Science & Technology Review >

2020 , Vol. 38 >Issue 2: 59 - 68

DOI: https://doi.org/10.3981/j.issn.1000-7857.2020.02.007

Papers

Research progress of fracture criteria in linear elastic fracture mechanics of materials

  • YANG Liyun ,
  • WANG Qingcheng ,
  • WANG Yuwei ,
  • XU Longning ,
  • SONG Ye ,
  • WANG Guidong
Expand
  • School of Mechanics and Civil Engineering, China University of Mining and Technology-Beijing, Beijing 100083, China

Received date: 2019-06-10

  Revised date: 2019-10-20

  Online published: 2020-04-01

Fold

Abstract

The fracture criterion is of great significance in predicting the time, the position and the crack propagation path for materials containing crack. In this paper, the fracture criteria of the linear elastic materials are reviewed, including the common fracture criteria, such as the stress intensity factor criterion, the maximum energy release rate criterion, the maximum tensile stress criterion, the maximum tensile strain criterion and the minimum strain energy density criterion, as well as their advantages and limitations. In view of the insufficient consideration of the stress components and the critical radius in the commonly used fracture criteria, some modified fracture criteria were proposed at home and abroad, including those considering the influence of the T-stress (non-singular term) and the variable critical radius rc. The application of these fracture criteria in brittle materials such as rock and concrete is analyzed. In view of the problems existing in the prediction of the fracture behavior based on these fracture criteria, it is suggested that the propagation path and the deflection angle of the crack can be predicted more accurately when the T-stress, the higher-order term of the stress field at the crack tip, is considered.

Key words： material crack; linear elastic fracture; fracture criterion

Cite this article

YANG Liyun , WANG Qingcheng , WANG Yuwei , XU Longning , SONG Ye , WANG Guidong . Research progress of fracture criteria in linear elastic fracture mechanics of materials[J]. Science & Technology Review, 2020 , 38(2) : 59 -68 . DOI: 10.3981/j.issn.1000-7857.2020.02.007

