientations on deformation behavior. The obtained contours of the cross-section, strain components distribution and also the shift of neutral layer indicate that the extended Drucker yield function can well predict the final geometric configuration of the deformed Zirconium beam.

Characterization of Adhesion Properties by Delamination of Ceramic-Metal Interfaces in Four Point Bending

The adhesive strength of ceramic - copper interfaces was measured in four point bending using a central notch for crack initiation. According to our method, plastic deformation may occur during the delamination process. FEM simulations were employed in order to separate elastic and plastic contributions to the energy consumption of the experiment. In conclusion, a novel delamination criterion based on the stress intensity at the crack tip was established. Here, the stress invariant J3is used as indicator for delamination of the interface. Agreement between experiments and theoretical interpretation is demonstrated for copper layers directly bonded to aluminum oxide.