Brittle fracture, theory

This equation for lap joint failure is surprising in a number of ways. It is equivalent to Griffith s brittle fracture theory for glass [4], Moreover, it fits the puzzling historic results for lap joint failure which showed that the overlap length was not important for long joints, and the strength increased with sheet thickness d and stiffness E. Additionally, it is now clear why chemical environment can weaken the Joint because the failure depends on work of adhesion W, which decreases markedly with surface contamination. 

Basically the brittle fracture theory assumes that stress at the vicinity of a crack (Fig. 4.16) due to a load applied perpendicular to the direction of crack is given by the following expressions ... 

Carpick, R.W., Enachescu, M., Ogletree, D.F. and Salmeron, M., Making, breaking, and sliding of nanometer-scale contacts. In Beltz, G.E., Selinger, R.L.B., Kim, K.-S. and Marder, M.P., (Eds.), Fracture and Ductile vs. Brittle Behavior-Theory, Modeling and Experiment. Materials Research Society, Warrendale, PA, 1999, pp. 93-103. 

An example of a theory is the Griffith theory. It expresses the strength of a material in terms of crack length and fracture surface energy. Brittle fracture is based on the idea that the presence of cracks determines the brittle... 

The relationship of brittle fracture to plastic deformation has, of course, been elaborated in various ways with the aid of dislocation theory, e.g. nucleation of microcracks has been discussed in terms of piling-up of dislocations [124]. Davies [145] has shown that embrittlement requires the presence of islands of martensite (about 1 pm in size) and has suggested that cracks are initiated in the martensite or at the martensite-ferrite interface. 

G.I. Barenblatt, Mathematical Theory of Equilibrium Cracks in Brittle Fracture, Advanced Applied Mechanics, Vol.7,1962, p.55. 

Volume 539— Fracture and Ductile vs. Brittle Behavior—Theory, Modelling and... 

Applications of linear elastic fracture mechanics (primarily) to the brittle fracture of solid polymers is discussed by Professor Williams. For those not versed in the theory of fracture mechanics, this paper should serve as an excellent introduction to the subject. The basic theory is developed and several variants are then introduced to deal with weak time dependence in solid polymers. Previously unpublished calculations on failure times and craze growth are presented. Within the framework of brittle fracture mechanics and testing this paper provides for a systematic approach to the faOure of engineering plastics. 

It will be shown in Chapter 11 that the correlations developed in this monograph can be combined with other correlations that are found in the literature (preferably with the equations developed by Seitz in the case of thermoplastics, and with the equations of rubber elasticity theory with finite chain extensibility for elastomers), to predict many of the key mechanical properties of polymers. These properties include the elastic (bulk, shear and tensile) moduli as well as the shear yield stress and the brittle fracture stress. In addition, new correlations in terms of connectivity indices will be developed for the molar Rao function and the molar Hartmann function whose importance in our opinion is more of a historical nature. A large amount of the most reliable literature data on the mechanical properties of polymers will also be listed. The observed trends for the mechanical properties of thermosets will also be discussed. Finally, the important and challenging topic of the durability of polymers under mechanical deformation will be addressed, to review the state-of-the-art in this area where the existing modeling tools are of a correlative (rather than truly predictive) nature at this time. 

Weibull developed his statistical theory of brittle fracture on the basis of the weakest link hypothesis, i.e. the specimen fails if its weakest element fails [6, 7], In its simplest form and for an uniaxial homogenous and tensile stress state, ct, and for specimens of the volume, F, the so called Weibull distribution of the probability of failure, F, is given by ... 

The Griffith theory of brittle fracture postulates that the fracture is due to ... 

There is, however, no generally accepted theory for predicting the brittle-ductile transition or relating it to other properties of the polymer, although for some polymers it is closely related to the glass transition. The type of failure is also affected by geometrical factors and the precise nature of the stresses applied. Plane-strain conditions, under which one of the principal strains is zero, which are often found with thick samples, favour brittle fracture. Plane-stress conditions, xmder which one of the principal stresses is zero, which are often found with thin samples, favour ductile fracture. The type of starting crack or notch often deliberately introduced when fracture behaviour is examined can also have an important effect ... 

There are two principal theories, or models, that attempt to describe what happens during brittle fracture, the Griffith fracture theory and the Irwin model. Both assume that fracture takes place through the presence of preexisting cracks or flaws in the polymer and are concerned with what happens near such a crack when a load is applied. Each leads to the definition of a fracture-toughness parameter and the two parameters are closely related to each other. The Griffith theory is concerned with the elastically stored energy near the crack, whereas the Irwin model is concerned with the distribution of stresses near the crack. Both theories apply strictly only for materials that are perfectly elastic for small strains and are therefore said to describe linear fracture mechanics. 

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