Effect of Loading on Stress Intensification Factors

The basic objective of this investigation is to determine the effect of loading on the stress intensification factors of Markl’s fatigue evaluation method for metal piping. Markl’s method is based on the fatigue testing of 4 in. schedule 40 carbon steel cantilever piping. Subsequent testing using a four-point loading showed that the S-N data were different from that predicted by the procedure and equation developed by Markl. Markl’s method is based on determining the elastic-plastic forces in a piping system by multiplying the elastic system stiffness by the actual deflection. In this manner a fictitious force is calculated to determine piping stresses assuming the elastic beam bending equation, Mc/I, applies even in partially plastic pipes. Previous analytical work on this topic by Rodabaugh and Scavuzzo (“Fatigue of Butt Welded Pipe and the Effect of Testing Methods–Report 2: Effect of Testing Methods on Stress Intensification Factors,” Welding Research Bulletin 433, July 1998) showed that these measured differences should occur between cantilever and four-point tests using Markl’s method. The basic assumption in this analytical comparison is that strain-cycle correlations lead to the correct prediction of fatigue life. Using the measured alternating strain, both types of test geometries lead to the same prediction of fatigue life using these strain-cycle correlations. In this study, the same analytical assumptions used by Rodabaugh and Scavuzzo (above) are applied to a pipe where the load is varied from a four-point loading through its extremes. Loads were varied from a cantilever to an end moment by changing the dimensions of four-point loading. Also, the shape of a bilinear stress-strain curve was varied from a perfectly plastic material to various degrees of work hardening by increasing the tangent modulus in the plastic regime. The results of the study indicate that Markl’s method is conservative by predicting too short a fatigue life for four-point loading for a given stress. As indicated by this study, the differences can be very large in the low-cycle regime for a perfectly plastic material and for a four-point loading approaching an end moment. Thus, piping could be over designed with unnecessary conservatism using the current ASME Code method based on stress intensification factors.