Scholarly article on topic 'Evaluating the Conditions When Warm Pre-stressing does not Produce a Benefit in Apparent Toughness'

Evaluating the Conditions When Warm Pre-stressing does not Produce a Benefit in Apparent Toughness Academic research paper on "Materials engineering"

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{"Fracture Toughnes" / "Monte Carlo Simulation" / "Warm Pre-stress" / "Chell model ;"}

Abstract of research paper on Materials engineering, author of scientific article — D.G.A. Van Gelderen, J.D. Booker, D.J. Smith

Abstract Warm pre-stressing (WPS) is the process of subjecting a pre-cracked component to a load cycle at a temperature higher than subsequent operating temperatures. This process is widely acknowledged as being able to enhance the load to fracture, especially in ferritic steels which exhibit lower shelf cleavage fracture. Although accurate estimates of the toughness distributions can be obtained, the accuracy of WPS predictions may be limited by the sample size. It can be argued that the experiments conducted to date are devised to show that the WPS enhancement is always successful, however there are circumstances when a specimen might fail prematurely during the WPS path. Focus is drawn on predicting the number of prematurely failed specimens at different temperatures and pre-load levels.

Academic research paper on topic "Evaluating the Conditions When Warm Pre-stressing does not Produce a Benefit in Apparent Toughness"

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Materials Today: Proceedings 2S (2015) S401 - S407

materialstoday:

PROCEEDINGS

Joint 3rd UK-China Steel Research Forum & 15th CMA-UK Conference on Materials Science

and Engineering

Evaluating the conditions when warm pre-stressing does not produce a benefit in apparent toughness

D.G.A. Van Gelderen*, J.D. Booker, D.J. Smith

Department of Mechanical Engineering, University ofBristol, Queen's Building, BS8 1TR, UK

Abstract

Warm pre-stressing (WPS) is the process of subjecting a pre-cracked component to a load cycle at a temperature higher than subsequent operating temperatures. This process is widely acknowledged as being able to enhance the load to fracture, especially in ferritic steels which exhibit lower shelf cleavage fracture. Although accurate estimates of the toughness distributions can be obtained, the accuracy of WPS predictions may be limited by the sample size. It can be argued that the experiments conducted to date are devised to show that the WPS enhancement is always successful, however there are circumstances when a specimen might fail prematurely during the WPS path. Focus is drawn on predicting the number of prematurely failed specimens at different temperatures and pre-load levels.

© 2015The Authors.PublishedbyElsevier Ltd. Thisisan open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Selection and Peer-review under responsibility of the Chinese Materials Association in the UK (CMA-UK).

Keywords:Fracture Toughnes; Monte Carlo Simulation; Warm Pre-stress; Chell model;

1. Introduction

Warm pre-stressing, (WPS), is a process where a cracked metallic component or structure is subjected to a given pre-load in tension at a temperature, termed 71. This generates localised yielding at existing crack tips. Subsequently, the load required to fracture the warm pre-stressed cracked component at a temperature lower than Tt,

* Corresponding author. Tel.:+44 1173315941. E-mail address: D.VanGelderen@bristol.ac.uk

2214-7853 © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Selection and Peer-review under responsibility of the Chinese Materials Association in the UK (CMA-UK). doi:10.1016/j.matpr.2015.05.055

typically termed T3, is found to be greater than a component without prior load history [1 -7]. This enhancement in apparent toughness has a significant impact on the integrity of nuclear reactor pressure vessels, particularly during severe loading conditions, such as pressurised thermal shock, (PTS), where the vessel is cooled down rapidly with a possible subsequent increase in pressure. The change in apparent toughness depends not only on the load but the temperature paths associated with the prior loading and subsequent operation.

Nomenclature

01, °2, &3 Yield strengths at Pre-loading, Unloading, Fracture temperatures.

Ke Elastic component of the Fracture Toughness.

KIc Fracture Toughness.

mK, K0, Kmin Parameters of Weibull distribution.

Ti, T2, T3 Temperatures at Pre-loading, Unloading, Fracture.

