### Torsion v. Tension in View of the Static Strengths

Akimasa ONO
1965 Proceedings of the Japan Academy
Foreword By way of recapitulation (see these Proceedings, vol. 38 (1962)r p. 520), we express the critical stress state of breaking section in material by the distance pN of a tangent line of the stress circle from the origin of the diagram reading as -(a l-a3) T -(c1+ ~'3)C=pN, 2 2 where a1, a3=the principal stresses, maximum and minimum, C = cos cp with cp denoting the angle made by pH to the axis of ar pN = ao -aR + bM, ao representing the initial strength, and R, M the greatest
more » ... ences, vibratory and static r respectively. As applied to static strengths, aR vanishes so that pN = ao + b(a1--a3), bM being solely responsible to affect ao proper to the given materiall in one or the other way according to the kinds of stress. For uni-axial tension we put a1= aB and a3 = 0, aB being the breaking tensile stress acting on the fractured surface, which can be specified by C=1, and for torsion a1= -a3=zb, this being defined as it is. Since C drops out in the second case, the original formula becomes in these cases ao=aB (1-b)=zb (1-2b'), b' being written for b in the last expression to denote a negative number, because zb falls below o by yielding in contrast to aB rising up. As for ao we have ao = a1= a2 = a3 in the critical state under uniform tension. But this test appears less feasible, while ao can be estimated conveniently from the vibratory strengths by making a certain assumption (loc, cit., p. 524). It is possible in this way to compute ao and determine the relations of aB and zb to ao by adjusting b and b'. As a result of such calculation it is made known that b is some 0.33 or simply 1/3 in steels undergoing ductile fracture in. tension. To approach b' without knowing zb exactly we may resort to the ratio zb : aB, which is thought not less than 1/2, since we have then -2b'1-2b, <_ i.e. -b'1/6 _< for b=1/3. At any rate b and b' as such result from plastic strain in yielding. In case of no yielding b = b' = 0 corresponding to that ao = aB = zb.