花岗岩动态断裂韧性的试验研究以及有限元分析
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摘要
随着科技的发展,裂纹在动态载荷下的稳定性问题变得日趋重要,关于材料动态断裂问题的试验技术和理论研究已成为多年以来学术界普遍关注的热点。然而由于问题的复杂性,至今都没有形成一个公认的,规范的裂纹动态起始判据,对这个问题还需要进行大量的、长时间的研究。目前动态断裂韧性的测试和表征大多集中在金属材料,然而矿产资源的开发等均涉及岩石类材料,岩石的稳定与破坏是岩石力学研究的两大问题。为了预防在地下工程结构出现岩石爆裂造成的灾难性的破坏,因此很有必须了解岩石材料的动态力学性能进而提供研究其动态破坏机理的方法。
本文提出使用中心裂纹圆盘试件来测试脆性材料的动态断裂韧性。中心裂纹圆盘试件能够方便的实现纯Ⅰ型、纯Ⅱ型和Ⅰ+Ⅱ复合型加载条件,且应力强度因子具有解析解,故在脆性材料断裂韧性测试方面得到了广泛的关注。通过对岩石试件进行纯Ⅰ型的加载试验,利用试件两端的平均载荷推广准静态下应力强度因子用于动态情形,计算得到了花岗岩在不同速率下动态断裂韧性；计算结果表明该批花岗岩断裂韧性在5-17MPa-m1/2之间,在5×104-25×104MPa·m1/2·s-1的加载速率范围内,随着加载速率的增加,岩石的断裂韧性也随之增加,大致呈现线性增加趋势,但随着加载速率的增大动态断裂韧性增加趋势明显减弱。
本文以实测的载荷时间历程为输入,即将实测载荷转化为相应的压力载荷施加在入射杆带入有限元进行计算,由有限元计算结果直接得到裂尖处的动态数值解进而得到动态断裂韧性。从数值计算结果和试验结果对比可以看出,在平均加载速率为6.57×104MPa·m1/2·s-1下,花岗岩的动态断裂韧性为7.42MPa-m1/2,有限元计算结果与试验所得动态断裂韧度误差平均为6.2%。这说明用试件两端的平均载荷代入计算,推广准静态公式用于动态情形是可行的。
With the development of science and technology, the stability problem of the crack under the dynamic loading are becoming increasing important. Theoretical and Experimental technology research on the dynamic fracture problem cause great attention in academic for many years. However, due to the complexity of the problem there has no formed recognition or standardized criterion on this issue so it still needs lots of time to study. Dynamic fracture toughness testing and characterization are mostly concentrated on the metal material and the exploitation of mineral resources involved in the rock material, the stability and destruction are the two major problems of rock mechanic studies. In order to avoid the possibility of disaster, we must understand the mechanism dynamic failure and study the dynamic mechanical properties.
In this paper, the central cracked circular disk specimens were used to study the dynamic fracture toughness of brittle materials.The CCCD specimen has been widely used to test the fracture toughness subjected to pure mode I,pure mode II and mixed-mode loading. We promote the equation of quasi-static stress intensity factor for dynamic fracture toughness calculation.the maximum load under the balance dynamic force was substituted into the equation to get the value of dynamic fracture toughness. The results show that the fracture toughness is between5-17MPa-m1/2and the loading rate range from5×104-25x104MPa· m1/2·s-1, with increasing loading rate, Test verified the dynamic fracture toughness and loading rate has good correlation,
In this paper, The load used in finite element computation is an average load of test. Dynamic finite element analysis is carried out to determine the SIF evolution,and then get the fracture toughness. In spite of an average error of6.2%between the finite element results and test processing,the dynamic fracture toughness of granite is7.42MPa·w1/2with an average loading rate of6.57×104MPa·m1/2s-1.It is feasible to promote the quasi-static formula to the dynamic situation.
