Predicting the failure of ultrasonic spot welds by pull-out from sheet metal

AbstractA methodology for determining the cohesive fracture parameters associated with pull-out of spot welds is presented. Since failure of a spot weld by pull-out occurs by mixed-mode fracture of the base metal, the cohesive parameters for ductile fracture of an aluminum alloy were determined and then used to predict the failure of two very different spot-welded geometries. The fracture parameters (characteristic strength and toughness) associated with the shear and normal modes of ductile fracture in thin aluminum alloy coupons were determined by comparing experimental observations to numerical simulations in which a cohesive-fracture zone was embedded within a continuum representation of the sheet metal. These parameters were then used to predict the load–displacement curves for ultrasonically spot-welded joints in T-peel and lap-shear configurations. The predictions were in excellent agreement with the experimental data. The results of the present work indicate that cohesive-zone models may be very useful for design purposes, since both the strength and the energy absorbed by plastic deformation during weld pull-out can be predicted quite accurately

Equilibrium and dynamical properties of the ANNNI chain at the multiphase point

We study the equilibrium and dynamical properties of the ANNNI (axial next-nearest-neighbor Ising) chain at the multiphase point. An interesting property of the system is the macroscopic degeneracy of the ground state leading to finite zero-temperature entropy. In our equilibrium study we consider the effect of softening the spins. We show that the degeneracy of the ground state is lifted and there is a qualitative change in the low temperature behaviour of the system with a well defined low temperature peak of the specific heat that carries the thermodynamic ``weight'' of the ground state entropy. In our study of the dynamical properties, the stochastic Kawasaki dynamics is considered. The Fokker-Planck operator for the process corresponds to a quantum spin Hamiltonian similar to the Heisenberg ferromagnet but with constraints on allowed states. This leads to a number of differences in its properties which are obtained through exact numerical diagonalization, simulations and by obtaining various analytic bounds.Comment: 9 pages, RevTex, 6 figures (To appear in Phys. Rev. E

The Ten Martini Problem

We prove the conjecture (known as the ``Ten Martini Problem'' after Kac and Simon) that the spectrum of the almost Mathieu operator is a Cantor set for all non-zero values of the coupling and all irrational frequencies.Comment: 31 pages, no figure

Sample-size dependence of the ground-state energy in a one-dimensional localization problem

We study the sample-size dependence of the ground-state energy in a one-dimensional localization problem, based on a supersymmetric quantum mechanical Hamiltonian with random Gaussian potential. We determine, in the form of bounds, the precise form of this dependence and show that the disorder-average ground-state energy decreases with an increase of the size $R$ of the sample as a stretched-exponential function, $\exp( - R^{z})$, where the characteristic exponent $z$ depends merely on the nature of correlations in the random potential. In the particular case where the potential is distributed as a Gaussian white noise we prove that $z = 1/3$. We also predict the value of $z$ in the general case of Gaussian random potentials with correlations.Comment: 30 pages and 4 figures (not included). The figures are available upon reques

Absolute Continuity of the Integrated Density of States for the Almost Mathieu Operator with Non-Critical Coupling

We show that the integrated density of states of the almost Mathieu operator is absolutely continuous if and only if the coupling is non-critical. We deduce for subcritical coupling that the spectrum is purely absolutely continuous for almost every phase, settling the measure-theoretical case of Problem 6 of Barry Simon's list of Schr\"odinger operator problems for the twenty-first century.Comment: 13 pages, to appear in Inv. Mat

Metastable States in Spin Glasses and Disordered Ferromagnets

We study analytically M-spin-flip stable states in disordered short-ranged Ising models (spin glasses and ferromagnets) in all dimensions and for all M. Our approach is primarily dynamical and is based on the convergence of a zero-temperature dynamical process with flips of lattice animals up to size M and starting from a deep quench, to a metastable limit. The results (rigorous and nonrigorous, in infinite and finite volumes) concern many aspects of metastable states: their numbers, basins of attraction, energy densities, overlaps, remanent magnetizations and relations to thermodynamic states. For example, we show that their overlap distribution is a delta-function at zero. We also define a dynamics for M=infinity, which provides a potential tool for investigating ground state structure.Comment: 34 pages (LaTeX); to appear in Physical Review

A parametric study of the peel test

The force required to peel a film from a substrate is generally a complex function of geometry, the constitutive properties of the film and substrate, and the interfacial cohesive properties. In most analyses, the effects of the transverse shear force that is an integral aspect of almost any peel test are neglected, although they can be incorporated in an indirect fashion through models that invoke a root-rotation angle. In this study, a complete elastic solution that incorporates all the components contributing to crack-tip deformation, including bending moment, transverse shear force and axial force, is derived in a self-consistent way. In particular, it is shown that, for a strong interface that requires a reasonably large peel strain, the transverse shear results in a significant deviation of the phase angle from earlier analyses that neglected the shear term. The present analysis also links the transverse shear component to the root-rotation angle. A cohesive-zone analysis is presented for the peeling of an elastic–plastic film. In this analysis, the interface is modeled using cohesive elements, and the film is modeled by a full, two-dimensional, finite-element analysis. This analysis allows the full effects of bending, axial loading, and transverse shear to evolve, with no a-priori assumptions being made about their relative magnitudes. The numerical results show how the peel force depends on the film thickness. When the film is relatively thin, the peel force increases with an increase in thickness as the extent of plasticity increases. This increase in plasticity is associated with (i) an increase in the contribution of bending to the deformation at the crack tip, relative to the contribution of transverse shear, and (ii) an increase in the physical limits imposed by the dimensions of the film on the volume of any crack-tip plastic zone. When the film is relatively thick, elasticity dominates the deformation of the film, and small-scale yielding effects become important. The peel force is dictated by the toughness of the interface and by crack-tip plasticity (if any) induced by the cohesive stresses. Therefore, peel forces tend to minimum values for both thick and thin films. A maximum peel force is exhibited for films with an intermediate thickness