A semi-infinite edge dislocation model for the proportionality limit stress of metals under high strain rate. (English) Zbl 1479.74018

Summary: Micromechanics of strain rate dependent elastic response, within the proportionality limit in metals is investigated, on the basis of dislocation kinetics. It is postulated that, the strain rate dependence of proportionality limit stress is dominated by inertia of dislocations, over drag controlled mechanisms. Subsequently, kinetic energy of accelerating edge dislocation at its incipient motion, is expressed. The proposed, inertia-dominated model is non dissipative in nature when compared with that of Frank-Read dislocation nucleation-based model and dislocation-drag mechanism-based model at high strain rates. Using Hamiltonian formalism, a new rate dependent slip criterion with corresponding threshold shear stress is derived. Experimental data on FCC samples, Aluminium-1100-0 and Oxygen free Copper; and BCC samples, pure Iron and mild steel, within a benchmark strain rate of \(10^4\) \(\mathrm{s}^{-1}\), are used to validate the model prediction. Reported theory on dislocation drag controlled model is compared with the proposed inertia-based theory, using published experimental data.


74C10 Small-strain, rate-dependent theories of plasticity (including theories of viscoplasticity)
74A60 Micromechanical theories
Full Text: DOI


[1] Langseth, M.; Lindholm, US; Larsen, PK; Lian, B., Strain-Rate Sensitivity of Mild Steel Grade St52-3N, J Eng Mech, 117, 719-732 (1991)
[2] Marsh, KJ; Campbell, JD, The effect of strain rate on the post-yield flow of mild steel, J Mech Phys Solids (1963)
[3] Singh, NK; Cadoni, E.; Singha, MK; Gupta, NK, Dynamic tensile and compressive behaviors of mild steel at wide range of strain rates, J Eng Mech © ASCE, 139, 1197-1207 (2013)
[4] Wang, W.; Ma, Y.; Yang, M., Strain rate effect on tensile behavior for a high specific strength steel: From quasi-static to intermediate strain rates, Metals (Basel) (2018)
[5] Campbell, JD; Ferguson, WG, The temperature and strain-rate dependence of the shear strength of mild steel, Philos Mag, 21, 63-82 (1970)
[6] Abo-Elkhier, M., Modeling of high-temperature deformation of commercial pure aluminum (1050), J Mater Eng Perform, 13, 241-247 (2004)
[7] Davies, RG; Magee, CL, The effect of strain-rate upon the tensile deformation of materials, J Eng Mater Technol, 97, 151-155 (1975)
[8] Johnson GR, Cook WH (1983) A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures. In: Proc 7th Int Symp Ballist
[9] Johnson, GR; Cook, WH, Fracture characteristics of three metals subjected to various strains, strain rates, temperatures and pressures, Eng Fract Mech, 21, 31-48 (1985)
[10] Harding, J., High-rate straining and mechanical properties of materials, Explos Weld Form Compact (1983)
[11] Timmel, M.; Kaliske, M.; Kolling, S.; Mueller, R., On configurational forces in hyperelastic materials under shock and impact, Comput Mech, 47, 93-104 (2011) · Zbl 1398.74241
[12] Hirth, JP; Lothe, J., Theory of Dislocations (1982), Malabar, Florida: Krieger publishing company, Malabar, Florida · Zbl 1365.82001
[13] Hirth, JP; Zbib, HM; Lothe, J., Forces on high velocity dislocations, Model Simul Mater Sci Eng, 6, 165-169 (1998)
