*3.1. "121" Model*

The *J*-resistance curves of different "121" models under different material constraints are shown in Figure 5. It can be found that increasing of the width of 52Mb from 0 to 8 mm, the *J*-resistance curves of the "121" models increase. When the width of 52Mb is up to 8 mm, the *J*-resistance curves remain steady and will not change with the increasing of the 52Mb's width.

**Figure 5.** The *J*-resistance curves of different "121" models.

Because material A508 has lower strength than material 52Mb, the "121" model is an over-matched joint. In this model, when the *W*52Mb = 0 mm, it is the same with the homogeneous material A508; when the *W*52Mb = 80 mm, it is the same with the homogeneous material 52Mb. Thus, the results in Figure 5 show that for an over-matched joint, the *J*-resistance curve of the joint is higher than the base material. In addition, a notable phenomenon is that when the width of 52Mb is up to 8 mm, the *J*-resistance curves of the "121" models are same with the *J*-resistance curve of homogeneous material 52Mb. It means that the crack is out of the effect range of the material constraint induced by the A508/52Mb interface. In this condition, it does not matter even if the material on the outside is soft or hard. That is, when the crack locates out of the effect range of material constraint, the fracture resistance curve of the weld joint no longer influenced by the material constraint anymore. Of course, the effect range is also related to different materials and models.

Figure 6 shows the distributions of equivalent plastic strain *ε<sup>p</sup>* = 0.1 isoline at crack tip at the same *J*-integral (*J* = 1600 kJ/m2) for different "121" models. It can be found that though the distributions of equivalent plastic strain are different for different models, but the equivalent plastic strains surrounded by *ε<sup>p</sup>* = 0.1 isoline are within the scope of 8 mm for all the models. When the interface is located within this scope, the *J*-resistance curve will be affected by the material constraint; when the interface is located outside this scope, the *J*-resistance curve will not be affected by material constraint. This scope is the effect range of the material constraint.

**Figure 6.** *Cont*.

**Figure 6.** The distributions of *ε<sup>p</sup>* = 0.1 isoline at crack tip at *J* = 1600 kJ/m2.

In addition, the areas surround by the *ε<sup>p</sup>* = 0.1 isoline reflect the same change rule with the *J*-resistance curves, as shown in Figure 7. Because the constraint is the resistance of a structure against plastic deformation, at the same *J*-integral (driving force) a lower plastic deformation reflects a higher constraint and a lower *J*-resistance curve, and vice versa. The same change rules between *J*-resistance curves and areas can prove each other and also reflect the change rules are related to the constraint.

Furthermore, Figure 7 also shows that the *J*-resistance curve of material is controlled by the strain fields at crack tip rather than stress fields. It should be noted that the *ε<sup>p</sup>* = 0.1 isoline was selected here, when a small *ε<sup>p</sup>* value was selected, the scope will beyond the 8 mm. Therefore, there may exist a main control value or control zone. For this study, the main control value is *ε<sup>p</sup>* = 0.1.

**Figure 7.** The areas surround by the *εp* = 0.1 isoline at the same *J*-integral for "121" model.