References

[1] Dally J W, Fourney W L, Irwin G R. On the uniqueness of the stress intensity factor:Crack velocity relationship[J]. International Journal of Fracture, 1985, 27(3-4):159-168.
[2] Erdogan F, Sih G C. On the crack extension in plates under plane loading and transverse shear[J]. Journal of Basic Engineering, 1997, 12(4):527-535.
[3] Palaniswamy K. Crack propagation under general inplane loading[D]. Pasadena:California Institute of Technology, 1972.
[4] Sih G C. Strain-energy-density factor applied to mixed mode crack problems[J]. International Journal of Fracture, 1974, 10(3):305-321.
[5] Sih G C. Some basic problems in fracture mechanics and new concepts[J]. Engineering Fracture Mechanics, 1973, 5(2):365-377.
[6] Xu S L, Reinhardt H W. Determination of double-K, criterion for crack propagation in quasi-brittle fracture, Part II:Analytical evaluating and practical measuring methods for three-point bending notched beams[J]. International Journal of Fracture, 1999, 98(2):151-177.
[7] Kumar S, Barai S V. Determining the double-K fracture parameters for three-point bending notched concrete beams using weight function[J]. Fatigue & Fracture of Engineering Materials & Structures, 2010, 33(10):645-660.
[8] Yu K Q, Lu Z D. Determining residual double-K fracture toughness of post-fire concrete using analytical and weight function method[J]. Materials and Structures, 2013, 47(5):839-852.
[9] 徐世烺, 赵国藩. 混凝土结构裂缝扩展的双K断裂准则[J]. 土木工程学报, 1992, 25(2):32-38.
[10] 马颖利. 实验研究混凝土双参数模型和双K断裂准则[D]. 大连:大连理工大学, 2002.
[11] 杨锋平, 孙秦, 罗金恒, 等. 平面状态下EWK延性断裂准则与K准则对比研究[J]. 船舶力学, 2011, 15(5):506-512.
[12] 王殿富. 可靠性设计对断裂力学K-准则的一个应用[J]. 哈尔滨工业大学学报, 1980(4):15-21.
[13] Vallejo L E. The brittle and ductile behavior of clay samples containing a crack under mixed mode loading[J]. Theoretical & Applied Fracture Mechanics, 1988, 10(1):73-78.
[14] Selcuk S, Hurd D S, Crouch S L, et al. Prediction of interfacial crack path:A direct boundary integral approach and experimental study[J]. International Journal of Fracture, 1994, 67(1):1-20.
[15] Plank R, Kuhn G. Fatigue crack propagation under nonproportional mixed mode loading[J]. Engineering Fracture Mechanics, 1999, 62(2-3):203-229.
[16] 刘小妹, 刘一华, 梁拥成. V型切口脆性断裂的最大周向应力准则[J]. 合肥工业大学学报(自然科学版), 2004, 27(9):1043-1046.
[17] 刘一华, 崔书文, 陈继光. 结合材料界面端脆性断裂的最大周向应力准则[J]. 合肥工业大学学报(自然科学版), 2007, 30(2):200-202.
[18] Chang K J. On the maximum strain criterion-a new approach to the angled crack problem[J]. Engineering Fracture Mechanics, 1981, 14(1):107-124.
[19] 金浏, 杜修力, 黄景琦. 多轴加载下混凝土细观破坏模拟的强度准则探讨[J]. 计算力学学报, 2015, 32(3):322-331.
[20] 翟越, 赵均海, 艾晓芹, 等. 基于统一强度理论的巴西圆盘劈裂强度分析[J]. 建筑科学与工程学报, 2015, 32(3):46-51.
[21] 沈成康. 断裂力学[M]. 上海:同济大学出版社, 1996.
[22] Kipp M E, Sih G C. The strain energy density failure criterion applied to notched elastic solids[J]. International Journal of Solids & Structures, 1975, 11(2):153-173.
[23] Gdoutos E E, Brock L M. Problems of mixed mode crack propagation[M]. Leiden:Martinus Nijhoff Press, 1984.
[24] 尹华杰. 复合型裂纹的脆性断裂应变能密度因子理论的精确解法[J]. 郑州工学院学报, 1989, 10(4):105-110.
[25] Maiti S K, Smith R A. Comparison of the criteria for mixed mode brittle fracture based on the preinstability stress-strain field[J]. International Journal of Fracture, 1984, 24(1):5-22.
[26] 孙倩, 李树忱, 冯现大, 等. 基于应变能密度理论的岩石破裂数值模拟方法研究[J]. 岩土力学, 2011, 32(5):1575-1582.
[27] 张少琴, 朱永昭, 胡海平. 关于复合材料单层板Ⅰ型裂纹应变能密度因子的推导和讨论[J]. 太原重型机械学院学报, 1986, 7(3):25-32.
