Abstract
Some fundamental problems on the optical method of caustics, which is used to determine the value of the stress-intensity factor, are studied. The paper shows that the radiusr o of the initial curve considerably affects the results and describes a method to eliminate this effect. This method is also applied to the biaxial-stress fracture problem. It is shown that the biaxial stress affects the fracture toughness of thin specimens of Plexiglas sheets and that the fatigue-crack-growth rate is increased due to the compressive stress along the crack line.
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Abbreviations
- a :
-
half crack length
- B :
-
biaxial-stress ratio
- c 1,c 2 :
-
stress-optical constants
- c 0,c ′0 :
-
optical constants in eq (1) in the air and in the immersion liquid, respectively
- D λ :
-
diameter of caustic
- E :
-
Young's modulus
- K I,K II :
-
stress-intensity factors of Mode I and Mode II, respectively
- K c :
-
values ofK at initiation of unstable fracture
- n :
-
refractive index
- P x,P y :
-
loads in x and y directions, respectively
- r 0 :
-
radius of the initial curve defined by eq (2)
- t :
-
thickness of specimen
- x,y :
-
coordinates in Figs. 1 and 7
- z 0 :
-
distance between the specimen and the screen
- z i :
-
distance between the specimen and the focal point of the lens
- da/dN :
-
fatigue-crack-growth rate
- μ:
-
Poisson's ratio
- σ1, σ2 :
-
principal stresses
- σ x , σ y :
-
stresses in x and y directions, respectively
- σ ys :
-
yield stress
- λ:
-
magnification factor defined by eq (3)
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Shimizu, K., Takahashi, S. & Shimada, H. Some propositions on caustics and an application to the biaxial-fracture problem. Experimental Mechanics 25, 154–160 (1985). https://doi.org/10.1007/BF02328806
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DOI: https://doi.org/10.1007/BF02328806