大理岩动态劈裂拉伸强度和裂纹起裂扩展特性
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摘要
确定岩石动态拉伸强度的方法是岩石力学研究领域中的重要课题之一。对岩石的动力学参数的实验测试,无论是在理论上还是在测试技术上,都存在诸多困难,寻找或建立新的动态拉伸测试技术已成为迫切需要解决的问题。
本文首次把平台巴西圆盘试样引入动态劈裂试验,利用直径100mm的分离式Hopkinson压杆(split Hopkinson pressure bar—SHPB)对大理岩巴西圆盘和平台巴西圆盘试样进行了宽应变率范围(14.6s~(-1)—163s~(-1))的动态劈裂实验,得到了不同尺寸的大理岩试样在不同应变率下的破坏应变。研究了试样有无平台、应变率、弹速、气压、温度对动态劈裂拉伸强度的影响。试验表明,通过粘贴在巴西圆盘中心的应变片来测量大理岩等脆性材料的动态拉伸强度,是一种简便高效的试验方法。另外,在试样表面加载直径方向粘贴一系列电阻应变片,用来记录试样加载直径上各点的应变随时间的变化曲线,通过记录其应变历程,可以判断劈裂试样的起裂应变、起裂位置和时刻,以及裂纹的扩展路径和裂纹扩展的速度。为岩石的动态断裂力学参数的测试找到了一条新的途径。
此外,还基于有限元分析,将数字信号处理领域的迭加积分法(卷积和杜阿美尔积分)引入到线弹性动态应力集中系数的求解中来,从理论和计算两个方面验证迭加积分法的可行性。
The research of rock dynamic question is a frontal topic in rock mechanics, up to now, there are many difficulties in testing the dynamic mechanics properties of rock not only in theory but also in measure technique. So finding or establishing new methods for testing rock dynamic properties becomes an urgently question to be resolved in the rock engineering.In this paper, the flattened Brazilian disc samples were first used in the dynamic split tests. The dynamic split tests of marble using both ordinary Brazilian disc and flattened Brazilian disc were performed at wide range of strain rate(14.6s~(-1) —163s~(-1)) with split Hopkins pressure bar(SHPB) of 100mm diameter. With the analysis of finite element method we deduced and got the dynamic tension strength for different sizes of marble and gained the typical failure mode of the Brazilian disc and the flattened Brazilian disc. The paper also researched the dynamic tension strength influenced by the flat ends of the sample, strain rate, projectile speed, pressure, and temperature. It is a simple, effective and ideal method to stick strain gages on the center of the sample in order to gain the dynamic tensile strength for brittle materials. In addition, from a series of electrical resistance strain gauges stuck on the sample surfaces along the loading diameter to record the strain histories, we could detect the initiation strain, the time and position of the crack initiation, and infer the consequence and the velocity of the crack propagation.In addition, based on analysis of finite element method, the superposition integral method was also introduced to calculate the dynamic stress concentration factor.
