PSI - Issue 42

Vitor S. Barbosa et al. / Procedia Structural Integrity 42 (2022) 1177–1184 V. S. Barbosa and C. Ruggieri / Structural Integrity Procedia 00 (2019) 000–000

1182

6

Table 2. Maximum likelihood estimates of the characteristic toughness, K 0 , for the measured distributions of the K Jc -values at varying test temper atures and the corresponding reference temperatures, T 0 , evaluated from the single temperature and multi-temperature methods.

ˆ K 0

T

K 0

ˆ α 0

T 0

T 0 − MT ( o C)

α

− S T (MPa √ m ) ( o C)

(MPa √ m )

( o C)

50 4

112

6.9

115

47

(94, 134)

(104, 127)

60 4

141

14.9

144

41

44

(119, 167)

(138, 151)

70 4

155

13.7

158

45

(130, 185)

(150, 167)

the MC procedure. To illustrate this issue, Table 2 also provides both Weibull parameters, ˆ α and ˆ K 0 , obtained from a standard ML estimation procedure and the corresponding 90% confidence bounds for K 0 (Mann et al., 1974; Thoman et al., 1969). Clearly, while large di ff erences in parameter α are evidenced in these approaches, the sensitivity of the estimated K 0 -value to the Weibull modulus are fairly small. Therefore, we can conclude that even substantial changes in the Weibull modulus, which are associated with the degree of agreement between the Weibull distribution defined by Eq. (1) and the experimental data, result in only modest variations in parameter K 0 and, thus, have little e ff ect on the T 0 evaluation for the martensitic steel addressed next.

4. Temperature E ff ects on Fracture Toughness

This section address the applicability of the Master Curve approach to describe the e ff ects of temperature on fracture toughness in terms of the reference temperature T 0 for the tested ultra high strength steel. Figures 3(a)- 3(c) describe the dependence of K Jc − med , with temperature for three test temperatures: T = 50 o C, 60 o C and 70 o C. In these plots, the solid lines define the master curve of median toughness, K Jc − med , whereas the dashed lines define the 5% and 95% tolerance bounds derived from ASTM E1921 procedure (American Society for Testing and Materials, 2019). The measured K Jc -values at the these test temperatures are also included in the plot to facilitate assessing the master curve indexed by T 0 and, at the same time, how well the tolerance bounds envelop the measured fracture toughness data. Table 2 presents the corresponding single temperature T 0 -values for each temperature, here denoted as T 0 − S T . Examination of these results reveals that, while there is no clear trend of a relationship between test temperature and the reference temperature, the estimated T 0 exhibits a relatively weak dependence over the range considered. This trend could be explained in terms of the somewhat small data set and the relatively poor fitting of the three parameter Weibull distribution with α = 4 to the experimental toughness values − refer to Fig. 2 and Table 2. A noteworthy additional feature of these results is that the estimated T 0 -values and, thus, the test temperatures for the cases under consideration are much closer to T 0 − 41J for the tested material than T 0 − 28J - recall that the hyperbolic tangent curve fitting gave T 0 − 28J = − 20 . 8 o C and T 0 − 41J = 66 o C. While one would generally anticipate that T 0 − 28J provides good estimates of T 0 in the case of ferritic steels, the present results suggest that T 0 − 41J gives better estimates of the reference temperature for the ultra high strength steel under analysis. While the method based on a single test temperature described previously provides a straightforward procedure to determine T 0 with adequate reliability, application of the multi-temperature method defined by Eq. (7) gives additional insight into the e ff ectiveness of the MC methodology to evaluate the T 0 for the tested martensitic steel. Figure 3(d) shows the Master Curve and associated confidence bounds based on the multi-temperature method using cleavage fracture toughness values measured from standard 1T SE(B) specimens tested at 50 o C, 60 o C and 70 o C. Table 2 provides the corresponding T 0 -value, here denoted as T 0 − MT . This analysis is rather conclusive. The reference temperature evaluated by the multi-temperature method result in a T 0 estimate that is in close agreement with other single temperature estimates. Observe, however, that taking T 0 − MT as the “correct” reference temperature, it can be seen that the estimated T 0 − S T -values at T = 50 o C and 70 o C are slightly larger whereas the estimated T 0 − S T -