Experimental Measurement of Neck Formation Time and its Probabilistic Model Description

Authors: Teraud V.V. Published: 27.09.2018
Published in issue: #5(80)/2018  
DOI: 10.18698/1812-3368-2018-5-83-98

Category: Physics | Chapter: Instrumentation and Methods of Experimental Physics  
Keywords: experiment, creep, necking, non-contact measurement, probabilistic model

The paper considers the phenomenon of strain localisation (neck formation) in flat tensile specimens undergoing high-temperature creep. Localisation is known to cause the material to lose its bearing strength, becoming unable to withstand the loads applied; subsequent strain mostly occurs locally in the neck. Only approximate theoretical estimates of neck formation time are possible during such testing. Our experiments investigated flat aluminium alloy specimens using an original instrument for non-contact high-temperature measurements that allowed us to measure the specimen geometry and displacement of its surface points over the course of our high-temperature experiment. We obtained experimental neck formation times for various initial tensile stresses and values of the parameter indicating sensitivity to necking. We considered the natural distribution of creep data in terms of statistics. We used the normal distribution to develop a probability density model of neck formation time. We computed theoretical probability of neck formation during a given period of time and described a method for estimating reliability, that is, work not involving strain localisation

The study was partially supported by RFBR grant (project no. 16-38-60200) and grant of the President of the Russian Federation (MK-4321.2018.1)


[1] Kuznetsov A.P., Trubiy V.A. The spread in creep curves. Journal of Applied Mechanics and Technical Physics, 1972, vol. 13, iss. 5, pp. 760–763. DOI: 10.1007/BF00850895

[2] Chalal H., Abed-Meraim F. Numerical predictions of the occurrence of necking in deep drawing processes. Metals, 2017, no. 7, pp. 455–473. DOI: 10.3390/met7110455

[3] Chalal H., Abed-Meraim F. Determination of forming limit diagrams based on ductile damage models and necking criteria. Latin American Journal of Solids and Structures, 2017, vol. 14, pp. 1872–1892.

[4] Swift H. Plastic instability under plane stress. J. Mechanics Physics Solids, 1952, vol. 1, iss. 1, pp. 1–18. DOI: 10.1016/0022-5096(52)90002-1

[5] Hill R. On discontinuous plastic states, with special reference to localized necking in thin sheets. J. Mechanics Physics Solids, 1952, vol. 1, iss. 1, pp. 19–30. DOI: 10.1016/0022-5096(52)90003-3

[6] Hora P., Tong L., Reissner J. A prediction method for ductile sheet metal failure in FE-simulation. Proc. NUMISHEET96 Conf., 1996, pp. 252–256.

[7] Michel B., Patrice C. Predictions of necking with analytical criteria and comparisons with experimental. Materials Processing and Design. Modeling, Simulation and Applications. NUMIFORM07, 2007, vol. 908, pp. 81–89.

[8] Nirmal K. Constant-load tertiary creep in nickel-base single crystal superalloys. Materials Science and Engineering: A, 2006, vol. 432, iss. 1-2, pp. 129–141. DOI: 10.1016/j.msea.2006.05.134

[9] Malygin G. Influence of the grain size on the resistance of micro and nanocrystalline metals against the neck like localization of plastic deformation. Physics of the Solid State, 2011, vol. 53, iss. 2, pp. 363–368. DOI: 10.1134/S1063783411020168

[10] Srinivas B., Janaki P., Ganesh R. Application of a few necking criteria in predicting the forming limit of unwelded and tailor-welded blanks. J. Strain Analysis. Eng. Des., 2009, vol. 45, iss. 2, pp. 79–96. DOI: 10.1243/03093247JSA562

[11] Veklich N.A. Probability-theoretical simulation of creep in uniaxial tension of specimens. Strength of Materials, 2013, vol. 45, iss. 2, pp. 179–186. DOI: 10.1007/s11223-013-9445-2

[12] Doyar I.A., Poshivalov V.P. A variant of probabilistic estimation of time to fracture in creep. Tekhn. Mekhanika [Technical Mechanics], 2013, no. 2, pp. 99–108 (in Russ.).

[13] Lehmayr B., Staudacher S. A statistical model for scatter representation in stress life curves. FFEMS, 2012, vol. 35, iss. 4, pp. 347–358. DOI: 10.1111/j.1460-2695.2011.01625.x

[14] Teraud V.V., Valisovskiy N.E. Experimental research of particularities of strain localization in the plane tensile specimens at high temperature creep. Mashinostroenie i inzhenernoe obrazovanie, 2015, no. 2, pp. 40–47 (in Russ.).

[15] Teraud V.V. Experimental criteria of creep deformations localization in rectangular specimens at high temperatures. Vestnik mashinostroeniya, 2017, no. 7, pp. 28–34 (in Russ.).

[16] Teraud W. Localization of the creep in rectangular samples at high temperature. Russian Engineering Research, 2017, vol. 37, iss. 10, pp. 850–856. DOI: 10.3103/S1068798X17100215

[17] Barenblatt G.I., Volodchenkov V.A., Kershteyn I.M., Pavlov D.Ya. Isothermal spread of neck in polymers. Comparison with the creep process. MTT, 1974, no. 5, pp. 144–156 (in Russ.).

[18] Lokoshchenko A.M. Creep and long-term strength of metals. CRC Press, 2018. 564 p.

[19] Novikov A.P., Voronin A.I., Purikova I.A., Dimitryuk Yu.S. Vysokotemperaturnaya polzuchest i dlitelnaya prochnost zharoprochnykh splavov pri slozhnykh temperaturno-vremennykh rezhimakh nagruzheniya [High-temperature creep and long-term strength of heat-resistant alloys in complex temperature-time loading modes]. Nevinnomyssk, NGGTI Publ., 2011. 243 p.

[20] Khokhlov A.V. Analysis of creep curves general properties under step loading generated by the Rabotnov nonlinear relation for viscoelastic plastic materials. Vestn. Mosk. Gos. Tekh. Univ. im. N.E. Baumana, Estestv. Nauki [Herald of the Bauman Moscow State Tech. Univ., Nat. Sci.], no. 3, pp. 93–123 (in Russ.). DOI: 10.18698/1812-3368-2017-3-93-123

[21] Radchenko V.P., Nebogina E.V., Andreeva E.A. Structural model of material softening at creep under complex stress conditions. Vestn. Sam. Gos. Tekh. Un-ta. Ser. Fiz.-Mat. Nauki [Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences], 2009, no. 1, pp. 75–84 (in Russ.).

[22] Pavlov I.V. Probability model of strength estimation of articles by results of testing of their fragments. Vestn. Mosk. Gos. Tekh. Univ. im. N.E. Baumana, Estestv. Nauki [Herald of the Bauman Moscow State Tech. Univ., Nat. Sci.], 2009, no. 3, pp. 66–83 (in Russ.).