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A new statistical local criterion for cleavage fracture in steel. Part II - Application to an offshore structural steel

S. R. Bordet a , A. D. Karstensen a , D. M. Knowles b , C. S. Wiesner a ,*

a TWI, Granta Park, Great Abington, Cambridge, CB1 6AL, U.K.
b Gracefield Research Centre, Gracefield Road, PO Box 31-310, Lower Hutt 6009, New Zealand

Paper published in Engineering Fracture Mechanics vol.72. issue 3. February 2005. pp.453 - 474

View part 1

Abstract

In the first part of this paper, a new model for cleavage fracture in steel was presented, based on a new statistical local criterion, which expresses the necessity of simultaneously fulfilling the conditions for both cleavage microcrack nucleation and propagation. In this second part, the assumptions and predictive capabilities of the new model are assessed using a modern offshore structural steel plate (Grade 450EMZ). It is shown that the model assumptions are consistent with the cleavage fracture behaviour of the steel and that the new model has the potential of correctly quantifying the effects of size, constraint, temperature and strain rate on cleavage fracture risk.

Introduction

In the first part of this paper [1], a new statistical local criterion for cleavage fracture in steel was presented, which allowed writing the cleavage fracture probability in steel as a Weibull distribution:

√m, had only minor effects on the overall predictions 7 . Obviously, K min is quite influential at very low fracture probabilities, since it sets the zero probability of macroscopic cleavage. Thus, to avoid being overly conservative, K min should be included in the analysis if the model is used for fracture assessment purposes.

 

6 This over-conservatism is somewhat illustrated in Fig.26, (as well as in Fig.29 presented in the next section), by the fact that the model tends to over-predict the experimental median rank probabilities at low probability, whatever the evolution of P f might be at higher fracture probabilities.

7 It did however improve statistical inference at low probability (cf. previous footnote).

High strain rate toughness predictions

Fig.27 shows a comparison between toughness results of the 50x50 mm 2 SENB specimens at load line velocity (LLV) of 10 mm/s and the predictions based on the set of material parameters determined from the quasi-static NT tests at -196°C. As for the quasi-static case, the only varying parameter is the yield strength, whose evolution with temperature and strain rate is given by Eq. (7). Fig.28 presents the same comparisons for LLV = 120 mm/s. For both strain rates, the predictions are in good general agreement. However, it is noticed that the results are increasingly underpredicted as the temperature is raised, although the targeted toughness values (filled symbols in Figs.27 and 28) are within the range where Group 1 cleavage type is expected to be the dominant initiation mechanism (cf. Fig.25). Comparison of the predictions at -100°C between Figs.27 and 28 shows that while this underprediction is pronounced for LLV = 10 mm/s, this is not the case for LLV = 120 mm/s. This is apparent on Fig.29, where, as for the quasi-static case, P f is compared with median rank probabilities for the dynamic δ c -results, belonging to Group 1 initiation mechanism (filled symbols in Figs.27 and 28). The model predicts the shape of the experimental toughness distribution well for both LLVs. However, whereas the model suitably predicts the position of the experimental toughness distribution with respect to CTOD for LLV = 120 mm/s, the predicted P f curve is noticeably shifted to the left 8 relative to the median rank probabilities for LLV = 10 mm/s.

8 Note that underpredictions of the model in toughness vs. temperature diagrams ( Figs.25, 27 and 28) appear as overpredictions in P f vs. CTOD diagrams ( Figs.26 and 29).



spcswfeb05pt2f27.gif
Fig.27. Cleavage toughness predictions for LLV = 10 mm/s using Eqs. (1) and (3)

spcswfeb05pt2f28.gif
Fig.28. Cleavage toughness predictions for LLV = 120 mm/s using Eqs. (1) and (3)

Fig.29. Comparison between predicted failure probabilities (solid lines) and median rank probabilities for the dynamic δ c -results (symbols) at -100°C with load line velocities (LLVs) of (a) 10 mm/s and (b) 120 mm/s. The dashed lines represent the 90% confidence limits for the estimates of the experimental rankprobabilities
spcswfeb05pt2f29.gif

