The Effect of Bi-Axial Stress on Limit Loads of Structures Containing Surface-Breaking Flaws and its Influence on Structural Integrity Assessments

Abstract

Fracture assessment diagram (FAD) based fracture assessment procedures are universally adopted by standards/documents including BS7910, R6, API579-1/ASME FFS-1 and FITNET. In the use of a FAD for structural integrity assessment, one important consideration is to determine the load ratio (Lr) which is defined by two equivalent definitions: Lr is either defined as the ratio of reference stress (σref) to yield strength (σY) as in BS7910, or as the ratio of applied load to plastic limit load as in R6. The solutions of reference stress or limit load are given in the assessment procedures for commonly encountered flawed structures such as a plate containing a surface crack and a cylinder containing an external surface crack. Although the solutions given in the various standards are not all the same, they were invariably derived on the basis of analysis of the force and moment equilibrium with regard to a flawed section and none of them has taken into account the effects of bi-axial stressing on a flawed section, thus leading to the likelihood of an overly conservative assessment. In this work, finite element analysis (FEA) of various flawed geometries (plate and cylinder containing surface cracks) was performed to compute plastic limit load, with the focus on understanding the effects of bi-axial stressing on plastic limit load. The geometries assessed include a plate with a surface crack subjected to both uni-axial and bi-axial loading, and a cylinder with circumferentially internal and external surface cracks sustaining a combination of axial loading and internal pressure. The investigation of these cases has demonstrated a significant increase in plastic limit load arising from bi-axial stressing. Comparison of the results of plastic limit load obtained from FEA with those derived from BS 7910 reference stress solutions was carried out to assess the extent of conservatism when the standard solutions are used in the applications containing bi-axial stresses. The implication for structural integrity assessment due to bi-axial stressing was also addressed. A comparison between BS 7910 Level 2B (material-specific FAD) and Level 3C (based on a FAD generated with FEA) procedures was also made and it was shown that whether the Level 3C procedure can reduce the conservatism in an assessment is dependent on individual cases.