Dynamic Crack Tip Equation of Motion: High-speed Oscillatory Instability

A dynamic crack tip equation of motion is proposed based on the autonomy of the near-tip nonlinear zone of scale $\ell_{nl}$, symmetry principles, causality and scaling arguments. Causality implies that the asymptotic linear-elastic fields at time $t$ are determined by the crack path at a {\bf retarded time} $t-\tau_d$, where the delay time $\tau_d$ scales with the ratio of $\ell_{nl}$ and the typical wave speed $c_{nl}$ within the nonlinear zone. The resulting equation is shown to agree with known results in the quasi-static regime. As a first application in the fully dynamic regime, an approximate analysis predicts a high-speed oscillatory instability whose characteristic scale is determined by $\ell_{nl}$. This prediction is corroborated by experimental results, demonstrating the emergence of crack tip inertia-like effects.Comment: 4 pages, 2 figures; minor change

Reconstruction of potential energy profiles from multiple rupture time distributions

We explore the mathematical and numerical aspects of reconstructing a potential energy profile of a molecular bond from its rupture time distribution. While reliable reconstruction of gross attributes, such as the height and the width of an energy barrier, can be easily extracted from a single first passage time (FPT) distribution, the reconstruction of finer structure is ill-conditioned. More careful analysis shows the existence of optimal bond potential amplitudes (represented by an effective Peclet number) and initial bond configurations that yield the most efficient numerical reconstruction of simple potentials. Furthermore, we show that reconstruction of more complex potentials containing multiple minima can be achieved by simultaneously using two or more measured FPT distributions, obtained under different physical conditions. For example, by changing the effective potential energy surface by known amounts, additional measured FPT distributions improve the reconstruction. We demonstrate the possibility of reconstructing potentials with multiple minima, motivate heuristic rules-of-thumb for optimizing the reconstruction, and discuss further applications and extensions.Comment: 20 pages, 9 figure

Full-field optical measurement of curvatures in ultra-thin-film–substrate systems in the range of geometrically nonlinear deformations

This article describes coherent gradient sensing (CGS) as an optical, full-field, real-time, nonintrusive, and noncontact technique for the measurement of curvatures and nonuniform curvature changes in film-substrate systems. The technique is applied to the study of curvature fields in thin Al films (6 mum) deposited on thin circular silicon wafers (105 mum) of "large" in-plane dimensions (50.8 mm in diameter) subjected to thermal loading histories. The loading and geometry is such that the system experiences deformations that are clearly within the nonlinear range. The discussion is focused on investigating the limits of the range of the linear relationship between the thermally induced mismatch strain and the substrate curvature, on the degree to which the substrate curvature becomes spatially nonuniform in the range of geometrically nonlinear deformation, and finally, on the bifurcation of deformation mode from axial symmetry to asymmetry with increasing mismatch strain. Results obtained on the basis of both simple models and more-detailed finite-element simulations are compared with the full-field CGS measurements with the purpose of validating the analytical and numerical models

Autonomy and Singularity in Dynamic Fracture

The recently developed weakly nonlinear theory of dynamic fracture predicts $1/r$ corrections to the standard asymptotic linear elastic $1/\sqrt{r}$ displacement-gradients, where $r$ is measured from the tip of a tensile crack. We show that the $1/r$ singularity does not automatically conform with the notion of autonomy (autonomy means that any crack tip nonlinear solution is uniquely determined by the surrounding linear elastic $1/\sqrt{r}$ fields) and that it does not automatically satisfy the resultant Newton's equation in the crack parallel direction. We show that these two properties are interrelated and that by requiring that the resultant Newton's equation is satisfied, autonomy of the $1/r$ singular solution is retained. We further show that the resultant linear momentum carried by the $1/r$ singular fields vanishes identically. Our results, which reveal the physical and mathematical nature of the new solution, are in favorable agreement with recent near tip measurements.Comment: 4 pages, 2 figures, related papers: arXiv:0902.2121 and arXiv:0807.486

