抽油杆杆体表面裂纹应力强度因子近似式研究

本文以拉伸无限体中椭圆片裂纹应力强度因子的精确解析解为基础,引入抽油杆杆体自由表面边界影响系数M,并将抽油杆杆体局部表面缺陷简化为部份椭圆表面裂纹,于是就将有局部表面缺陷的抽油杆杆体问题简化为有部份椭圆表面裂纹的拉伸圆杆问题。在假设拉伸圆杆部份椭圆表面裂纹的变形为“部份椭球”的条件下,得到了M与该表面裂纹嘴中心张开位移Δ₀之间的关系,简称M-Δ₀公式,用变载勾线法勾画不同裂纹形状,用实验测定相应Δ₀,用M-Δ₀公式计算相应的M值,将不同裂纹形状下的M数据进行数学回归,得到了系数M(a/r,a/c)函数,从而得到了抽油杆杆体局部表面裂纹应力强度因子近似式。将对应的表面裂纹形状最深点的数值与文献的结果进行了比较,比较表明,二者大体一致。

AN APPROXIMATE EXPRESSION OF STRESS INTENSITY FACTOR IN SUCKER ROD STRING WITH SURFACE CRACK

This article suggess a free surface boundary influence coefficient M in a sucker rod string, the partial surface defect is simplified to a partially elliptical surface crack. On the basis of an exact analytical solution of the stress intensity factor of an infinite elastic tension body with flat elliptical crack, the problem of a sucker rod string with partial surface defect is simplified to a problem of a round tension rod with partially elliptical surface crack. Assuming that the deformation of the surface crack in the round tension rod is a partial ellipsoid,the relation between M and center opening displacement Δ₀ of surface crack mouth are obtained.It is called simply as a M-Δ₀ equation. The coefficient functtion M (a/r, a/c) is obtained by using marking techniques in fatigue crack growth to delineate the different crack shanes, determining their corresponding displacement by experiments,computing the corresponding values M by M-Δ₀ equation, and making regression on data M in different crack shapes. Thus we get an approximate expression of the stress intensity factor of a sucker rod string with partial surface crack. A comparison of the numerical values on the deepest point of corresponding surface crack shape with the results in literature shows that they are somewhat con-sistant to each other.