Abstract The critical Crack Tip Opening Angle (CTOAC) has been proved to be a promising parameter to characterize the crack arrest toughness of natural gas pipeline. However, the accuracy and consistency of its experimental measuring results are seriously affected by the uncertainties in locating the crack tips and the points on both crack surfaces at a certain distance behind the crack tips. Load-displacement curve is a comprehensive reflection of geometry, mechanical property and fracture behaviour of a loaded specimen. It would be highly advantageous to deduce CTOAC from load-displacement curve directly. This is exactly what this paper has done. Firstly, in order to combine the load, displacement and deformation of single edge notched bend (SENB) specimen together organically, the Martinelli-Venzi ductile fracture model is used to analyze its dynamic fracture process together with energy equilibrium theory and a correlation between CTOA and the slope of the energy-load curve is established. Secondly, based on the fact that load decreases almost linearly with the increment of displacement during steady-state crack growth, attempts have been made to regress the load-displacement curve linearly and express the slope of the energy-load curve by the linear regression equation. Thirdly, the correlation between the load-displacement curve and instantaneous CTOA is found by the bridge of energy load gradient. Finally, CTOAC can be determined by averaging the stable state CTOA values. The experiments and corresponding finite element simulations of SENB specimens with X80 pipeline steel are conducted. CTOAC results obtained by both methods are in good agreements with the theoretical ones, indicating that the method proposed in this paper is satisfactory. The CTOAC derived from the published Drop Weight Tear Test (DWTT) load-displacement curves is also consistent with the experimental results, which further proves its wide applicability in different steel grades and loading rates. The method presented in this paper can significantly improve the analysis efficiency and has great potentialities for industry application.

中文翻译：

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一种直接通过载荷位移曲线确定临界 CTOA 的新方法

摘要 临界裂纹尖端张角（CTOAC）已被证明是表征天然气管道止裂韧性的一个很有前景的参数。然而，其实验测量结果的准确性和一致性受到裂纹尖端和裂纹尖端后面一定距离处两个裂纹表面点定位的不确定性的严重影响。载荷-位移曲线是加载试样几何形状、力学性能和断裂行为的综合反映。直接从载荷-位移曲线推导出 CTOAC 将是非常有利的。这正是本文所做的。首先，为了将单边缺口弯曲（SENB）试样的载荷、位移和变形有机地结合在一起，采用Martinelli-Venzi韧性断裂模型结合能量平衡理论分析其动态断裂过程，建立CTOA与能量-载荷曲线斜率的相关性。其次，基于稳态裂纹扩展过程中载荷随位移的增加几乎呈线性下降的事实，尝试将载荷-位移曲线线性回归，并用线性回归方程表示能量-载荷曲线的斜率. 第三，通过能量负载梯度桥找到负载-位移曲线与瞬时CTOA之间的相关性。最后，可以通过对稳定状态 CTOA 值求平均值来确定 CTOAC。用X80管线钢对SENB试样进行了实验和相应的有限元模拟。两种方法得到的CTOAC结果与理论值吻合较好，表明本文提出的方法是令人满意的。由公布的落锤撕裂试验（DWTT）载荷-位移曲线得出的 CTOAC 也与实验结果一致，进一步证明了其在不同钢种和载荷速率下的广泛适用性。本文提出的方法可以显着提高分析效率，具有很大的工业应用潜力。这进一步证明了其在不同钢种和装载率下的广泛适用性。本文提出的方法可以显着提高分析效率，具有很大的工业应用潜力。这进一步证明了其在不同钢种和装载率下的广泛适用性。本文提出的方法可以显着提高分析效率，具有很大的工业应用潜力。