三维裂纹板条动态断裂参量的线弹簧有限元法研究
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摘要
本文将线弹簧模型与有限元软件ANSYS相结合，对弹性表面裂纹的动态断裂参量进行了研究，所进行的工作主要有：
将传统的用于静态表面裂纹分析的线弹簧模型推广用于动态断裂分析，导出了相应的线弹簧本构关系，并与有限元(ANSYS)相结合，建立了相应的求解技术。
对含内埋椭圆裂纹的板条进行了静态和瞬态分析，得到的结果与已有的解吻合良好，对影响瞬态响应的因素如裂纹形状、裂纹深度、板条长度、板条厚度做了分析比较。
在ANSYS中提出了一种新的线弹簧单元用于表面裂纹分析，并分别用于表面裂纹静态与动态的分析，所得结果与已有解吻合良好，说明此单元模型的建立是成功的，最后对影响表面裂纹动态应力强度因子的因素做了分析。
本文所建立的三维裂纹动态断裂参量的分析方法，较之全三维有限元法大大简化了前处理过程和节省了计算机时。同时，保证了一定的分析精度。因此，作为一种工程数值分析方法，是非常适合的。
This paper presents a method to calculate elastodynamic fracture parameters of surface crack by using the elastic line-spring model combined with perfect ANSYS software. The main content includes :
The traditional line-spring model which is used in the static analysis of surface crack is extended to the dynamic case, the corresponding constitutive relations are derived and combined with the software ANSYS, and then the corresponding computational technique is formulated.
A static and a transient analysis of an embedded crack in a long elastic strip are carried out. The results are approximate to the ones that existed. And the effects of the factors including the crack configuration, the crack depth, the strip length and the strip thickness on the transient response are discussed.
A new line-spring element is established and combined into ANSYS ,which is used to analysis of surface crack . And static case and dynamic case are solved respectively, the results are consistent well with the accepted numerical solutions. It is shown that established element is successful , And the effects of the factors on the transient response are examined in detail.
This method provided in this paper can simplify pre-process and drastically reduces computer time and achieve some certain accuracy as compared to full 3-D finite element method. It has shown that as an engineering numerical method ,it is suitable.
将传统的用于静态表面裂纹分析的线弹簧模型推广用于动态断裂分析，导出了相应的线弹簧本构关系，并与有限元(ANSYS)相结合，建立了相应的求解技术。
对含内埋椭圆裂纹的板条进行了静态和瞬态分析，得到的结果与已有的解吻合良好，对影响瞬态响应的因素如裂纹形状、裂纹深度、板条长度、板条厚度做了分析比较。
在ANSYS中提出了一种新的线弹簧单元用于表面裂纹分析，并分别用于表面裂纹静态与动态的分析，所得结果与已有解吻合良好，说明此单元模型的建立是成功的，最后对影响表面裂纹动态应力强度因子的因素做了分析。
本文所建立的三维裂纹动态断裂参量的分析方法，较之全三维有限元法大大简化了前处理过程和节省了计算机时。同时，保证了一定的分析精度。因此，作为一种工程数值分析方法，是非常适合的。
This paper presents a method to calculate elastodynamic fracture parameters of surface crack by using the elastic line-spring model combined with perfect ANSYS software. The main content includes :
The traditional line-spring model which is used in the static analysis of surface crack is extended to the dynamic case, the corresponding constitutive relations are derived and combined with the software ANSYS, and then the corresponding computational technique is formulated.
A static and a transient analysis of an embedded crack in a long elastic strip are carried out. The results are approximate to the ones that existed. And the effects of the factors including the crack configuration, the crack depth, the strip length and the strip thickness on the transient response are discussed.
A new line-spring element is established and combined into ANSYS ,which is used to analysis of surface crack . And static case and dynamic case are solved respectively, the results are consistent well with the accepted numerical solutions. It is shown that established element is successful , And the effects of the factors on the transient response are examined in detail.
This method provided in this paper can simplify pre-process and drastically reduces computer time and achieve some certain accuracy as compared to full 3-D finite element method. It has shown that as an engineering numerical method ,it is suitable.