本文提出使用中心裂纹圆盘试件来测试脆性材料的动态断裂韧性。中心裂纹圆盘试件能够方便的实现纯Ⅰ型、纯Ⅱ型和Ⅰ+Ⅱ复合型加载条件,且应力强度因子具有解析解,故在脆性材料断裂韧性测试方面得到了广泛的关注。通过对岩石试件进行纯Ⅰ型的加载试验,利用试件两端的平均载荷推广准静态下应力强度因子用于动态情形,计算得到了花岗岩在不同速率下动态断裂韧性；计算结果表明该批花岗岩断裂韧性在5-17MPa-m1/2之间,在5×104-25×104MPa·m1/2·s-1的加载速率范围内,随着加载速率的增加,岩石的断裂韧性也随之增加,大致呈现线性增加趋势,但随着加载速率的增大动态断裂韧性增加趋势明显减弱。
本文以实测的载荷时间历程为输入,即将实测载荷转化为相应的压力载荷施加在入射杆带入有限元进行计算,由有限元计算结果直接得到裂尖处的动态数值解进而得到动态断裂韧性。从数值计算结果和试验结果对比可以看出,在平均加载速率为6.57×104MPa·m1/2·s-1下,花岗岩的动态断裂韧性为7.42MPa-m1/2,有限元计算结果与试验所得动态断裂韧度误差平均为6.2%。这说明用试件两端的平均载荷代入计算,推广准静态公式用于动态情形是可行的。
With the development of science and technology, the stability problem of the crack under the dynamic loading are becoming increasing important. Theoretical and Experimental technology research on the dynamic fracture problem cause great attention in academic for many years. However, due to the complexity of the problem there has no formed recognition or standardized criterion on this issue so it still needs lots of time to study. Dynamic fracture toughness testing and characterization are mostly concentrated on the metal material and the exploitation of mineral resources involved in the rock material, the stability and destruction are the two major problems of rock mechanic studies. In order to avoid the possibility of disaster, we must understand the mechanism dynamic failure and study the dynamic mechanical properties.
In this paper, the central cracked circular disk specimens were used to study the dynamic fracture toughness of brittle materials.The CCCD specimen has been widely used to test the fracture toughness subjected to pure mode I,pure mode II and mixed-mode loading. We promote the equation of quasi-static stress intensity factor for dynamic fracture toughness calculation.the maximum load under the balance dynamic force was substituted into the equation to get the value of dynamic fracture toughness. The results show that the fracture toughness is between5-17MPa-m1/2and the loading rate range from5×104-25x104MPa· m1/2·s-1, with increasing loading rate, Test verified the dynamic fracture toughness and loading rate has good correlation,
In this paper, The load used in finite element computation is an average load of test. Dynamic finite element analysis is carried out to determine the SIF evolution,and then get the fracture toughness. In spite of an average error of6.2%between the finite element results and test processing,the dynamic fracture toughness of granite is7.42MPa·w1/2with an average loading rate of6.57×104MPa·m1/2s-1.It is feasible to promote the quasi-static formula to the dynamic situation.
引文
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[2]范天佑,断裂动力学进展,力学进展1986；2：1-13.
[3]Nishioka T., Atluri SN, Computational methods in dynamic fracture, In Computation Methods in Mechanics of Fracture, Atluri SN etc.Amsterdam,North-Holland(1986):356-383.
[4]赵亚溥,裂纹动态起始问题的研究进展,力学进展,1996,Vo1.26 No3：362-375.
[5]宫能平,弹塑性材料动态断裂韧性的理论与实验研究——表征与测试,博士学位论文,中国科技大学,2001.
[6]范天佑,断裂动力学引论,北京理工大学出版社,1990.
[7]范天佑,断裂理论基础,科学出版社,2003.
[8]沈成康,断裂力学,同济大学出版社,1996.
[9]Sih GC., Loeber JF. J. Acoustical Society of American1968;44:1237-1245.
[10]Sih GC., Loeber JF. J. Acoustical Society of American 1969;46:711-721.
[11]Stabkopf AK,et al,Crack and Fracture,ASTM ATP601(1976):291-311.