These discrepancies reflect the effects of temperature on work of fracture, stress relaxation, carbide debonding etc. [1], which become stronger as temperature is increased and which are not presently modelled. The fact that the model underpredicts dynamic CTOD ranges, which were suitably predicted in the quasi-static loading case, reveals that a higher strain rate cannot fully compensate for an increase in temperature. For example, a temperature shift Δ T, causing the same change in yield strength as an imposed strain rate shift Δ ε p , will have a stronger effect on carbide stress relaxation due to diffusional processes than Δ ε p . Also, once a carbide crack or a ferrite microcrack is running, the strain rates generated at their tips are far superior to the strain rates imposed by the dynamic loading conditions, so that the temperature is likely to have stronger effects than Δ ε p for equivalent change in yield strength. The work of fracture behind the moving cleavage crack, involving the elongation and rupture of ductile ligaments, will also vary more as a function of Δ T than Δ ε p . The temperature shift observed between two toughness curves of the same steel at different strain rates is therefore smaller than what would be obtained if all temperature dependent parameters, with the exception of the yield strength, were kept constant. The model, only considering the effect of temperature on the yield strength, will therefore predict a transition temperature higher than the actual one. As a result, the model will predict a lower shelf toughness region extending to temperatures for which the actual toughness already belongs to the fast increasing ductile-brittle transition region, which explains why the model increasingly underpredicts cleavage toughness as the temperature is raised in Figs.27 and 28. This also explains why the model underpredicts experimental toughness data at -100°C for LLV = 10 mm/s ( Fig.27), but not for LLV = 120 mm/s ( Fig.28), if one considers that the model overestimation of the probability of cleavage fracture at small probabilities in Fig.29(b) is principally due to assuming δ min = 0. This arises from the fact that the higher the loading rate, the higher the ductile-brittle transition (DBT) temperature. For LLV = 120 mm/s, the experimental cleavage toughness values at -100°C still belong to the lower shelf, whereas those for LLV = 10 mm/s belong to the lower part of the DBT region, hence a greater gap with the model predictions in the second case.

Concluding remarks

Microscopic work has shown that the model assumptions are consistent with the cleavage fracture behaviour of a modern offshore structural steel plate (Grade 450EMZ). The model parameters were calibrated from notched tensile (NT) fracture specimens, tested at -196°C, and then used to predict the lower shelf toughness transition curve of the steel. Good predictions were obtained, validating the ability of the model to predict effects of size, constraint and temperature on cleavage toughness, and confirming that the critical stress criterion is a valid assumption for characterising cleavage fracture, given that the nucleation stage is accounted for in the local criterion. The new model also showed potential to correctly predict the effect of dynamic loading on toughness, although it appeared too conservative, due to temperature effects on material parameters not presently modelled.

Calibration of the shape parameter m must be done in a stress-varying geometry if a single testing geometry is used, i.e. a geometry where the stress field is not self-similar (as is the case in deeply cracked SENB and CT geometries). The NT geometry is recommended because it allows an accurate and conservative estimation of the lower critical stress, σ th , and because testing, modelling, and parameter calibration are made easier compared with other geometries, such as Charpy-type notch bend tests for example. In addition, there already exists an ESIS guidance document [14] for the calculation of the Local Approach parameters which employs this geometry, and which could easily be adapted to the new model. The fact that the stress field in the NT geometry is relatively homogeneous is also favourable in terms of statistical inference, especially if the number of tests is low. However, because σ th will usually be quite close to the lowest critical stress value recorded in the weakest NT test, the m-estimate will be strongly dependent on the value of σ th . It is therefore advisable, if not necessary, to use a second geometry tested at the same temperature and select the set of ( σ th , m) parameters that produce the same scaling parameter, σ u *, in both geometries. The approach is similar to the GRD (Gao-Ruggieri-Dodds) procedure [15] , with the difference that m is cross-checked through the classical calibration procedure on the NT fracture data.

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