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Three-dimensional stress relief displacement resulting from drilling a blind hole in acrylic

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Abstract

Analyses of optically based, hole-drilling stress measurements require accurate knowledge of the three-dimensional relaxation displacements induced by the drilling of a blind hole into the surface of a stressed object. These displacements are calculated using two closed-form solutions proposed earlier and a numerical finite element technique. Double exposure holographic fringe patterns calculated from the analytic displacements are in poor agreement with those observed in a controlled laboratory calibration experiment on a block of acrylic subject to a known uniaxial compressive stress. However, the fringe positions predicted by the finite element modeling match those obtained from the observed fringe pattern using image-processing procedures, although some drilling-related discrepancies remain near the stress-relieving hole. The stressstrain behavior of acrylic is extremely temperature sensitive; the discrepancies near the stress relief hole may result from drilling induced heat. Despite these near hole disagreements between the predicted and observed fringe patterns, the overall correspondence indicates that the finite element method adequately provides the desired three-dimensional relaxation displacements necessary for determination of stress magnitudes in some blind hole drilling measurements employing coherent optical recording.

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Abbreviations

ϱ:

dimensionless radial coordinater/a

ε:

radial strain

ϕ:

azimuth fromx-axis

ν:

Poisson's ratio

σ:

applied uniaxial stress (MPa)

λ:

wavelength of coherent light

σ ′ r :

relaxed radial stress

σ ′θ :

relaxed circumferential stress

τ ′ rθ :

relaxed shear stress

ʵ ′ z :

relaxed surface normal strain

x, y, z :

coordinate axes

σ p , σ q :

principal in plane stresses applied to halfspace at infinity

σ H :

hydrostatic stress

σ s :

pure shear stress

A, B :

constants

H :

depth of blind hole

P :

a point on surface of object

P′:

new position of pointP after displacement

Δl :

change in length of ray path due to displacement

u i :

displacement vector for surface positioni

d i :

geometric vector for surface positioni

u :

displacement vector

d :

geometric vector

e i :

unit directional vectors

K :

sensitivity vector

n :

fringe order

r :

radial distance from hole center

a :

hole radius

t x, ty, tz :

x, y, z translational displacements common to all surface points

u ϕ :

relaxed circumeferential displacement

u r :

relaxed radial displacement

u z :

relaxed surface normal displacement

u Rr :

radial displacement coefficient

u Rθ :

circumferential displacement coefficient

u Rz :

surface normal displacement coefficient

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Authors and Affiliations

  1. Department of Physics, University of Alberta, T6G 2JI, Edmonton, Alberta, Canada

    D. R. Schmitt (Professor) & Y. Li (Graduate Student)

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  1. D. R. Schmitt
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  2. Y. Li
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Schmitt, D.R., Li, Y. Three-dimensional stress relief displacement resulting from drilling a blind hole in acrylic. Experimental Mechanics 36, 412–420 (1996). https://doi.org/10.1007/BF02328586

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  • DOI: https://doi.org/10.1007/BF02328586

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