基于完全剪切耦合 Gurson 模型的损伤断裂评估曲线研究

Study on the Damage Fracture Assessment Curve Based on a Fully Shear-Coupled Gurson Model

摘要

全尺寸管道结构在断裂评估中的保守性问题日益突出,目前以 Hutchinson-Rice-Rosengren 解为基础的工程临界评估程序,无法准确预测韧性撕裂条件下的断裂评估结果,主要原因在于缺少统一的耦合损伤模型和考虑损伤因素的失效评估方法．根据现有研究中的不足,在 Gurson-Tvergaard-Needleman(GTN)模型基础上,提出了完全剪切耦合 Gurson(SCG)模型,以捕捉完整的损伤断裂演化过程．对比小尺寸单边缺口拉伸 SE(T)试样数值模拟仿真断裂截面与拉伸试验断口结果,验证采用完全剪切耦合损伤系数$C_{Z}^{-1} \omega(\sigma)$可准确预测断口高、低应力三轴度状态下韧性断裂机制．利用 SE(T)试样与全尺寸管道裂纹尖端拘束状态的相似性,通过小尺寸SE(T)试验标定SCG 模型,并重新定义断裂评估曲线方程为$f\left(L_{\mathrm{r}}\right)=\sqrt{\delta_{\mathrm{e}} / \delta_{\text {damage }}}$．在外载荷作用下,根据 Irwin-Orowan 能量守恒定律推断,因裂纹尖端存在不同程度的撕裂情况,经典弹塑性断裂评估程序未考虑形成新裂纹面引起的驱动力减小,从而导致其评估曲线保守．通过469 组已发表的全尺寸管道断裂试验结果对损伤断裂评估程序进行验证．结果表明:SCG 模型可以准确预测高应力三轴度状态(η＞0.4)主导的多孔隙率断裂和低应力三轴度状态(0≤η≤0.4)下发生的低孔隙化断裂,基于 SCG 模型获得损伤断裂评估曲线,预测 469 组全尺寸管道断裂试验,其可靠度为 98.8%,为管道结构安全冗余设计提供可量化的全新评估方法,同时加深了对环焊缝断裂行为的认知．

Abstract

Conservatism in the fracture assessment of full-scale pipeline structures has become an increasingly prominent issue. Current engineering critical assessment procedures,which are primarily based on the Hutchinson-Rice-Rosengren solution,fail to accurately predict the fracture outcomes under ductile tearing conditions. This limitation stems from the lack of a unified coupled damage model and a fracture assessment approach that incorporates the damage effects. To address these limitations,a fully shear-coupled Gurson(SCG)model is proposed,based on the classical phenomenological Gurson-Tvergaard-Needleman model,to capture the complete evolution of ductile fracture. A comparative analysis between numerically simulated fracture sections of small-sized single edge-notched tension(SE(T))specimens and the corresponding experimental fracture surfaces validates that the SCG model,with an appropriately defined shear-coupling damage coefficient $C_{Z}^{-1} \omega(\sigma)$ ,can accurately predict the ductile fracture mechanisms under high- and low-stress triaxiality conditions. Given the similarity in crack-tip constraint conditions between SE(T)specimens and full-scale pipes,the SCG model is calibrated using small-sized SE(T)tests and a revised fracture assessment curve(FAC)is subsequently formulated as $f\left(L_{\mathrm{r}}\right)=\sqrt{\delta_{\mathrm{e}} / \delta_{\text {damage }}}$. According to the Irwin-Orowan energy conservation principle,crack-tip tearing contributes to a reduction in the driving force owing to the formation of new crack surfaces. However,this effect is not accounted for in the traditional elastic-plastic fracture assessment procedure,leading to conservative predictions. The proposed damage fracture assessment method is validated against 469 published full-scale pipeline fracture tests. The results demonstrate that the SCG model accurately captures the high-cavitation fracture dominated by high triaxiality(η＞0.4) as well as the low-cavitation fracture under low triaxiality(0≤η≤0.4). The damage FAC derived from the SCG model achieves a prediction reliability of 98.8% across the 469 full-scale pipeline tests,offering a novel and quantifiable methodology for structural integrity design with safety redundancy. Moreover,it deepens the understanding of fracture behavior in circumferential-welded joints.

