数值模拟带裂纹中心开孔巴西圆盘的K因子公式
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摘要
文章采用有限元方法对纯Ⅰ型单边裂纹及双边裂纹的中心开孔巴西圆盘应力强度因子(K因子)进行了数值模拟,运用量纲分析法,在大量算例的基础上总结其规律,拟合出纯Ⅰ型的K因子公式。该公式具有试样不受尺寸大小限制、适用范围广、精确度高等优点。在单边裂纹及双边裂纹的中心开孔巴西圆盘纯Ⅰ型试验中,当相对裂纹长度a/(R-r)为0.10～0.80,内外圆半径比a/R为0.05～0.60,拟合公式求得的数值和有限元模拟得到的数值误差在3%以内。通过对比相同条件下,双、单边裂纹中心开孔巴西圆盘K因子之间的比值关系,分析了单、双边裂纹相对长度及内外圆半径比对中心开孔巴西圆盘K因子影响的相对大小。
In this paper, finite element method was used to calculate the stress intensity factor(K factor) of Brazilian disc with central hole and pure Ⅰ-type single-side cracks and bilateral cracks. Through the dimensional analysis which was based on plenty of examples, the formulas of K factor of pure Ⅰ-type cracks were summed up. The formulas have the advantages such as unlimited sizes of the specimen, wide range of application and high degree of accuracy and so on. In the numerical simulation experiment of Brazilian disc with single-side cracks and bilateral cracks, it is shown that the formulas match the values calculated by finite element method perfectly with an error of only 3% when the relative crack length a/(R-r) ranges from 0.10 to 0.80 and the inner and outer circle radius ratio a/R ranges from 0.05 to 0.60. By comparing the ratio of K factor of single-side cracks and bilateral cracks under the same circumstance, the effect of both a/(R-r) and a/R on K factor of Brazilian disc with central hole was analyzed.
In this paper, finite element method was used to calculate the stress intensity factor(K factor) of Brazilian disc with central hole and pure Ⅰ-type single-side cracks and bilateral cracks. Through the dimensional analysis which was based on plenty of examples, the formulas of K factor of pure Ⅰ-type cracks were summed up. The formulas have the advantages such as unlimited sizes of the specimen, wide range of application and high degree of accuracy and so on. In the numerical simulation experiment of Brazilian disc with single-side cracks and bilateral cracks, it is shown that the formulas match the values calculated by finite element method perfectly with an error of only 3% when the relative crack length a/(R-r) ranges from 0.10 to 0.80 and the inner and outer circle radius ratio a/R ranges from 0.05 to 0.60. By comparing the ratio of K factor of single-side cracks and bilateral cracks under the same circumstance, the effect of both a/(R-r) and a/R on K factor of Brazilian disc with central hole was analyzed.
引文
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[2]张盛,王启智.用5种圆盘试件的劈裂试验确定岩石断裂韧度[J].岩土力学,2009,30(1):12-18.
[3]胡凤辉,巫绪涛,顾颖,等.基于数值模拟的含裂纹BD试验和SCB试验的K因子公式[J].合肥工业大学学报(自然科学版),2015,38(1):95-97.
[4]HUDSON J A.Tensile strength and the ring test[J].International Journal of Rock Mechanics and Mining Sciences&Geomechanics Abstracts,1969,6(1):91-97.
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[6]WANG Q Z.The flattened Brazilian disc specimen used for determining elastic modulus tensile strength and fracture toughness of brittle rocks:experimental results[J].International Journal of Rock Mechanics and Mining Sciences,2004,41(2):26-30.
[7]AHMAD J,ASHBAUGH N E.Constant KⅠcrack-propagation test specimens[J].International Journal of Fracture,1982,19(2):115-129.
[8]张盛,梁亚磊.预制裂缝宽度对HCFBD试件确定岩石断裂韧度的影响[J].实验力学,2013,28(4):517-523.
[9]CHEN C S,HSU S C.Measurement of indirect tensile strength of anisotropic rocks by the ring test[J].Rock Mechanics and Rock Engineering,2001,34(4):293-321.
[10]TANG T,BAZANT Z P,YANG S C,et al.Variable-notch one-size test method for fracture energy and process zone length[J].Engineering Fracture Mechanics,1996,55(3):383-404.
[11]CHEN C H,CHEN C S,WU J H.Fracture toughness analysis on cracked ring disks of anisotropic rock[J].Rock Mechanics and Rock Engineering,2008,41(4):539-562.
[12]周妍,张财贵,杨井瑞,等.圆孔内单边(或双边)裂纹平台巴西圆盘应力强度因子的全面标定[J].应用数学和力学,2015,36(1):16-30.
[13]张洪才.ANSYS 14.0理论解析与工程应用实例[M].北京:机械工业出版社,2012:456-486.
[2]张盛,王启智.用5种圆盘试件的劈裂试验确定岩石断裂韧度[J].岩土力学,2009,30(1):12-18.
[3]胡凤辉,巫绪涛,顾颖,等.基于数值模拟的含裂纹BD试验和SCB试验的K因子公式[J].合肥工业大学学报(自然科学版),2015,38(1):95-97.
[4]HUDSON J A.Tensile strength and the ring test[J].International Journal of Rock Mechanics and Mining Sciences&Geomechanics Abstracts,1969,6(1):91-97.
[5]HOBBS D W.An assessment of a technique for determining the tensile strength of rock[J].British Journal of Applied Physics,1965,16(2):259-268.
[6]WANG Q Z.The flattened Brazilian disc specimen used for determining elastic modulus tensile strength and fracture toughness of brittle rocks:experimental results[J].International Journal of Rock Mechanics and Mining Sciences,2004,41(2):26-30.
[7]AHMAD J,ASHBAUGH N E.Constant KⅠcrack-propagation test specimens[J].International Journal of Fracture,1982,19(2):115-129.
[8]张盛,梁亚磊.预制裂缝宽度对HCFBD试件确定岩石断裂韧度的影响[J].实验力学,2013,28(4):517-523.
[9]CHEN C S,HSU S C.Measurement of indirect tensile strength of anisotropic rocks by the ring test[J].Rock Mechanics and Rock Engineering,2001,34(4):293-321.
[10]TANG T,BAZANT Z P,YANG S C,et al.Variable-notch one-size test method for fracture energy and process zone length[J].Engineering Fracture Mechanics,1996,55(3):383-404.
[11]CHEN C H,CHEN C S,WU J H.Fracture toughness analysis on cracked ring disks of anisotropic rock[J].Rock Mechanics and Rock Engineering,2008,41(4):539-562.
[12]周妍,张财贵,杨井瑞,等.圆孔内单边(或双边)裂纹平台巴西圆盘应力强度因子的全面标定[J].应用数学和力学,2015,36(1):16-30.
[13]张洪才.ANSYS 14.0理论解析与工程应用实例[M].北京:机械工业出版社,2012:456-486.