By Shiva P.
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We need, clearly, to express the nominal stress s in terms of σ. 7) ///. Thus, the value of s corresponding to any point B in Fig. 7 is given by the slope of the line OB or, equivalently, the intercept on the line //<> = 1. Therefore as the load on the specimen increases the point B travels along the curve, until it reaches the point, Γ, where OB touches the curve, when the load cannot be increased SPECIFICATION OF AN IDEAL PLASTIC MATERIAL 25 any more. Any subsequent elongation of the bar must take place with falling load, and for a value of s below the maximum value there are now two possible paths (both lying on a line of slope s from the origin); one (TC) involving more plastic deformation and the other (TD) involving elastic unloading.
18 shows the combined principal stress/principal strain increment space, viewed along the leading diagonal, as before. In order to associate each strain increment vector with the corresponding stress vector, we plot it with the corresponding stress point as a "floating" origin. 12)) and they are in fact perpendicular to the (Tresca) C-curve locally. Similar relationships apply to the other sides of the hexagon. 13), but the strain increment vector lies between the normals to adjacent sides. 11) ensures that the strain increment vector is always parallel to the π-plane which in 44 ENGINEERING PLASTICITY turn is perpendicular to the faces of the yield surface.
In this book we shall be concerned not so much with the way the yield locus changes its shape or size as the load point "pierces" it, but with the general form of the locus for an elementary block of material at a given stage in its history of plastic deformation. 8. Yield Surface for Three-dimensional Stress In general the state of stress at a point in a body is specified by the values of the six independent stress components σΧ9 σ„, σζ, Tyr, τζχ, Txy referred to an arbitrary set of orthogonal x, y, z axes SPECIFICATION OF AN IDEAL PLASTIC MATERIAL 33 (see Fig.