[28] Qian R J. Applying strain energy density factor theory to propagation estimating of surface crack in tubular Tjoints[J]. Engineering Fracture Mechanics, 1996, 53(6):849-851, 853-858.
[29] Nuismer R J. An energy release rate criterion for mixed mode fracture[J]. International Journal of Fracture, 1975, 11(2):245-250.
[30] Griffith A A. The phenomena of rupture and flow in solids[J]. Philosophical Transactions of the Royal Society of London, 1921, 221(2):163-198.
[31] 赵诒枢. 最大能量释放率准则及其近似[J]. 机械强度, 1984(4):29-34.
[32] 赵诒枢. 广义最大能量释放率断裂准则[J]. 华中工学院学报, 1985, 13(1):57-60.
[33] Wu C H. Maximum-energy-release-rate criterion applied to a tension-compression specimen with crack[J]. Journal of Elasticity, 1978, 8(3):235-257.
[34] Claydon P W. Maximum energy release rate distribution from a generalized 3D virtual crack extension method[J]. Engineering Fracture Mechanics, 1992, 42(6):961-969.
[35] Lim I L, Johnston I W, Choi S K, et al. Fracture testing of a soft rock with semi-circular specimens under threepoint bending(Part 1-mode I)[J]. International Journal of Rock Mechanics & Mining Sciences & Geomechanics Abstracts, 1994, 31(3):185-197.
[36] Aliha M R M, Ashtari R, Ayatollahi M R. Mode I and mode II fracture toughness testing for a coarse grain marble[J]. Applied Mechanics & Materials, 2006, 5:181-188.
[37] Khan K, Al-Shayea N A. Effect of specimen geometry and testing method on mixed mode I-II fracture toughness of a limestone rock from Saudi Arabia[J]. Rock Mechanics and Rock Engineering, 2000, 33(3):179-206.
[38] Williams M L. On the stress distribution at the base of a stationary crack[J]. Journal of Applied Mechanics, 1959, 24:109-114.
[39] Williams J G, Ewing P D. Fracture under complex stress:The angled crack problem[J]. International Journal of Fracture Mechanics, 1972, 8(4):441-446.
[40] Smith D J, Ayatollahi M R, Pavier M J. The role of Tstress in brittle fracture for linear elastic materials under mixed-mode loading[J]. Fatigue & Fracture of Engineering Materials & Structures, 2010, 24(2):137-150.
[41] Aliha M R M, Ayatollahi M R, Smith D J, et al. Geometry and size effects on fracture trajectory in a limestone rock under mixed mode loading[J]. Engineering Fracture Mechanics, 2010, 77(11):2200-2212.
[42] Ayatollahi M R, Aliha M R M, Hassani M M. Mixed mode brittle fracture in PMMA:An experimental study using SCB specimens[J]. Materials Science & Engineering:A, 2006, 417(1):348-356.
[43] 赵艳华, 陈晋, 张华. T应力对Ⅰ-Ⅱ复合型裂纹扩展的影响[J]. 工程力学, 2010, 27(4):5-12.
[44] 唐世斌, 黄润秋, 唐春安, 等. 考虑T应力的最大周向应变断裂准则研究[J]. 土木工程学报, 2016, 49(9):87-95.
[45] Akbardoost J, Ayatollahi M R. Experimental analysis of mixed mode crack propagation in brittle rocks:The effect of non-singular terms[J]. Engineering Fracture Mechanics, 2014, 129:77-89.
[46] Mirsayar M M. Mixed mode fracture analysis using extended maximum tangential strain criterion[J]. Materials & Design, 2015, 86:941-947.
[47] Mirsayar M M, Razmi A, Aliha M R M, et al. EMTSN criterion for evaluating mixed mode I/II crack propagation in rock materials[J]. Engineering Fracture Mechanics, 2018, 190:186-197.
[48] Hua W, Dong S, Pan X, et al. Mixed mode fracture analysis of CCBD specimens based on the extended maximum tangential strain criterion[J]. Fatigue & Fracture of Engineering Materials & Structures, 2017, 40(12):2118-2127.