本文首次把平台巴西圆盘试样引入动态劈裂试验,利用直径100mm的分离式Hopkinson压杆(split Hopkinson pressure bar—SHPB)对大理岩巴西圆盘和平台巴西圆盘试样进行了宽应变率范围(14.6s~(-1)—163s~(-1))的动态劈裂实验,得到了不同尺寸的大理岩试样在不同应变率下的破坏应变。研究了试样有无平台、应变率、弹速、气压、温度对动态劈裂拉伸强度的影响。试验表明,通过粘贴在巴西圆盘中心的应变片来测量大理岩等脆性材料的动态拉伸强度,是一种简便高效的试验方法。另外,在试样表面加载直径方向粘贴一系列电阻应变片,用来记录试样加载直径上各点的应变随时间的变化曲线,通过记录其应变历程,可以判断劈裂试样的起裂应变、起裂位置和时刻,以及裂纹的扩展路径和裂纹扩展的速度。为岩石的动态断裂力学参数的测试找到了一条新的途径。
此外,还基于有限元分析,将数字信号处理领域的迭加积分法(卷积和杜阿美尔积分)引入到线弹性动态应力集中系数的求解中来,从理论和计算两个方面验证迭加积分法的可行性。
The research of rock dynamic question is a frontal topic in rock mechanics, up to now, there are many difficulties in testing the dynamic mechanics properties of rock not only in theory but also in measure technique. So finding or establishing new methods for testing rock dynamic properties becomes an urgently question to be resolved in the rock engineering.In this paper, the flattened Brazilian disc samples were first used in the dynamic split tests. The dynamic split tests of marble using both ordinary Brazilian disc and flattened Brazilian disc were performed at wide range of strain rate(14.6s~(-1) —163s~(-1)) with split Hopkins pressure bar(SHPB) of 100mm diameter. With the analysis of finite element method we deduced and got the dynamic tension strength for different sizes of marble and gained the typical failure mode of the Brazilian disc and the flattened Brazilian disc. The paper also researched the dynamic tension strength influenced by the flat ends of the sample, strain rate, projectile speed, pressure, and temperature. It is a simple, effective and ideal method to stick strain gages on the center of the sample in order to gain the dynamic tensile strength for brittle materials. In addition, from a series of electrical resistance strain gauges stuck on the sample surfaces along the loading diameter to record the strain histories, we could detect the initiation strain, the time and position of the crack initiation, and infer the consequence and the velocity of the crack propagation.In addition, based on analysis of finite element method, the superposition integral method was also introduced to calculate the dynamic stress concentration factor.
引文
1.蔡美峰,何满潮,刘东燕.岩石力学与工程[M].北京:科学出版社,2002.
2.谢和平,陈忠辉.岩石力学[M]北京:科学出版社,2004.
3.沈荣明.岩体力学[M].上海:同济大学出版社,1998.
4.李夕兵,刘德顺.岩石冲击动力学[M].长沙:中南工业大学出版社,1994.
5.叶明亮,续建科,牟宏,洪海春.岩石抗拉强度试验方法的探讨[J].贵州工业大学学报(自然科学版),2001,30(6):19-25.
6. ISRM. Suggested methods for determining tensile strength of rock materials [J]. Int.J.Rock Mech. Min. Sci.& Geomech. Abstr., 1978, 15:99-103.
7.GB/T50799-99.工程岩体试验方法标准[S].北京:中国计划出版社,1999.20.
8.SL264-2001.水利水电工程岩石试验规程[S].北京:水利水电出版社,2001.32-33.
9.王启智,贾学明.平台巴西圆盘试样确定脆性岩石的弹性模量、拉伸强度和断裂韧度——第一部分:解析与数值结果[J].岩石力学与工程学报,2002,21(9):1285-1289.
10.王启智,吴礼舟.用平台巴西圆盘试样确定脆性岩石的弹性模量、拉伸强度和断裂韧度——第二部分:实验结果[J].岩石力学与工程学报,2004,23(2):199-204.
11.王启智,戴峰,贾学明.对“平台圆盘劈裂的理论和实验”一文的回复[J].岩石力学与工程学报2004,23(1):175-178.
12.李夕兵,刘德顺.岩石冲击动力学[M].中南工业大学出版社,长沙.1994.
13.苏碧军,王启智.平台巴西圆盘试样岩石动态拉伸特性的实验研究[J].长江科学院院报,2004,21(1):22-25.
14.陶振宇.试论岩石力学的最新进展[J].力学进展,1992,22(2):161-172.
15.黎振兹,张静宜,刘大安.岩石断裂力学测试与理论研究[J].中国有色金属学报,1994,4(41:18-21.
16. Kolsky H. An investigation of the mechanical properties of materials at very high rates of loading. Proc. Roy. Soc. Lon.B,62:676-700.
17. Zhao J, Li H B. Experimental determination of dynamic tensile properties of a granite [J]. Int J Rock Mech. Min. Sci, 2000, 37:861-866.
18. Lambert D E, Ross C A. Strain rate effects on dynamic fracture and strength [J]. International Journal of Impact Engineering, 2000, 24: 985-998.