引文
1．范天佑．断裂动力学引论．北京理工大学出版社，1990．6
2．杨宏伟，马大为，王更新，王志群．厚壁筒内裂纹深度与动态应力强度因子的关系．南京理工大学学报，1996，20(6)
3．薛河，刘金依，徐尚龙，朱华双．ANSYS中断裂参量的计算及分析．重型机械，2002，2
4．尹奇志，肖金生．孔边应力集中和裂纹尖端应力强度因子的有限元分析．武汉理工大学学报，2002，26(1)：47-50
5．杨广里．断裂力学及其应用．中国铁道出版社，1990
6．黄玲珍，聂毓琴，孟广伟．计算断裂力学的现状与进展．吉林工业大学学报．1995，1
7．钟明，张永元．用时域边界元法分析半圆表面裂纹的动态应力强度因子．应用数学和力学，2001，22(11)
8．范天佑．应用断裂动力学基础．北京理工大学出版社，1992
9．侯晓宁．有限差分法及动态能量积分在断裂力学中的应用．北京理工大学硕士论文，1987
10．Chen Y M, Wilkins M L. Numerical analysis of dynamic crack problems[A]. In: M H Aliabadi Ed. Dynamic Fracture Mechanics[C],1977
11．刘云忠．边界元法计算厚板表面裂纹问题的应力强度因子．固体火箭技术，1996，19(3)
12．刘涛，杨凤鹏．精通ANSYS．清华大学出版社，2001．9
13．谭建国．使用ANSYS6．0进行有限元分析．北京大学出版社，2001
14．王勖成，邵敏．有限单元法基本原理和数值方法．清华大学出版社，1995．12
15. J. J. Yin, Numerical computation of dynamic stress intensity by BEM. Proceedings of Int. (vnf. On Fracture and fracture Mechanics), ShangHai, China, 1987, 150-154
16. T. Y. Fan, H. G..Hahn, D. Tenhaeff and C. P. Fritzen, Computer-realization of boundary integral equation method in static and dynamic fracture methanics. J. of Beijing Institute of Technology, Vol. 4(1984), No. 3, 1-20
17．赵明颢，刘元杰，程昌钧．Ressiner型板表面裂纹应力强度因子的线弹簧—不连续位移边界积分方程解法．计算结构力学及其应用，1996，13(1)
18．李英贤．冲击载荷作用下动态应力强度因子的研究．南京航天航空大学学报，1996，28
(3)
19．杨宏伟，吕爱民，王英林．数值积分法求解厚壁筒的动态应力强度因子．计算结构力学及其应用，1996，13(3)
20．欧贵宝，朱加铭，饶意中，张正国．动载荷下应力强度因子的边界元计算．工程力学，1994，11(2)
21．陈卫江，柳春图．平面断裂动力学问题的奇异积分方程解法．兰州大学学报，1996，32(1)
22．欧贵宝，张正国，潘信吉．用边界元法计算裂纹的瞬态和稳态问题．应用力学学报，1996，13(3)
23. Freund L B. The oblique reflection of a Rayleigh wave from a creak tip. Int J Solids Strut,1971, 7: 1199-1210
24. Achenbach J D, Gautesen A. Elastodynamic stress intensity factors for a semi-infinite crack under 3-D loading. J Appl Mech, 1977, 44:243-249
25. Freund L B. The stress intensity factor due to three dimensional transient loading of the faces ora crack. J Mech Phys Solids, 1987, 35:61-72
26. Ramirez J C. The three dimensional stress intensity factor due to the motion of a load on the faces of a crack. Q Appl Math XLV 1987:361-376
27．李湘平，柳春图．运动载荷下的三维裂纹应力强度因子．固体力学学报，1994，15(2)
28. Sladek J, Sladek V. Dynamic stress intensity factors studied by boundary integro-differential equatitions [J]. Int J Numer Methods Engng, 1986, 23 (5): 919-928
29. Zhang Y Y, Shi W. Transient analysis of three-dimensional crack problems by the Laplace transform boundary element method[J]. Engng Fracture Meth, 1994, 47(5): 715-722
30. Wen. P.H. Dynamic Fracture Mechanics: Displacement Discontinuity Method[M]. Southampton, Boston: Comput Meeh Publication, 1996
31. Fedelinski P, Aliabadi M H, Rooke D P. Cracks in the three dimensions: dynamic dual boundary element analysis [J]. Comput Methods in Appl Mech Engng, 1998, 167 (1-2): 139-151
32. Wen P H, Aliabadi M H, Rooke D P, A variational technique for boundary element analysis of 3D fracture mechanics weight functions: Dynamic[J]. Int J Numer Meth Engng, 1998,
42(8): 1425-1439
33. Hirose S, Achenbach J D. Time-domain boundary element analysis of elastic wave interaction with a crack[J]. Int J Numer Methods Engng, 1989, 28 (1-3): 629-644
