き裂進展の非線型欠陥モデル

概要

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In the previous paper, a Nonlineer-Defect-Model of the crack initiation by tensile deformations was proposed. Based on the assumption that there is a defect of mechanically nonlinear character in a one-dimensional crystal, at which Young's modulus E veries with the strain ε as E=E_0(1-β_ε), where E_0 and β are constants, it has been found that the strain at the defect ε is given in terms of the stress σ as ε=1/2β(1±√<1-4βσ/E_0>) and also β governs the fructure stress σ_c=E_0/4β. In this paper, the above model is developed further in order to explain explicitly the crack propagation. When it is assumed that nonlinear character of E depends on ε with a small time lag ξ as E=E_0(1-βε+βξ(dε/dt)), then ε is defined as the solution of the following equation [numerical formula]. The analytical solution has been obtained for each case of σ⪋σ_c. Of special interest is the solution for σ>σ_c, which is the formulated expression of the crack propagation when ε increases with time to infinity. Lastly, the applicability of the present model on the actual crack propagation in a three-dimensional body has been discussed.
社団法人日本材料学会の論文
1972-11-15