Engineering topics

Bouchbinder, Eran

Publications and source records attributed to Bouchbinder, Eran.

4 records

DOE OSTI2018

Universality and Stability Phase Diagram of Two-Dimensional Brittle Fracture

The two-dimensional oscillatory crack instability, experimentally observed in a class of brittle materials under strongly dynamic conditions, has been recently reproduced by a nonlinear phase-field fracture theory. Here, we highlight the universal character of this instability by showing that it is present in materials exhibiting widely different near crack tip elastic nonlinearity, and by demonstrating that the oscillations wavelength follows a universal master curve in terms of dissipation-related and nonlinear elastic intrinsic length scales. Moreover, we show that upon increasing the driving force for fracture, a high-velocity tip-splitting instability emerges, as experimentally demonstrated. The analysis culminates in a comprehensive stability phase diagram of two-dimensional brittle fracture, whose salient properties and topology are independent of the form of near tip nonlinearity.

36 MATERIALS SCIENCE↗

DOE OSTI2017

Instability in dynamic fracture and the failure of the classical theory of cracks

Cracks, the major vehicle for material failure, undergo a micro-branching instability at ~40% of their sonic limiting velocity in three dimensions. Recent experiments showed that in thin systems cracks accelerate to nearly their limiting velocity without micro-branching, until undergoing an oscillatory instability. Despite their fundamental importance, these dynamic instabilities are not explained by the classical theory of cracks, which is based on linear elasticity and an extraneous local symmetry criterion to predict crack paths. We develop a two-dimensional theory for predicting arbitrary paths of ultrahigh-speed cracks, which incorporates elastic nonlinearity without extraneous criteria. We show that cracks undergo an oscillatory instability controlled by small-scale, near crack-tip, elastic nonlinearity. This instability occurs above an ultrahigh critical velocity and features an intrinsic wavelength proportional to the ratio of the fracture energy to the elastic modulus, in quantitative agreement with experiments. As a result, this ratio emerges as a fundamental scaling length assumed to play no role in the classical theory of cracks, but shown here to strongly influence crack dynamics.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2016

Notch Fracture Toughness of Glasses: Dependence on Rate, Age, and Geometry

Understanding the fracture toughness (resistance) of glasses is a fundamental problem of prime theoretical and practical importance. Here we theoretically study its dependence on the loading rate, the age (history) of the glass, and the notch radius ρ. Reduced-dimensionality analysis suggests that the notch fracture toughness results from a competition between the initial, age- and history-dependent, plastic relaxation time scale τ$ ^{pl}_0 $ and an effective loading time scale τ ext ($ \dot{K} $ I , ρ ), where KI is the tensile stress-intensity-factor rate. The toughness is predicted to scale with ρ independently of ξ≡τ ext /τ$ ^{pl}_0 $ for ξ «1, to scale as T$ \sqrt{ρ} $log(ξ) for ξ«1 (related to thermal activation, where T is the temperature), and to feature a nonmonotonic behavior in the crossover region ξ~ O (1) (related to plastic yielding dynamics). These predictions are verified using 2D computations, providing a unified picture of the notch fracture toughness of glasses. Here, the theory highlights the importance of time-scale competition and far-from-steady-state elasto-viscoplastic dynamics for understanding the toughness and shows that the latter varies quite significantly with the glass age (history) and applied loading rate. Experimental support for bulk metallic glasses is presented, and possible implications for applications are discussed.

36 MATERIALS SCIENCE↗

DOE OSTI2015

An Eulerian projection method for quasi-static elastoplasticity

A well-established numerical approach to solve the Navier-Stokes equations for incompressible fluids is Chorin's projection method, whereby the fluid velocity is explicitly updated, and then an elliptic problem for the pressure is solved, which is used to orthogonally project the velocity field to maintain the incompressibility constraint. In this paper, we develop a mathematical correspondence between Newtonian fluids in the incompressible limit and hypo-elastoplastic solids in the slow, quasi-static limit. Using this correspondence, we formulate a new fixed-grid, Eulerian numerical method for simulating quasi-static hypo-elastoplastic solids, whereby the stress is explicitly updated, and then an elliptic problem for the velocity is solved, which is used to orthogonally project the stress to maintain the quasi-staticity constraint. We develop a finite-difference implementation of the method and apply it to an elasto-viscoplastic model of a bulk metallic glass based on the shear transformation zone theory. We show that in a two-dimensional plane strain simple shear simulation, the method is in quantitative agreement with an explicit method. Like the fluid projection method, it is efficient and numerically robust, making it practical for a wide variety of applications. We also demonstrate that the method can be extended to simulate objects with evolving boundaries. Here, we highlight a number of correspondences between incompressible fluid mechanics and quasi-static elastoplasticity, creating possibilities for translating other numerical methods between the two classes of physical problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