C(T) Compact Tension.

CF Cool - Fracture loading regime - Case 3 of Chell model.

LCF Load - Cool - Fracture loading regime - Case 2 of Chell model.

LUCF Load - Unload - Cool - Fracture loading regime - Case 1 of Chell model.

MCS Monte Carlo Simulation.

PTS Pressurised Thermal Shock.

WPS Warm Pre-stress.

Systematic studies have focussed on simplified loading paths using a relatively small number of laboratory specimens. Typical loading paths are shown in Figure 1. Cool and fracture (CF) is the conventional loading path used to carry out a fracture toughness test. However, typical WPS loading paths are load, complete unload, cool and fracture (LUCF) and load, cool and fracture (LCF). Recent WPS studies have explored different pre-stressing conditions in order to evaluate the limitations associated with this enhancement; investigating the effects of biaxiality [8-10], complex loading paths [11], active plasticity [12] and irradiation [13]. The overall conclusion obtained from these experiments suggests that this enhancement is always successful, which, when concerned with a nuclear RPV's structural integrity, is a very desirable outcome. However, there are cases where specimens can fail during WPS loading paths. As such, this raises the possibility that current WPS tests are performed under conditions which always ensure an observable benefit. Whilst the_underlying theory governing this enhancement is very well established, since several models have been produced to estimate this effect [7, 16-18];the main issue is determining how to treat prematurely failed data and subsequently understand its effect on the resultant WPS failure distribution.

Fracture Kf

Fracture

i-rac ll

Pre-load Ki

No Unload K2 = Ki

Fracture Kf

Pre-load Ki

U nload K2 = 0

T3 Temperature Ti

T3 Temperature Ti

T3Temperature T2 Ti

Fig. 1. Schematic of temperature-load cycles applied to fracture specimens: (a) Cool and Fracture (CF) cycle; (b) Load, Cool and Fracture (LCF);

(c) Load, Unload, Cool and Fracture (LUCF) cycle.

The purpose of this paper is to predict the number of specimens failing prematurely during a set WPS loading path, and identify the conditions when there is no increase in apparent fracture toughness. This is achieved using a probabilistic modelling approach (based on the Chell model [7]) to not only evaluate the minimum pre-load level required to induce an enhancement, but also to estimate based on preliminary fracture toughness results, how many specimens in a sample would fail during the pre-loading sequence at a set temperature.

2. Experimental Results

A substantial fracture toughness data set was generated in order to apply the reformulated Chell model, and perform the predictive analysis, which is described in further detail in Section 3. Compact tension, C(T), specimens, 25mm thick with L-T orientations, side-grooves (to avoid shear lips) and wire EDM pre-cracks, were extracted from 55mm thick steel plates. The fracture tests were conducted at -160oC using a 500kN capacity Dartec hydraulic test machine fitted with a temperature controlled chamber. Figure 2 shows the C(T)'s conceptual drawing and specimens post fracture. The specimens were cooled at a rate of -2oC/min, ensuring no thermal shock was seen, until T3 = -160oC was reached. Once T3 had been reached, the specimen would rest at the desired temperature, monitored using 3 type-K thermocouples, for 10mins in order to reach thermal equilibrium. The tests were conducted in displacement control, with a loading rate of 0.2mm/min in order to give quasi-static loading conditions. A calibrated low temperature clip gauge was used to measure the CMOD, in order to evaluate both Ke and KJC. All specimens were manufactured and tested according to the regulations imposed by ASTM E399-09 [19]. Composition and results tables (Tables 1 & 2) are shown below.

Table 1. Chemical composition of C-Mn steel plate BS1501-224 28B.

C Si Mn Al P S 0.15 0.28 1.27 0.022 0.007 0.005

(a) (b) (c)

Fig. 2. (a) Engineering drawing of C(T) specimen; (b) Fractured C(T) immediately after test; Fractured C(T) conducted at T3 = -160oC

Table 2. Fracture Toughness, Kc, data at -160oC.

