引張試験における拡散くびれに及ぼす周辺圧力の影響に関する理論的考察

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At some value of the elongation a loss of uniquencess of the uniaxial state can be expected signaling the onset of necking. A problem of some interest in the theory of plastic instability arises from considering a tensile test conducted on a metal specimen whose lateral surface is simultaneously subjected to uniform fluid pressure. The question is this : What effect does the fluid-pressure have on the amount of uniform elongation that is possible before the onset of necking? The effect of hydrostatic pressure on the necking of plastic solids has long been a point of controversy. However, Hill first proved that lateral pressure does not affect the tensile necking. Hill^<(4)> used his sufficient criterion for unique solution in his proof, and in the discussion of specimen subjected to lateral pressure p the stress σ_<ij >appearing in his criterion was replaced by σ_<ij>+pδ_<ij>. This replacement cannot be complied with because the stress σ_<ij> is introduced from the definition of nominal stress rate. Therefore, his argument is unsatisfactory. We proposed recently criterion for multiplicity, and in applying the criterion it must be emphasized to consider the condition of load instability which can lead the state of specimen to active eigenstate. In this paper we apply criteria of multiplicity and load instability to the discussion of tensile instability, and make a detailed study of their relationship in evaluating the onset of necking. The result shows the strain at which necking occurs dependent on hydrostatic pressure.
1999-11-25

引張試験における拡散くびれに及ぼす周辺圧力の影響に関する理論的考察

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