Fracture, dynamic/elastic

The most common conditions of possible failure are elastic deflection, inelastic deformation, and fracture. During elastic deflection a product fails because the loads applied produce too large a deflection. In deformation, if it is too great it may cause other parts of an assembly to become misaligned or overstressed. Dynamic deflection can produce unacceptable vibration and noise. When a stable structure is required, the amount of deflection can set the limit for buckling loads or fractures. 

Geophysical method Depth to bedrock Stratigraphy Lithology Fractured zones Fault displacements Dynamic elastic moduli Density Rippability Cavity detection Buried artefacts... 

Material Brazed Specimens Creep Cyclic Density Dynamic Elasticity Fracture Hardness Interrupted Material... 

Balankin, A. S. (1991). A Fractals Elastic Properties, Transverse Strain Effect and Sohd Bodies Free Fracture Dynamics. DokladyAN SSSR, 319(5), 1098-1101. 

Balankin, A. S. (1992). Fractal Elastic Properties and Solids Brittle Fracture Dynamics FizikaTverdogo Tela, 34(4), 1245-1258. 

The static (mechanical) elastic modulus is determined in the linear part of the elastic deformation at the strain-deformation diagram of the sample at static load. The difficulty in determining the static elastic modulus is in the fact that the deformation before the fracture is only microns and a precise apparatus is required. The static elastic modulus may be measured at strength tests (compression, bending, tensile), and, of course, the sample will be broken. In reality, the measurement of the dynamic elastic modulus is more popular. 

A.S. Rizkalla and D. W. Jones. (2004) Indentation fracture toughness and dynamic elastic moduli for commercial feldspathic dental porcelain materials. Dent Mater. 20 198-206. 

The plastic strain at fracture decreases markedly with time as the cement ages also the elastic modulus increases (Wilson, Paddon Crisp, 1979 Barton et al., 1975). There is an increase in dynamic modulus with time (Barton et al., 1975). 

Many variables used and phenomena described by fracture mechanics concepts depend on the history of loading (its rate, form and/or duration) and on the (physical and chemical) environment. Especially time-sensitive are the level of stored and dissipated energy, also in the region away from the crack tip (far held), the stress distribution in a cracked visco-elastic body, the development of a sub-critical defect into a stress-concentrating crack and the assessment of the effective size of it, especially in the presence of microyield. The role of time in the execution and analysis of impact and fatigue experiments as well as in dynamic fracture is rather evident. To take care of the specihcities of time-dependent, non-linearly deforming materials and of the evident effects of sample plasticity different criteria for crack instability and/or toughness characterization have been developed and appropriate corrections introduced into Eq. 3, which will be discussed in most contributions of this special Double Volume (Vol. 187 and 188). 

The scope of the series covers the entire spectrum of solid mechanics. Thus it includes the foundation of mechanics variational formulations computational mechanics statics, kinematics and dynamics of rigid and elastic bodies vibrations of solids and structures dynamical systems and chaos the theories of elasticity, plasticity and viscoelasticity composite materials rods, beams, shells and membranes structural control and stability soils, rocks and geomechanics fracture tribology experimental mechanics biomechanics and machine design. 

The above refers primarily to linear elastic fracture mechanics (LEFM) studies related to the onset of brittle fracture as well as fatigue. The states of the sciences of ductile and dynamic fracture, which only became of serious concern in the early 1960s and 1970s, respectively, have not reached a similar level of maturity despite the immense research efforts expended on these topics in recent years. Yet to be resolved in the former is a viable ductile fracture criterion in view of the recently uncovered uncertainties regarding the /-integral as a crack tip parameter.5,6 As for the latter, a reliable dynamic crack propagation criterion is yet to be established, as will become apparent in subsequent sections of this chapter. 

Ceramics and the matrix in ceramic composites exhibit cleavage fracture at room temperature as well as at elevated temperatures. This is fortunate since most of the theoretical developments in dynamic fracture are confined to linear elastic fracture mechanics which is then applicable to fracture of the ceramic matrix. However, the additional complexities of crack deflection and fiber-matrix interface cracking, as well as fiber/whisker/particulate pull-outs, are at this time yet to be addressed. 

Note that for the asymptotic equations of Eqns. (2) and (3) to be valid, r

characteristic length, and is normally the crack length or the remaining ligament, whichever is the smaller, of a fracture specimen. Also, the above asymptotic equations are not valid for an orthotropic elastic continuum, such as a ceramic fiber/ceramic matrix composite. While the static crack tip state for an orthotropic elastic continuum has been derived, to the author s knowledge, no dynamic counterpart is available to date. Nevertheless, the above crack tip state should be applicable to particulate/whisker-filled ceramic matrix composites which macroscopically behave like an isotropic homogeneous continuum. 

The mechanical properties of rapidly polymerizing acrylic dispersions, in simulated bioconditions, were directly related to microstructural characteristics. The volume fraction of matrix, the crosslinker volume in the matrix, the particle size distribution of the dispersed phase, and polymeric additives in the matrix or dispersed phase were important microstructural factors. The mechanical properties were most sensitive to volume fraction of crosslinker. Ten percent (vol) of ethylene dimethacrylate produced a significant improvement in flexural strength and impact resistance. Qualitative dynamic impact studies provided some insight into the fracture mechanics of the system. A time scale for the elastic, plastic, and failure phenomena in Izod impact specimens was qualitatively established. The time scale and rate sensitivity of the phenomena were correlated with the fracture surface topography and fracture geometry in impact and flexural samples. 

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