Skip to main content Accessibility help
×
Home
  • Print publication year: 2021
  • Online publication date: May 2021

3 - Continuum Plasticity

Summary

The handling of stress and strain during elastic deformation is covered in the preceding chapter. However, the situation becomes more complex after the onset of plastic deformation. Whereas elastic straining essentially occurs just via changes in interatomic spacing, the mechanisms involved in plastic (permanent) deformation are far from simple. These mechanisms are described in some detail in the next chapter. The current chapter is based, as is the previous one, on treating the material as a homogeneous continuum, albeit one that may be anisotropic (i.e. exhibit different responses in different directions). Much of the coverage concerns conditions for the onset of plasticity (often described as “yielding”) and subsequent rises in applied stress that are required for further plastic straining (“work hardening”). Two yielding criteria are in common use and these are described. The work-hardening behavior is often quantified using empirical constitutive laws and two of the most prominent of these are also outlined. This chapter also covers the representation of temporal effects – both the changes in stress–strain characteristics that occur when high strain rates are imposed and the progressive straining that can take place over long periods under constant stress, which is often termed “creep.”

Related content

Powered by UNSILO
1.Hosford, WF, Generalized isotropic yield criterion. Journal of Applied Mechanics, 1972. 39(2): 607609.
2.Yang, WH, A generalized Von Mises criterion for yield and fracture. Journal of Applied Mechanics: Transactions of the ASME, 1980. 47(2): 297300.
3.Goo, E and Park, KT, Application of the Von Mises criterion to deformation twinning. Scripta Metallurgica, 1989. 23(7): 10531056.
4.Capsoni, A and Corradi, L, Variational formulations for the plane strain elastic–plastic problem for materials governed by the Von Mises criterion. International Journal of Plasticity, 1996. 12(4): 547560.
5.Ponter, ARS and Engelhardt, M, Shakedown limits for a general yield condition: implementation and application for a Von Mises yield condition. European Journal of Mechanics A: Solids, 2000. 19(3): 423445.
6.Lagioia, R and Panteghini, A, On the existence of a unique class of yield and failure criteria comprising Tresca, Von Mises, Drucker–Prager, Mohr–Coulomb, Galileo–Rankine, Matsuoka–Nakai and Lade–Duncan. Proceedings of the Royal Society A: Mathematical Physical and Engineering Sciences, 2016. 472(2185).
7.Hollomon, JH, Tensile deformation. Transactions of the American Institute of Mining and Metallurgical Engineers, 1945. 162: 268290.
8.Voce, E, The relationship between stress and strain for homogeneous deformation. Journal of the Institute of Metals, 1948. 74(11): 537562.
9.Zhao, YH, Guo, YZ, Wei, Q, Topping, TD, Dangelewicz, AM, Zhu, YT, Langdon, TG and Lavernia, EJ, Influence of specimen dimensions and strain measurement methods on tensile stress-strain curves. Materials Science and Engineering A: Structural Materials Properties Microstructure and Processing, 2009. 525(1–2): 6877.
10.Arrayago, I, Real, E and Gardner, L, Description of stress–strain curves for stainless steel alloys. Materials & Design, 2015. 87: 540552.
11.Umbrello, D, M’Saoubi, R and Outeiro, JC, The influence of Johnson–Cook material constants on finite element simulation of machining of AISI 316L steel. International Journal of Machine Tools & Manufacture, 2007. 47(3–4): 462470.
12.Johnson, GR and Cook, WH, A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures, in Proceedings of the 7th International Symposium on Ballistics, 1983. 21: 541547.
13.Molinari, A and Ravichandran, G, Fundamental structure of steady plastic shock waves in metals. Journal of Applied Physics, 2004. 95(4): 17181732.
14.Rule, WK and Jones, SE, A revised form for the Johnson–Cook strength model. International Journal of Impact Engineering, 1998. 21(8): 609624.
15.Lin, YC, Chen, XM and Liu, G, A modified Johnson–Cook model for tensile behaviors of typical high-strength alloy steel. Materials Science and Engineering A: Structural Materials Properties Microstructure and Processing, 2010. 527(26): 69806986.
16.He, A, Xie, GL, Zhang, HL and Wang, XT, A comparative study on Johnson–Cook, modified Johnson–Cook and Arrhenius-type constitutive models to predict the high temperature flow stress in 20CrMo alloy steel. Materials & Design, 2013. 52: 677685.
17.Manes, A, Peroni, L, Scapin, M and Giglio, M, Analysis of strain rate behavior of an A1 6061 T6 alloy, in 11th International Conference on the Mechanical Behavior of Materials, Guagliano, M and Vergani, L, eds. Amsterdam: Elsevier, 2011, pp. 34773482.
18.Roberto-Pereira, FF, Campbell, JE, Dean, J and Clyne, TW, Extraction of superelasticity parameter values from instrumented indentation via iterative FEM modelling. Mechanics of Materials, 2019. 134: 143152.
19.Clyne, TW and Hull, D, An Introduction to Composite Materials. 3rd ed. Cambridge: Cambridge University Press, 2019.
20.Meguid, SA, Shagal, G, Stranart, JC and Daly, J, Three-dimensional dynamic finite element analysis of shot-peening induced residual stresses. Finite Elements in Analysis and Design, 1999. 31(3): 179191.
21.Hong, T, Ooi, JY and Shaw, B, A numerical simulation to relate the shot peening parameters to the induced residual stresses. Engineering Failure Analysis, 2008. 15(8): 10971110.
22.You, C, Achintha, M, Soady, KA, Smyth, N, Fitzpatrick, ME and Reed, PAS, Low cycle fatigue life prediction in shot-peened components of different geometries, part I: residual stress relaxation. Fatigue & Fracture of Engineering Materials & Structures, 2017. 40(5): 761775.
23.Guan, J, Wang, LQ, Mao, YZ, Shi, XJ, Ma, XX and Hu, B, A continuum damage mechanics based approach to damage evolution of M50 bearing steel considering residual stress induced by shot peening. Tribology International, 2018. 126: 218228.
24.Burley, M, Campbell, JE, Dean, J and Clyne, TW, Johnson–Cook parameter evaluation from ballistic impact data via iterative FEM modelling. International Journal of Impact Engineering, 2018. 112: 180192.