Dynamic Photoelasticity and Holography Applied to Crack and Wave Propagation
The field of elastodynamics covers the class of problems in solid mechanics where the inertia term on the right hand side of the equations of motion where e is the dilatation and ω is the in-plane rotation of an element, may not be neglected because of ra
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PHoTOELASTICITY A~ HOLOGRAPHY APPLIED TO CRACK A~ID 1.~AVE PRoPAGATION
H.P. R o s s m a n i t h Institute of Mechanics Technical University Vienna, Austria W.L. F o u r n e y Department of Mechanical Engineering University of Maryland, USA
The field of elastodynamics covers the class of problems in solid mechanics where the inertia term on the right hand side of the equations of motion
where e is the dilatation and w is the in-plane rotation of an element, may not be neglected because of rapid changes of stress and displacement in time. These variations of the stresses are due to loads or displacements which change in time, or they are due to relatively sudden changes in the geometry of the body. From the broad field of elastodynamics only stress wave propagation, fracture propagation and their interaction, and penetration ( high speed impact) problems will be highlighted here. Collision impact and vibration with possible exception of ultrasonic excitation both involve time-varying forces which, in general, are relatively long compared· to the observation period. Because of cyclic force application and the difficulties involved in the proper photoelastic
H. P. Rossmanith (ed.), Rock Fracture Mechanics © Springer-Verlag Wien 1983
210
H.P. Rossmanith - W.L. Fourney
scaling of material damping, dynamic photoelasticity has not been extensively employed in problems of vibration. Although, in collision impact problems the developement of stresses depends upon the velocity of impact and the elastic wave transmission characteristics of the colliding bodies, the stress waves are often of such a low magnitude that fringe multiplication techniques are required to develop a feasable isochromatic pattern. Quasistatic problems, such as transient thermal stress problems, where the inertia term. is negligible, can be investigated using normal methods of recording photoelastic fringe patterns.
1.
Photoe"lasticity
This section summarizes the basic relationships of the theory of photoelasticity. Many transparent noncrystalline materials that are optically isotropic in a stress free condition become temporarily birefringent when subjected to stress loading. This optical anisotropy persists while the material is stressed but disappears when the stresses are removed. The method of photomec~anics is based on this physical phenomenon. Maxwell formulated the relationship between the change in
th~
indices
of refraction of a material exhibiting temporary birefringence and the loads applied (for plane stress)/1,2/: (1)
where o1,o2 =principal stress at point, n0 = refractive index associated with unstressed state, n1,n 2= refractive indices associated with stressed state and d1,d 2= stress optic coefficients. From equ.(1) follows (2)
where d0 is the relative stress optic coefficient. During birefringence the two perpendicular components of a light ray propagate with different speeds (3)
Dynamic Photoelasticity and Holography
211
with c' the speed.of light in vacuum. Upon passage of a plane layer of thickness h the retardati
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