Engineering Plasticity by C. R. Calladine and B. G. Neal (Auth.)

By C. R. Calladine and B. G. Neal (Auth.)

Nice classic engineering booklet!

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Extra resources for Engineering Plasticity

Sample text

All we can say in these circumstances is (8 €l , Se2, 8e3) = λ (1, 0, - 1 ) + μ (1, - 1 , 0), λ ^ 0, μ > 0. 13) It is instructive to plot plastic strain increments in a space whose axes are parallel to the principal stress axes. 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· The "Normality" Rule The "normality" of the associated plastic strain increment vector to the yield surface for the Tresca plastic material is indeed FIG. 18. Normality of the strain-increment vector to the Tresca yield surface. not accidental. "Normality" is a general rule which applies not only to plastic material but also, as we shall see, in the appropriate load-space, to structures made of plastic material. Its generality may be appreciated to some extent by means of the idea of maximum plastic work.

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.

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