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C. Dumont reported a 1939 experimental study of stress around a circular hole in an aluminum-alloy plate under out-of-plane bending. The primary NACA record retains that exact initial-only name and lists an Aluminum Company of America affiliation.^[ref]

Dumont measured plate deflection and strain for two loads. The largest hole-edge stresses were tangential at the ends of the transverse diameter. The reported maximum was 1.59 times a computed net-section stress and 1.85 times the computed stress for an otherwise solid plate subjected to the same bending forces.^[ref]

Those ratios demonstrate why a stress concentration factor requires a stated denominator. For an original numerical illustration, stipulate a local peak $37\mathrm{MPa}$. Reference stresses $37/1.85=20.0\mathrm{MPa}$ and $37/1.59\approx 23.27\mathrm{MPa}$ then reproduce the two ratios for the same peak. These invented stresses illustrate normalization; they are not recovered loads or stresses from Dumont's experiment.

The bending result is also distinct from the factor three in the in-plane tensile Kirsch equations. Geometry, stress components and boundary loading differ. Dumont's comparison of strain and deflection provided complementary local and overall observations rather than assuming a universal circular-hole amplification.

For a linear-elastic model, doubling the load at fixed geometry doubles both strain and deflection. Taking measurements at more than one load can therefore test proportionality. Agreement at two loads alone would not establish fatigue life or the onset of yielding. This explains the value and the limits of the experiment without expanding the initial C. or assigning an unverified biography.

The Kirsch equations describe the stress tensor around a traction-free circular hole in an infinite linear elastic plate under uniform remote tension. For remote stress ${\sigma }_{\infty }$ along $x$, hole radius $a$ and polar coordinates $(r,\theta )$ measured from that direction, put $q=a^2/r^2$. In the classical isotropic plane stress model,The fields satisfy equilibrium and the prescribed boundary tractions. They can be obtained using an Airy stress function satisfying the biharmonic compatibility equation.^[ref]

At $r=a$, $q=1$, so ${\sigma }_{rr}={\sigma }_{r\theta }=0$ whileThe tangential stress is $3{\sigma }_{\infty }$ at the top and bottom of the hole and $-{\sigma }_{\infty }$ at its sides. A traction-free boundary does not require every stress component to vanish: the outward boundary normal is radial, so radial normal and shear tractions must vanish.

For an original distance comparison along $\theta =\pi /2$, the tangential stress is ${\sigma }_{\infty }(1+q/2+3q^2/2)$. At $r=2a$ it is $1.21875{\sigma }_{\infty }$, already far below the edge value three. At large distance the polar components approach those of the original uniform Cartesian tension.

A finite-width plate, internal hole pressure, plasticity or out-of-plane bending changes the boundary-value problem. The stress concentration factor three is therefore specific to the stated remote-tension model. The MIT laboratory uses local strain measurements and photoelasticity to examine how actual geometries compare with ideal concentration fields.^[ref]

A stress concentration is a localized increase of stress caused by geometry or another disturbance of the load path. Holes, notches and abrupt section changes can make the largest local normal stress much greater than a stress calculated from the total force divided by a reference cross-sectional area. A stress concentration factor $K_t={\sigma }_{\max }/{\sigma }_{\mathrm{ref}}$ is meaningful only after both the stress component and its reference have been specified.

The Kirsch equations give an instructive exact result for a circular hole of radius $a$ in an infinite, isotropic linear elastic elastic plate under remote tensile stress ${\sigma }_{\infty }$ in one direction, using a plane stress model. Measure the polar angle $\theta$ from the loading direction. At the hole boundary,At $\theta =\pi /2,3\pi /2$, the tangential normal stress reaches $3{\sigma }_{\infty }$, giving $K_t=3$ relative to remote stress. At $\theta =0,\pi$, it is $-{\sigma }_{\infty }$. A traction-free hole therefore does not require every component of its stress tensor to vanish: it requires zero traction on the radial boundary.^[ref]

For a finite plate, distinguish gross and net reference areas. A plate of width $W$, thickness $t$ and central hole diameter $d$ transmits force $P$ through gross area $A_g=tW$ and minimum net area $A_n=t(W-d)$. Defining ${\sigma }_g=P/A_g$ and ${\sigma }_n=P/A_n$ gives the exact conversionThis is a change of normalization, not a solution for the finite plate's stress field. For an original numerical example, take $W=40\mathrm{mm}$, $t=2\mathrm{mm}$, $d=10\mathrm{mm}$ and $P=800\mathrm{N}$. The reference stresses are $10$ and $13.333\mathrm{MPa}$. If the local maximum is stipulated as $32\mathrm{MPa}$, the same physical maximum gives $K_{tg}=3.2$ and $K_{tn}=2.4$. Neither number changes the local stress by choosing a different denominator.

The distinction appears in real historical measurements. In 1939, C. Dumont loaded a perforated aluminum-alloy plate in out-of-plane bending and measured strain and deflection at two loads. The reported peak tangential stress was 1.59 times the computed net-section stress, but 1.85 times the computed stress for an unperforated plate under the same bending forces. These are bending results for that geometry, rather than the infinite-plate tensile factor three.^[ref]

Modern demonstrations can combine a metal plate instrumented with strain gauges and a transparent polymer viewed in a polariscope. The latter uses stress-induced birefringence; its fringes respond to differences of principal stresses. The MIT laboratory compares local and remote strain measurements with qualitative photoelasticity observations around holes and a slot.^[ref]

The elastic stress concentration factor is dimensionless. It differs from the stress intensity factor used to describe a sharp crack's singular field. Local yielding or a crack changes the mechanical problem; multiplying a remote stress by the elastic $K_t$ does not, by itself, establish a failure load.