Research Papers: Materials and Fabrication

Variation of Beremin Model Parameters With Temperature by Monte Carlo Simulation

[+] Author and Article Information
K. Bhattacharyya

Department of Mechanical Engineering,
Jadavpur University,
188, Raja S. C. Mallick Road,
Kolkata, West Bengal 700032, India
e-mail: bhattacharyyakushal3@gmail.com

S. Acharyya, S. Dhar

Department of Mechanical Engineering,
Jadavpur University,
188, Raja S. C. Mallick Road,
Kolkata, West Bengal 700032, India

J. Chattopadhyay

Reactor Safety Division,
Bhabha Atomic Research Centre,
Mumbai 400085, India

Contributed by the Pressure Vessel and Piping Division of ASME for publication in the JOURNAL OF PRESSURE VESSEL TECHNOLOGY. Manuscript received May 7, 2018; final manuscript received November 17, 2018; published online February 21, 2019. Assoc. Editor: Kiminobu Hojo.

J. Pressure Vessel Technol 141(2), 021401 (Feb 21, 2019) (7 pages) Paper No: PVT-18-1094; doi: 10.1115/1.4042121 History: Received May 07, 2018; Revised November 17, 2018

In this work, variation of the Beremin parameters with temperature for reactor pressure vessel material 20MnMoNi55 steel is studied. Beremin model is used, including the effect of plastic strain as originally formulated in the Beremin model. A set of six tests are performed at a temperature of −110 °C in order to determine reference temperature (T0) and master curve for the entire ductile-to-brittle transition (DBT) region as per the ASTM Standard E1921. Monte Carlo simulation is employed to produce a large number of 1 T three-point bending specimen (TPB) fracture toughness data randomly drawn from the scatter band obtained from the master curve, at different temperatures of interest in the brittle dominated portion of DBT region to determine Beremin model parameters variation with temperatures.

Copyright © 2019 by ASME
Your Session has timed out. Please sign back in to continue.


