Axisymmetric Thermo-Elastic-Plastic Problem Under Plane Stress Conditions
Chapter
First Online:
Abstract
Thin annular discs subject to various loading conditions are a class of commonly used structures in mechanical engineering. Particular examples are aircraft structures and reciprocating machinery. The mechanical analysis and design of such discs may be based either on elastic or elastic/plastic solutions. This monograph deals with the latter approach.
References
- 1.Reid L (1997) Incorporating hole cold expansion to meet durability and damage tolerance airworthiness objectives. SAE International, SAE Paper No 972624Google Scholar
- 2.Ghorashi M, Daneshpazhooh M (2001) Limit analysis of variable thickness circular plates. Comput Struct 70:461–468CrossRefGoogle Scholar
- 3.Durban D (1987) An exact solution for the internally pressurized, elastoplastic, strain-hardening, annular plate. Acta Mech 66:111–128CrossRefMATHGoogle Scholar
- 4.Guven U (1998) Elastic-plastic stress distribution in a rotating hyperbolic disk with rigid inclusion. Int J Mech Sci 40:97–109CrossRefGoogle Scholar
- 5.Guven U (1998) Stress distribution in a linear hardening annular disk of variable thickness subjected to external pressure. Int J Mech Sci 40:589–601CrossRefGoogle Scholar
- 6.Guven U, Altay O (2000) Elastic-plastic solid disk with nonuniform heat source subjected to external pressure. Int J Mech Sci 42:831–842CrossRefGoogle Scholar
- 7.Eraslan AN (2002) Inelastic deformations of rotating variable thickness solid disks by Tresca and von Mises criteria. Int J Comput Eng Sci 3:89–101CrossRefGoogle Scholar
- 8.Eraslan AN (2003) Elastoplastic deformations of rotating parabolic solid disks using Tresca’s yield criterion. Eur J Mech A Solids 22:861–874CrossRefMATHGoogle Scholar
- 9.Eraslan AN (2003) Elastic-plastic deformations of rotating variable thickness annular disks with free, pressurized and radially constrained boundary conditions. Int J Mech Sci 45:643–667Google Scholar
- 10.Eraslan AN, Orcan Y (2002) On the rotating elastic-plastic solid disks of variable thickness having concave profiles. Int J Mech Sci 44:1445–1466CrossRefMATHGoogle Scholar
- 11.Arslan E, Mack W, Eraslan AN (2008) Effect of a temperature cycle on a rotating elastic-plastic shaft. Acta Mech 195:129–140CrossRefMATHGoogle Scholar
- 12.You LH, Zhang JJ (1999) Elastic-plastic stresses in a rotating solid disk. Int J Mech Sci 41:269–282Google Scholar
- 13.You LH, Tang YY, Zhang JJ, Zheng CY (2000) Numerical analysis of elastic-plastic rotating disks with arbitrary variable thickness and density. Int J Solids Struct 37:7809–7820CrossRefMATHGoogle Scholar
- 14.You XY, You LH, Zhang JJ (2004) A simple and efficient numerical method for determination of deformations and stresses in rotating solid shafts with non-linear strain-hardening. Commun Numer Methods Eng 20:689–697CrossRefMATHGoogle Scholar
- 15.Eraslan AN, Argeso A (2002) Limit angular velocities of variable thickness rotating disks. Int J Solids Struct 39:3109–3130CrossRefMATHGoogle Scholar
- 16.Debski R, Zyczkowski M (2002) On decohesive carrying capacity of variable-thickness annular perfectly plastic disks. Z Angew Math Mech 82:655–669CrossRefMATHMathSciNetGoogle Scholar
- 17.Vivio F, Vullo L (2010) Elastic-plastic analysis of rotating disks having non-linearly variable thickness: residual stresses by overspeeding and service stress state reduction. Ann Solid Struct Mech 1:87–102CrossRefGoogle Scholar
