Authors: Toshiyuki Meshii
Source: Fatigue & Fracture of Engineering Materials & Structures (article, 2021-11-04)
Field: Materials Science — Materials Chemistry

Data‐driven approach to construct a fracture toughness master curve for ferritic steels based on tensile properties The characterization of the fracture toughness (KJc) of ferritic steels in the ductile-to-brittle transition (DBT) region, which is vital for analyzing the structural integrity of cracked structures subjected to large temperature changes, has been pursued by researchers and practitioners. This is because KJc is associated with a large temperature dependence (a change of approximately 400% corresponding to a temperature change of 100°C), specimen thickness dependence (approximately KJc ∝ 1/(specimen thickness)1/4), and large scatter (approximately ±100% variation around the median value). Therefore, a large amount of KJc data is required for structural integrity assessment. Constructing a KJc master curve (MC) that can predict KJc for arbitrary ferritic steel, temperature, and specimen size is expected to benefit the engineering community, as KJc testing is time- and material-consuming because of the above-mentioned issues. While the ASTM E19211 MC provides one solution, a failure in predicting KJc for some ferritic steels has been reported.2, 3 Hence, considering a data-driven approach and reexamining the physical background of KJc temperature dependence may enable the construction of a KJc MC that is applicable to all ferritic steels. The constructed KJc MC considers tensile properties as explanatory parameters and avoids time- and material-consuming KJc tests, thus holding higher merit than that of the ASTM E1921 MC. This led to a hypothesis that KJc should have a uniform relationship with (σYSRT–σYS), and it was selected as the main explanatory parameter. On the basis of this selection, realization of the KJc MC based on tensile properties was expected because Equation 1 is an MC. In addition, considering that (σB/σYS) for the reactor pressure vessel (RPV) and non-RPV steel is approximately 1.2 and 1.7, respectively,2 σB at RT was added as an explanatory parameter to represent (σB/σYS) at RT; it was assumed that (σB/σYS) exhibits a small temperature dependence in the considered temperature range. Finally, specimen width W (mm) was selected as an explanatory parameter to represent the specimen size effect, and the KJc data used for regression were limited to those with a thickness-to-width ratio B/W of 0.5. This section presents a KJc MC construction that requires only tensile test data at the temperature of interest and RT under the aforementioned physical assumptions: (i) KJc temperature dependence has a direct correlation with that of SED; (ii) KJc temperature dependence is fundamentally described by that of σYS, with some modification by σB; and (iii) σB/σYS changes minimally with temperature from its value at RT. First, by applying a Box–Cox transformation7 to the 531 KJc data collected in literature8 (i.e., cases of B/W = 0.5 in the downloadable data), function g was derived as a logarithmic. Then, GLM regression using the Bayesian approach was conducted by assuming prior distribution for all the coefficients in Equation 2 as a uniform distribution (corresponding to a noninformative prior distribution) and a Gamma distribution with a shape parameter of 0.01 and scaling parameter of 0.01 for the Weibull distribution-specific parameter α (shape factor). For the Markov chain Monte Carlo samples, eight chains of 20,000 iterations each were considered, with 10,000 warmup iterations. The simulation was confirmed to converge by checking whether was less than 1.17 for all the unknowns. The 50% confidence value of α was 4.04, which is close to the fixed value of 4 in the ASTM E1921 MC. In this study, a KJc MC based on tensile properties was developed by applying the Bayesian approach to 531 KJc data, and the KJc MC prediction at 5%, 50%, and 95% was obtained as KJc (x%) = cx% KJcnRT × exp[0.00458(σYSRT − σYS)]. A Weibull distribution was assumed for the case. The developed MC can predict KJc for an arbitrary ferritic steel by specifying σYS at the temperature at which KJc is to be predicted, as well as the RT tensile properties σYSRT and σBRT. If the temperature dependence of σYS can be clearly described by the Z–A σYS MC, only σYSRT and σBRT are required for KJc prediction. Therefore, the developed KJc MC does not require time- and material-consuming fracture toughness tests. The data-driven approach applied in this study is categorized as “data regression” to predict the objective variable KJc from the explanatory variables related to the tensile properties and test specimen size. Another prospective category of the data-driven approach in KJc research is “determining hidden law” in fracture. For example, the mechanics-oriented approach derived a useful and simple relationship of KJc ∝ 1/(specimen thickness)1/4, but it failed to explain the existence of the lower bound KJc along with its size. Thus, the mechanics-oriented approach has limitations. Meanwhile, predicting KJc using the constructed MC and conducting elastic–plastic finite element analysis (EP-FEA) enable the construction of a 3D failure criterion for cracked specimens, which can predict the KJc temperature and size dependence. Although this data-driven 3D failure criterion is a “black box,” integrating it with an EP-FEA post-processor is expected to enable the fracture prediction of the complicated structures with cracks. Our future research aims to investigate the mechanics of the above-mentioned “black box” failure criterion. The data that support the findings of this study are openly available in Appendix E (https://doi.org/10.1016/j.engfailanal.2020.104713). Materials science ; Fracture toughness ; Ultimate tensile strength ; Brittleness ; Toughness ; Fracture (geology) ; Tensile testing ; Composite material ; Metallurgy ; Structural engineering ; Engineering Nuclear Materials and Properties ; Fatigue and fracture mechanics ; High-Velocity Impact and Material Behavior