Showing papers by "John W. Hutchinson published in 1976"

Bounds and Self-Consistent Estimates for Creep of Polycrystalline Materials

Abstract: A study of steady creep of face centred cubic (f.c.c.) and ionic polycrystals as it relates to single crystal creep behaviour is made by using an upper bound technique and a self-consistent method. Creep on a crystallographic slip system is assumed to occur in proportion to the resolved shear stress to a power. For the identical systems of an f.c.c. crystal the slip-rate on any system is taken as $\gamma =\alpha (\tau /\tau \_{0})^{n}$ where $\alpha $ is a reference strain-rate $\tau $ is the resolved shear stress and $\tau \_{0}$ is the reference shear stress. The tensile behaviour of a polycrystal of randomly orientated single crystals can be expressed as $\overline{\epsilon}=\alpha (\overline{\sigma}/\overline{\sigma}\_{0})^{n}$ where $\overline{\epsilon}$ and $\overline{\sigma}$ are the overall uniaxial strain-rate and stress and $\overline{\sigma}\_{0}$ is the uniaxial reference stress. The central result for an f.c.c. polycrystal in tension can be expressed as $\overline{\sigma}\_{0}=h(n)\tau \_{0}$. Calculated bounds to $h(n)$ coincide at one extreme $(n=\infty)$ with the Taylor result for rigid/perfectly plastic behaviour and at the other $(n=1)$ with the Voigt bound for linear viscoelastic behaviour. The self-consistent results, which are shown to be highly accurate for $n=1$, agree closely with the upper bound for $n\geq 3$. Two types of glide systems are considered for ionic crystals: A-systems, {110} $\langle 110\rangle $, with $\gamma =\alpha (\tau /\tau \_{\text{A}})^{n}$; and B-systems, {100} $\langle 110\rangle $, with $\gamma =\alpha (\tau /\tau \_{\text{B}})^{n}$. The upper bound to the tensile reference stress $\overline{\sigma}\_{0}$ is shown to have the simple form $\overline{\sigma}\_{0}\leq A(n)\tau \_{\text{A}}+B(n)\tau \_{\text{B}};A(n)$ and $B(n)$ are computed for the entire range of $n$, including the limit $n=\infty $. Self-consistent predictions are again in good agreement with the bounds for high $n$. Upper bounds in pure shear are also calculated for both f.c.c. and ionic polycrystals. These results, together with those for tension, provide a basis for assessing the most commonly used stress creep potentials. The simplest potential based on the single effective stress invariant is found to give a reasonably accurate characterization of multiaxial stress dependence.

Analytical and Numerical Study of the Effects of Initial Imperfections on the Inelastic Buckling of a Cruciform Column

Abstract: The inelastic buckling of a cruciform column is investigated by a combination of analytical and numerical methods. An exact asymptotic analysis for the effect of small imperfections on the maximum load reveals clearly how it is possible for an exceedingly small imperfection to have a very large influence. As long as the strain hardening is sufficiently low, the numerical analysis confirms the Onat- Drucker conclusion that unavoidably small imperfections, together with the use of J2 flow theory, give rise to a maximum load prediction which is approximated by the bifurcation load prediction based on a deformation theory of plasticity.