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Damage evolution in an expanding/contracting hollow sphere at large strains. (English) Zbl 1272.74582

Summary: A generalization of one of the classical problems of plasticity theory, expansion/contraction of a hollow sphere, is proposed assuming that the conventional constitutive equations for rigid plastic, hardening material are supplemented with an arbitrary ductile damage evolution law. No restriction is imposed on the hardening law in the analytic part of the solution. The initial/boundary value problem is reduced to two equations in characteristic coordinates. A numerical scheme to solve these equations is proposed. An illustrative example is given.

MSC:

74R20 Anelastic fracture and damage
74S20 Finite difference methods applied to problems in solid mechanics
74C15 Large-strain, rate-independent theories of plasticity (including nonlinear plasticity)
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[1] Hill R.: The Mathematical Theory of Plasticity. Clarendon Press, Oxford (1950) · Zbl 0041.10802
[2] Kachanov L.M.: Introduction to Continuum Damage Mechanics. Kluwer, Dordrecht (1986) · Zbl 0596.73091
[3] Atkins A.G.: Fracture in forming. J. Mater. Process. Technol. 56, 609–618 (1996) · doi:10.1016/0924-0136(95)01875-1
[4] Lemaitre J.: A continuous damage mechanics model for ductile fracture. Trans. ASME J. Eng. Mater. Technol. 107, 83–89 (1985) · doi:10.1115/1.3225775
[5] Chandrakanth S., Pandey P.C.: A new ductile damage evolution model. Int. J. Fract. 60, R73–R76 (1993)
[6] Chica, E.L., Iban, A.L., Teran, J.M.G.: Influence of ductile damage evolution on the collapse load of frames. Trans. ASME J. Appl. Mech. 77, Paper 034502 (2010).
[7] Gurson A.L.: Continuum theory of ductile rupture by void nucleation and growth: Part 1 – Yield criteria and flow rules for porous ductile media. Trans. ASME. J. Eng. Mater. Technol. 99, 2–15 (1977) · doi:10.1115/1.3443401
[8] Druyanov B.: Technological Mechanics of Porous Bodies. Clarendon Press, New York (1993) · Zbl 0784.73003
[9] Hambli R.: Comparison between Lemaitre and Gurson damage models in crack growth simulation during blanking process. Int. J. Mech. Sci. 43, 2769–2790 (2001) · Zbl 1082.74543 · doi:10.1016/S0020-7403(01)00070-4
[10] Behrens A., Just H.: Verification of the damage model of effective stresses in cold and warm forging operations by experimental testing and FE simulations. J. Mater. Process. Technol. 125–126, 295–301 (2002) · doi:10.1016/S0924-0136(02)00404-1
[11] Hartley P., Hall F.R., Chiou J.M., Pillinger I.: Elastic-plastic finite-element modelling of metal forming with damage evolution. In: Predeleanu, M., Gilormini, P. (eds) Advanced Methods in Materials Processing Defects, pp. 135–142. Elsevier, Amsterdam (1977)
[12] Roberts S.M., Hall F.R., Bael A.V., Hartley P., Pillinger I., Sturgess C.E.N., Houtte P.V., Aernoudt E.: Benchmark tests for 3-D, elasto-plastic, finite-element codes for the modeling of metal forming processes. J. Mater. Process. Technol. 34, 61–68 (1992) · doi:10.1016/0924-0136(92)90090-F
[13] Helsing J., Jonsson A.: On the accuracy of benchmark tables and graphical results in the applied mechanics literature. Trans. ASME J. Appl. Mech. 69, 88–90 (2002) · Zbl 1110.74478 · doi:10.1115/1.1427691
[14] Tomkins B., Atkins A.G.: Crack initiation in expanded fully plastic thick-walled rings and rotating discs. Int. J. Mech. Sci. 23, 395–412 (1981) · doi:10.1016/0020-7403(81)90078-3
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