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The Shadow Optical Method of Caustics

  • Jörg F. Kalthoff
Part of the International Centre for Mechanical Sciences book series (CISM, volume 290)

Abstract

The shadow optical method of caustics is a relatively new experimental technique in stress strain analysis. It was introduced by Manogg1,2 in 1964. The method is sensitive to stress gradients and therefore is an appropriate tool for quantifiying stress concentration problems. Manogg originally used the method for investigating crack tip stress intensifications. The technique was extended later by Theocaris3–5, Rosakis6,7, and the author and his colleagues8–11 to different conditions of loading, material behavior, in static as well as dynamic situations. Shadow optical images of test specimens under loading in general are characterized by very simple geometric patterns which can be easily evaluated. Because of the simplicity of shadow patterns, the method can also be successfully applied for investigating rather complex phenomena, for example transient problems. Despite the complexity which may be inherent in the problems to be investigated the clearness of the generated recordings allows the derivation of reliable informative data. The author and his colleagues have applied the caustic technique to investigate various problems of practical interest in the field of fracture dynamics, in particular to the behavior of propagating and subsequently arresting cracks and the behavior of cracks under different impact loading conditions.

Keywords

Stress Intensity Factor Crack Velocity Dynamic Stress Intensity Factor Shadow Pattern Caustic Curve 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of Symbols

a

Crack length

a,b

Elasto-optical constants

A,B

Material constants in Maxwell-Neumann’s law

α

Velocity dependent factor

a2,3,4...

Coeffients of higher order terms in crack tip stress distribution

c

Shadow optical constant

co

Sound wave speed

c1

Longitudinal wave speed

c2

Transverse wave speed

C

Compliance of specimen

d

1. Specimen thickness

2. Distance between two cracks in double crack configuration

deff

Effective thickness of the specimen

D

Characteristic length parameter for caustic evaluation

Do,i

Outer, inner characteristic length parameter

Dmax,min

Maximum, minimum length parameter of mixed mode caustics

e

Index characterizing elastic behavior

E

Young’s modulus

ε

Strain

f

Numerical factor for caustic evaluation

fo,i

Numerical factor for evaluating outer, inner caustic

g

Numerical factor for KI-determination from mixed mode caustics

G

1. Function

2. Lamé’s constant, G = E/2(1+ν)

H

Height of specimen

In

Numerical Factor in the HRR stress field equations

J

J-Integral

K

Stress intensity factor

n

1. Refractive index

2. Strain hardening coefficient

ν

Poisson’s ratio

O

Origin of coordinate system

p

Edge load, unit N/m

P

Index characterizing plastic behavior

p,q

Biaxial stresses in y,x-direction

R

Radius of circular hole

r,φ

Polar coordinate system in object plane (specimen)

r′,φ′

Polar coordinate system in image (reference) plane

Polar coordinate system at the tip of a moving crack

ro

Radius of initial curve

rpl

Radius of plastically deformed region around the crack tip

rps

Smallest radius around the center of stress concentration outside which a state of plane stress exists

ρ

1. Density of the material

2. Notch tip radius

3. Wedge tip radius

S

Support span

s

Optical path length

σ

Normal stress

σo

Tensile yield stress

t

Time

λ

Coefficient of anisotropy

τ

1. Shear stress

2. Period of the oscillation of impacted specimen

µ

Ratio of the mode II to mode I stress intensity factor, KII/KI

u,v,w

Displacements in x,y,z-direction

W

Width of the specimen

x,y

Cartesian coordinates system in object plane (specimen)

x′,y′

Cartesian coordinates system in image (reference) plane

Cartesian coordinates system at the tip of a moving crack

z

Direction of optical axis

zo

Distance between object plane (specimen) and image (reference) plane

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Copyright information

© Springer-Verlag Wien 1987

Authors and Affiliations

  • Jörg F. Kalthoff
    • 1
  1. 1.Fraunhofer-Institut für WerkstoffmechanikFreiburgFederal Republic of Germany

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