简化扩展有限元法精度的验证及在DCT试验中的应用
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摘要
在扩展有限元方法(XFEM)和相互作用积分的基础上,建立了不含裂尖增强函数的简化XFEM法.并通过该方法计算了经典算例的应力强度因子,与传统的J积分方法和应力强度因子手册中的解析解进行了对比分析.结果表明,简化XFEM法与传统的J积分法相比,其精度更高且不需划分过密的网格.之后,采用简化XFEM法对沥青混合料圆盘拉伸试验(DCT)进行了数值模拟分析,通过与室内试验对比发现,简化XFEM法模拟的裂纹扩展路径和试验结果接近,并有助于分析试验过程中的断裂机理.该简化XFEM法能为非均质材料等更复杂问题断裂模拟提供新的解决思路.
Based on the extended finite element method(XFEM) combined with interaction integral method, the simplified XFEM without tip-enriched functions is established. Using this method, the stress intensity factor of a typical example is studied, and compared with the traditional J integral method and analytical solution of stress intensity factor handbook. The results show that the simplified XFEM has a higher precision than the J integral method, and there is no need to divide too dense meshes. Afterwards, simplified XFEM is employed to simulate the disk-shaped compact tension test(DCT). Based on the comparison of numerical results and experimental data, it can be concluded that the simplified XFEM can serve as an efficient tool to simulate crack initiation and propagation, and analyze the fracture mechanism during the actual experiment. The method established in this paper could provide new solutions for the fracture process of non-homogeneous materials.
Based on the extended finite element method(XFEM) combined with interaction integral method, the simplified XFEM without tip-enriched functions is established. Using this method, the stress intensity factor of a typical example is studied, and compared with the traditional J integral method and analytical solution of stress intensity factor handbook. The results show that the simplified XFEM has a higher precision than the J integral method, and there is no need to divide too dense meshes. Afterwards, simplified XFEM is employed to simulate the disk-shaped compact tension test(DCT). Based on the comparison of numerical results and experimental data, it can be concluded that the simplified XFEM can serve as an efficient tool to simulate crack initiation and propagation, and analyze the fracture mechanism during the actual experiment. The method established in this paper could provide new solutions for the fracture process of non-homogeneous materials.
引文
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[7] 王志勇, 马力, 吴林志, 等. 基于扩展有限元法的颗粒增强复合材料静态及动态断裂行为研究[J]. 固体力学学报, 2011, 32(6): 566-573. Wang Zhiyong, Ma Li, Wu Linzhi, et al. Investigation of static and dynamic fracture behavior of particle-reinforced composite materials by the extended finite element method[J]. Chinese Journal of Solid Mechnaics, 2011, 32(6): 566-573.
[8] Yu H, Wu L, Guo L, et al. Investigation of mixed-mode stress intensity factors for nonhomogeneous materials using an interaction integral method[J]. International Journal of Solids and Structures, 2009,46(20): 3710-3724.
[9] Yu H, Wu L, Guo L, et al. Interaction integral method for the interfacial fracture problems of two nonhomogeneous materials[J]. Mechanics of Materials, 2010, 42(4): 435-450.
[10] Wagoner M, Buttlar W, Paulino G, et al. Investigation of the fracture resistance of hot-mix asphalt concrete using a disk-shaped compact tension test[J]. Journal of the Transportation Research Board, 2005, (1929): 183-192.
[11] Seong H. Fracture of asphalt concrete: a cohesive zone model approach considering viscoelastic effects[D]. University of Illinois at Urbana-Champaign, 2006: 57-66.
[12] 朱月风, 张洪亮, 宋彬. 再生沥青混合料的黏弹性动态响应及疲劳性能[J]. 北京工业大学学报,2017, 43(1):135-142. Zhu Yuefeng, Zhang Hongliang, Song Bin. Visco-elastic dynamic response property and fatigue performance of recycled asphalt mixture[J]. Journal of Beijing University of Technology, 2017, 43(1): 135-142.
[13] 朱兴一, 黄志义, 陈伟球. 基于复合材料细观力学模型的沥青混凝土弹性模量预测[J]. 中国公路学院, 2010, 23(3): 29-34. Zhu Xingyi, Huang Zhiyi, Chen Weiqiu. Elastic modulus prediction of asphalt concrete based on composite material micromechanics model[J]. China Journal of Highway and Transport, 2010, 23(3): 29-34.