- 18.Budiansky B, Mangasarian DL (1960) Plastic stress concentration at a circular hole in an infinite sheet subjected to equal biaxial tension. Trans ASME J Appl Mech 27:59–64CrossRefMATHMathSciNetGoogle Scholar
- 19.Papanastasiou P, Durban D (1997) Elastoplastic analysis of cylindrical cavity problems in geomaterials. Int J Numer Anal Mech Geomech 21:133–149CrossRefMATHGoogle Scholar
- 20.Durban D, Papanastasiou P (1997) Cylindrical cavity expansion and contraction in pressure sensitive geomaterials. Acta Mech 122:99–122Google Scholar
- 21.Bradford IDR, Durban D (1998) Stress and deformation fields around a cylindrical cavity embedded in a pressure-sensitive elastoplastic medium. Trans ASME J Appl Mech 65:374–379Google Scholar
- 22.Chen PCT (1973) A comparison of flow and deformation theories in a radially stressed annular plate. Trans ASME J Appl Mech 40:283–287CrossRefGoogle Scholar
- 23.Roberts SM, Hall FR, Bael AV, Hartley P, Pillinger I, Sturgess CEN, Houtte PV, Aernoudt E (1992) Benchmark tests for 3-D, elasto-plastic, finite-element codes for the modeling of metal forming processes. J Mater Process Technol 34:61–68CrossRefGoogle Scholar
- 24.Helsing J, Jonsson A (2002) On the accuracy of benchmark tables and graphical results in the applied mechanics literature. Trans ASME J Appl Mech 69:88–90CrossRefMATHGoogle Scholar
- 25.Ball DL (1995) Elastic-plastic stress analysis of cold expanded fastener holes. Fat Fract Eng Mater Struct 18:47–63CrossRefGoogle Scholar
- 26.Hill R (1950) The mathematical theory of plasticity. Clarendon Press, OxfordMATHGoogle Scholar
- 27.Bland DR (1956) Elastoplastic thick-walled tubes of work-hardening material subject to internal and external pressures and to temperature gradients. J Mech Phys Solids 4:209–229CrossRefMATHMathSciNetGoogle Scholar
- 28.Rees DWA (1990) Autofrettage theory and fatigue life of open-ended cylinders. J Strain Anal Eng Des 25:109–121CrossRefGoogle Scholar
- 29.Luxmoore AR, Light MF, Evans WT (1977) A comparison of finite-element and experimental studies on plane stress crack geometries. J Strain Anal Eng Des 12:208–216CrossRefGoogle Scholar
- 30.Simo JC, Taylor RL (1986) A return mapping algorithm for plane stress elastoplasticity. Int J Numer Meth Eng 22:649–670CrossRefMATHMathSciNetGoogle Scholar
- 31.Jetteur P (1986) Implicit integration algorithm for elastoplasticity in plane stress analysis. Eng Comput 3:251–253CrossRefGoogle Scholar
- 32.Kleiber M, Kowalczyk P (1996) Sensitivity analysis in plane stress elasto-plasticity and elasto-viscoplasticity. Comput Meth Appl Mech Eng 137:395–409CrossRefMATHGoogle Scholar
- 33.Valoroso N, Rosati L (2009) Consistent derivation of the constitutive algorithm for plane stress isotropic plasticity. Part 1: Theoretical formulation. Int J Solids Struct 46:74–91CrossRefMATHGoogle Scholar
- 34.Triantafyllou SP, Koumousis VK (2012) An hysteretic quadrilateral plane stress element. Arch Appl Mech 82:1675–1687CrossRefMATHGoogle Scholar
- 35.Rees DWA (2006) Basic engineering plasticity. Elsevier, AmsterdamGoogle Scholar
- 36.Yoshida S, Oguchi A, Nobuki M (1971) Influence of high hydrostatic pressure on the flow stress of copper polycrystals. Trans Jpn Inst Met 12:238–242CrossRefGoogle Scholar
- 37.Spitzig WA, Sober RJ, Richmond O (1976) The effect of hydrostatic pressure on the deformation behavior of maraging and HY-80 steels and its implications for plasticity theory. Metall Trans 7A:1703–1710CrossRefGoogle Scholar
- 38.Spitzig WA (1979) Effect of hydrostatic pressure on plastic-flow properties of iron single crystals. Acta Metall 27:523–534CrossRefGoogle Scholar
