中心直裂纹圆盘无量纲应力强度因子获取精度研究

Analysis on accuracy of dimensionless stress intensity factor of central straight through Brazilian disc

岩石断裂韧性是岩石抵抗裂纹扩展能力的表征,而无量纲应力强度因子是计算断裂韧性的关键参数,目前众多国内外学者采用Atkinson给出的中心裂纹圆盘试件的近似公式获取中心直裂纹圆盘的无量纲应力强度因子。对Atkinson给出的无量纲应力强度因子近似公式及中心裂纹圆盘试件的级数解精度进行了研究,并给出了较广范围的产生纯Ⅱ型裂纹加载条件,还采用有限元方法标定了不同预制裂纹宽度时中心直裂纹圆盘Ⅰ型裂纹的无量纲应力强度因子。分析结果表明:YⅠ随着相对裂纹宽度增大逐渐减小,且当相对裂纹宽度大于0.01后,YⅠ变化幅度逐渐减小;不同裂纹宽度条件下,YⅠ随加载角变化的规律相同。当裂纹宽度仅为0.1 mm时,其无量纲应力强度因子解析解与数值解会产生很大偏差,因此在断裂韧性测试中应根据实测的裂纹宽度对无量纲应力强度因子进行标定。

Rock fracture toughness is a factor describing the ability of resisting rock crack propagation,and the dimension-less stress intensity factor（ DSIF） is an essential parameter to calculating the fracture toughness. At present,many scholars still adopt the approximate formula given by C. Atkinson for the central straight through Brazilian disc specimen to obtain the DSIF values. We research the accuracies of C. Atkinson formula and the series solution for the center crack disk specimen,and put forward the loading conditions of pure type II crack at a wide range of load angle and relative crack length. We also adopt finite element method to calculate the dimensionless stress intensity factor of crack I for CSTBD specimens with different prefabricated crack width. The analysis results show that YI gradually decreases with increase of the relative crack width,and the change amplitude of YI gradually reduces after the relative crack width exceeds 0. 01; for the different crack width,the change law of YI is the same. In addition,when the crack width is only 0. 1 mm,the analytical solution of DSIF will deviate from the numerical solution. Therefore,in the fracture toughness test,the dimensionless stress intensity factor must be calibrated by the measured crack width.