# Effect Range of the Material Constraint in Different Strength Mismatched Laboratory Specimens
## 1 Introduction  
Constraint is the resistance of a specimen or structure against plastic deformation. It contains geometry constraint and material constraint. The geometry constraint is affected by the dimension of specimen, whereas the material constraint is affected by the strength mismatch between different materials. Both of them can affect the fracture behavior of the material significantly.  
The material constraint was first proposed by [PERSON] et al. [1] and [PERSON] et al. [2] to show the changing of slip-line fields with the yield strength of the base material. Then, some parameters were established to characterize the material constraint. [PERSON] et al. [3] established a material constraint parameter \(M\) to investigate the two-material problem where the crack was located in the interface of two dissimilar materials. [PERSON] et al. [4] defined another material constraint parameter \(\beta_{m}\) which suited the overmatched welded joints. [PERSON] et al. [5; 6; 7] proposed a unified constraint parameter \(A_{p}\) which can characterize both material constraint and geometry constraint.  
In addition, the fracture resistance curve, crack propagation path, fracture toughness, crack-tip fields of the strength mismatched structures, especially in welded joint, affected by the material constraint were also investigated widely.  
[PERSON] et al. [8; 9] and [PERSON] et al. [10] investigated the fracture resistance curve of dissimilar metal welded joint (DMWJ) influenced by material constraint. [PERSON] et al. [11; 12; 13] studied the fracture resistance curve of bi-material welded joint influenced by material constraint. [PERSON] et al. [14] and [PERSON] et al. [15] studied the deviation of crack propagation path in DMWJ influenced by material constraint. [PERSON] et al. [16] and [PERSON] et al. [17] focused on their studies on the fracture toughness of DMWJ affected by material constraint. [PERSON] et al. [18] and [PERSON] et al. [19] studied the crack-tip fields of DMWJ influenced by material constraint. [PERSON] et al. [20] and [PERSON] et al. [21] studied the crack-tip fields of welded joint affected by material heterogeneity. [PERSON] et al. [22; 23] studied the structure of stress fields for stationary crack in welded joint influenced by material constraint.  
Nevertheless, most studies above focused their attention on the strength mismatch of both sides of the crack, such as over-match and under-match. There is another interesting issue, the effect range of the material constraint, which also needs to be clarified. This includes whether exists an effect range of material constraint or not, who effects it, and whether the fracture resistance and crack propagation path are affected by the material which is located outside the effect range or not.  
In the previous studies [24; 25], the effect range of the material constraint has been studied and verified in the single-edge-notched bend (SENB) specimen. However, it is not enough to arrive at a conclusion that the effect range of material constraint exists in all the structures with different geometries and loading configurations. Thus, in this study, more laboratory specimens which contain the compact tension (CT), single edge-notched tensile (SENT), and central-cracked tension (CCT) specimens with various specimen geometries, loading configurations, and initial cracks were selected to further study the effect range of the material constraint.