A comparison of reaction rate models for the fracture of solids

Henderson, C. B.; Graham, Peter; Robinson, Courtland N.

doi:10.1007/bf00183657

Cited by 37 publications

(12 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This essential tail property, along with the Weibull distribution itself, was first derived in 1928 by Fisher and Tippett (1928) from the stability postulate of extreme value statistics of a set of independent, identically distributed, random variables. Of course, the RVEs in a material are not perfectly statistically independent, but the stability postulate can also be justified for correlated random systems (such as percolation models, Bazant, 2000Bazant, , 2002van der Hofstad and Redig, 2006) using renormalization group methods, which homogenize the system recursively up to a scale (of the RVE) where correlations become negligible. Aside from the assumption of independence, however, the FisherTippett argument has nothing to do with physics per se, and for a long time it has not been clear whether the power-law tail would apply only for probabilities so small (e.g.…”

Section: Strength Statisticsmentioning

confidence: 98%

Unified nano-mechanics based probabilistic theory of quasibrittle and brittle structures: I. Strength, static crack growth, lifetime and scaling

Bažant

Bazant

2011

Journal of the Mechanics and Physics of Solids

164

134

View full text Add to dashboard Cite

Section: Strength Statisticsmentioning

confidence: 98%

Unified nano-mechanics based probabilistic theory of quasibrittle and brittle structures: I. Strength, static crack growth, lifetime and scaling

Bažant

Bazant

2011

Journal of the Mechanics and Physics of Solids

164

134

View full text Add to dashboard Cite

“…The offset approach [as seen in Eq. 1, but also revised elsewhere (Henderson et al, 1970;Bartenev, 1973)] considers that the applied stresses decrease the energy barrier for bond breakage. Some simulation studies (Gagnon et al, 2001) support this interpretation, but they also give a very different mechanistic description of crack propagation, following the coalescence of voids forming ahead of the crack tip; a model that seems to be at odds with the most recent experimental investigation (Wiederhorn et al, 2013a).…”

Section: Application To Experimental Datamentioning

confidence: 99%

Parametrization in Models of Subcritical Glass Fracture: Activation Offset and Concerted Activation

et al. 2017

View full text Add to dashboard Cite

There are two established but fundamentally different empirical approaches to parametrize the rate of subcritical fracture in brittle materials. While both are relying on a thermally activated reaction of bond rupture, the difference lies in the way as to how the externally applied stresses affect the local energy landscape. In the consideration of inorganic glasses, the strain energy is typically taken as an offset on the activation barrier. As an alternative interpretation, the system's volumetric strain energy is added to its thermal energy. Such an interpretation is consistent with the democratic fiber bundle model. Here, we test this approach of concerted activation against macroscopic data of bond cleavage activation energy, and also against ab initio quantum chemical simulation of the energy barrier for cracking in silica. The fact that both models are able to reproduce experimental observation to a remarkable degree highlights the importance of a holistic consideration toward non-empirical understanding.

show abstract

“…20, which neglects any bond reformation process, was confirmed by experiments on several metals and polymers. With the advent of fracture mechanics, this approach was subsequently applied to model crack propagation rate [29,30].…”

Section: Fracture Modelsmentioning

confidence: 99%

On the Commonality Between Theoretical Models for Fluid and Solid Friction, Wear and Tribochemistry

2015

View full text Add to dashboard Cite

Tribology is concerned with the influence of mechanically applied forces on interfacial phenomena that accompany and control sliding. A wide range of models has been developed to describe these phenomena, which include frictional dissipation, wear and tribochemical reactions. This paper shows that these apparently disparate models are based on the same fundamental concept that an externally applied force accelerates the rate of thermal transition of atoms or molecules across energy barriers present in solid and liquid materials, thereby promoting flow, slip or bond cleavage. Such ''stress-assisted'' effects and the associated thermal activation concepts were developed independently and in different forms by Prandtl (Z Angew Math Mech 8:85, 1928) and Eyring (J Chem Phys 4(4): [283][284][285][286][287][288][289][290][291] 1936). These two works have underpinned subsequent theories of dry friction, boundary lubrication, EHD rheology, tribochemistry and nanoscale wear modelling. This paper first reviews the historical development of the concepts, focussing in particular on the models of Prandtl and Eyring and how they have subsequently been used and adapted by others. The two approaches are then compared and contrasted, noting that although superficially similar, they contain quite different assumptions and constraints. First, the Prandtl model assumes that the force is exerted through a compliant spring, while constant force sliding is assumed by Eyring. Second, different approximations are made in the two models to describe the change in energy barrier with external force. Prandtl explores the asymptotic behaviour of the energy barrier as the applied force become sufficiently high to reduce it to zero, while Eyring assumes that the energy barrier is reduced by an amount equal to the external work carried out on the system. The theoretical underpinnings of these differences are discussed along with the implications of compliant coupling and constant force sliding on the velocity and temperature dependence of the friction forces for the two models.

show abstract

A comparison of reaction rate models for the fracture of solids

Cited by 37 publications

References 9 publications

Unified nano-mechanics based probabilistic theory of quasibrittle and brittle structures: I. Strength, static crack growth, lifetime and scaling

Unified nano-mechanics based probabilistic theory of quasibrittle and brittle structures: I. Strength, static crack growth, lifetime and scaling

Parametrization in Models of Subcritical Glass Fracture: Activation Offset and Concerted Activation

On the Commonality Between Theoretical Models for Fluid and Solid Friction, Wear and Tribochemistry

Contact Info

Product

Resources

About