Applications of the Optical Method of Caustics to the Study of Viscoelastic Dynamic Fracture and Static Blunt Crack Fronts
Dickerson, Kevin Lee
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https://hdl.handle.net/2142/71695
Description
Title
Applications of the Optical Method of Caustics to the Study of Viscoelastic Dynamic Fracture and Static Blunt Crack Fronts
Author(s)
Dickerson, Kevin Lee
Issue Date
1987
Doctoral Committee Chair(s)
Kim, Kyung S.,
Department of Study
Theoretical and Applied Mechanics
Discipline
Theoretical and Applied Mechanics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Applied Mechanics
Abstract
The opto-mechanical relation, as used in the optical methods of photoelasticity and caustics, are extended to linearly viscoelastic materials. The Maxwell-Neumann relation for the stress-optic constants, which is good for linearly elastic behavior, is replaced by an expression derived from the Clausius-Mosotti-Lorentz-Lorenz (CMLL) equation. The opto-mechanical relation is given explicitly in terms of the mechanical and dielectric properties of the material. In the limiting case of elastic behavior, the present result is consistent with the Maxwell-Neumann relation. Approximations to the CMLL equation are discussed and compared with experiment.
The derived opto-mechanical relations are applied to the steady-state propagation of a crack in a viscoelastic material. Numerical computation of the caustic and initial curves are performed. The caustic shape changes very little from the elastic case. However, the size is dependent on the crack speed and temperature of the material.
Numerical calculations are used to determine the stress intensity factors of previously performed crack propagation experiments. The dynamic fracture toughness for Homalite 100 shows a strong temperature dependence for temperature variations below the glass transition temperature. Also, the crack branching toughness shows no dependence on temperature or crack speed and remains constant within the limits of the experimental error.
In order to address the accuracy and validity of the experimental measurement of the stress intensity factor, the stress field for a static blunt crack tip is investigated. The stress field surrounding a keyhole crack is given in terms of the eigenfunctions for a sharp crack. The eigenfunction stress field expansion for the keyhole crack contains additional coefficients of higher singularity than the usual square root singularity. The coefficients are determined by the boundary collocation method, which truncates the infinite series to satisfying the traction-free boundary condition on the face of the keyhole crack. The stress field is checked experimentally using the method of caustics. Numerically generated caustics are computed from the derived stress field. The caustic shapes compare well with experiment. The validity of using the caustic diameter alone to determine the stress intensity factor is discussed. The aspect ratio of the caustic appears to be a good indicator of the accuracy of the stress intensity factor measurement.
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