5-1 求取裂縫尖端應力強度因子之方法
(1)首先在已建立模型的裂縫尖端預設刻槽，比例分別為：2s/a=0.1、2s/a=0.2、2s/a=0.3、
2s/a=0.4、2s/a=0.5、2s/a=0.6。如圖 5-1 所示。
(2)再將各比例之預設刻槽的應力強度因子以位移外插法計算出。
(3)最後將所求得各預設刻槽的破裂韌度值，以線性迴歸方式求得裂縫尖端的應力強度因子。
圖5-1 假想之裂紋擴展刻槽
5-2 無圍束作用試體應力強度因子
各比例計算出的應力強度因子結果如表5-1 所示。由圖 5-2 可知應力強度因子先隨間距 比增加而增加，至間距比為0.25 時最大，之後隨之下降。破裂韌度值約在 0.20-0.41MPa*m1/2 之間。
表5-1裂縫間距比與破壞時之應力強度因子(無圍束)( 單位：MPa*m1/2) 破壞時之應力強度因子(破壞韌度) a/w
平面應變狀況 平面應力狀況
0.1 0.204 0.205
0.15 0.222 0.227
0.2 0.325 0.341
0.25 0.413 0.414
0.3 0.392 0.407
5-3 具圍束作用試體應力強度因子
推求出各種裂縫比率之裂縫幾何校正函數，繪出其校正曲線，如圖5-4 所示。
最後將本研究所求出之結果與Kemeny (2006) 校正曲線做比較，發現隨著裂縫間距比增 加校正係數亦會跟著增加而非Wakins (1985) 所提出幾何校正係數為常數。
0.0 0.1 0.2 0.3 0.4
0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26 0.28 0.3 裂縫間距比(a/w)
裂縫幾何函數F(a/w)
具圍束作用之試體 (本研究,2007)"
無圍束作用之試體 (Watkins&Liu,1985)
"
具圍束作用之試體 (Kemeny,2006)"
圖5-5 與前人文獻幾何校正曲線圖
六、 結論
參考文獻
1. Atkinson, C., Smelser, R.E., Sanchez, J. (1982), “Combined mode fracture via the cracked Brazilian disk test,” International Journal of Fracture, 18, 279-291.
2. Awaji, H., Sato, S. (1978), “Combined mode fracture toughness measurement by the disk test,” Journal of Engineering Materials and Technology, 100, 175-182.
3. Ayatollahi, M.R., Aliha, M.R.M. (2005), “Cracked Brazilian disc specimen subjected to mode II deformation,” Engineering Fracture Mechanics, 72, 493-503.
4. Ayatollahi, M.R., Aliha, M.R.M. (2006), “On determination of mode II fracture toughness using semi-circular bend specimen,” International Journal of Solids and Structures, 43, 5217-5227.
5. Ballatore, E., Carpinteri, A., Ferrara, G., Melchiorri, G. (1990), “Mixed mode fracture energy of concrete,” Engineering Fracture Mechanics, 35, 145-157.
6. Banks-Sills, L., Arcan, M. (1983), “An edge-cracked mode II fracture specimen,”
Experimental Mechanics, 23,257-261.
7. Banks-Sills, L., Arcan, M., Bui, H.D. (1983), “Toward a pure shear specimen for KIIc determination,” International Journal of Fracture, 22, R9-R14.
8. Bansal, A., Kumosa, M. (1995), “Application of the biaxial Iosipescu method to mixed-mode fracture of unidirectional composites,” International Journal of Fracture, 71, 131-150.
9. Barr, B., Derradj, M. (1990), “Numerical study of a shear (mode II) type test specimen geometry,” Engineering Fracture Mechanics, 35, 171-180.
10. Barret, J.D., Foschi, R.O. (1977), “Mode II stress-intensity factors for cracked wood beams,”
Engineering Fracture Mechanics, 9, 371-378.
11. Bažant, Z.P., Pfeiffer, P.A. (1986), “Shear fracture test of concrete,” Materials and Structures, 110, 111-121. Biolzi, L. (1990), “Mixed mode fracture in concrete beams,” Engineering Fracture Mechanics, 35, 187-193.
12. Blandford, G.E., Ingraffea, A.R., Liggett, J.A. (1981), “Two-dimentional stress intensity factor computations using the boundary element method,” International Journal for Numerical Method in Engineering, 17, 387-404.
13. Bocca, P., Carpinteri, A., Valente, S. (1990), “Size effect in the mixed mode crack propagation:
softening and snap-back analysis,” Engineering Fracture Mechanics, 35, 159-170.
14. Chisholm, D.B., Jones, D.L. (1977), “An analytical and experimental stress analysis of a practical mode II fracture test specimen,” Experimental Mechanics, 17, 7-13.
15. Chong, K.P., Kuruppu, M.D. (1984), “New specimen for fracture toughness determination for rock and other materials,” International Journal of Fracture, 26, R59-R62.
16. Cramer, S.M., Pugel, A.D. (1987), “Compact shear specimen for wood mode II fracture investigations,” International Journal of Fracture, 35, 163-174.
17. Davanport, J.C.W., Simth, D.J. (1993), “A study of superimposed fracture modes I, II, III on PMMA,” Fatigue and Fracture of Engineering Materials and Structures, 16, 1125-1133.
18. Davies, J., Morgan, T.G., Yim, A.W. (1985), “The finite element analysis of a punch-through shear specimen in mode II,” International Journal of Fracture, 28, R3-R10.
