Limit loads for cracked elbows under in-plane bending moment

Elbows are the type of components widely used in a piping system, and are particularly important from the point of view of structural behaviour. In practice, the existence of cracks in excess of the defect limit cannot be excluded. So it is very important to know the effect of cracks on limit loads of elbows for integrity assessment of the piping system. The existing closed-form limit loads for axial cracked elbows under in-plane bending moment are either too conservative or inadequate, therefore, the present studies focused on limit loads of elbows with axial cracks and the crack configurations were assumed to be constant-depth rectangle, subjected to in plane opening and closing bending moments respectively. The crack-like defects were postulated to be in crown of elbows with different crack sizes. The limit loads and residual strength factors (RSFs) (M_L/M_0L )of cracked elbows with various ratios of t/r_m and relative bending radius R/r_m were investigated in detail, by using of three-dimensional (3D) non-linear finite element (FE) analyses, assuming elastic perfectly-plastic material behaviour and taking geometric nonlinearity into account. The non-linear finite element (FE) analyses indicate that under the open/close bending modes, elbows exhibit different behaviour obviously at the elastic plastic states. The results from comprehensive parametric studies indicate that the limit loads of cracked elbows may reduce with the increasing of crack length, and these trends are more serious for long radius elbows. Generally speaking, the thickness-radius ratio t/r_m of elbow has insignificant effects on RSFs. Based on extensive limit load numeric data and comprehensive parametric studies, the revised closed form equations for cracked elbows involving effect of tangent pi