By William F. Hosford

This booklet is perfect for these curious about designing sheet steel forming strategies. wisdom of plasticity is vital for the pc simulation of steel forming techniques, and figuring out the advances in plasticity idea is vital to formulating sound analyses. during this booklet, William Hosford makes the themes basic via fending off notations utilized by experts in mechanics. R. Hill's authoritative e-book, Mathematical thought of Plasticity (1950), offered a finished therapy of continuum plasticity thought as much as that point; even supposing a lot of the therapy during this e-book covers an analogous floor, it makes a speciality of more effective issues. Hosford has additionally integrated contemporary advancements in continuum conception, together with a more moderen therapy of anisotropy that has resulted from calculations of yielding according to crystallography, research of the function of defects, and forming restrict diagrams. this article additionally places a miles larger emphasis on deformation mechanisms, and contains chapters on slip and dislocation concept and twinning

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**Example text**

VON MISES CRITERION It might seem reasonable to assume that yielding would be affected by the intermediate principal stress. Yielding cannot depend on the average of the diameters of the three Mohr’s circles, [(σ1 − σ2 ) + (σ2 − σ3 ) + (σ1 − σ3 )]/3, because the intermediate stress term, σ2 , drops out of the average, [(σ1 − σ2 ) + (σ2 − σ3 ) + (σ1 − σ3 )]/3 = (2/3)(σ1 − σ3 ), so an average diameter criterion reduces to the Tresca criterion. The effect of the intermediate principal stress can, however, be included by assuming that yielding depends on the root-mean-square diameter of the three Mohr’s circles.

At yielding, σx = σ3 = −Y, σy = σz = σ2 = σ3 = 0. Therefore, (σ2 − σ3 ) > (σ1 − σ2 ), so criterion 2 applies, and C = (σ1 − σ3 ) + (σ2 − σ3 ) = −(−2Y) or C2 = 2Y. 7). 7. Another isotropic yield locus. 7), and using symmetry to construct the left hand half, this criterion extends the yield locus the maximum amount into the first quadrant, with σx /Y = 4/3. 8. 8. Equivalent regions of an isotropic yield locus. From W. F. Hosford, The Mechanics of Crystals and Textured Polycrystals, Oxford University Press (1993).

Tresca, Comptes Rendus Acad. Paris v. 59 (1864). ¨ R. Von Mises, Gottin. Nachr. Math. Phys. v. 1 (1913). W. Lode, Z. Phys v. 36 (1926). G. I. Taylor and H. Quinney, Phil. Trans. Roy. Soc A. v. 230 (1931). B. Paul, in Fracture, An Advanced Treatise, Mathemetical Fundamentals, Liebowitz ed, v. Academic Press (1968). 6. W. F. Hosford, J. Appl. Mech. (Trans. ) v. 39E (1972). 7. M. Levy, Comptes Rendus Acad. Paris v. 7 (1870). 8. W. F. Hosford and R. M. Caddell, Metal Forming: Mechanics and Metallurgy, 4th ed, Cambridge University Press (2011).