[14] Pellegrini, Y-P, Dynamic Peierls-Nabarro equations for elastically isotropic crystals, Phys Rev B, 81, 024101 (2010)
[15] Brandl, C.; Derlet, PM; Van Swygenhoven, H., Strain rates in molecular dynamics simulations of nanocrystalline metals, Philos Mag, 89, 3465-3475 (2009)
[16] Shao, JL; Wang, P.; Zhang, FG; He, AM, Hcp/fcc nucleation in bcc iron under different anisotropic compressions at high strain rate: molecular dynamics study, Sci Rep, 8, 1-10 (2018)
[17] Marais, ST; Tait, RB; Cloete, TJ; Nurick, GN, Material testing at high strain rate using the split Hopkinson pressure bar, Lat Am J Solids Struct, 1, 319-337 (2004)
[18] Schlick, T., Molecular modeling and simulation: an interdisciplinary Guide (2010), Berlin: Springer, Berlin · Zbl 1320.92007
[19] Bianchini, F.; Glielmo, A.; Kermode, JR; De Vita, A., Enabling QM-accurate simulation of dislocation motion in γ-Ni and α-Fe using a hybrid multiscale approach, Phys Rev Mater (2019)
[20] Ansart, JP; Dormeval, R.; Tokuda, M., About the strain rate dependence of yield stress and flow stress of materials, Advances in plasticity, 371-374 (1989), Amsterdam: Elsevier, Amsterdam
[21] El-Magd, E., Mechanical properties at high strain rates, J Phys IV, 04, C8-149 (1994)
[22] Gordeliy, E.; Detournay, E., Displacement discontinuity method for modeling axisymmetric cracks in an elastic half-space, Int J Solids Struct, 48, 2614-2629 (2011)
[23] Crouch, SL, Solution of plane elasticity problems by the displacement discontinuity method. I. Infinite body solution, Int J Numer Methods Eng, 10, 301-343 (1976) · Zbl 0322.73016
[24] Orowan, E., ZurKristallplastizität III Zeitschrift für Phys, 89, 605-613 (1934)
[25] Taylor, GI, The mechanism of plastic deformation of crystals. part ii. theoretical, Proc R Soc A Math Phys Eng Sci, 145, 388-404 (1934) · JFM 60.0713.01
[26] Polanyi, M., Lattice distortion which originates plastic flow, Zeitschrift fur Phys, 89, 660-664 (1934)
[27] Tang, Y., Uncovering the inertia of dislocation motion and negative mechanical response in crystals, Sci Rep (2018)
[28] Markenscoff, X.; Ni, L., The transient motion of a dislocation with a ramp-like core, J Mech Phys Solids, 49, 1603-1619 (2001) · Zbl 0989.74037
[29] Pellegrini, YP, Screw and edge dislocations with time-dependent core width: from dynamical core equations to an equation of motion, J Mech Phys Solids, 60, 227-249 (2012) · Zbl 1244.74035
[30] Shishvan, SS; Van der Giessen, E., Distribution of dislocation source length and the size dependent yield strength in freestanding thin films, J Mech Phys Solids, 58, 678-695 (2010)
[31] Gurrutxaga-Lerma, B.; Balint, DS; Dini, D., The role of homogeneous nucleation in planar dynamic discrete dislocation plasticity, J Appl Mech, 82, 071008 (2015)
[32] Özdemir, I.; Yalçinkaya, T., Modeling of dislocation-grain boundary interactions in a strain gradient crystal plasticity framework, Comput Mech (2014)
[33] Suzuki, T.; Takeuchi, S.; Yoshinaga, H., Dislocation Dynamics and Plasticity (1991), Berlin Heidelberg, Berlin, Heidelberg: Springer, Berlin Heidelberg, Berlin, Heidelberg
[34] Taylor, G., Thermally-activated deformation of BCC metals and alloys, Prog Mater Sci (1992)
[35] Nadgornyi, E., Dislocation dynamics and mechanical properties of crystals, Prog Mater Sci, 31, 1-530 (1988)
