A generating function for the yield criterion of isotropic and anisotropic polycrystalline materials |
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Authors: | W Crans |
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Institution: | (1) Laboratorium voor Metaalkunde, Technische Hogeschool Delft, The Netherlands |
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Abstract: | Summary A yield criterion for elastic pure-plastic polycrystalline materials is generated under simplified conditions by assuming that for yielding a certain fraction Q
c of the total number of slip planes in the material has to be active. This fraction Q
c is called the critical active quantity. We suppose Q
c to be independent of the state of stress. The yield criterion is mathematically expressed as an integral, which is a function of Q
c. This criterion can also be used for anisotropic materials.For isotropic materials the ratio (r) of the yield stress in torsion to that in tension is calculated as a function of Q
c. We find 0.5r0.61.The value r=0.5 (Tresca's criterion) is obtained for Q
c=0 and Q
c=1. The value r=0.577 (von Mises criterion) is obtained for Q
c=0.34 and Q
c=0.79. The difference between two criteria with the same r is the magnitude of the yield stress. We think the value Q
c=0.79 corresponds to the experiments for f.c.c. materials, since a rough estimation gives Q
c>0.75 for yielding.The independence of Q
c on the state of stress brings on that r>0.5 is more probable. This is caused by the slower increase to Q
c in torsion compared with the case of tension.From the theory follows that in the general case (Q
c0) the middle principal stress has influence on yielding.In this paper we don't determine Q
c, but adapt its value to the experimental results. However, a rough estimation of Q
c is given for isotropic materials. |
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