Notch fracture toughness of glasses: Rate, age and geometry dependence

Abstract

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 $\rho$. Reduced-dimensionality analysis suggests that the notch fracture toughness results from a competition between the initial, age- and history-dependent, plastic relaxation timescale ${\tau }_0^{pl}$ and an effective loading timescale ${\tau }^{ext}({\dot{K}}_I,\rho )$, where ${\dot{K}}_I$ is the tensile stress-intensity-factor rate. The toughness is predicted to scale with $\sqrt{\rho }$ independently of $\xi \equiv {\tau }^{ext}/{\tau }_0^{pl}$ for $\xi \ll 1$, to scale as $T\sqrt{\rho }\log (\xi )$ for $\xi \gg 1$ (related to thermal activation, where $T$ is the temperature) and to feature a non-monotonic behavior in the crossover region $\xi \sim \mathcal{O}(1)$ (related to plastic yielding dynamics). These predictions are verified using novel 2D computations, providing a unified picture of the notch fracture toughness of glasses. The theory highlights the importance of timescales 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.

arXiv comment9 pages, 6 figures

References in corpus (18)

• Dynamics of Viscoplastic Deformation in Amorphous Solids
• Deformation and Failure of Amorphous Solidlike Materials
• Shear-transformation-zone theory of plastic deformation near the glass transition
• Strain localization in a shear transformation zone model for amorphous solids
• Dynamics of Shear-Transformation Zones in Amorphous Plasticity: Formulation in Terms of an Effective Disorder Temperature
• Nonequilibrium Thermodynamics of Amorphous Materials II: Effective-Temperature Theory
• Athermal Shear-Transformation-Zone Theory of Amorphous Plastic Deformation I: Basic Principles
• Rate dependent shear bands in a shear transformation zone model of amorphous solids
• Nonequilibrium Thermodynamics of Amorphous Materials III: Shear-Transformation-Zone Plasticity
• Nonequilibrium Thermodynamics of Amorphous Materials I: Internal Degrees of Freedom and Volume Deformation
• Two-temperature continuum thermomechanics of deforming amorphous solids
• Athermal Shear-Transformation-Zone Theory of Amorphous Plastic Deformation II: Analysis of Simulated Amorphous Silicon
• Linear Response Theory for Hard and Soft Glassy Materials
• An Eulerian projection method for quasi-static elastoplasticity
• Variable-amplitude oscillatory shear response of amorphous materials
• Dynamic Failure in Amorphous Solids via a Cavitation Instability
• Age dependent modes of extensional necking instability in soft glassy materials
• The Stability of an Expanding Circular Cavity and the Failure of Amorphous Solids

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