Measurement of Residual Stresses by the Hole-Drilling Strain Gage Method

Principle and Theory The Hole-Drilling Strain Gage Method The introduction of a hole (even of very small diameter) into a residually stressed body relaxes the stresses at that location. This occurs because every perpendicular to a free surface (the hole surface, in this case) is necessarily a principal axis on which the shear and normal stresses are zero. The elimination of these stresses on the hole surface changes the stress in the immediately surrounding region, causing the local strains on the surface of the test object to change correspondingly. This principle is the foundation for the hole-drilling method of residual stress measurement, first proposed by Mathar (Ref 2 ). In most practical applications of the method, the drilled hole is blind, with a depth which is: (a) about equal to its diameter, and (b) small compared to the thickness of the test object. Unfortunately, the blind-hole geometry is sufficiently complex that no closed-form solution is available from the theory of elasticity for direct calculation of the residual stresses from the measured strains -- except by the introduction of empirical coefficients. A solution can be obtained, however, for the simpler case of a hole drilled completely through a thin plate in which the residual stress is uniformly distributed through the plate thickness. Because of this, the theoretical basis for the hole-drilling method will first be developed for the throughhole geometry, and subsequently extended for application to blind holes.

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