Specimen Code KicMPa^ m Specimen Code KicMPaV m Specimen Code KicMPaV m Specimen Code KicMPaV m Specimen Code KicMPaV m

S1A01 101.26 S1A02 71.73 S1A04 102.19 S2A02 146.52 S2B02 101.45

S2A01 88.86 S2A03 36.75 S2A04 108.96 S2B01 101.33 S2B03 116.63

S2B04 127.06 S2A06 127.47 S2A10 69.04 S2A14 98.53 S2A18 130.99

S2B14 126.72 S2B17 127.38 S2B08 137.24 S2B06 102.30 S2B10 122.36

S3B18 144.19 S2A08 149.32 S2A11 127.83 S2A17 117.85 S2A09 121.74

S2A12 82.15 S2A05 77.95 S2A07 73.11 S2A13 116.91 S1B06 125.80

An additional scoping study was carried out to investigate the fracture transition with temperature for this specific material. The results are shown in Figure 4(a).

3. Monte-Carlo Simulations of Warm Pre-Stress

Monte-Carlo simulation is a numerical method which involves the use of simulated random numbers to estimate some function of a probability distribution, and is often used to model cases where there is a significant uncertainty, e.g. cleavage fracture toughness [20]. The Monte Carlo Simulations (MCS) are applied to the revised Chell model, and the details of this analysis can be found in [21]. A 3 parameter Weibull analysis is used to represent the scatter associated with the fracture toughness data. All three parameters are freely determined, and those which provide the highest linear regression coefficient were selected to govern the Weibull distribution. The distribution mapping the experimental results can be seen in Figure 4(b).

The fracture community cares about low probability events, which corresponds to the tails of the fracture toughness distribution. Generally the master curve [17] is used to evaluate the maximum pre-load level, K1, by attributing the KIc value which has a 5% probability of failure. However,it is believed that there is insufficient amount of experimental tests conducted at each temperature step to evaluate such low probability events. As such, an analysis was conducted on the Euro data set [22-23], in order to evaluate a statistically suitable sample size. Specific Weibull parameters were used to generate 100 KIc data points and 5 to 95 points were randomly progressively removed. A new distribution was fitted to the reduced sample, and the variation in both the shape and scale parameters with the number of specimens in the sample was investigated, as shown in Figure 3. Since the scatter observed is a direct result of the reduction in sample size, this process was repeated 20 times._Applying the Mann-Whitney test [24] to the resulting parameter datasets, it was deemed that a sample size of 30 would be statistically acceptable, in order to minimise the potential variation in these fitting parameters.

S É ?

0Bhii - ?

Number of specimens in sample

° o ? 8 o

Number of specimens in sample (b)

Fig. 3. Scatter in Weibull parameters vs Number of specimens, (a) Shape parameter; (b) Scale parameter.

The input variables required for the Chell model are the virgin fracture toughness (KIc), pre-load magnitude (K1), unload magnitude (K2), and the yield strengths at both the fracture and pre-load temperatures (oi, o3). As previously mentioned, a 3 parameter Weibull distribution is used to generate the KIc distribution, however, the elastic component of the stress intensity factor is required in order for the Chell model to be valid. The pre-load magnitude, in this analysis, follows a uniform distribution, with limits of ± 3.2MPaVm. This type of variation is not uncommon, especially if WPS tests are conducted under displacement control [4, 25-26]. Finally, the yield strength values are attributed a 5% coefficient of variation [27]. This analysis also fits 3 parameter Weibull distributions to the KIc data performed at T3 = -140oC to -80oC, in order to evaluate the conditions when K1>KIc(T1), and subsequently eliminate the specimens which would fail prematurely. The pre-load level was increased from K1 = 100 to 400 MPaV m, and applied at T1 = -80 to -140oC. The results obtained from this analysis are displayed in Figure 4(c).