[36] Hirth, JP; Lothe, J.; Nabarro, FRN; Smoluchowski, R., Theory of dislocations and theory of crystal dislocations, Phys Today, 21, 85-86 (1968)
[37] Eshelby, JD, The interaction of kinks and elastic waves, Proc R Soc A Math Phys Eng Sci, 266, 222-246 (1962) · Zbl 0106.44703
[38] Sietsma, J.; Pereloma, E., Nucleation and growth during the austenite-to-ferrite phase transformation in steels after plastic deformation, Phase Transformations in Steels, 505-526 (2012), Amsterdam: Elsevier, Amsterdam
[39] Vítek, V., Intrinsic stacking faults in body-centred cubic crystals, Philos Mag, 18, 773-786 (1968)
[40] Peierls, R., The size of a dislocation, Proc Phys Soc, 52, 34-37 (1940)
[41] Nabarro, FRN, Dislocations in a simple cubic lattice, Proc Phys Soc, 59, 256-272 (1947)
[42] Eshelby, JD, LXXXII. Edge dislocations in anisotropic materials, London, Edinburgh, Dublin Philos Mag J Sci, 40, 903-912 (1949) · Zbl 0033.04801
[43] Eshelby, JD, Uniformly moving dislocations, Proc Phys Soc Sect A, 62, 307-314 (1949)
[44] Peach, M.; Koehler, JS, The forces exerted on dislocations and the stress fields produced by them, Phys Rev, 80, 436-439 (1950) · Zbl 0039.23301
[45] Gurrutxaga-Lerma, B.; Balint, DS; Dini, D.; Sutton, AP, Elastodynamic image forces on dislocations, Proc R Soc A Math Phys Eng Sci (2015) · Zbl 1371.74150
[46] Gurrutxaga-Lerma, B.; Balint, DS; Dini, D., A dynamic discrete dislocation plasticity method for the simulation of plastic relaxation under shock loading, Proc R Soc A Math Phys Eng Sci, 469, 20130141 (2013) · Zbl 1371.74052
[47] Gurrutxaga-Lerma B, Balint DS, Dini D, et al (2014) Dynamic Discrete Dislocation Plasticity. In: Bordas S (ed) Advances in Applied Mechanics. Elsevier Inc., pp 93-224
[48] Gurrutxaga-Lerma, B.; Balint, DS; Dini, D., Attenuation of the dynamic yield point of shocked aluminum using elastodynamic simulations of dislocation dynamics, Phys Rev Lett, 114, 1-5 (2015)
[49] Agnihotri, PK; Van Der Giessen, E., On the rate sensitivity in discrete dislocation plasticity, Mech Mater, 90, 37-46 (2015)
[50] Roos, A.; De Hosson, JTM; Van der Giessen, E., High-speed dislocations in high strain-rate deformations, Comput Mater Sci, 20, 19-27 (2001)
[51] Shehadeh, MA; Zbib, HM; De La Rubia, TD, Multiscale dislocation dynamics simulations of shock compression in copper single crystal, Int J Plast, 21, 2369-2390 (2005) · Zbl 1101.74317
[52] Shehadeh, MA; Bringa, EM; Zbib, HM, Simulation of shock-induced plasticity including homogeneous and heterogeneous dislocation nucleations, Appl Phys Lett, 89, 2004-2007 (2006)
[53] Van der Giessen, E.; Needleman, A., Discrete dislocation plasticity: a simple planar model, Model Simul Mater Sci Eng, 3, 689-735 (1995)
[54] Zbib, HM; Diaz de la Rubia, T., A multiscale model of plasticity, Int J Plast, 18, 1133-1163 (2002) · Zbl 1062.74008
[55] Shehadeh, MA; Zbib, HM; Diaz De La Rubia, T., Modelling the dynamic deformation and patterning in fee single crystals at high strain rates: dislocation dynamics plasticity analysis, Philos Mag, 85, 1667-1685 (2005)
[56] Wang, ZQ; Beyerlein, IJ; Lesar, R., Dislocation motion in high strain-rate deformation, Philos Mag, 87, 2263-2279 (2007)
[57] Wang, ZQ; Beyerlein, IJ; LeSar, R., The importance of cross-slip in high-rate deformation, Model Simul Mater Sci Eng, 15, 675-690 (2007)