19. Lifshit.z J M, Leber H. Data processing in the split Hopkinson pressure bar tests[J].Int. J. Impact Eng, 1994,15(6):723-733.
20. Zhao H and Gary G. On the use of SHPB techniques to determine the dynamic behavior of materials in the range of small strains[J]. Int. J. Solids Structures, 1996, 33(23):3363-3375.
21. Frew D J, Forrestal M J and Chen W. A split Hopkinson pressure bar technique to determine compressive stress-strain data for rock matedals[J]. Experimental Mechanics, 2001, 41(1):40-46
22. Tedesco J W, Ross C A and Brunair R M. Numerical analysis of dynamic split cylinder tests[J]. Computers & Structures, 1989,32(3/4):609-624.
23. Tedesco J W, Hughes M L and Ross C A. Numerical simulation of high strain rate concrete compression tests[J]. Computers & Structures, 1994,51 (1):65-77.
24. Hughes M L, Tedesco J W, and Ross C A. Numerical analysis of high strain rate splitting-tensile tests[J]. Computers & Structures, 1993, 47(4/5):653-671.
25. Rodrigue J, Navarro C. Splitting test:an alternative to determine the dynamic tensile strength of ceramic materials[J]. Journal de Physique. 1994. Vol. 4,c8101-c8106.
26.胡时胜.霍普金森亚杆技术[J].兵器材料科学与工程,1991,(11),40-47
27.王鲁明,赵坚,华安增,赵晓豹.脆性材料SHPB实验技术的研究[J].岩石力学与工程学报,2003,22(11):1798-1802.
28.刘剑飞,胡时胜,王道荣.用于脆性材料的Hopkinson压杆动态实验新方法[J].实验力学,2001,16(3):283-290.
29.刘剑飞,王正道,胡时胜.低阻抗多孔介质材料的SHPB实验技术[J].实验力学,1998,13(2):218-223.
30.孟益平,胡时胜.混凝土材料冲击压缩实验中的一些问题[J].实验力学,2003,18(1):108-111.
31.李夕兵.岩石在不同加载波下的σ-ε-&关系[J].中国有色金属学报.1994,4(3):16-22.
32. Birkimer D L. A possible fracture criterion for the dynamic tensile strength of rock, Poe. 12th US Symp. Rock Mech.(Ed. GB Clark), Society of Mining, Metallurgical and Petroleum Engineers, New York, 1971:573-590.
33. Bazant Z P, Chen E P. Scaling of structure failure [J]. Appl. Mech. Rev., 1997, 50: 593-627.中译本:Bazant Z P,Chen E P.王文标等译.结构破坏的尺度律[J].力学进展,1999,29: 383～433.
34.张永兴.岩石力学[M].北京:中国建筑工业出版社,2004.
35.虞吉林.动态断裂理论何试验研究进展[J].力学与实践,1992,14(5):7-14.
36. Xie H, Sanderson D J. Fractal effects of crack propagation on dynamic stress intensity factors and crack velocities[J]. International journal of fracture, 1995,74(1):29-42.
37. Xie H, Sanderson D J. Fractal kinematics of crack propagation in geomaterials[J]. Engineering fracture mechanics, 1995,50(4):529-536.
38.谢和平.矿山岩体力学及工程的研究进展与展望[J].中国工程科学.2003,5(3):31-37.
39. Tedesco J W, Ross A C, Kuennen S T. Experimental and numerical analysis of high strain rate splitting tensile tests [J]. ACI materials journal, 1993, 90(2): 162-169.
40.鲍亦兴,毛昭宙著,刘殿魁,苏先樾译.弹性波的衍射与动应力集中[M].北京:科学出版社,1993.
41.刘殿魁,盖秉政,陶贵源.论孔附近的动应力集中[J].力学学报特刊,1981:65-77.
42.胡超,黄文虎,邵成勋.含孔平面力板弹性波散射与动应力分析[J].哈尔滨理工大学学报,2000,5(3):81-85.
