Stress linearization is fundamentally based on the assumption that the stress is linearly distributed along the path and any stress deviated from the linear path is caused by stress concentration.
With this fact, if the stress is highly nonlinearly distributed along the stress path, it is recommended not to use stress linearization method, as linearized stress is not conservative enough. An elasticplastic method is more appropriate. ASME BPVC Sec VIII Div 2 states that if the ratio of the thickness of the wall t to the insider radius R is larger than 0.25, then stress linearization method should not be used.