Fracture Temperature /°C

Q 0.4 0

â 0.3

Fracture Toughness / MPa m

250 1/2

ra 40 c

Ke Data. T3 = -160°C Kfl Distribution, T3 = -160°C " m°K = 4.39, Kg = 115.69, Km,n = 0.00

- K, = 100MPa M"'

- K, = 150MPa M11 K, = 200MPa M1* K, = 250MPa M1" K, = 300MPa M11 K, = 350MPa M11

- K = 400MPa m"

-140 -120 -100 -

Pre-load Temperature

Fig. 4. (a) KIC data vs Temperature; (b) Ke distribution at T3 = -160oC; (c) Percentage of survival of sample after pre-load K1 is applied at T1.

4. Discussion

The results of this analysis have revealed two cases where no benefit is observed after a pre-load has been applied. The first instance occurs when the pre-load reaches a critical magnitude which is larger than the original fracture toughness of that specimen. Whilst the Chell model would normally be used to simply predict the potential enhancement, this analysis takes into account the potential elimination of specimens in a sample if premature failure occurs. Figure 5(a) and (b) show the results obtained from using input parameters K1 = 250 MPaVm, T1 = -120oC, and T3 = -160oC. Figure 5(a) shows the generated KIc data points and predicted enhancements, and displays the ranked predictions made from eliminating the prematurely failed specimens. Figure 5(b) shows the probability distribution functions made from fitting 3 parameter Weibull distributions to the results displayed in Figure 5(a). The main observation is that the modified prediction shows a curtailing of the original distribution. Since the lower tail (specimens with low fracture toughness) has effectively been removed, it causes the percentage confidence in the enhancement to increase. This gives a false indication of the true distribution, and degree of enhancement. Discarding the specimens which have failed during the pre-loading sequence, would cause the results to be perceived as even more beneficial, which is effectively incorrect as a proportion of the sample has not survived the WPS loading path.

Fig. 5. Results obtained from LUCF simulation^ = -160oC, T, = -120oC, K, = 250 MPaVm, (a) Cumulative distribution; (b) Probability distribution; (c) Results obtained from LUCF simulation^ = -160oC, T, = -80oC, K, = 100 MPaVm.

The second case is identifying the minimum pre-load level required to cause a benefit in the apparent toughness. Theoretically, the Chell model can provide an estimate of the minimum pre-load necessary determined from yield strength ratios [20]. This corresponds to Case 3 of the Chell model, which states that the specimen's fracture toughness, KIc, is too large for the given pre-load, K1. However, the analysis results predicts an actual number of

specimens in a sample which might not see this enhancement. Figure 5(c) shows that 3 specimens will not see an enhancement, for K1 = 100MPaVm at T1 = -80oC, since their fracture toughness would be too high for the applied pre-load. Since the predictions made from this analysis are to be validated experimentally, obtaining an estimate of how many specimens will not see an enhancement is very important. It is impossible to know both the fracture toughness and apparent toughness post WPS of the same specimen, and therefore impossible to know if a given specimen has seen an enhancement or not. However, with an original fracture toughness data set of 30 specimens at T3 = -160oC, these current predictions will help determine whether a specimen has seen an enhancement or not. Finally, the data collected at T = -140 to -80oC is insufficient to evaluate the tails of its associated fracture toughness distributions. Therefore, the WPS experiments will focus on pre-load magnitudes around the means of the associated Weibull distributions.

5. Conclusions and Future Work

Whilst previous experiments have focussed on loading paths which ensure there is a benefit, this paper has shown that there are 2 cases where no enhancement in apparent fracture toughness is seen. Firstly, there is a risk of premature failure during pre-load. Secondly, it is shown that if the pre-load magnitude is not significantly large enough, there will be no enhancement in the apparent toughness. As such the model used in this analysis defines the parameter space for future WPS experiments. The next step involves experimental validation of the predictions made by the reformulated Chell model. These tests will occur within the transition region using conditions where the risk of premature failure is detectable, whilst the confidence in enhancement is acceptable.

Acknowledgements

The authors are grateful for the financial support for Derreck Van Gelderen's research from EPSRC and EDF Energy. David Smith is supported by the Royal Academy of Engineering, EDF Energy and Rolls-Royce plc.

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