Abstract
A method is described for the rapid, accurate determination of residual stresses from a holographic interference fringe pattern. The pattern is generated by the displacement field caused by localized relief of residual stresses via the introduction of a small, shallow hole into the surface of a component or test specimen. The theoretical development of the holographic method is summarized. An example is given showing how the method can be applied to a typical experimentally observed fringe pattern to determine principal residual stresses and directions.
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Abbreviations
- \(\tilde a,\tilde b,\tilde c\) :
-
nondimensional coefficients derived from\(\tilde A,\tilde B,\tilde C\)
- h :
-
depth of a blind hole
- n :
-
fringe order
- n 0 :
-
fringe order in a fringe pattern that does not include out-of-plane displacements
- n (1),n (1′) :
-
fringe orders at diametrically opposite points around a hole
- n (i),n (i′) :
-
fringe orders at diametrically opposite points around a hole
- r :
-
radial coordinate
- r 0 :
-
radius of a blind hole
- t :
-
specimen thickness
- u x ,u y ,u z :
-
displacement components in a Cartesian coordinate system
- u r ,u θ ,u z :
-
displacement components in a cylindrical coordinate system
- z vp :
-
z-coordinate of the observer's position
- \(\tilde A,\tilde B,\tilde C\) :
-
coefficients in the expressions for the displacement field [eq (2)]
- C ij :
-
elements of the matrix of coefficients in eqs (19) and (21)
- D :
-
diameter of a blind hole
- E :
-
Young's modulus
- K x ,K y ,K z :
-
Cartesian components of the sensitivity vector
- K 0 x ,K 0 y ,K 0 z :
-
Cartesian components of the sensitivity vector when the observer is at infinity
- \(\bar e_x ,\bar e_y ,\bar e_z \) :
-
unit vectors in a Cartesian coordinate system
- \(\bar k_1 \) :
-
propagation vector in the illumination direction
- \(\bar k_2 \) :
-
propagation vector in the viewing direction
- ū:
-
displacement vector
- \(\bar K\) :
-
sensitivity vector
- \(\bar K^0 \) :
-
sensitivity vector when the observer is at infinity
- α:
-
angle defined by tan−1(r/z vp )
- β:
-
orientation of the principal axes
- \(\gamma _1 \) :
-
grazing angle of illumination
- ζ:
-
inclination of the illumination direction
- θ:
-
circumferential coordinate in a cylindrical coordinate system
- λ:
-
wavelength of the illumination source
- ν:
-
Poisson's ratio
- ρ:
-
ratio of hole radius to radial coordinate (r 0 /r)
- \(\sigma _{xx} ,\sigma _{yy} ,\tau _{xy} \) :
-
components of the stress tensor (Cartesian coordinate system)
- \(\sigma _1 ,\sigma _2 \) :
-
principal stresses
- ϕ:
-
phase shift
- ϕ(x, y), ϕ(r, θ):
-
fringe function
- \(\Phi _0 \) :
-
net phase shift of the object beam
- \(\Phi _R \) :
-
net phase shift of the reference beam
- ΔΦ:
-
net phase shift change
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Makino, A., Nelson, D. Residual-stress determination by single-axis holographic interferometry and hole drilling—Part I: Theory. Experimental Mechanics 34, 66–78 (1994). https://doi.org/10.1007/BF02328443
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DOI: https://doi.org/10.1007/BF02328443