# Variation of Fracture Toughness with Biaxial Load and T-Stress under Mode I Condition
## 5 Conclusions  
By applying a biaxial load on the cross-shaped specimen, the experiment of changing T-stress in the specimen with the same geometry is realized in the current paper. The test results show that the value of the stress intensity coefficient at the moment of fracture initiation is not a constant, but a variable with the change of T-stress. This proves from one side that even in mode I fracture, the influence of the higher-order term of the stress field at the crack tip on the fracture behavior cannot be ignored; that is, there is a distance \(r_{c}\) from the ideal crack tip, and the stress-strain state at RC controls the crack growth or not. Furthermore, through the calculation and analysis of crack-bending characteristic parameters, the parameter controlling crack growth should be the stress at the critical distance, which is more consistent with the phenomenon of crack curving.  
In another similar study by [PERSON] and [PERSON] [20], the critical distance is 2.3 mm (from the stress-controlled fracture) or 0.86 mm (from the strain-controlled fracture). The critical distance from the stress-controlled fracture is consistent with the current paper, but the critical distance from the strain-controlled fracture is very different. This makes us believe that it is a universal conclusion to use the stress at the critical distance as the assumption to judge whether the crack is in the critical state. It must be admitted that using the stress at the critical distance as the parameter of crack propagation can explain the phenomenon of crack curving and fracture toughness changing with T-stress to a certain extent, but it cannot predict the crack initiation angle well. One possible explanation for this is that the critical distance is not a constant, but a variable that varies with the angle at which the maximum circumferential stress is located. In other words, when \(\theta_{c}=0\), \(r_{c}\) is a constant, and when a is not equal to zero, \(r_{c}\) will change with the change of \(\theta_{c}\).  
\begin{table}
\begin{tabular}{c c c c c c} \hline  & \multicolumn{2}{c}{\(T_{c}/K_{c}\)} & \multicolumn{2}{c}{\(T_{c}/K_{c}\sqrt{r_{c}}/8K_{c}\)} & \multicolumn{2}{c}{**Curve Or Not**} \\  & **Left** & **Right** & **Left** & **Right** & **Curve Or Not** \\ \hline
**1** & \(-0.1078\) & \(-0.1053\) & \(-0.0950\) & \(-0.0917\) & NO \\
**2** & \(-0.0824\) & \(-0.0780\) & \(-0.0717\) & \(-0.0664\) & NO \\
**3** & \(-0.0714\) & \(-0.0688\) & \(-0.0588\) & \(-0.0558\) & NO \\
**4** & \(-0.0408\) & \(-0.0400\) & \(-0.0293\) & \(-0.0280\) & NO \\
**5** & \(-0.0061\) & \(-0.0060\) & \(0.0021\) & \(0.0022\) & NO \\
**6** & \(0.0143\) & \(0.0147\) & \(0.0234\) & \(0.0239\) & NO \\
**7** & \(0.0690\) & \(0.0690\) & \(0.0789\) & \(0.0793\) & YES \\
**8** & \(0.0929\) & \(0.0930\) & \(0.1086\) & \(0.1093\) & YES \\
**9** & \(-0.0153\) & \(-0.0140\) & \(-0.0054\) & \(-0.0040\) & NO \\
**10** & \(0.0297\) & \(0.0300\) & \(0.0398\) & \(0.0404\) & NO \\ \hline \end{tabular}
\end{table}
Table 2: Characteristic Parameters of Crack Curving.  
**Author Contributions:** Conceptualization, C.C., Z.Z. and S.Z.; Data curation, C.C. and S.Z.; Formal analysis, C.C.; Funding acquisition, C.C., Z.L., C.X., Z.Z. and S.Z.; Investigation, C.C. and Z.Z.; Methodology, C.C.; Project administration, C.C., Z.L., C.X. and Z.Z.; Resources, C.C., Z.Z. and S.Z.; Software, C.C. and C.X.; Supervision, C.C., Z.L. and Z.Z.; Validation, C.C. and Z.Z.; Visualization, C.C., Z.L. and Z.Z.; Writing--original draft, C.C., C.X. and Z.Z.; Writing--review & editing, C.C. and Z.Z. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research received no external funding.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** Data is contained within the article.  
**Conflicts of Interest:** The authors declare no conflict of interest.