Defect assessment of a weld zone is important in fitness-for-service evaluation of plant components. Typically a J and $C^*$ estimation method for a defective homogeneous component is extended to a mismatched component, by incorporating the effect due to the strength mismatch between the weld metal and the base material. The key element is a mismatch limit load. For instance, the R6/R5 procedure employs an equivalent material concept, defined by a mismatch limit load. A premise is that if a proper mismatch limit load solution is available, the same concept can be used for any defect location (either a weld centre defect or a heat affected zone (HAZ) defect) and for any material combination (either two-material or multi-material combinations; either similar or dissimilar joints). However, validation is still limited, and thus a more systematic investigation is needed to generalise the suggestion to any geometry, any defect location and any material combination. This paper describes the effect of structural geometry on the $C^*$ integral for defective similar welds, based on systematic elastic-creep 2-D and 3-D finite element (FE) analyses, to attempt to elucidate the questions given above. It is found that the existing 'equivalent material' concept is valid only for limited cases, although it provides conservative estimates of $C^*$ for most of cases. A modification to the existing equivalent material concept is suggested to improve accuracy.