By T. Z. Blazynski
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Additional info for Applied Elasto-plasticity of Solids
1c, the externally applied system of loading results in the presence of direct stresses a, and shear stresses T, acting on all the faces of our elementary cube . The notation used there indicates the interchangeability of the subscripts i and j, which denote the surface on which the stress is present and the direction in which it acts. Direct stresses are thus denoted by i = j and shear stresses by i =1= j. 1c that this condition is satisfied if the nine com- ponent forces of the system are considered to be mutually balanced in the three perpendicular directions.
YdA. C 1 0.. xdA. 4 By projecting the component forces in directions normal and tangential to CD, we obtain the following equations SNdA N = axxdA N sin6 0 + ayydAN coslO - 2a x ydA N sin 0 cos 0 SgdA N = axxdA N sin 0 cos 0 --- ayydA N cos 0 sin 0 + axydA N (sin20 - cos20) or SN = 1(ax x + ayy) + 1(ayy -- axx)cos 20 -- a x y sin 20 Sg = 1(ayy -- a x x) sin 20 + ax y cos 20 The above equations give the variation of stress components with the angle O. To locate the principal planes , we consider the maximum and minimum values of sN respectively .
7 These depend for practical and theoretical reasons on (a) retaining in the same indentation, the incremental nature of loading, with the increments not exceeding 2 per cent in the plastic range, (b) maintaining the ratio b/h between 2 and 4 by changing the dies when required and (c) ensuring that w/b > 6. The basic stress-strain curve for the material thus obtained will be that of true stress and natural strain . 4 Torsion test The distortion of the specimen experienced in tensile and compressive testing, on the one hand, and the relatively low rates of straining obtainable, on the other , have led to the increasing use of the torsion test.