Crack wave interaction

Brittle fracture, dynamic crack branching, crack wave interaction... 

For thin shell structures, the most promising methods are those based in the analysis of the propagation of elastic waves. The wave propagation methods have often used piezoelectric wafer active sensors (PWAS) as transmitters to generate waves and simultaneously as receivers to measure the echo signals due to the defects. A time-frequency analysis allows an estimation of crack size on the basis of the relationship between new and baseline response. The sensitivity of Lamb waves to defects depends largely on the frequency, and for complex structures the dispersive Lamb waves interact with reinforcements with partial reflections and refractions. These systems have not reached the level of maturity required for industrial applications. A full discussion with alternatives is presented in the book by Giurgiutiu (2008). 

The beam-defect interaction is modelled using Kirchhoff s diffraction theory applied to elastodynamics. This theory (see [10] for the scattering by cracks and [11] for the scattering by volumetric flaws) gives the amplitude of the scattered wave in the fonn of coefficients after interaction with defects and takes account of the possible mode-conversion that may occur. 

Wallner lines are formed when sonic waves generated during fracture interact with principal stress driving the propagating crack front. Wallner lines appear as a series of arc shaped steps as shown in Figure 2.33. 

When the sound wave generated from the branched microcrack or reflected from the boundary of the plate interact with the crack, the singular stress fields at the tip of the crack are modulated in such form as given by Eqs. (25), which are proportional to cos((wr - P x). On the other hand the 1-st order fields consist of two terms which are proportional either to cos(o>r- p x) or sin(o>r-/5 jX). The latter term, for example, comes from the real part of such term. 

This type of smooth undulating feature on the fracture surface is exemplified in Wallner lines. In Figure 9.3, the Wallner lines are the curved features on the fracture surface. Wallner lines are often created by stress pulses generated as the crack interacts with inclusions in the body or with surface imperfections. (Those stress pulses usually consist of a compression followed by a dilatation so that the general wave form approximates the O stress in Figure 3.2a.)... 

Ravi-Chandar, K. and Kjiauss, W.G., An investigation into dynamic fracture. Ill - On steady-state crack propagation and branching. Int. J. Fract., 26, 141-154 (1984), Ravi-Chandar, K. and Knauss, W.G., An investigation into dynamic fracture. IV - On the interaction of stress wave with propagating cracks. Int. J. Fract., 26, 189-200 (1984). Pocius, A., Verbal communication, 1998. 

During propagation, a crack interacts with the microstructure of the material, the stress, and with elastic waves that are generated these interactions produce distinctive features on the fracture surface. Furthermore, these features provide important information on where the crack initiated and the source of the crack-producing defect. In addition, measurement of the approximate fracture-produdng stress may be useful stress magnitude is indicative of whether the ceramic piece was excessively weak or the in-service stress was greater than anticipated. 

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