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National Advisory Committee for Aeronautics, Technical Notes - Stress and Strain Concentration at a Circular Hole in an Infinite Plate

Stress concentration factors have been universally computed on the
basis of the theory of elasticity. If, however, the material is stressed
into the plastic range, the theory of elasticity no longer applies and
stress concentration factors computed on that basis are in error.

Experimental data on the stress and strain concentration at a
circular hole in a large, wide sheet of 2hS-T3 aluminum alloy in tension
were published in reference 1. If the material remains elastic, the
theory of elasticity predicts concentration factors of 3 for both stress
and strain at the point of maximum stress. Values close to 3 were
actually found experimentally when no part of the sheet was stretched
beyond the elastic range. When the sheet was further stressed into the
plastic range, the stress concentration factor-(based on applied stress
instead of net-section stress as was done in reference I) decreased
to l.h and the strain concentration factor increased to 8.6.

This paper considers the theoretical problem of the stress distri-
bution in an infinitely large sheet with a circular hole for the general
case where the material may have any stress-strain curve. The plate is
assumed to be under uniform tension at a large distance from the hole.
The'material is taken to be isotropic and incompressible.

The calculation, as presented in the appendix, gives the formula
for the stress concentration at a circular hole in an infinite sheet as
where (E5)a,fl 2 is the secant modulus at the point of maximum stress
and (Es)0° is the secant modulus at points far removed from the hole,
Where the load is applied. A numerical trialaand—error procedure is
required to solve for the stress concentration factor.

In reference 1, experimental data were given on the stress and
strain concentration factors for a wide sheet of 2hS-T3 aluminum alloy
with a circular hole under tension. A curve of Es/E for this material
was determined and is shown in figure 1. From this curve, which was
taken from the stress—strain curve ending at point E in figure h of
reference 1, stress and strain concentration factors can be easily
computed to compare with figure 5 of reference I.

Such a comparison is shown in figure 2 of the present paper. The stress
concentration factor appears to be given by the formula with accuracy which
is adequate. The factors for strain are somewhat lower than those reported
in reference 1; the apparent discrepancy is prdbably due in part to the
peculiarities of the stress-strain curve, which permit a slight error
in stress to be enormously magnified in strain, and in part to the use
of 1/2 for Poisson‘s ratio.