Models brittle fracture

The way of modelling brittle fracture of fibres is paved by LEFM, and good agreement between experimental results has been found. Future refinements will improve the accuracy of the predictions, in particular for anisotropic fibres where cracks propagate in mixed mode. More inputs from fractography and physical aspects of fracture will be helpful in modelling defects able to initiate cracks. 

Fig. 1.7 is a schematic plot of stress versus strain, where curve (1) models brittle fracture and curve (2) ductile fracture with large deformation. The two extreme cases... 

It is very important, from one hand, to accept a hypothesis about the material fracture properties before physical model building because general view of TF is going to change depending on mechanical model (brittle, elasto-plastic, visco-elasto-plastic, ete.) of the material. From the other hand, it is necessary to keep in mind that the material response to loads or actions is different depending on the accepted mechanical model because rheological properties of the material determine type of response in time. The most remarkable difference can be observed between brittle materials and materials with explicit plastic properties. 

Hydrogen can decrease the strength of the metal-metal bond, thereby facilitating brittle fracture. Both the decohesion and surface energy models are based on this premise. 

Film-induced cleavage models. It has been suggested that dealloying and/or vacancy injection could induce brittle fracture. The model assumes that a brittle crack initiates in a surface film or layer and this crosses the film/matrix without loss of speed. The brittle crack will continue in the ductile matrix until it eventually blunts and arrests. Verification of this model needs better understanding of the surface films and brittle fracture. (Jones)5... 

Adsorption-induced brittle fracture. This model is based on the hypothesis that adsorption of environmental species lowers the interatomic bond strength and the stress required for cleavage. This model of chemical adsorption can explain the fact that a certain alloy is susceptible to specific ions. An important factor in support of this mechanism is the existence of a critical potential below which the SCC does not occur in some systems, and this model underlines the relation between the potential value and the capacity of adsorption of the aggressive ion. It also explains the preventive action of SCC for some systems by cathodic protection. This model may interpret the rupture of plastic materials or glass. It is referred to as the stress-sorption model, and similar mechanisms have been proposed for HE and LME. In this model, the crack should propagate in a continuous way at a rate determined by the arrival of the embrittling species at the crack tip. The model does not explain how the crack maintains a sharp tip in a normally ductile material.156... 

Figure 27.19 shows the variation of U/A as a function of A, according to the proposed model of crack initiation and propagation energies. From the intercept of this plot, a fracture energy value of 4.7 kJ/m2 can be obtained for ABS. This value is much lower than that determined above, using the method developed for brittle fracture or the constant fracture energy consideration. 

Bernstein, N. Multiscale modelling of materials. In Multiscale Simulations of Brittle Fracture and the Quantum-Mechanical Nature of Bonding in Silicon, MRS 2000 Fall Meeting Proceedings, Pittsburgh, 2001 Kubin, L.P., Bassani, J.L., Cho, K., Gao, H., Selinger, R.L.B., Eds. Materials Research Society, 653. 

Fracture Stress and Strain. Yielding and plastic deformation in the schematic representation of tensile deformation were associated with microfibrillation at the interface and stretching of the microfibrils. Because this representation was assumed to apply to both the core-shell and interconnected-interface models of compatibilization, the constrained-yielding approach was used without specific reference to the microstructure of the interface. In extending the discussion to fracture, however, it is useful to consider the interfacial-deformation mechanisms. Tensile deformation culminated in catastrophic fracture when the microfibrillated interface failed. This was inferred from the quasi-brittle fracture behavior of the uncompatibilized blend with VPS of 0.5, which indicated that the reduced load-bearing cross section after interfacial debonding could not support plastic deformation. Accordingly, the ultimate properties of the compatibilized blend depended on interfacial char-... 

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. 

As indicated in section 8.1, fracture can take place in essentially two ways, either following macroscopic yield, when the fracture is said to be ductile fracture, or without macroscopic yield, when it is called brittle fracture. The present section is concerned with the brittle fracture of polymers. Experimental studies of brittle fracture can be divided broadly into two types, those that are undertaken with a view to understanding the details of what happens during fracture and those that are aimed at providing engineering data about a polymer. Experiments of the former type are often designed to test the predictions of a theoretical model, whereas experiments... 

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. 

Tests on tin oxide fiber coatings in model composite systems indicated some crack deflection at the coating-fiber interface (Siadati et al., 1991 Venkatesh and Chawla, 1992). However, tensile tests of tin oxide coated alumina fiber-reinforced alumina matrix composites demonstrated a decrease in the extent of fiber pullout as the density of the matrix phase was increased. This led to increasingly brittle fracture behavior in these composites (Goettler, 1993). Tin oxide also has thermal stability problems at elevated temperatures (Norkitis and Hellmann, 1991). For example, in the presence of air at temperatures above 1300°C (2,372°F), tin oxide (solid) decomposes into SnO (gas) and Oj (gas). This decomposition occurs at even lower temperatures when the partial pressure of oxygen in the test environment is reduced. 

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