有限要素法による切欠き材のクリープ解析

In recent years much attention has been paid to the application of the finite element method to the continum mechanics, partly due to the rapid development of digital computers. In the present work, report is made of the method that was adopted to analyze the creep due to stress and that to strain in double edge V notched plates and circumference V notched round bars. The time dependent variation of stresses and strains in the transient stage of creep was calculated on the basis of a time-hardening hypothesis. The following results have been obtained:<br>(1) The Neuber's stress concentration factor K_t(Neuber) is smaller than the stress concentration factor K_t(FEM) obtained by the finite element analysis. Between the two the following relation is found both for the notched plates and for the notched round bars.<br>[K_t(FEM)-1]/[K_t(Neuber)-1]=1.3<br>(2) The maximum elastic stress at the notch root relaxes by creep, reaching its steady state after a certain lapse of time. The stress redistribution occurs more rapidly in the notched plates than in the notched bars having the same stress concentration factor and subject to the same magnitude of nominal stress.<br>(3) Steady stresses in the axial and tangential direction on the minimum cross section of the notched bars have their maximum values at a point below the notch root unlike those of the notched plates. The position of the maximum values of stress moves away from the notch root as the stress concentration factor decreases and the applied nominal stress increases. The results are closely related to the sharpness of strain concentration near the notch root and the extent of restraint of creep peformation on the specimen axis.<br>(4) The stress concentration factor K_σ for the steady stress is under a half of the elastic stress concentration factor K_t. The strain concentration factor K_ε at the time when the stresses reach their steady state is larger than K_σ, and K_ε is smaller than K_t, showing that the Neuber's rule does not hold in this case.<br>(5) The von Mises effective stress σ^* on the minimum cross section is maximum at the notch root both for the notched plates and for the notched bars. The mean value of the effective stress across the minimum cross section is smaller than the nominal stress.<br>(6) In the creep condition, the hydrostatic component of stress σ_m on the minimum cross section has its maximum value at a point below the notch root. This may be one of the factors which explain the experimental results on the origin of cracks lying just below the notch surface.