Introduction to structural integrity

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# 3.4.4 Stress concentration at joint

Although it is known that a round hole in a flat sample will theoretically produce a stress concentration of about 3, the issue was decided experimentally. A tensile test at 25 °C was undertaken on an intact eye-bar-pin assembly from the bridge, being some 8 m long and from a lower part of the chain. It yielded at about 7 MN, and fractured in the shank at a stress of about 770 MPa. The yield stress in the shank was about 520 MPa, and the failed eye bar showed ductile behaviour with a reduction in area of 30% at an elongation of 8.5%. By putting strain gauges at various points in the hole of the bar, the stress concentration was calculated to be about 2.62 at the opposing faces of the inner side of the hole where fracture had occurred in eye bar 330.

## Exercise 9

Suggest why, in the tensile tests, fracture occurred in the shank rather than at the hole of the eye bar. What factors contribute to where failure occurs?

### Answer

The shank dimensions are 51 mm by 305 mm, giving a section area of 15.6 × 10−3 m2, while the limbs at each side of the hole are each 203 by 51 mm, giving a total section of 20.7 × 10−3 m2. So the section area is about a third greater in the limb compared with the shank, giving a correspondingly lower stress.

Nevertheless, the greater stress concentration at the edges of the hole should have ensured failure here rather than in the shank.

Surface roughness effects can be critical, so if the pin and eye-bar hole surfaces were smooth and the shank surface was rough, failure in the shank would be preferred.

It is worth emphasising that stress concentrations are of less importance in ductile compared with brittle-type failures. After all, a material that usually fails in a ductile manner, such as steel, can yield locally at the root of a notch or the edge of a hole. By contrast, during brittle fracture there is no mechanism for absorbing excessive load by deforming plastically, and the stress at the root of a crack may be extremely high.

The experiment established that brittle cracks had not developed in the lower eye bar: if they had, this test bar would have failed at the hole rather than in the shank.

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