き裂成長形態の予測に関する基礎研究

(その2) き裂成長経路の安定性について

抄録

In order to obtain the precise failure process of structures, the importance has recently been recognized for the crack growth path of structures under tensile loading conditions. Several criteria had been proposed for the determination of the crack growth direction, i. e. the criteria of maximum hoop stress, minimum strain energy density, locally symmetric deformation, and maximum energy release rate. Using these criteria the finite initial branch angle of the crack growth can be predicted, if the stress intensity factor of the in-plane shear mode, K_II, exists at the pre-existing crack tip.
The abrupt crack curving is, however, often observed even if K_II≅0 at the crack tip, where severe bending or biaxial stress condition holds. Recently Cotterell and Rice examined this problem, and proposed the T-stress theory by using a small perturbation technique, in which they introduced the concept of stability for the crack growth path. T-stress is defined as the constant component of the normal stress acting parallel to the crack line, when the near tip stress field is expanded in terms of the distance from the crack tip. In their theory, if T>0, the crack growth path is unstable, i. e. the abrupt crack curving is expected, and vice versa. In case of biaxially stressed plate, this theory is successful in predicting the crack path stability, while the crack path is stable for the compact-tension specimen even though the T-stress is positive. Therefore the generality of the theory is still open to question.
In the present paper, based upon the crack path prediction obtained in the first report, the authors introduce the concept of intermediate range of stability for the crack growth path. This stability concept includes the length parameter corresponding to the crack growth, while only the immediate range of stability is considered by the theory of Cotterell and Rice. Numerical calculations are performed by using the finite element method, and the stability of the present theory is determined for various stress conditions at the crack tip. The numerical results clarify the difference of the present and Cotterell-Rice theories, and also confirm the stable crack growth path for the compact-tension type specimen.
Finally experiments are performed for the cases corresponding to the numerical calculations. The test specimens, which are made of PMMA, are prepared, and quasi-statically fractured under the monotonically increasing displacement with practically Mode I loading conditions. Various stable and unstable crack growth paths are observed, and the theoretical prediction of the stability for the crack growth path agrees quite well with the experimental results.