[12]Server WL,Impact three-point bend testing for notched and pre-cracked Specimens. J.of test and evaluation 1978;6:29-34.
[13]Liu YN et al,Engng.Fract Mech1991;39:955-964.
[14]J.Beinert,J. F. Kalthoff. Mechanics of Fracture Edited by G. C.Sih(1981)281-330.
[15]Costin LS, Duffy J and Freund LB, ASTM ATP627,1977.Elastic-Plastic.
[16]Nakamura T, Shih CF and Freund LB, Elastic-Plastic analysis of a dynamically loaded circumferential notched round bar, Engng.Fract Mechl985;22(3):437-452.
[17]T. Yokoyama,K. Kishiad,Exp.Mech.,7(1989) 188-194.
[18]Rao SG, Xia YM, Dynamic Elastic-Plastic FEM Analysis of a fracture Specimens under Plane Stress State, Engng.Fract Mech1995;52(4):755-763.
[19]Xia YM, Rao SG and Yang BC, A novel method for measuring plane Stress Dynamic fracture toughness, Engng.Fract Mech1994;48:17-24.
[20]Gong NP, Xia YM, Elastic-Plastic FEM Analysis for bar-bar tensile impact apparatus with a circumferentially notched short metal bar. Acta Mechanic Solida Sinica 2002;23(2):223-231.
[21]汪洋,夏源明.杆杆型冲击拉伸试验装置一维试验原理的有效性论证[J].实验力学,1997,12(1)：126-134.
[22]Nakano M, Kishida K. Dynamic fracture initiation in brittle materials under combined mode I/II loading[J]. Journal De physique Ⅳ,1994.
[23]Liu C, Huang Y, Lovato ML and Stout MG Measurement of the fracture toughness of a fiber-reinforced composite using the Brazilian disk geometry[J]. International Journal of Fracture, 1997(87):241-263.
[24]Lambert DE, Ross CA, Strain rate effects on Dynamic Fracture and strength, Int J Impact Engng2000;24:985-998.
[25]ISRM Testing Commission (co-ordinator: F.Ouchterlony). Suggested methods for determining the fracture toughness of rock[J]. International Journal of Rock Mechanics and Mining Sciences,1988(25):71-96.
[26]ISRM Testing Commission (co-ordinator: R.J.Fowell). Suggested methods for determining mode I fracture toughness using cracked chevron notched Brazilian disc specimens[J]. International Journal of Rock Mechanics and Mining Sciences,1995(32):57-64.
[27]M.J.Iqbal,B-Mohanty,Experimental calibration of stress intensity factors of the ISRM suggested cracked chevron-notched Brazilian disk specimen used for determination of mode-I fracture toughness. Internationnal Journal of Rock Mechanics and Mining Sciences 43(2006) 1270-1276.
[28]P.Jonsen et al,Tensile strength and fracture engergy of pressed metal powder by diametral compression test.Powder technology 176(2007)148-155.
[29]M.R.Ayatoollahi,M.R.M.Aliha.Cracked Brazilian disk specimen subjected to mode II deformation. Engineerin Fracture Mechanics 72(2005)493-503.
[30]王启智等.采用中心圆孔裂缝平台巴西圆盘确定岩石的动态断裂韧度[J].岩士工程学报,2006,28(6)：723-728.
[31]李战鲁,王启智.加载速率对岩石动态断裂韧度影响的实验研究[J].岩土工程学报,2006,28(12)：2116-2120.
[32]张宗贤,赵清等,用短棒试件测定岩石的动静态断裂韧度,北京科技大学学报,1992.3,Vol.14,No.2.
[33]张宗贤,俞洁等,高温状态下岩石动态断裂的试验研究,有色金属,1999.2,Vol.51,No.1。
[34]Z.X.Zhang,S.Q.Kou,L.G.Jiang,Effects of loading rate on rock fracture:fracture characteristics and engergy partitioning,Internationnal Journal of Rock Mechanics and Mining Sciences 37(2002).
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