[49] Deda Y, Ikeda K, Yao T, et al. Characteristics of brittle fracture under general combined modes including those under bi-axial tensile loads[J]. Engineering Fracture Mechanics, 1983, 18(6):1131-1158.
[50] Ewing P D, Williams J G. The fracture of spherical shells under pressure and circular tubes with angled cracks in torsion[J]. International Journal of Fracture, 1974, 10(4):537-544.
[51] Maiti S K, Smith R A. Comparison of the criteria for mixed mode brittle fracture based on the preinstability stress-strain field[J]. International Journal of Fracture, 1984, 24(1):5-22.
[52] 高文, 王生楠. T应力对线弹性材料脆性断裂的影响[J]. 西北工业大学学报, 2015, 33(6):928-935.
[53] Ayatollahi M R, Moghaddam M R, Berto F. A generalized strain energy density criterion for mixed mode fracture analysis in brittle and quasi-brittle materials[J]. Theoretical & Applied Fracture Mechanics, 2015, 79:70-76.
[54] Marsavina L, Berto F, Negru R, et al. An engineering approach to predict mixed mode fracture of PUR foams based on ASED and micromechanical modelling[J]. Theoretical & Applied Fracture Mechanics, 2017, 91:148-154.
[55] Moghaddam M R, Ayatollahi M R, Berto F. Mixed mode fracture analysis using generalized averaged strain energy density criterion for linear elastic materials[J]. International Journal of Solids & Structures, 2017, 120:137-145.
[56] Hou C, Jin X C, Fan X L, et al. A generalized maximum energy release rate criterion for mixed mode fracture analysis of brittle and quasi-brittle materials[J]. Theoretical and Applied Fracture Mechanics, 2019, 100:78-85.
[57] Lazzarin P, Zambardi R. A finite-volume-energy based approach to predict the static and fatigue behavior of components with sharp V-shaped notches[J]. International Journal of Fracture, 2001, 112(3):275-298.
[58] Theocaris P S, Andrianopoulos N P. The Mises elasticplastic boundary as the core region in fracture criteria[J]. Engineering Fracture Mechanics, 1982, 16(3):425-432.
[59] Theocaris P S, Andrianopoulos N P. The T-criterion applied to ductile fracture[J]. International Journal of Fracture, 1982, 20(4):R125-130.
[60] Khan S M A, Khraisheh M K. Analysis of mixed mode crack initiation angles under various loading conditions[J]. Engineering Fracture Mechanics, 2000, 67(5):397-419.
[61] Ukadgaonker V G, Awasare P J. A new criterion for fracture initiation[J]. Engineering Fracture Mechanics, 1995, 51(2):265-274.
[62] Yan X Q, Zhang Z H, Du S Y. Mixed-mode fracture criteria for the materials with different yield strengths in tension and compression[J]. Engineering Fracture Mechanics, 1992, 42(1):109-116.
[63] 李贺. 岩石断裂力学[M]. 重庆:重庆大学出版社, 1988.
[64] 孙欣, 朱哲明, 谢凌志, 等. 基于SENDB试样的砂岩复合脆性断裂行为研究[J]. 岩石力学与工程学报, 2017, 36(12):2884-2894.
[65] 李部, 黄润秋, 吴礼舟. 类岩石脆性材料非闭合裂纹的Ⅰ-Ⅱ压剪复合型断裂准则研究[J]. 岩土工程学报, 2017, 39(4):662-668.
[66] 侯泉林, 程南南, 石梦岩, 等. 不同构造层次岩石变形准则的融合与发展[J]. 岩石学报, 2018, 34(6):1792-1800.
[67] 李智慧, 师俊平, 汤安民. 复杂应力状态下岩石的破坏形式及断裂准则探讨[J]. 固体力学学报, 2015, 36(Supple 1):50-57.
[68] 代继飞. 基于双K准则的多尺寸聚丙烯纤维混凝土断裂韧性研究[D]. 重庆:重庆大学, 2017.
[69] 许斌, 江见鲸. 混凝土Ⅰ-Ⅱ复合型断裂判据研究[J]. 工程力学, 1995, 12(2):13-21.
[70] 黄作宾. 断裂力学基础[M]. 北京:中国地质大学出版社, 1991.
Options
Outlines

/

〈 〉

Contact

  • Add：No. 86 Xueyuan South Road, Haidian District, Beijing　 Postal Code：100081
  • Tel: +86-10-62138113　Fax: +86-10-62138113
  • E-mail：kjdbbjb@cast.org.cn

    • Visited

      Total visitors:
      Visitors of today:
      Now online:
    Copyright © Science & Technology Review, All Rights Reserved.