中心裂纹圆盘断裂参数的有限元标定  

Calibration of Finite Element of the Fracture Parameters of Central Cracked Circular Disk

作　　者：段国胜 Duan Guosheng(Qinghai Communications Technical College,Xining 810000,China)

机构地区：[1]青海交通职业技术学院

出　　处：《甘肃科学学报》2019年第5期129-134,共6页Journal of Gansu Sciences

基　　金：青海东部地区公路泥石流特征及快速抢修技术研究项目(2018-ZJ-733)

摘　　要：圆盘试件作为最受研究人员青睐的式样类型,被广泛用于测试和研究脆性材料(如岩石、聚合材料及陶瓷等)的Ⅰ、Ⅱ型及复合型断裂韧性。Williams级数解的常数项,即平行于裂纹方向的T应力对裂纹的断裂行为存在很大影响,进一步的研究表明,裂纹尖端Williams级数解的更高阶非奇异项(n=3)对中心直裂纹圆盘断裂特征的影响同样显著。研究采用有限元法获得了裂纹尖端多个节点的位移值,建立超静定方程组,采用最小二乘法对其进行求解,对Williams级数解的奇异项应力强度因子KⅠ和KⅡ,常数项T应力以及更高阶系数A3和B3进行求解。最后,给出了不同相对裂纹长度a/R及裂纹倾角的中心裂纹圆盘裂纹尖端的应力强度因子K*Ⅰ及K*Ⅱ,以及更高阶项断裂参数A*3和B*3。结果表明:T*随裂纹倾角增大逐渐增大且保持为负值;B*3均为正值且随裂纹倾角的增大呈现先增大后减小的趋势;K*Ⅰ、A*3均随裂纹倾角的增大逐步减小,而K*Ⅱ随裂纹倾角的增大而增大;中心裂纹圆盘的纯Ⅱ型断裂裂纹倾角随相对裂纹长度的增大而减小,而Ⅱ型无量纲应力强度因子随裂纹长度的增大而增大。As the most popular pattern type for researchers,disk test specimen are widely used to test and study the Ⅰ,Ⅱ and composite fracture toughness of brittle materials such as rocks,polymeric materials and ceramics.The constant term of Williams series solution,namely T stress parallel to the direction of the crack,has a great influence on the fracture behavior of the crack,and further studies show that the higher-order non-singular term ( n =3) of Williams series solution at the crack tip has same critical impact on the fracture characteristics of the disk with central vertical crack.In this paper,the finite element method was used to obtain the displacement value of multiple nodes at the crack tip,and the statically indeterminate equation group that was solved by means of the ordinary least squares techniques was established,and the stress intensity factors K Ⅰ and K Ⅱof singular term of Williams series solution,stress T of constant term and higher-order coefficients A 3 and B 3 were solved.Finally,the stress intensity factors K *Ⅰand K *Ⅱ of crack tip of central cracked disk and higher-order fracture parameters A * 3 and B * 3 are given at different relative crack length a/R and crack inclination angle.The results show that:T * increases gradually with the growing crack inclination and remains negative;B * 3 is positive and shows the tendency of increasing and then decreasing with the increase of crack inclination;K *Ⅰand A * 3 falls with the increase of the crack inclination,while K *Ⅱ enlarges with the increase of the crack inclination;the inclination of the pure type Ⅱ crack on the central cracked disk decreases with the increase of the relative crack length,while the dimensionless stress intensity factor of type Ⅱ increases with the growth of the crack length.

关 键 词：中心裂纹圆盘 断裂参数 Williams级数解 应力强度因子 高阶项 

分 类 号：TD713[矿业工程—矿井通风与安全]