[14] 金光来, 黄晓明, 梁彦龙. 两种不同模式下的沥青混合料断裂过程研究[J]. 湖南大学学报(自然科学版), 2014, 41(6): 120-126. Jin Guanglai, Huang Xiaoming, Liang Yanlong. A numerical analysis of the fracture behavior of asphalt concrete under two different modes[J]. Journal of Hunan University(Natural Sciences), 2014, 41(6): 120-126.
[2] 陈金龙, 战楠, 张晓川. 基于扩展有限元法的裂尖场精度研究[J].计算力学学报, 2014, 31(4): 425-430. Chen Jinlong, Zhan Nan, Zhang Xiaochuan. Numerical study on the accuracy of crack tip field by extended finite element method[J]. Chinese Journal of Computational Mechanics, 2014, 31(4): 425-430.
[3] Belytschko T, Black T. Elastic crack growth in finite elements with minimal remeshing[J]. International Journal for Numerical Methods in Engineering, 1999, 45:601-620.
[4] Belytschko T, Hao H, Xu J, Zi G. Dynamic crack propagation based on loss of hyperbolicity and a new discontinuous enrichment[J]. International Journal of Numerical Methods in Engineering, 2003, 58(12): 1873-1905.
[5] Motamedi D, Mohammadi S. Dynamic crack propagation analysis of orthotropic media by the extended finite element method[J]. International Journal of Fracture, 2010, 161(1): 21-39.
[6] 苏毅, 王生楠, 高文. 广义扩展有限元及其在裂纹扩展中的应用[J]. 西北工业大学学报, 2015, 33(6): 921-927. Su Yi, Wang Shengnan, GAO Wen. Generalized extended finite element method and its application in crack grow[J]. Journal of Northwestern Polytechnical University, 2015, 33(6): 921-927.
[7] 王志勇, 马力, 吴林志, 等. 基于扩展有限元法的颗粒增强复合材料静态及动态断裂行为研究[J]. 固体力学学报, 2011, 32(6): 566-573. Wang Zhiyong, Ma Li, Wu Linzhi, et al. Investigation of static and dynamic fracture behavior of particle-reinforced composite materials by the extended finite element method[J]. Chinese Journal of Solid Mechnaics, 2011, 32(6): 566-573.
[8] Yu H, Wu L, Guo L, et al. Investigation of mixed-mode stress intensity factors for nonhomogeneous materials using an interaction integral method[J]. International Journal of Solids and Structures, 2009,46(20): 3710-3724.
[9] Yu H, Wu L, Guo L, et al. Interaction integral method for the interfacial fracture problems of two nonhomogeneous materials[J]. Mechanics of Materials, 2010, 42(4): 435-450.
[10] Wagoner M, Buttlar W, Paulino G, et al. Investigation of the fracture resistance of hot-mix asphalt concrete using a disk-shaped compact tension test[J]. Journal of the Transportation Research Board, 2005, (1929): 183-192.
[11] Seong H. Fracture of asphalt concrete: a cohesive zone model approach considering viscoelastic effects[D]. University of Illinois at Urbana-Champaign, 2006: 57-66.
[12] 朱月风, 张洪亮, 宋彬. 再生沥青混合料的黏弹性动态响应及疲劳性能[J]. 北京工业大学学报,2017, 43(1):135-142. Zhu Yuefeng, Zhang Hongliang, Song Bin. Visco-elastic dynamic response property and fatigue performance of recycled asphalt mixture[J]. Journal of Beijing University of Technology, 2017, 43(1): 135-142.
[13] 朱兴一, 黄志义, 陈伟球. 基于复合材料细观力学模型的沥青混凝土弹性模量预测[J]. 中国公路学院, 2010, 23(3): 29-34. Zhu Xingyi, Huang Zhiyi, Chen Weiqiu. Elastic modulus prediction of asphalt concrete based on composite material micromechanics model[J]. China Journal of Highway and Transport, 2010, 23(3): 29-34.
[14] 金光来, 黄晓明, 梁彦龙. 两种不同模式下的沥青混合料断裂过程研究[J]. 湖南大学学报(自然科学版), 2014, 41(6): 120-126. Jin Guanglai, Huang Xiaoming, Liang Yanlong. A numerical analysis of the fracture behavior of asphalt concrete under two different modes[J]. Journal of Hunan University(Natural Sciences), 2014, 41(6): 120-126.