The current paper presents the application of three-dimensional (3D) constraint-based fracture mechanics for the determination of R-curves (J-R curves and CTOD-R curves) of thermal aged 16MND5 bainitic forging steel. First, the fracture toughness test results of 16MND5 steel using different sized clamped single edge notched tension (SENT) specimens under various thermal aging durations were summarized. Then, 3D finite element method (FEM) was applied to determine constraint parameters for the tested clamped SENT specimens. From the analysis results, it is shown that the T₁₁ and the independent portion of T₃₃ normalized by the nominal stress, named F₁₁ and V₃₃, can accurately quantify the in-plane and out-of-plane constraint levels, respectively. In addition, for all thermal aging condition, the thickness strain and V₃₃ have a good linear relationship, which proves the applicability of V₃₃ to quantify out-of-plane constraint effect from the experimental point of view. Next, the in-plane and out-of-plane constraint dependent R-curves were developed. Results showed that the developed R-curves can reproduce the experimental J-R curves and CTOD-R curves of thermal aged RPV steel obtained by clamped SENT specimens with generally good agreements. The combined effects of in-plane constraint, out-of-plane constraint and thermal aging on the fracture toughness were revealed and quantified. Finally, the R-curves of 16MND5 steel with various in-plane and out-of-plane constraint levels, and thermal aging durations were predicted, and compared to available test data.

当前纸张呈现三维（3D）基于约束的骨折为测定力学的应用- [R -curves（JR热老化16MND5贝氏体锻造用钢的曲线和CTOD-R曲线）。首先，总结了16MND5钢在不同热老化持续时间下使用不同尺寸夹紧单刃缺口拉伸（SENT）试样的断裂韧性测试结果。然后，应用 3D 有限元方法 (FEM) 来确定测试的夹紧 SENT 试样的约束参数。分析结果表明，T ₁₁和T ₃₃的独立部分被名义应力归一化，命名为F ₁₁和V₃₃，可以分别准确地量化平面内和平面外的约束水平。此外，对于所有热时效条件，厚度应变与V ₃₃具有良好的线性关系，这从实验的角度证明了V ₃₃用于量化面外约束效应的适用性。接下来，开发了平面内和平面外约束相关的R曲线。结果表明，开发的R曲线可以重现实验JR通过夹紧 SENT 试样获得的热时效 RPV 钢的曲线和 CTOD-R 曲线具有普遍良好的一致性。揭示并量化了面内约束、面外约束和热老化对断裂韧性的综合影响。最后，预测了具有各种平面内和平面外约束水平以及热老化持续时间的 16MND5 钢的R曲线，并与可用的测试数据进行了比较。