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The Quarterly Journal of Mechanics and Applied Mathematics 1949 2(1):40-52; doi:10.1093/qjmam/2.1.40
© 1949 by Oxford University Press
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THE PLASTIC YIELDING OF NOTCHED BARS UNDER TENSION

R. HILL

( Cavendish Laboratory Cambridge )

The state of stress in the core of a notched bar is analysed at the moment when pronounced plastic yielding begins. The theory is two-dimensional and an ideal plastic-rigid material is assumed. Following a general analysis of the problem, the magnitude of the constraint factor is calculated for a deep notch with a semicircular root. The correct approach to problems of plane plastic strain is discussed, and is further illustrated by a re-examination of the classical work of Prandtl on indentation (which is closely related in principle with the notched bar problem).


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