34．钟明，张永元．用时域边界元法分析半圆表面裂纹的动态应力强度因子．应用数学和力学，2001，22(11)
35．崔振源．表面裂纹理论及其应用．西北工业大学出版社．1985，12
36．胡宗陵．线弹簧模型在断裂力学中的拓展．华东交通大学学报，1996
37．杨伯源，胡宗陵．线弹簧模型柔度与裂纹开裂角之间的关系．合肥工业大学学报，1998，21(3)
38．黄正中，高庆，王光钦．表面裂纹平板应力强度因子的杂交应力元—线弹簧模型方法．计算结构力学及其应用，1992，9(1)
39. Rice J R, Levy N. The part-through surface crack in an elastic plate. J Appl Mech Trans ASME, 1972, 185-194
40. E. DE Langre, L. Ebersolt. The use of a new line-spring shell element for elastic surface crack analysis[J]. Fatigue & Fracture of Engineering Materials & Structures, 10(1987), 305-311
41．曾昭景，戴树和．分析表面裂纹的一种新方法．应用数学和力学，1993，14(8)
42. Noriyuki Miyazaki. An application of a line-spring model to a transient analysis of the dynamic stress intensity factor. Int. J. of Fracture, 1989 39 R77-R80
43. Noriyuki Miyazak, Hideaki Kaneko. On the combination of the boundary element method and the line-spring model. Int. J. of Fracture, 1986 31 R3-R10
44. Fan Xuejun, Yu Shouwen, Hwang Kehchih. The line spring model with arbitrary loads on crack surface and its applications in thermal shock analysis. ACTA Mechanica Sinica, 1990 6 (3)
45. T Miyoshi, M Shiratori, Y Yoshida. Analysis of J-integral and crack growth for surface cracks by line spring method. J. of Pressure Vessel Technology, 1986 VOL108 305-311
46. Shih C F, Needleman A. Fully plastic crack problem. J Appl Mech, 1984, 51:51-64
47. Matteo Chiesa, Bjorn Shallerud, Dietmar Gross. Closed from line spring yield surface for deep and shallow cracks: formulation and numerical performance. Computer and structures,2002, (80): 533—545
48. Bo Wang, Ning Hu. Study of a spherical shell with a surface crack by the line-spring
model. Engineering stucture, 2000 (22): 1006—1012
49．王勇．弹塑性边界元法及其在表面裂纹分析中的应用．浙江工业大学学报，1997，25(2)
50. Hyungyil Lee, David M.Parks. Enhanced elastic-plastic line-spring finite element. Int. J. solids structure, 1995, 32 (16): 2393—2418
51. Miyoshi T, Shiratori M, Tanabe O. Stress intensity factors for surface cracks with Arbitrary Shape in Plates and Shells. Fracture Mechanics, 1985, 521—534
52. V. Kumar, M D Garman, B I Schumacher. Analysis of elastic surface cracks in clinders using the line-spring model and shell finite element method [J]. Int Press Vessel Tech, 1985, 107:403-419
53．李皓月，周田朋，刘相新．ANSYS工程计算应用教程．北京大学出版社中国铁道出版社，2003
54．袁杰红，唐国金，周建平，范瑞祥．无限平板内埋裂纹线弹簧模型．固体力学学报，1999，20(1)：69-76
55．袁杰红，周建平，唐国金，宋先村．多个共面任意分布表面裂纹的应力强度因子．力学季刊，2000，21(1)
56．袁杰红，唐国金，周建平，范瑞祥．椭圆形半露头裂纹的线弹簧模型．工程力学，1999，16(2)
57．柴国钟，顾立成，洪起超，王勇．表面裂纹弹塑性分析的线弹簧模型法．浙江工业大学学报，1996，24(2)
58．易大义，陈道琦．数值分析引论．浙江大学出版社，1996
59．中国航空研究院．应力强度因子手册．科学出版社，1981
60．彭凡，刘忠，马石城．局部应力场中表面裂纹的线弹簧模型分析．Natural Science Journal of Xiangtan University，1998，6
61．袁杰红，周建平，唐国金．含内埋裂纹的板条瞬态响应分析．固体力学学报，2001，20(1)：69-76
62. Noriyuki Miyazaki. An application of a line-spring model to a transient analysis of the dynamic stress intensity factor. Int. J. of Fracture, 1989 39 R77-RS0
63．俞载道．结构动力学基础．同济大学出版社，1985
