## 1 Introduction  
The original idea of application of conventional fracture mechanics was that a single parameter, such as crack tip opening displacement (CTOD) and \(J\)-integral, could well characterize the crack-tip stress filed. Additionally, the unique fracture resistance curve, \(J\)-R or CTOD-R, was enough to reflect the material behavior. The shortages of such idealized one-parameter theory, however, become increasingly clear by studying the diversified crack-tip fields [1; 2; 3]. Thus, two-parameter fracture theory (i.e., elastic \(T\)-stress [4] and \(J\)-Q theory [5; 6]) has been developed to characterize the crack-tip stress field and measure the constraint levels for various geometries and loading configurations in elastic-plastic materials. Crack-like defects always produce during in-service operation or fabrication for pipelines. The single edge notched bending (SENB) specimen is usually treated as an experimental standard. While the researches make it clear that the standard SENB has certain conservatism due to its remarkably higher geometry constraint than actual pipes with circumferential surface cracks. The single edge notched tension (SENT) specimen has been frequently suggested for its more similar geometry constraint as the cracks in pipes in front of the crack tip [7; 8; 9; 10]. Weldments commonly exist in engineering structures and they tend to be the most critical part of welded structures for the instability of fracture. Weld strength mismatch plays a crucial role in structural integrity assessment. For this known reason, researches focused on characterizing the local stress fields of weldment and heat affected zone (HAZ) [11; 12; 13] were carried out in recent decades. For such a mismatched weldment, there are two types of constraints consisting of geometric constraint induced by specimen dimensions, loading modes and crack size, and the material constraint induced by inhomogeneous material properties [14; 15]. [PERSON] et al. [14] proposed the mismatch constraint parameter \(M\) to describe the influence of material mismatch on the crack tip stress field. Furthermore, a so-called _J-Q-M_ theory (see e.g., [PERSON] et al. [14; 16; 17]), where both constraint effects were considered to characterize the local stress field near the crack tip was developed by SINTEF/NTNU. Recently, [PERSON] reviewed the fracture results of inhomogeneous microstructure for materials testing and failure assessment [18]. The [PERSON] group examined the effect of weld strength mismatch and crack sizes (a/W ratios) on J and CTOD ductile fracture parameters while using SENT specimens based on plastic \(\eta\)-factors and load separation analysis [19; 20]. On the other hand, the similar investigation about strength mismatch effect on fracture mechanical behavior for SA 508-Alloy 52 narrow gap dissimilar metal weld was conducted by microstructural and fracture resistance characterizations [21]. The results showed that the mismatch state caused the crack to propagate towards the fusion boundary. When the crack initiated from HAZ, the crack propagation occurred towards the weld zone for the undermatched condition [22]. Recently, [PERSON] et al. studied ductile crack growth behaviors at different locations of a weld joint for an X80 pipeline steel by experimental and numerical methods, it demonstrated that the Gurson-Tvergaard-Needleman (GTN) model can differentiate the constraint conditions and predict the J-R curves at different joint locations for SENB and SENT specimens accurately [23]. There are no reported studies so far on the ductile fracture resistance behavior for strength-mismatched welding pipe under large scale yielding conditions to the best of our knowledge. Thus, present work mainly investigates the effects of specimen geometry and weld strength mismatch on the ductile fracture resistance of welding pipe. Additionally, the constraint state ahead of a propagating crack is taken into account.