19. Davies, J., So, K.W. (1986), “Further development of fracture test in mode II,” International Journal of Fracture, 31, R19-R21.
20. Debaise, G.R. (1972), “Morphology of wood shear fracture,” Journal of Materials, 7, 568-572.
21. Moura, M.F.S.F., Silva, M.A.L., de Morais, A.B., Morais, J.J.L. (2006), “Equivalent crack based mode II fractuer charactreization of wood,” Engineering Fracture Mechanics, 73, 978-993.
22. Hallbäck, N., Jönsson, N. (1996), “T-stress evaluations of mixed mode I/II fracture specimens and T-effects on mixed mode failure of aluminium,” International Journal of Fracture, 76, 141-168.
23. Huang, J., Wang, S. (1985), “An experimental investigation concerning the comprehensive fracture toughness of some brittle rocks,” International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 22, 99-104.
24. Hunt, D.G., Croager, W.P. (1982), “Mode II fracture toughness of wood measured by a mixed-mode test method,” Journal of materials science letters, 1, 77-79.
25. Iosipescu, N. (1967), “New accurate procedure for single shear testing of metals,” Journal of Materials, 2, 537-566.
26. Jones, D.J., Chisholm, D.B. (1975), “An investigation of the edge-sliding mode in fracture mechanics,” Engineering Fracture Mechanics, 7, 261-270.
27. Ko, T.Y., Kemeny J. (2006), “Determination of mode II stress intensity factor using short beam compression test,” In: Leung, C.F., Zhou, Y.X. (eds.) Chapter 7.2. In-Situ and Laboratory Tests, ISRM International Symposium 2006- 4th Asian Rock Mechanics Symposium.
28. Kumosa, M., Hull, D. (1987), “Mixed-mode fracture of composites using Iosipescu shear test,”
International Journal of Fracture, 35, 83-102.
29. Laqueche, H., Rousseau, A., Valentin, G. (1986), “Crack propagation under mode I and mode II loading in slate schist,” International Journal of Rock Mechanics and Mining Sciences &
Geomechanics Abstracts, 23, 347-354.
30. Liu, K., Barret, B.I.G., Watkins, J. (1985), “Mode II fracture of fibre reinforced concrete materials,” The International Journal of Cement Composites and Lightweight Concrete, 7, 93-101.
31. Luong, M.P. (1990), “Tensile and shear strengths of concrete and rock,” Engineering Fracture Mechanics, 35, 127-135.
32. Mahajan, R.V., Ravi-Chandar, K. (1989), “An experimental investigation of mixed-mode fracture,” International Journal of Fracture, 41, 235-252.
33. Mall, S., Murphy, J.F., Shottafer, J.E. (1983), “Criterion for mixed mode fracture in wood,”
ASCE-Journal of Engineering Mechanics, 109, 680-690.
34. Raju, K.R. (1981), “On the sliding mode stress intensity factors for a three-point bend KII
specimen and mode II fracture toughness,” International Journal of Fracture, 17, R193-R197.
35. Rao, Q., Sun, Z., Stephansson, O., Li, C., Stillborg, B. (2003), “Shear fracture (mode II) of brittle rock,” International Journal of Rock Mechanics and Mining Sciences, 40, 355-375.
36. Reinhardt, H. W., Xu, S. (1998), “Experimental determination of K of normal strength
energy GIIF for concrete,” International Journal of Fracture, 105, 107-125.
38. Richard, H.A. (1981), “A new compact shear specimen,” International Journal of Fracture, 17, R105-R107.
39. Swartz, S.E., Lu, L.W., Tang, L.D., Refai, T.M.E. (1988), “Mode II fracture-parameter estimates for concrete from beam specimens,” Experimental Mechanics, 28,146-153.
40. Swartz, S.E., Taha, N.M. (1990), Engineering Fracture Mechanics, 35, 137-144.
41. Watkins, J. (1983), “Fracture toughness test for soil-cement samples in mode II,” International Journal of Fracture, 23, R135-R138.
42. Watkins, J., Liu, K.L.W. (1985), “A finite element study of the short beam test specimen under mode II loading,” The International Journal of Cement Composites and Lightweight Concrete, 7, 37-47.
43. Williams, J.G., Birch, M.W. (1976), “Mixed mode fracture in anisotropic media,” in Cracks and Fractures, ASTM STP 601, ASTM, 125-137.
44. Woo, C.W., Kuruppu, M.D. (1982), “Use of finite element method for determining stress intensity factors with a conic-section simulation model of crack surface,” International Journal of Fracture, 20, 163-178.
45. Wu, E.M. (1967), “Application of fracture mechanics to anisotropic plates,” Journal of Applied Mechanics, 12, 967-974.
46. Xu, S., Reinhardt, H. W., Gappoev, M. (1996), “Mode II fracture testing method for highly orthotropic materials like wood,” International Journal of Fracture, 75, 185-214.
47. 黃國彰，’’人工岩石材料之節理面的剪力強度研究’’，國立成功大學土木工程研究所碩 士論文，2004。
48. 鄭富書，’’軟弱岩盤承載行為研究（I）’’，行政院國家科學委員會專題研究計畫成果報 告，1994。
附錄A
2008 年發表於礦冶期刊
附錄B
2008 年發表於 Journal of Testing and Evaluation 相關文章(審查中)