Non-universality in Micro-branching Instabilities in Rapid Fracture: the Role of Material Properties

In spite of the apparent similarity of micro-branching instabilities in different brittle materials, we propose that the physics determining the typical length- and time-scales characterizing the post-instability patterns differ greatly from material to material. We offer a scaling theory connecting the pattern characteristics to material properties (like molecular weight) in brittle plastics like PMMA, and stress the fundamental differences with patterns in glass which are crucially influenced by 3-dimensional dynamics. In both cases the present ab-initio theoretical models are still too far from reality, disregarding some fundamental physics of the phenomena.Comment: 4 pages, 6 figures, PRL submitte

Dislocation plasticity in thin metal films

This article describes the current level of understanding of dislocation plasticity in thin films and small structures in which the film or structure dimension plays an important role. Experimental observations of the deformation behavior of thin films, including mechanical testing as well as electron microscopy studies, will be discussed in light of theoretical models and dislocation simulations. In particular, the potential of applying strain-gradient plasticity theory to thin-film deformation is discussed. Although the results of all studies presented follow a “smaller is stronger” trend, a clear functional dependence has not yet been established

Strain induced stabilization of stepped Si and Ge surfaces near (001)

We report on calculations of the formation energies of several [100] and [110] oriented step structures on biaxially stressed Si and Ge (001) surfaces. It is shown that a novel rebonded [100] oriented single-height step is strongly stabilized by compressive strain compared to most well-known step structures. We propose that the side walls of ``hut''-shaped quantum dots observed in recent experiments on SiGe/Si films are made up of these steps. Our calculations provide an explanation for the nucleationless growth of shallow mounds, with steps along the [100] and [110] directions in low- and high-misfit films, respectively, and for the stability of the (105) facets under compressive strain.Comment: to appear in Appl. Phys. Lett.; v2=minor corrections,figs resize

Finite Element Analysis of Strain Effects on Electronic and Transport Properties in Quantum Dots and Wires

Lattice mismatch in layered semiconductor structures with submicron length scales leads to extremely high nonuniform strains. This paper presents a finite element technique for incorporating the effects of the nonuniform strain into an analysis of the electronic properties of SiGe quantum structures. Strain fields are calculated using a standard structural mechanics finite element package and the effects are included as a nonuniform potential directly in the time independent Schrodinger equation; a k-p Hamiltonian is used to model the effects of multiple valence subband coupling. A variational statement of the equation is formulated and solved using the finite element method. This technique is applied to resonant tunneling diode quantum dots and wires; the resulting densities of states confined to the quantum well layers of the devices are compared to experimental current-voltage I(V) curves.Comment: 17 pages (LaTex), 18 figures (JPEG), submitted to Journal of Applied Physic

Dissipative Visco-plastic Deformation in Dynamic Fracture: Tip Blunting and Velocity Selection

Dynamic fracture in a wide class of materials reveals "fracture energy" $\Gamma$ much larger than the expected nominal surface energy due to the formation of two fresh surfaces. Moreover, the fracture energy depends on the crack velocity, $\Gamma=\Gamma(v)$. We show that a simple dynamical theory of visco-plasticity coupled to asymptotic pure linear-elasticity provides a possible explanation to the above phenomena. The theory predicts tip blunting characterized by a dynamically determined crack tip radius of curvature. In addition, we demonstrate velocity selection for cracks in fixed-grip strip geometry accompanied by the identification of $\Gamma$ and its velocity dependence.Comment: 4 pages, 1 figures; presentation improved, refs. changed, figure omitte

The DVCS Measurement at HERA

The recent results of the studies of Deeply Virtual Compton Scattering (DVCS) events at HERA are presented. The possibility offered by this process to gain information about skewed parton distributions (SPD) is emphasized.Comment: Talk given at New Trends in HERA Physics 2001, Ringberg Castle, Tegernsee, Germany, 17-22 Jun 2001, 13 pages, 10 figures, recent ZEUS data discussed, references update