Hojo, K., Muroya, I., and Brückner-Foit, 1997, “ Fracture Toughness Transition Curve Estimation From a Notched Round Bar Specimen Using the Local Approach Method,” Nucl. Eng. Des., 174(3), pp. 247–258. [CrossRef]
Gao, X. , Zhang, G. , and Srivatsan, T. S. , 2006, “ A Probabilistic Model for Prediction of Cleavage Fracture in the Ductile-to-Brittle Transition Region and the Effect of Temperature on Model Parameters,” Mater. Sci. Eng. A., 415, pp. 264–472. [CrossRef]
Wasiluk, B. , Petti, J. P., and Dodds, R. H., Jr., 2006, “ Temperature Dependence of Weibull Stress Parameters: Studies Using the Euro-Material,” Eng. Fract. Mech., 73(8), pp. 1046–1069. [CrossRef]
Petti, J. P. , and Dodds, R. H., Jr. , 2005, “ Calibration of the Weibull Stress Scale Parameter, σu, Using the Master Curve,” Eng. Fract. Mech., 72(1), pp. 91–120. [CrossRef]
Wiesner, C. S. , and Goldthorpe, M. R. , 1996, “ The Effect of Temperature and Specimen Geometry on the Parameters of the ‘Local Approach’ to Cleavage Fracture. 1st European Mechanics of Materials Conference on Local Approach to Fracture ‘86–96,’” J. Phys. IV, France, 6(C6), pp. C6-295–C6-304. [CrossRef]
Khalili, A. , and Kromp, K. , 1991, “ Statistical Properties of Weibull Estimators,” J. Mater. Sci., 26(24), pp. 6741–6752. [CrossRef]
Bhowmik, S. , Sahoo, P., Acharyya, S. K., Dhar, S., and Chattopadhyay, J., 2015, “ Evaluation and Effect of Loss of Constraint on Master Curve Reference Temperature of 20MnMoni55 Steel,” Eng. Fract. Mech., 136, pp. 142–157. [CrossRef]
Ruggieri, C. , Savioli, R. G. , and Dodds, R. H., Jr. , 2015, “ An Engineering Methodology for Constraint Corrections of Elastic–Plastic Fracture Toughness—Part II: Effects of Specimen Geometry and Plastic Strain on Cleavage Fracture Predictions,” Eng. Fract. Mech., 146, pp. 185–209. [CrossRef]
Wallin, K. , 1984, “ The Scatter in KIC Result,” Eng. Fract. Mech., 19(6), pp. 1085–1093. [CrossRef]
Wallin, K. , 1999, “ The Master Curve Method: A New Concept for Brittle Fracture,” Int. J. Mater. Prod. Technol., 14(2/3/4), pp. 342–354. [CrossRef]
Wallin, K. , 1998, “ Master Curve of Ductile to Brittle Transition Region Fracture Toughness Round Robin Data. The ‘EURO’ Fracture Toughness Curve,” VTT Technical Research Centre of Finland, Espoo, Finland, Report No. 367. https://www.vtt.fi/inf/pdf/publications/1998/P367.pdf
IAEA, 2009, “ Master Curve Approach to Monitor Fracture Toughness of Reactor Pressure Vessels in Nuclear Power Plants,” International Atomic Energy Agency, Vienna, Austria, Standard No. IAEA-TECDOC-1613. https://www-pub.iaea.org/books/iaeabooks/8162/Master-Curve-Approach-to-Monitor-Fracture-Toughness-of-Reactor-Pressure-Vessels-in-Nuclear-Power-Plants
ASTM, 2013, “ Standard Test Method for Determination of Reference Temperature, TO, for Ferritic Steels in the Transition Range,” ASTM International, American Society for Testing and Materials, West Conshohocken, PA, Standard No. ASTM E1921-13. https://www.astm.org/DATABASE.CART/HISTORICAL/E1921-13.htm
Beremin, F. M. , 1983, “ A Local Criterion for Cleavage Fracture of a Nuclear Pressure Vessel Steel,” Metall. Trans., 14A, pp. 2277–2287. [CrossRef]
Bhowmik, S. , Chattopadhyaya, A., Bose, T., Acharyya, S. K., Sahooa, P., Chattopadhyay, J., and Dhara, S., 2011, “ Estimation of Fracture Toughness of 20MnMoNi55 Steel in the Ductile to Brittle Transition Region Using Master Curve Method,” Nucl. Eng. Des., 241(8), pp. 2831–2838. [CrossRef]
Bhowmik, S. , Sahoo, P., Acharyya, S. K., Chattopadhyay, J., and Dhara, S., 2012, “ Application and Comparative Study of Master Curve Methodology for Fracture Toughness Characterization of 20MnMoNi55 Steel,” Mater. Des., 39, pp. 309–317. [CrossRef]
Tiwari, A. , Avinash, G., Sunil, S., Singh, R. N., Per Ståhle, Chattopadhyay, J., and Chakravartty, J. K., 2015, “ Determination of Reference Transition Temperature of In-RAFMS in Ductile Brittle Transition Regime Using Numerically Corrected Master Curve Approach,” Eng. Fract. Mech., 142, pp. 79–92. [CrossRef]
Ruggieri, C. , Gao, X., and Dodds, R. H., Jr., 2000, “ Transferability of Elastic-Plastic Fracture Toughness Using the Weibull Stress Approach: Significance of Parameter Calibration,” Eng. Fract. Mech., 67(2), pp. 101–117. [CrossRef]


Grahic Jump Location
Fig. 1

Experimental arrangement for low temperature Jc test: (1) cryo-chamber, (2) controller, (3) operator panel, (4) support computer, (5) liquid nitrogen cylinder, and (6) temperature indicator

Grahic Jump Location
Fig. 2

Experimental setup of TPB specimen for low temperature Jc test: (7) TPB specimen, (8) crack tip opening displacement gauge, and (9) rigid roller

Grahic Jump Location
Fig. 3

Geometry of TPB specimen

Grahic Jump Location
Fig. 4

(a) Quarter TPB specimen model along with boundary conditions and (b) maximum principal stress (MPa) distribution in the fracture process zone

Grahic Jump Location
Fig. 5

(a) Comparison of load versus LLD at −110 °C and (b) Comparison of J-Integral versus LLD at −110 °C

Grahic Jump Location
Fig. 6

(a) Master curve from six test data set and (b) randomly generated KJc by master curve and temperature relation

Grahic Jump Location
Fig. 7

(a) Relation between Weibull modulus and the simulation number (test temperature −100 °C, average m = 32) and (b) relation between Weibull Modulus and the simulation number (test temperature −130 °C, average m = 41)

Grahic Jump Location
Fig. 8

(a) Relation between scale parameter and the simulation number (test temperature −100 °C, average σu = 2186 MPa) and (b) relation between scale parameter and the simulation number (test temperature −130 °C, average σu = 2092 MPa)

Grahic Jump Location
Fig. 9

(a) Variation of m with temperature and (b) Variation of σu with temperature

Grahic Jump Location
Fig. 10

Probability of failure versus Weibull stress distribution for −100 °C, −110 °C, −120 °C, −130 °C, and −140 °C



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In