弯折裂纹尖端应力强度因子值的近似计算方法

STUDY ON APPROXIMATE METHOD OF STRESS INTENSITY FACTOR VALUE AT BENDING CRACK TIP

工程结构中存在着大量分布不均的弯折裂纹,对结构稳定性有较大影响。为了能够简单快速地得到弯折裂纹尖端应力强度因子(K)值,应用近似方法,将弯折裂纹近似为等效直裂纹,通过计算等效直裂纹尖端K值得到弯折裂纹尖端K值。在已有近似方法 (水平投影法)的基础上,提出了三种新的近似方法,分别为:垂线投影法、中心旋转法和连线法。新提出的三种近似方法与已有近似方法对比可知:优化了得到等效直裂纹的近似过程;修正和扩大了近似计算方法的适用范围。计算弯折裂纹的主裂纹尖端K时,当主裂纹与荷载方向垂直且次裂纹与荷载所在方向的夹角小于45°时,垂线投影法为最优近似方法;但当次裂纹与荷载所在方向的夹角大于45°时,中心旋转法为最优近似方法。计算弯折裂纹的次裂纹尖端K_(Ⅰ)时,水平投影法为最优近似方法,当计算弯折裂纹的次裂纹尖端K_(Ⅱ)时,在弯折裂纹主次裂纹长度比b/a<0.3范围内,垂线投影法、中心旋转法均优于水平投影法。与水平投影法相比,连线法更适用于计算主裂纹与荷载所在方向的夹角较小情况下的K_(Ⅱ)值。

A large number of unevenly distributed bending cracks exist in engineering structures,which have great influence on the stability of structures.To obtain the stress intensity factor(K) values of the bending crack tips easily and quickly,the bending cracks are approximated as equivalent straight.By calculating the equivalent straight crack tip K value,the bending crack tip K value is obtained.Based on the existing approximate methods(horizontal projection method),three new approximate methods are proposed,which are vertical projection method,center rotation method and line method.The comparison of the three new approximation methods with the existing ones shows that the approximation process of obtaining equivalent straight cracks is optimized.The application range of approximate calculation method is modified and expanded.When calculating the main crack tip K of the bending crack,when the main crack is perpendicular to the load direction and the angle between the branch crack and the load direction is less than 45°,the vertical projection method is the best approximation method;but when the angle between the branch crack and the load direction is greater than 45°,the central rotation method is the best one.When calculating the branch crack tip K_(Ⅰ) of the bending crack,the horizontal projection method is the best approximate method.When the branch crack tip K_(Ⅱ) is calculated,the vertical projection method and the center rotation method are superior to the horizontal projection method in the range of the length ratio(b/a) of the main and branch cracks of the bending crack less than 0.3.Compared with the horizontal projection method,the line method is more suitable for the calculation of K_(Ⅱ) value when the angle between the main crack and the direction of load is small.