- 39.Kao AS, Kuhn HA, Spitzig WA, Richmond O (1990) Influence of superimposed hydrostatic pressure on bending fracture and formability of a low carbon steel containing globular sulfides. Trans ASME J Eng Mater Technol 112(1):26–30CrossRefGoogle Scholar
- 40.Wilson CD (2002) A critical reexamination of classical metal plasticity. Trans ASME J Appl Mech 69:63–68CrossRefMATHGoogle Scholar
- 41.Liu PS (2006) Mechanical behaviors of porous metals under biaxial tensile loads. Mater Sci Eng 422A:176–183Google Scholar
- 42.Drucker DC, Prager W (1952) Soil mechanics and plastic analysis for limit design. Q Appl Math 10:157–165MATHMathSciNetGoogle Scholar
- 43.Alexandrov S, Alexandrova N (2001) Thermal effects on the development of plastic zones in thin axisymmetric plates. J Strain Anal Eng Des 36:169–176CrossRefGoogle Scholar
- 44.Alexandrov S, Jeng Y-R, Lomakin E (2011) Effect of pressure-dependency of the yield criterion on the development of plastic zones and the distribution of residual stresses in thin annular disks. Trans ASME J Appl Mech 78:031012Google Scholar
- 45.Alexandrov SE, Lomakin EV, Jeng Y-R (2012) Solution of the thermoelasticplastic problem for a thin disk of plastically compressible material subject to thermal loading. Dokl Phys 57:136–139CrossRefGoogle Scholar
- 46.Alexandrov S, Jeng Y-R, Lyamina E (2012) Influence of pressure-dependency of the yield criterion and temperature on residual stresses and strains in a thin disk. Struct Eng Mech 44:289–303CrossRefGoogle Scholar
- 47.Pirumov A, Alexandrov S, Jeng Y-R (2013) Enlargement of a circular hole in a disc of plastically compressible material. Acta Mech 224:2965–2976CrossRefMATHMathSciNetGoogle Scholar
- 48.Alexandrov S, Jeng Y-R, Lomakin E (2014) An exact semi-analytic solution for residual stresses and strains within a thin hollow disc of pressure-sensitive material subject to thermal loading. Meccanica 49:775–794CrossRefMATHMathSciNetGoogle Scholar
- 49.Alexandrov S, Lyamina E, Jeng Y-R (2012) Design of an annular disc subject to thermomechanical loading. Math Prob Eng 2012, Article ID 709178Google Scholar
- 50.Wang Y-C, Alexandrov S, Jeng Y-R (2013) Effects of thickness variations on the thermal elastoplastic behavior of annular discs. Struct Eng Mech 47:839–856CrossRefGoogle Scholar
- 51.Alexandrov S, Lyamina E, Jeng Y-R (2013) Plastic collapse of a thin annular disk subject to thermomechanical loading. Trans ASME J Appl Mech 80:051006Google Scholar
- 52.Alexandrov S, Wang Y-C, Aizikovich S (2014) Effect of temperature-dependent mechanical properties on plastic collapse of thin discs. Proc IMechE Part C: J Mech Eng Sci 228:2483–2487CrossRefGoogle Scholar
- 53.Alexandrov S, Wang Y-C, Jeng Y-R (2014) Elastic-plastic stresses and strains in thin discs with temperature-dependent properties subject to thermal loading. J Therm Stresses 37:488–505CrossRefGoogle Scholar
- 54.Alexandrov S, Pham C (2014) Plastic collapse mechanisms in thin disks subject to thermo-mechanical loading. Asia Pacific J Comput Eng 1:7Google Scholar
- 55.Alexandrov S, Mustafa Y (2014) A qualitative comparison of flow rules of pressure-dependent plasticity under plane stress conditions. J Eng Math 89:177–191CrossRefMathSciNetGoogle Scholar
- 56.Alexandrova N, Alexandrov S (2004) Elastic-plastic stress distribution in a plastically anisotropic rotating disk. Trans ASME J Appl Mech 71:427–429CrossRefMATHGoogle Scholar
Copyright information
© The Author(s) 2015