64. Heliot J, Labbens R, Pellissier T A. Benchmark problem No. 1—semielliptical surface crack—resuits of computation. Int. J. Fracture, 1979, 15 (6): 197—202
65． Zhang Y Y, Shi W. Transient analysis of three-dimensional crack problems by the Laplace transform boundary element method[J]. Engng Fracture Meth, 1994, 47 (5) : 715-722
2．杨宏伟，马大为，王更新，王志群．厚壁筒内裂纹深度与动态应力强度因子的关系．南京理工大学学报，1996，20(6)
3．薛河，刘金依，徐尚龙，朱华双．ANSYS中断裂参量的计算及分析．重型机械，2002，2
4．尹奇志，肖金生．孔边应力集中和裂纹尖端应力强度因子的有限元分析．武汉理工大学学报，2002，26(1)：47-50
5．杨广里．断裂力学及其应用．中国铁道出版社，1990
6．黄玲珍，聂毓琴，孟广伟．计算断裂力学的现状与进展．吉林工业大学学报．1995，1
7．钟明，张永元．用时域边界元法分析半圆表面裂纹的动态应力强度因子．应用数学和力学，2001，22(11)
8．范天佑．应用断裂动力学基础．北京理工大学出版社，1992
9．侯晓宁．有限差分法及动态能量积分在断裂力学中的应用．北京理工大学硕士论文，1987
10．Chen Y M, Wilkins M L. Numerical analysis of dynamic crack problems[A]. In: M H Aliabadi Ed. Dynamic Fracture Mechanics[C],1977
11．刘云忠．边界元法计算厚板表面裂纹问题的应力强度因子．固体火箭技术，1996，19(3)
12．刘涛，杨凤鹏．精通ANSYS．清华大学出版社，2001．9
13．谭建国．使用ANSYS6．0进行有限元分析．北京大学出版社，2001
14．王勖成，邵敏．有限单元法基本原理和数值方法．清华大学出版社，1995．12
15. J. J. Yin, Numerical computation of dynamic stress intensity by BEM. Proceedings of Int. (vnf. On Fracture and fracture Mechanics), ShangHai, China, 1987, 150-154
16. T. Y. Fan, H. G..Hahn, D. Tenhaeff and C. P. Fritzen, Computer-realization of boundary integral equation method in static and dynamic fracture methanics. J. of Beijing Institute of Technology, Vol. 4(1984), No. 3, 1-20
17．赵明颢，刘元杰，程昌钧．Ressiner型板表面裂纹应力强度因子的线弹簧—不连续位移边界积分方程解法．计算结构力学及其应用，1996，13(1)
18．李英贤．冲击载荷作用下动态应力强度因子的研究．南京航天航空大学学报，1996，28
(3)
19．杨宏伟，吕爱民，王英林．数值积分法求解厚壁筒的动态应力强度因子．计算结构力学及其应用，1996，13(3)
20．欧贵宝，朱加铭，饶意中，张正国．动载荷下应力强度因子的边界元计算．工程力学，1994，11(2)
21．陈卫江，柳春图．平面断裂动力学问题的奇异积分方程解法．兰州大学学报，1996，32(1)
22．欧贵宝，张正国，潘信吉．用边界元法计算裂纹的瞬态和稳态问题．应用力学学报，1996，13(3)
23. Freund L B. The oblique reflection of a Rayleigh wave from a creak tip. Int J Solids Strut,1971, 7: 1199-1210
24. Achenbach J D, Gautesen A. Elastodynamic stress intensity factors for a semi-infinite crack under 3-D loading. J Appl Mech, 1977, 44:243-249
25. Freund L B. The stress intensity factor due to three dimensional transient loading of the faces ora crack. J Mech Phys Solids, 1987, 35:61-72
26. Ramirez J C. The three dimensional stress intensity factor due to the motion of a load on the faces of a crack. Q Appl Math XLV 1987:361-376
27．李湘平，柳春图．运动载荷下的三维裂纹应力强度因子．固体力学学报，1994，15(2)
28. Sladek J, Sladek V. Dynamic stress intensity factors studied by boundary integro-differential equatitions [J]. Int J Numer Methods Engng, 1986, 23 (5): 919-928
29. Zhang Y Y, Shi W. Transient analysis of three-dimensional crack problems by the Laplace transform boundary element method[J]. Engng Fracture Meth, 1994, 47(5): 715-722
30. Wen. P.H. Dynamic Fracture Mechanics: Displacement Discontinuity Method[M]. Southampton, Boston: Comput Meeh Publication, 1996
31. Fedelinski P, Aliabadi M H, Rooke D P. Cracks in the three dimensions: dynamic dual boundary element analysis [J]. Comput Methods in Appl Mech Engng, 1998, 167 (1-2): 139-151