43.薛慧,宋锦良,贾有权.三角波和阶跃波荷载作用下的动态应力集中系数[J].机械强度,1998,20(2):87-90.
44. Hiroyuki M, Tadaharu A, Yoshitaka K and Keiichi F. Analysis of the Dynamic Stress Concentration Factor by the Two-Dimensional Boundary Element Method [J]. JSME International Journal, Series Ⅰ,1990,33(1):37-43.
45. Nakayama N, Ohashi M, Takeishi H. Dynamic Stress Concentration in a Strip Plate with Fillet [J]. JSME International Journal, Series A, 1998,41(3):326-331.
46. Matsumoto H. Dynamic Stress Concentration in Notched Strips Subjected to Longitudinal Impact [J]. JSNDI, (in Japanese), 18(8):343.
2.谢和平,陈忠辉.岩石力学[M]北京:科学出版社,2004.
3.沈荣明.岩体力学[M].上海:同济大学出版社,1998.
4.李夕兵,刘德顺.岩石冲击动力学[M].长沙:中南工业大学出版社,1994.
5.叶明亮,续建科,牟宏,洪海春.岩石抗拉强度试验方法的探讨[J].贵州工业大学学报(自然科学版),2001,30(6):19-25.
6. ISRM. Suggested methods for determining tensile strength of rock materials [J]. Int.J.Rock Mech. Min. Sci.& Geomech. Abstr., 1978, 15:99-103.
7.GB/T50799-99.工程岩体试验方法标准[S].北京:中国计划出版社,1999.20.
8.SL264-2001.水利水电工程岩石试验规程[S].北京:水利水电出版社,2001.32-33.
9.王启智,贾学明.平台巴西圆盘试样确定脆性岩石的弹性模量、拉伸强度和断裂韧度——第一部分:解析与数值结果[J].岩石力学与工程学报,2002,21(9):1285-1289.
10.王启智,吴礼舟.用平台巴西圆盘试样确定脆性岩石的弹性模量、拉伸强度和断裂韧度——第二部分:实验结果[J].岩石力学与工程学报,2004,23(2):199-204.
11.王启智,戴峰,贾学明.对“平台圆盘劈裂的理论和实验”一文的回复[J].岩石力学与工程学报2004,23(1):175-178.
12.李夕兵,刘德顺.岩石冲击动力学[M].中南工业大学出版社,长沙.1994.
13.苏碧军,王启智.平台巴西圆盘试样岩石动态拉伸特性的实验研究[J].长江科学院院报,2004,21(1):22-25.
14.陶振宇.试论岩石力学的最新进展[J].力学进展,1992,22(2):161-172.
15.黎振兹,张静宜,刘大安.岩石断裂力学测试与理论研究[J].中国有色金属学报,1994,4(41:18-21.
16. Kolsky H. An investigation of the mechanical properties of materials at very high rates of loading. Proc. Roy. Soc. Lon.B,62:676-700.
17. Zhao J, Li H B. Experimental determination of dynamic tensile properties of a granite [J]. Int J Rock Mech. Min. Sci, 2000, 37:861-866.
18. Lambert D E, Ross C A. Strain rate effects on dynamic fracture and strength [J]. International Journal of Impact Engineering, 2000, 24: 985-998.
19. Lifshit.z J M, Leber H. Data processing in the split Hopkinson pressure bar tests[J].Int. J. Impact Eng, 1994,15(6):723-733.
20. Zhao H and Gary G. On the use of SHPB techniques to determine the dynamic behavior of materials in the range of small strains[J]. Int. J. Solids Structures, 1996, 33(23):3363-3375.
21. Frew D J, Forrestal M J and Chen W. A split Hopkinson pressure bar technique to determine compressive stress-strain data for rock matedals[J]. Experimental Mechanics, 2001, 41(1):40-46
22. Tedesco J W, Ross C A and Brunair R M. Numerical analysis of dynamic split cylinder tests[J]. Computers & Structures, 1989,32(3/4):609-624.