[58] Gurrutxaga-Lerma, B.; Balint, DS; Dini, D.; Sutton, AP, The mechanisms governing the activation of dislocation sources in aluminum at different strain rates, J Mech Phys Solids, 84, 273-292 (2015)
[59] Wang, W.; Ma, Y.; Yang, M., Strain rate effect on tensile behavior for a high specific strength steel: from quasi-static to intermediate strain rates, Metals (Basel) (2017)
[60] Liu, ZL; Liu, XM; Zhuang, Z.; You, XC, A multi-scale computational model of crystal plasticity at submicron-to-nanometer scales, Int J Plast, 25, 1436-1455 (2009) · Zbl 1235.74013
[61] Bulatov, VV; Cai, W., Computer simulations of dislocations (2006), Oxford: Oxford University Press, Oxford · Zbl 1119.74001
[62] Huh, H.; Kim, SB; Song, JH; Lim, JH, Dynamic tensile characteristics of TRIP-type and DP-type steel sheets for an auto-body, Int J Mech Sci, 50, 918-931 (2008) · Zbl 1388.74019
[63] Kontorova, T.; Frenkel, J., On the theory of plastic deformation and twinning, II Zh Eksp Teor Fiz, 8, 1340-1348 (1938) · Zbl 0021.08501
[64] Frank, FC, On the equations of motion of crystal dislocations, Proc Phys Soc Sect A, 62, 131 (1948) · Zbl 0033.24002
[65] Eshelby, JD, The equation of motion of a dislocation, Phys Rev, 90, 248-255 (1953) · Zbl 0051.23101
[66] Markenscoff, X., The transient motion of a nonuniformly moving dislocation, J Elast, 10, 193-201 (1980) · Zbl 0441.73142
[67] Landau, AI, The effect of dislocation inertia on the thermally activated low-temperature plasticity of materials, Phys Status Solidi, 61, 415-423 (1981)
[68] Markenscoff, X.; Clifton, RJ, The nonuniformly moving edge dislocation, J Mech Phys Solids, 29, 253-262 (1981) · Zbl 0463.73137
[69] Pillon, L.; Denoual, C.; Pellegrini, YP, Equation of motion for dislocations with inertial effects, Phys Rev B Condens Matter Mater Phys (2007)
[70] Kojima, H.; Suzuki, T., Electron drag and flow stress in niobium and lead at 4.2°K, Phys Rev Lett, 21, 896-898 (1968)
[71] Alers, GA; Buck, O.; Tittmann, BR, Measurements of plastic flow in superconductors and the electron-dislocation interaction, Phys Rev Lett, 23, 290-293 (1969)
[72] Marion, JB, Hamilton’s Principle—Lagrangian and Hamiltonian Dynamics, Stephen thornton classical dynamics of particles and systems, 214-266 (1965), Amsterdam: Elsevier, Amsterdam
[73] Armstrong, RW; Arnold, W.; Zerilli, FJ, Dislocation mechanics of shock-induced plasticity, Metall Mater Trans A Phys Metall Mater Sci A, 38, 2605-2610 (2007)
[74] Armstrong, RW; Walley, SM, High strain rate properties of metals and alloys, Int Mater Rev, 53, 105-128 (2008)
[75] Yaghoobi, M.; Voyiadjis, GZ, The effects of temperature and strain rate in fcc and bcc metals during extreme deformation rates, Acta Mater, 151, 1-10 (2018)
[76] Armstrong, R.; Codd, I.; Douthwaite, RM; Petch, NJ, The plastic deformation of polycrystalline aggregates, Philos Mag, 7, 45-58 (1962)
[77] Ni, L.; Markenscoff, X., The self-force and effective mass of a generally accelerating dislocation I: screw dislocation, J Mech Phys Solids, 56, 1348-1379 (2008) · Zbl 1171.74317
[78] Ni, L., The effective mass of an accelerating dislocation (2005), San Diego: University of California, San Diego
[79] Rosakis, P., Supersonic dislocation kinetics from an augmented Peierls model, Phys Rev Lett, 86, 95-98 (2001)