关键词

细观损伤力学 / 剪切修正 / 断裂评估曲线 / 管道环焊缝 / 耦合损伤模型

Key words

microscopic damage mechanics / shear modification / fracture assessment curve(FAC) / pipeline girth weld / damage coupled model

参考文献

[1] Hadley I, Horn A. Treatment of constraint in BS 7910:2013,ISO 27306 and DNVGL—RP—F108[J]. International Journal of Pressure Vessels and Piping, 2019, 169:77-93.

[2] Kouzoumis K, Hadley I, Mostafavi M. Validation of BS 7910；assessing the integrity of pipes containing axial flaws[J]. Procedia Structural Integrity, 2018, 13:868-876.

[3] 龚宝明, 万潇彬, 戴联双, 等. X80 管道环焊缝拉伸应变容量预测模型对比研究[J]. 天津大学学报(自然科学与工程技术版), 2024, 57(1):73-78.

[4] Gong Baoming, Wan Xiaobin, Dai Lianshuang, et al. Prediction of tensile strain capacity for X80 pipeline girth weld by different models[J]. Journal of Tianjin University(Science and Technology), 2024, 57(1):73-78(in Chinese).

[5] Kouzoumis K, Hadley I, Mostafavi M. Validation of BS 7910 fracture assessment procedures；wide plates and cylinders[J]. International Journal of Pressure Vessels and Piping, 2021, 190:104309.

[6] Lotsberg I, Sigurdsson G, Fjeldstad A. Probabilistic methods for planning of inspection for fatigue cracks in offshore structures[J]. Marine Structures, 2016, 46:167-192.

[7] Maljaars J, Steenbergen H, Vrouwevelder A. Probabilistic model for fatigue crack growth and fracture of welded joints in civil engineering structures[J]. International Journal of Fatigue, 2012, 38:108-117.

[8] Anderson T L. Fracture Mechanics:Fundamentals and Applications[M]. 4th ed. Boca Raton,USA:CRC Press, 2017.

[9] Gatea S, Ou H A, Lu B, et al. Modelling of ductile fracture in single point incremental forming using a modified GTN model[J]. Engineering Fracture Mechanics, 2017, 186:59-79.

[10] Tuhami A E O, Feld—Payet S, Quilici S, et al. A two characteristic length nonlocal GTN model:Application to cup—cone and slant fracture[J]. Mechanics of Materials, 2022, 171:104350.

[11] Kuroda M, Tvergaard V, Needleman A. Constraint and size effects in confined layer plasticity[J]. Journal of the Mechanics and Physics of Solids, 2021, 149:104328.

[12] Dunand M, Mohr D. On the predictive capabilities of the shear modified Gurson and the modified Mohr—Coulomb fracture models over a wide range of stress triaxialities and Lode angles[J]. Journal of the Mechanics and Physics of Solids, 2011, 59(7):1374-1394.

[13] Wierzbicki T, Bao Y, Lee Y W, et al. Calibration and evaluation of seven fracture models[J]. International Journal of Mechanical Sciences, 2005, 47(4/5):719-743.

[14] Lin M, Li Y, Roger Cheng J J, et al. Novel XFEM variable strain damage model for predicting fracture in small—scale SENT and full—scale pipe tests[J]. Engineering Fracture Mechanics, 2022, 271:108628.

[15] Pisarski H. Assessment of flaws in pipeline girth welds—A critical review[J]. Welding in the World, 2013, 57(6):933-945.

基金资助

国家自然科学基金资助项目(52075366)