Linking high and low temperature plasticity in bulk metallic glasses II: use of a log-normal barrier energy distribution and a mean field description of high temperature plasticity

A thermal activation model to describe the plasticity of bulk metallic glasses (Derlet and Maa\ss, Phil. Mag. 2013, DOI: 10.1080/14786435.2013.826396) which uses a distribution of barrier energies and some aspects of under-cooled liquid physics is developed further. In particular, a log-normal distribution is now employed to describe the statistics of barrier energies. A high temperature mean-field description of homogeneous macro-plasticity is then developed and is shown to be similar to a thermal activation picture employing a single characteristic activation energy and activation volume. In making this comparison, the activation volume is interpreted as being proportional to the average mean-square-value of the plastic shear strain magnitude within the material. Also, the kinetic fragility at the glass transition temperature is shown to represent the effective number of irreversible structural transformations available at that temperature.Comment: 28 pages, 2 figure

Linking high and low temperature plasticity in bulk metallic glasses: thermal activation, extreme value statistics and kinetic freezing

At temperatures well below their glass transition, the deformation properties of bulk metallic glasses are characterised by a sharp transition from elasticity to plasticity, a reproducible yield stress, and an approximately linear decrease of this stress with increasing temperature. In the present work it shown that when the well known properties of the under-cooled liquid regime, in terms of the underlying potential energy landscape, are assumed to be also valid at low temperature, a simple thermal activation model is able to reproduce the observed onset of macro-scopic yield. At these temperatures, the thermal accessibility of the complex potential energy landscape is drastically reduced, and the statistics of extreme value and the phenomenon of kinetic freezing become important, affecting the spatial heterogeneity of the irreversible structural transitions mediating the elastic-to-plastic transition. As the temperature increases and approaches the glass transition temperature, the theory is able to smoothly transit to the high temperature deformation regime where plasticity is known to be well described by thermally activated viscoplastic models.Comment: 43 pages, 9 figures, Appears in Philosophical Magazin

A probabilistic explanation for the size-effect in crystal plasticity

In this work, the well known power-law relation between strength and sample size, $d^{-n}$, is derived from the knowledge that a dislocation network exhibits scale-free behaviour and the extreme value statistical properties of an arbitrary distribution of critical stresses. This approach yields $n=(\tau+1)/(\alpha+1)$, where $\alpha$ reflects the leading order algebraic exponent of the low stress regime of the critical stress distribution and $\tau$ is the scaling exponent for intermittent plastic strain activity. This quite general derivation supports the experimental observation that the size effect paradigm is applicable to a wide range of materials, differing in crystal structure, internal microstructure and external sample geometry.Comment: 22 pages, 4 figures, to be published in Phil. Ma

AN INVESTIGATION OF THE POROUS SILICON OPTICAL-ABSORPTION POWER-LAW NEAR THE BAND-EDGE

A theoretical investigation of the absorption coefficient of p-type doped porous silicon near the band edge is presented. We assume that the absorption coefficient is constructed by taking an average over a distribution (in terms of band gap) of absorption coefficients of individual crystallites. Exploiting physics fundamental to the crystallite optical absorption process, we derive the relation between the absorption coefficient and the averaged conduction density of states near the band edge for porous silicon. By postulating a specific form for the effective conduction density of states we find excellent agreement with recent optical absorption data for p-type doped porous silicon. We attempt to explain the basis for this postulate phenomenologically by suggesting a certain large-scale behaviour of the particle size distribution. The implication of further experimental verification will be discussed

Thermal-activation model for freezing and the elastic robustness of bulk metallic glasses

Despite significant atomic-scale heterogeneity, bulk metallic glasses well below their glass transition temperature exhibit a surprisingly robust elastic regime and a sharp elastic-to-plastic transition. Here it is shown that, when the number of available structural transformations scales exponentially with system size, a simple thermal-activation model is able to describe these features, where yield corresponds to a change from a barrier energy dominated to a barrier entropy dominated regime of shear transformation activity, allowing the system to macroscopically exit its frozen state. A yield criterion is then developed, which describes well the existing experimental data and motivates future dedicated deformation experiments to validate the model

Shear-band arrest and stress overshoots during inhomogeneous flow in a metallic glass

At the transition from a static to a dynamic deformation regime of a shear band in bulk metallic glasses, stress transients in terms of overshoots are observed. We interpret this phenomenon with a repeated shear-melting transition and are able to access a characteristic time for a liquidlike to solidlike transition in the shear band as a function of temperature, enabling us to understand why shear bands arrest during inhomogenous serrated flow in bulk metallic glasses