[80] Pellegrini, YP, Equation of motion and subsonic-transonic transitions of rectilinear edge dislocations: s collective-variable approach, Phys Rev B Condens Matter Mater Phys, 90, 1-18 (2014)
[81] Weertman, J.; Weertman, JR, Elementary dislocation theory (1992), Oxford: Oxford University Press, Oxford · Zbl 0982.74004
[82] Gillis, PP; Kratochvil, J., Dislocation acceleration Philos Mag, 21, 425-432 (1970)
[83] Weertman J (1961) Response of metals to high velocity deformation. In: Shewmon, In: Paul G. VFZ (ed) Proceedings of a Technical Conference. Metallurgical society conferences . Interscience publishers, pp 205-246
[84] Po, G.; Cui, Y.; Rivera, D., A phenomenological dislocation mobility law for bcc metals, Acta Mater, 119, 123-135 (2016)
[85] Hu, J.; Liu, Z.; Van der Giessen, E.; Zhuang, Z., Strain rate effects on the plastic flow in submicron copper pillars: Considering the influence of sample size and dislocation nucleation, Extrem Mech Lett, 17, 33-37 (2017)
[86] Oren, E.; Yahel, E.; Makov, G., Dislocation kinematics: a molecular dynamics study in Cu, Model Simul Mater Sci Eng (2017)
[87] Mordehai, D.; Kelson, I.; Makov, G., Nonplanar core and dynamical behavior of screw dislocations in copper at high velocities, Phys Rev B Condens Matter Mater Phys (2006)
[88] Tsuzuki, H.; Branicio, PS; Rino, JP, Accelerating dislocations to transonic and supersonic speeds in anisotropic metals, Appl Phys Lett (2008)
[89] Kuksin, AY; Stegaĭlov, VV; Yanilkin, AV, Molecular-dynamics simulation of edge-dislocation dynamics in aluminum, Dokl Phys, 53, 287-291 (2008)
[90] Abu Al-Rub, RK; Voyiadjis, GZ, A finite strain plastic-damage model for high velocity impact using combined viscosity and gradient localization limiters: Part I—Theoretical formulation, Int J Damage Mech (2006)
[91] Khan, AS; Huang, S., Experimental and theoretical study of mechanical behavior of 1100 aluminum in the strain rate range 10-5-104s-1, Int J Plast, 8, 397-424 (1992)
[92] Bao, WP; Xiong, ZP; Ren, XP; Wang, FM, Effect of strain rate on mechanical properties of pure iron, Adv Mater Res, 705, 21-25 (2013)
[93] Regazzoni, G.; Kocks, UF; Follansbee, PS, Dislocation kinetics at high strain rates, Acta Metall, 35, 2865-2875 (1987)
[94] Taylor, GI, plastic strain in metals (1938), London: The Institute of Metals, London
[95] Shen, JH; Li, YL; Wei, Q., Statistic derivation of Taylor factors for polycrystalline metals with application to pure magnesium, Mater Sci Eng A, 582, 270-275 (2013)
[96] Kocks, UF; Mecking, H., Physics and phenomenology of strain hardening: the FCC case, Prog Mater Sci, 48, 171-273 (2003)
[97] Przybyla, CP; Adams, BL; Miles, MP, Methodology for determining the variance of the taylor factor: application in Fe-3
[98] Meyers, MA; Kumar Chawla, K., Mechanical behavior of materials (2009), Cambridge: Cambridge University Press, Cambridge · Zbl 1280.74002
[99] Weinberger, CR; Boyce, BL; Battaile, CC, Slip planes in bcc transition metals, Int Mater Rev (2013)
[100] Yogo, Y.; Sawamura, M.; Harada, R., Stress-strain curve of pure aluminum in a super large strain range with strain rate and temperature dependency, Procedia Eng, 207, 161-166 (2017)