32. Wen P H, Aliabadi M H, Rooke D P, A variational technique for boundary element analysis of 3D fracture mechanics weight functions: Dynamic[J]. Int J Numer Meth Engng, 1998,
42(8): 1425-1439
33. Hirose S, Achenbach J D. Time-domain boundary element analysis of elastic wave interaction with a crack[J]. Int J Numer Methods Engng, 1989, 28 (1-3): 629-644
34．钟明，张永元．用时域边界元法分析半圆表面裂纹的动态应力强度因子．应用数学和力学，2001，22(11)
35．崔振源．表面裂纹理论及其应用．西北工业大学出版社．1985，12
36．胡宗陵．线弹簧模型在断裂力学中的拓展．华东交通大学学报，1996
37．杨伯源，胡宗陵．线弹簧模型柔度与裂纹开裂角之间的关系．合肥工业大学学报，1998，21(3)
38．黄正中，高庆，王光钦．表面裂纹平板应力强度因子的杂交应力元—线弹簧模型方法．计算结构力学及其应用，1992，9(1)
39. Rice J R, Levy N. The part-through surface crack in an elastic plate. J Appl Mech Trans ASME, 1972, 185-194
40. E. DE Langre, L. Ebersolt. The use of a new line-spring shell element for elastic surface crack analysis[J]. Fatigue & Fracture of Engineering Materials & Structures, 10(1987), 305-311
41．曾昭景，戴树和．分析表面裂纹的一种新方法．应用数学和力学，1993，14(8)
42. Noriyuki Miyazaki. An application of a line-spring model to a transient analysis of the dynamic stress intensity factor. Int. J. of Fracture, 1989 39 R77-R80
43. Noriyuki Miyazak, Hideaki Kaneko. On the combination of the boundary element method and the line-spring model. Int. J. of Fracture, 1986 31 R3-R10
44. Fan Xuejun, Yu Shouwen, Hwang Kehchih. The line spring model with arbitrary loads on crack surface and its applications in thermal shock analysis. ACTA Mechanica Sinica, 1990 6 (3)
45. T Miyoshi, M Shiratori, Y Yoshida. Analysis of J-integral and crack growth for surface cracks by line spring method. J. of Pressure Vessel Technology, 1986 VOL108 305-311
46. Shih C F, Needleman A. Fully plastic crack problem. J Appl Mech, 1984, 51:51-64
47. Matteo Chiesa, Bjorn Shallerud, Dietmar Gross. Closed from line spring yield surface for deep and shallow cracks: formulation and numerical performance. Computer and structures,2002, (80): 533—545
48. Bo Wang, Ning Hu. Study of a spherical shell with a surface crack by the line-spring
model. Engineering stucture, 2000 (22): 1006—1012
49．王勇．弹塑性边界元法及其在表面裂纹分析中的应用．浙江工业大学学报，1997，25(2)
50. Hyungyil Lee, David M.Parks. Enhanced elastic-plastic line-spring finite element. Int. J. solids structure, 1995, 32 (16): 2393—2418
51. Miyoshi T, Shiratori M, Tanabe O. Stress intensity factors for surface cracks with Arbitrary Shape in Plates and Shells. Fracture Mechanics, 1985, 521—534
52. V. Kumar, M D Garman, B I Schumacher. Analysis of elastic surface cracks in clinders using the line-spring model and shell finite element method [J]. Int Press Vessel Tech, 1985, 107:403-419
53．李皓月，周田朋，刘相新．ANSYS工程计算应用教程．北京大学出版社中国铁道出版社，2003
54．袁杰红，唐国金，周建平，范瑞祥．无限平板内埋裂纹线弹簧模型．固体力学学报，1999，20(1)：69-76
55．袁杰红，周建平，唐国金，宋先村．多个共面任意分布表面裂纹的应力强度因子．力学季刊，2000，21(1)
56．袁杰红，唐国金，周建平，范瑞祥．椭圆形半露头裂纹的线弹簧模型．工程力学，1999，16(2)
57．柴国钟，顾立成，洪起超，王勇．表面裂纹弹塑性分析的线弹簧模型法．浙江工业大学学报，1996，24(2)
58．易大义，陈道琦．数值分析引论．浙江大学出版社，1996
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