(a): Schematic presentation of the relative positions of the two coincident laser beams of radius , penetrating down to depth in the material, and the crack of the characteristic length , and of the characteristic depth . (b): Schematic presentation of the relative positions of the region of laser radiation absorption (in gray color) and of the infinite plane crack ( interface) in the 1D geometry. The characteristic width of the light absorption region is equal to . The inset in (b) demonstrates that the surfaces of the crack are interacting by the force and the width of the crack is controlled by the relative displacement of the crack faces.
(a): Qualitative presentation of the dependence of the interaction force between the crack faces on the width of the crack. (b): The accepted piece-wise linear approximation of the interaction force between the crack faces on the width of the crack. (c): Illustration of the crack width variation under quasistatic loading. If the amplitude of the sinusoidal loading force does not exceed the maximum force , which the crack can support in its open state, the rigidity of the crack does not change with time, and the crack motion is linear. If the amplitude of the applied force exceeds the maximum force , which the crack can support in its open state, the rigidity of the crack abruptly changes twice during a single period of loading when the crack width is equal to and the crack motion is highly nonlinear.
(a): Graphical solution of the algebraic equation for the times and of crack opening and closing, respectively, under sinusoidal thermoelastic loading of the crack. (b): Nonsinusoidal variation in the crack relaxation frequency between its maximum minimum value in the open state of the crack and its maximum value in the closed state of the crack in response to sinusoidal loading presented in (a).
Spectrum of the side-lobes in the absence of hysteresis region in the force/width characteristic of the crack. (a): The envelope of the amplitudes of the side-lobes as a function of the side-lobe number for three discrete values of the amplitude of crack loading force relative to the maximum compression force that can be supported by the crack in open state. For the presentation of the envelope the discrete variable is treated as a continuous one. (b): The dependence of the amplitude of the side-lobes on the continuously varying amplitude of the normalized force loading the crack at low frequency . in the absence of hysteresis region in the force/width characteristic of the crack.
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