Quasi-elastic fracture

Irwin proposed the concept of quasi-elastic fracture, which allows us to extend the limits of applicability of Griffith s theory [11], Irwin s criterion is valid not only for brittle materials, but also for elastic-plastic materials with significant plastic deformation developing until the moment of actual destruction of a material. 

For many engineering applications, impact fracture behavior is of prime practical importance. While impact properties of plastics are usually characterized in terms of notched or un-notched impact fracture energies, there has been an increasing tendency to also apply fracture mechanics techniques over the last decade [1, 2 and 3]. For quasi-brittle fracture, a linear elastic fracture mechanics (LEFM) approach with a force based analysis (FBA) is frequently applied to determine fracture toughness values at moderate loading rates. 

High rate fracture parameters are important in the assessment of structural integrity, particularly in applications where there is a risk of rapid crack propagation. Linear elastic fracture mechanics provide a method for assessing fracture parameters under quasi-static conditions but under impact conditions various dynamic effects make both experimental measurement and analysis difficult. 

C/SiC composites show a quasi-ductile fracture behaviour, derived from mechanisms like crack deflection and fibre pullout. Figure 14 shows exemplarily these effects within a C/C-SiC composite. The linear-elastic behaviour of C/SiC is less pronounced than for example SiC/SiC composites due to the inherent microcracks in the matrix which occur during cooling-down from processing to room temperature because of the high thermal mismatch between C-fibres and SiC-matrix. 

The mechanical properties of asbestos fibre cements may be calculated from the law of mixtures or by using the fracture mechanics formulae from which can be seen the specific work of fracture and R-curve. Mai, et al. (1980) observed also that crack initiation was close to the bending strength, which was related to a quasi elastic and brittle behaviour. For specimens with a depth greater than 50 mm the size effect on mechanical behaviour was negligible. For smaller specimens the pull-out fibres across cracks could not be developed before quick crack propagation took place followed by the failure of the specimen. 

In this study we have investigated the structural and interaction parameters of ternary water/octane/CiaEs system by means of SAXS. Phase behavior of this system was studied by Kahlweit et al. [9]. This system shows interesting phase behavior (Fig. 1). One can study the structures of low-temperature microemulsion (LTM) phase, middle-temperature lamellar (MTL) phase and high-temperature microemulsion (HTM) phase by changing temperature only, provided that the sample contains approximately more than 12 wt% of surfactant at equal volume fraction of water and oil. Bodet et al. have clarified the structural evolution of this system by means of pulsed-field gradient spin-echo NMR, quasi-elastic light scattering and freeze-fracture transmission electron microscopy [10]. Local structure of the bilayer and monolayer of the same system was also studied by Strey et al. [11]. Recently, we have studied the mechanism of the phase transition [12]. 

Plastic deformation is especially pronounced in polymeric materials. The electron micrographs presented in Chapter 8 provide ample evidence of this fact. It will be necessary, therefore, to study whether and how the fracture mechanics approach derived for an elastic material can be applied to elastic-plastic solids as well. The effect of plastic deformation on the stress distribution at a crack tip is well documented [3—7]. An elastic-plastic material under quasi-elastic conditions, for instance, begins to deform plastically wherever the state of stress meets the yield or flow criterion. Plastic deformation begins in the region of largest stresses, i.e. in the proximity of the crack tip it limits the components of stress to the yield stress up. In... 

When an atmospheric spray specimen was subjected to a quasi-static test with an indenter of 1 mmcj), both the substrate and the bond coat were affected with marked plastic deformation, and in particular, the substrate underwent so drastically that the limit of elastic-plastic deformation was stepped over to present a porous zone with concentrated cracks. As the indenter size grew, the area of plastic deformation in the substrate and the bond coat was reduced, to present Hertz cone cracks in the cross-section. In addition to Hertz cone cracks, a number of cracks were seen in parallel to the substrate, which were thought to have occurred when the load was eliminated. With an indenter of 4 mmcj), the area of plastic deformation was reduced further, and lateral cracks were observed as the load was eliminated. Debonding between the bond coat and the substrate was observed only with the 4-mm indenter. Comparing to impact tests results(Fig. 7), qusi-static tests(Fig. 14) can reproduce similar fracture behavior. 

Thus quasi static and unsteady statement may be used for simulation of fracture propagation caused by viscous and inviscid fluid pumping. Rock deformation is described in scope of linear elasticity equation of homogeneous rmiform material. Classical (similar to one used in [1]) and dual bormdary element methods are used for this equations solution. Rock breaking caused by the fracture propagation is described by Irwin s criterion coupled with maximal circumferential stress criterion for calculation of propagation direction. Various approaches are used to obtain stress intensity factors that are necessary for both criteria. 

Figure 3 shows the load (P) - load line displacement (5) records obtained from fracture tests at room temperature and at quasi-static conditions (low loading rates) of propylene homopolymer, PPO, and thee controlled-rheology PPs. The mechanical response for all the materials presented clearly elastic-plastic behaviour and this justifies the use of the EPFM multiple specimen method to evaluate the fracture behaviour. In addition, all the curves deviated from linearity and at a certain deflection level, sudden instability occurred and the specimen broke in two halves. The difference in stiffness is due to the different initial crack lengths. 

The energy criterion for fracture is simply an extension of Griffith s hypothesis which describes quasi-static crack propagation as the conversion of the work done, Wd, by the external force and the available elastic energy stored in the bulk of the specimen, U, into surface free energy, y. It may be written ... 

Figure 8 Dependence of elastic modulus E (a) and fracture toughness Kk (b) on the degree of polymerization of polymer grafts in the CPB and SDPB regimes measured by nanoindentation of the quasi- one-componenf nanocomposite films. Black and blue dashed lines denote the measured f and for linear PS (M =300 000 g mol" ) and PMMA (/H,=1000 000 g mol ), respectively. The error bars represent standard deviations of the results for at least 20 indentations.

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