[101] Zhang, T.; Wang, Z.; Wang, Y.; Chen, Z., Experimental study on the mechanical properties of oxygen-free copper used in high energy physics detectors and accelerators, Nucl Inst Methods Phys Res A, 935, 8-16 (2019)
[102] Kim JS, Huh H (2011) Rate Dependent Material Properties of an OFHC copper Film. In: Conference Proceedings of the Society for Experimental Mechanics Series 99:459-465
[103] Roters, F., A new concept for the calculation of the mobile dislocation density in constitutive models of strain hardening, Phys Status Solidi Basic Res, 240, 68-74 (2003)
[104] Orlová, A., On the mobile dislocation density in creep, Czechoslov J Phys, 38, 502-504 (1988)
[105] Voyiadjis, GZ; Abed, FH, Effect of dislocation density evolution on the thermomechanical response of metals with different crystal structures at low and high strain rates and temperatures, Arch Mech, 57, 299-343 (2005) · Zbl 1126.74011
[106] Kelly, JM; Gillis, PP, Continuum descriptions of dislocations under stress reversals, J Appl Phys, 45, 1091-1096 (1974)
[107] Brindley, BJ; Barnby, JT, Dynamic strain ageing in mild steel, Acta Metall, 14, 1765-1780 (1966)
[108] Schafler, E.; Zehetbauer, M.; Borbely, A.; Ungar, T., Dislocation densities and internal stresses in large strain cold worked pure iron, Mater Sci Eng A, 234-236, 445-448 (1997)
[109] Nakashima, K.; Suzuki, M.; Futamura, Y., Limit of Dislocation Density and Dislocation Strengthening in Iron, Mater Sci Forum, 503-504, 627-632 (2006)
[110] Hu, Q.; Zhao, F.; Fu, H., Dislocation density and mechanical threshold stress in OFHC copper subjected to SHPB loading and plate impact, Mater Sci Eng A, 695, 230-238 (2017)
[111] May, J.; Dinkel, M.; Amberger, D., Mechanical properties, dislocation density and grain structure of ultrafine-grained aluminum and aluminum-magnesium alloys, Metall Mater Trans A Phys Metall Mater Sci A (2007)
[112] Orowan, E., Problems of plastic gliding, Proc Phys Soc, 52, 8-22 (1940)
[113] Lu, G.; Kioussis, N.; Bulatov, VV; Kaxiras, E., Dislocation core properties of aluminum: a first-principles study, Mater Sci Eng A (2001)
[114] Staker, MR; Holt, DL, The dislocation cell size and dislocation density in copper deformed at temperatures between 25 and 700°C, Acta Metall, 20, 569-579 (1972)
[115] Bitzek, E.; Weygand, D.; Gumbsch, P., Atomistic study of edge dislocations in FCC metals: drag and inertial effects, IUTAM Symp Mesoscopic Dyn Fract Process Mater Strength (2004)
[116] Bitzek, E.; Gumbsch, P., Atomistic study of drag, surface and inertial effects on edge dislocations in face-centered cubic metals, Mater Sci Eng A, 387-389, 11-15 (2004)
[117] Horstemeyer, MF; Baskes, MI; Plimpton, SJ, Length scale and time scale effects on the plastic flow of fcc metals, Acta Mater, 49, 4363-4374 (2001)
[118] Larose, A.; Brockhouse, BN, Lattice vibrations in copper at elevated temperatures studied by neutron scattering, Can J Phys, 54, 1990-2009 (2011)
[119] Ortiz, M., Computational micromechanics, Comput Mech, 18, 321-338 (1996) · Zbl 0890.73054
[120] Khoei, AR; Aramoon, A.; Jahanbakhshi, F.; Dormohammadi, H., A coupling atomistic-continuum approach for modeling mechanical behavior of nano-crystalline structures, Comput Mech, 54, 269-286 (2014) · Zbl 1334.74008
