摘 要 Jk積分與應力強度因子是研究具裂縫物體之破壞行為的重要參數，因此研究重點為針對不同材料與具有不同裂縫形狀之物體，計算其Jk積分與應力強度因子。首先依序針對具任意曲線形狀之二維裂縫問題以及具任意曲面形狀之三維裂縫問題，進行Jk積分式之理論推導。其中J2積分，因裂縫尖端附近的應力場具有奇異性，造成裂縫尖端附近區域之有限元素網格的形式對J2積分的計算影響很大，在數值計算上往往不能得到準確值，因此J2積分值的計算顯得非常困難。本文提出一解決此問題的簡易方法，在裂縫尖端附近不需使用奇異元素或是複雜的網格，即可求得準確的J2值，且分別對等向性線彈性材料與非等向性線彈性材料進行數值分析。 研究中，對於等向性材料之具裂縫物體，由於應力強度因子與Jk積分具有一簡易關係式，故應力強度因子可藉由數值分析所得之Jk積分值直接求得。對於非等向性材料之具裂縫物體，應力強度因子與J1積分亦具有一關係式，但J2積分尚無相關文獻之探討；因此，本文先針對J2積分推導其與應力強度因子之關係式，再利用此二關係式與數值分析所得之Jk積分值求得應力強度因子。 此外，當具固定裂縫物體在承受動態載重作用之下，可由動態之Jk積分求得隨時間變化之應力強度因子，進而計算出動態載重作用下之應力強度因子與擬靜態因子之放大因數。 ABSTRACT A method based on the Jk integrals for arbitrary 2-D curve and 3-D surface crack problems is presented in this research. Due to stress singularity around the crack tip, the finite element meshes near crack tip will affect the J2 numerical value and it is difficult to accurately calculate this value. A simple and convenient approach is developed to obtain the accurate J2 value without using singular elements or complicated meshes. Both isotropic and anisotropic linear elastic materials are considered in this thesis. For isotropic materials, there exists a relationship between the stress intensity factors and Jk integrals. Accordingly, the stress intensity factors can be calculated by using the equations and the Jk values obtained from numerical analysis. For anisotropic materials, specific J1 integral has a relationship with the stress intensity factors. Nevertheless, there were no studies on J2 integral. In this research, an equation which describes the relation between J2 integral and the stress intensity factors is derived. Accordingly, the stress intensity factors can be obtained by the equations and the Jk values obtained from numerical analysis. Moreover, for the cases of a stationary crack under dynamic loading, one can get the elastodynamic stress intensity factors varying with time by the Jk values obtained from numerical analysis. Accordingly, the amplification factor which is a ratio of the elastodynamic stress intensity factors and the quasi-static stress intensity factors can be obtained.
