岩石材料动态破坏的近场动力学方法数值模拟
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摘要
裂纹的聚集、扩展、分叉是岩石等脆性材料破坏失效的关键因素,本文在验证了近场动力学方法在研究岩石类材料裂纹动态扩展方面的有效性之后,采用近场动力学方法分别对冲击载荷作用下含有双裂纹岩石材料和单轴压缩作用下含单斜裂纹的岩石材料进行数值模拟.结果表明,对于双垂直裂纹,其裂纹扩展路径大致与预制裂纹成70°夹角;对于单裂纹,裂纹的扩展路径随裂纹倾角的变化而变化,最终导致构件的整体破坏.数值模拟结果表明近场动力学方法可以很好地模拟岩石等脆性材料的裂纹扩展直至破坏的过程,反映裂纹扩展的物理机理;其作为一种新的基于非局部理论的数值方法,在地下岩体工程方面及页岩气的开采方面会有很好的发展前景.
Crack propagation, aggregation, bifurcation plays the key role in the failure of brittle materials such as rock. In this paper, after verifying the effectiveness of the peridynamics in studying the crack dynamic growth of rock materials, the numerical simulations of rock with prefabricated double cracks under impacting loading, and rock with the pre-notch single crack under compression loading are carried out by using peridynamics method. The results show that for the pre-notch double vertical crack,the crack propagation path is approximately 70° from the pre-notch crack. For the pre-notch single crack, the crack propagation trajectory changes with the crack orientation angle, finally resulting in the overall failure of the component. The numerical simulation results show that the peridynamics can well simulate the propagation of cracks in brittle materials such as rocks, up to the failure status, and reflect the physical mechanism of crack propagation. As a new numerical method based on the nonlocal theory, peridynamics has very good application prospects in underground engineering and shale gas exploration.
Crack propagation, aggregation, bifurcation plays the key role in the failure of brittle materials such as rock. In this paper, after verifying the effectiveness of the peridynamics in studying the crack dynamic growth of rock materials, the numerical simulations of rock with prefabricated double cracks under impacting loading, and rock with the pre-notch single crack under compression loading are carried out by using peridynamics method. The results show that for the pre-notch double vertical crack,the crack propagation path is approximately 70° from the pre-notch crack. For the pre-notch single crack, the crack propagation trajectory changes with the crack orientation angle, finally resulting in the overall failure of the component. The numerical simulation results show that the peridynamics can well simulate the propagation of cracks in brittle materials such as rocks, up to the failure status, and reflect the physical mechanism of crack propagation. As a new numerical method based on the nonlocal theory, peridynamics has very good application prospects in underground engineering and shale gas exploration.
引文
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[21]吴凡,李书卉,段庆林,等.基于近场动力学方法的水力压裂过程数值模拟[J].计算机辅助工程,2017,26(1):1-6.
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[2]蒲成志,曹平,赵延林,等.单轴压缩下多裂隙类岩石材料强度试验与数值分析[J].岩土力学,2010,31(11):3661-3666.
[3]乔丕忠,张勇,张恒,等.近场动力学研究进展[J].力学季刊,2017,38(1):1-13.
[4]王海运.世界能源格局的新变化及其对中国能源安全的影响[J].上海大学学报:社会科学版,2013,30(6):1-11.
[5]SILLING S A.Reformulation of elasticity theory for discontinuities and long-range forces[J].Journal of the Mechanics and Physics of Solids,2000,48(1):175-209.
[6]黄丹,章青,乔丕忠,等.近场动力学方法及其应用[J].力学进展,2010,4(2):448-459.
[7]朱其志,倪涛,赵伦洋,等.岩石类材料裂纹扩展贯通的近场动力学方法模拟[J].岩土力学与工程学报,2016,34(11):3507-3515.
[8]谷新保,周小平.裂纹扩展和连接过程的近场动力学数值模拟[J].岩土力学,2017,38(2):610-616.
[9]SILLING S A,ASKAR E.A meshfree method based on the peridynamic model of solid mechanics[J].Computers and Structures,2005,83:1526-1535.
[10]BOBARU F,YANG M,ALVES L F,et al.Convergence adaptive refinement and scaling in 1Dperidynamics[J].International Journal for Numerical Methods in Engineering,2009,77:852-877.
[11]HA Y D,BOBARU F.Characteristics of dynamic brittle fracture captured with peridynamics[J].Engineering Fracture Mechanics,2011,78(6):1156-1168.
[12]HU Y L,MADENCI E.Bond-based peridynamics modeling of composite laminates with arbitrary orientation and satcking aequence[J].Composite Structures,2016,153:139-175.
[13]刘元雪,陈忱,周家伍,等.岩土损伤复合体理论的应力应变合成模式[J].后勤工程学院学报,2008,24(3):7-10,14.
[14]张慧娟.页岩动态本构关系及应用初探[D].成都:西南石油大学,2014.
[15]于永军.热力耦合作用下油页岩的损伤与断裂力学行为研究[D].太原:太原理工大学,2015.
[16]CHENG Z Q,LIU Y K,ZHAO J,et al.Numerical simulation of crack propagation and branching in functionally graded materials using peridynamic modeling[J].Engineering Fracture Mechanics,2018,191:13-32.
[17]HA Y,BOBARE F.Studies of dynamic crack propagation and crack branching with peridynamics[J].International Journal of Fracture,2010,162(1):229-244.
[18]YANG S Q,JING H W.Strength failure and crack coalescence behavior of brittle sandstone samples containing a single fissure under uniaxial compression[J].International Journal of Fracture,2011,168:227-250.
[19]王玉满,董大志,李建忠,等.川南下至留统龙马溪组页岩储气层特征[J].石油学报,2012,33(4):551-561.
[20]梁利喜,何顺平,张安东.CCNBD试样测试页岩Ⅰ型断裂韧性[J].西部探矿工程,2016,11:41-46.
[21]吴凡,李书卉,段庆林,等.基于近场动力学方法的水力压裂过程数值模拟[J].计算机辅助工程,2017,26(1):1-6.
[22]顾鑫,章青,黄丹.基于近场动力学方法的混凝土板侵彻问题研究[J].震动与冲击,2016,35(6):52-58.