[121] Ye, W.; Paliwal, B.; Goh, WH, Finite element modeling of dislocation in solids and its applications to the analysis of GaN nanostructures, Comput Mater Sci, 58, 154-161 (2012)
[122] Kolednik, O.; Ochensberger, W.; Predan, J.; Fischer, FD, Driving forces on dislocations—An analytical and finite element study, Int J Solids Struct, 190, 181-198 (2020)
[123] Sasaki, K.; Kishida, M.; Ekida, Y., Stress analysis in continuous media with an edge dislocation by finite element dislocation model, Int J Numer Methods Eng (2002) · Zbl 1034.74047
[124] Song, Y.; Voyiadjis, GZ, Constitutive modeling of dynamic strain aging for HCP metals, Eur J Mech A/Solids (2020) · Zbl 1473.74004
[125] Voyiadjis, GZ; Song, Y.; Rusinek, A., Constitutive model for metals with dynamic strain aging, Mech Mater (2019)
[126] Jin, T.; Mourad, HM; Bronkhorst, CA; Livescu, V., Finite element formulation with embedded weak discontinuities for strain localization under dynamic conditions, Comput Mech, 61, 3-18 (2018) · Zbl 1451.74207
[127] Kreuzer, HGM; Pippan, R., Discrete dislocation simulation of nanoindentation, Comput Mech (2004) · Zbl 1067.74549
[128] Bin Jamal, MN; Kumar, A.; Lakshmana Rao, C.; Basaran, C., Low cycle fatigue life prediction using unified mechanics theory in Ti-6Al-4V alloys, Entropy (2019)
[129] Basaran, C., Introduction to unified mechanics theory with applications (2020), Berlin: Springer International Publishing, Berlin
[130] Basaran, C., Entropy based fatigue, fracture, failure prediction and structural health monitoring, Entropy, 22, 1-4 (2020)
[131] Sosnovskiy, LA; Sherbakov, SS, On the development of mechanothermodynamics as a new branch of Physics, Entropy (2019)
[132] Bendikiene, R.; Bahdanovich, A.; Cesnavicius, R., Tribo-fatigue behavior of austempered ductile iron monica as new structural material for rail-wheel system, Medziagotyra (2020)
[133] Sherbakov, SS; Kuo, C-H, Three-dimensional stress-strain state of a pipe with corrosion damage under complex loading, Tribology—lubricants and lubrication, 139-172 (2011), Rijeka, Croatia: InTech, Rijeka, Croatia
[134] Bahdanovich, A.; Bendikiene, R.; Cesnavicius, R., Research on tensile behaviour of new structural material MoNiCa, Medziagotyra (2019)
[135] Sosnovskii, LA; Komissarov, VV; Shcherbakov, SS, A method of experimental study of friction in a active system, J Frict Wear, 33, 136-145 (2012)
[136] Sherbakov, SS; Zhuravkov, MA, Interaction of several bodies as applied to solving tribo-fatigue problems, Acta Mech, 224, 1541-1553 (2013) · Zbl 1398.74016
[137] Shcherbakov, SS, Modeling of the damaged state by the finite-element method on simultaneous action of contact and noncontact loads, J Eng Phys Thermophys, 85, 472-477 (2012)
[138] Shcherbakov, SS, Spatial stress-strain state of tribofatigue system in roll-shaft contact zone, Strength Mater, 45, 35-43 (2013)
[139] Sosnovskii, LA; Komissarov, VV; Shcherbakov, SS, Comparative experimental study of friction parameters in a tribopair and a force system, J Frict Wear, 33, 203-207 (2012)
[140] Sherbakov, SS, Measurement and real time analysis of local damage in wear-and-fatigue tests, Devices Methods Meas, 10, 207-214 (2019)
[141] Brown, LM, The self-stress of dislocations and the shape of extended nodes, Philos Mag, 10, 441-466 (1964) · Zbl 0125.25701
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.