23. Tedesco J W, Hughes M L and Ross C A. Numerical simulation of high strain rate concrete compression tests[J]. Computers & Structures, 1994,51 (1):65-77.
24. Hughes M L, Tedesco J W, and Ross C A. Numerical analysis of high strain rate splitting-tensile tests[J]. Computers & Structures, 1993, 47(4/5):653-671.
25. Rodrigue J, Navarro C. Splitting test:an alternative to determine the dynamic tensile strength of ceramic materials[J]. Journal de Physique. 1994. Vol. 4,c8101-c8106.
26.胡时胜.霍普金森亚杆技术[J].兵器材料科学与工程,1991,(11),40-47
27.王鲁明,赵坚,华安增,赵晓豹.脆性材料SHPB实验技术的研究[J].岩石力学与工程学报,2003,22(11):1798-1802.
28.刘剑飞,胡时胜,王道荣.用于脆性材料的Hopkinson压杆动态实验新方法[J].实验力学,2001,16(3):283-290.
29.刘剑飞,王正道,胡时胜.低阻抗多孔介质材料的SHPB实验技术[J].实验力学,1998,13(2):218-223.
30.孟益平,胡时胜.混凝土材料冲击压缩实验中的一些问题[J].实验力学,2003,18(1):108-111.
31.李夕兵.岩石在不同加载波下的σ-ε-&关系[J].中国有色金属学报.1994,4(3):16-22.
32. Birkimer D L. A possible fracture criterion for the dynamic tensile strength of rock, Poe. 12th US Symp. Rock Mech.(Ed. GB Clark), Society of Mining, Metallurgical and Petroleum Engineers, New York, 1971:573-590.
33. Bazant Z P, Chen E P. Scaling of structure failure [J]. Appl. Mech. Rev., 1997, 50: 593-627.中译本:Bazant Z P,Chen E P.王文标等译.结构破坏的尺度律[J].力学进展,1999,29: 383～433.
34.张永兴.岩石力学[M].北京:中国建筑工业出版社,2004.
35.虞吉林.动态断裂理论何试验研究进展[J].力学与实践,1992,14(5):7-14.
36. Xie H, Sanderson D J. Fractal effects of crack propagation on dynamic stress intensity factors and crack velocities[J]. International journal of fracture, 1995,74(1):29-42.
37. Xie H, Sanderson D J. Fractal kinematics of crack propagation in geomaterials[J]. Engineering fracture mechanics, 1995,50(4):529-536.
38.谢和平.矿山岩体力学及工程的研究进展与展望[J].中国工程科学.2003,5(3):31-37.
39. Tedesco J W, Ross A C, Kuennen S T. Experimental and numerical analysis of high strain rate splitting tensile tests [J]. ACI materials journal, 1993, 90(2): 162-169.
40.鲍亦兴,毛昭宙著,刘殿魁,苏先樾译.弹性波的衍射与动应力集中[M].北京:科学出版社,1993.
41.刘殿魁,盖秉政,陶贵源.论孔附近的动应力集中[J].力学学报特刊,1981:65-77.
42.胡超,黄文虎,邵成勋.含孔平面力板弹性波散射与动应力分析[J].哈尔滨理工大学学报,2000,5(3):81-85.
43.薛慧,宋锦良,贾有权.三角波和阶跃波荷载作用下的动态应力集中系数[J].机械强度,1998,20(2):87-90.
44. Hiroyuki M, Tadaharu A, Yoshitaka K and Keiichi F. Analysis of the Dynamic Stress Concentration Factor by the Two-Dimensional Boundary Element Method [J]. JSME International Journal, Series Ⅰ,1990,33(1):37-43.
45. Nakayama N, Ohashi M, Takeishi H. Dynamic Stress Concentration in a Strip Plate with Fillet [J]. JSME International Journal, Series A, 1998,41(3):326-331.
46. Matsumoto H. Dynamic Stress Concentration in Notched Strips Subjected to Longitudinal Impact [J]. JSNDI, (in Japanese), 18(8):343.