Geometrically nonlinear bending of thin-walled shells and plates under creep-damage conditions

Computational Mechanics

Naumenko

1997

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A phenomenological constitutive model for the characterization of creep-damage processes of metals is applied to the numerical analysis of thin-walled shells and plates. The governing equations of the theory of shallow shells are used taking into account geometrical nonlinearities connected with ®nite time-dependent de¯ections by moderate bending. The solutions of the initial-boundary value problem are obtained for thin rectangular plates in order to show the in¯uence of geometrical nonlinearity on results of time-dependent deformation and stress redistribution as well as on estimations of the failure time. IntroductionAnalysis and design of thin-walled structures operating at high temperature conditions require the consideration of time dependent creep behaviour. Creep strains cause signi®cant stress redistributions in the structure and can give rise to creep buckling even by moderate loading. Another type of creep failure is associated with the progressive material softening during tertiary creep stage. For an adequate prediction of long-time strength of thin shells and plates it is necessary to formulate constitutive models giving an accurate approximation of the creep strain rate and the irreversible changes of material properties (such as nucleation and growth of microcavities) as they depend on the stress state. As shown in Altenbach et al. (1986), Betten and Borrmann (1987) stress redistributions in shells of revolution are strongly in¯uenced if the dependence of the creep strain rate on the kind of loading (e.g. tension, compression) is taken into account. Similar effects caused by sensitivity of the damage evolution to tensile and compressive stress states have been established by Bondar and Chrzanowski (1991), Naumenko (1996) by rupture life-time prediction of rectangular plates.On the other hand, suitable shell theories including geometrically nonlinear equations of kinematics and equilibrium have to be used in creep analysis. Geometrically nonlinear equations have been conventionally used in numerical models of creep-buckling analysis of shells, e.g. Miuazaki (1987) and in shell problems associated with large-strain plasticity, e.g. Kra Ètzig and On Äate (1990). In the present paper a geometrically nonlinear model will be formulated in order to predict creep-damage evolution of thin shells and plates.By means of the continuum damage mechanics approach, see Hayhurst (1994), Lemaitre and Chaboche (1990) we introduce the initial-boundary value problem which contains creep-damage material equations with a single scalar damage parameter and governing equations of the shell theory undergoing moderate rotations, e.g. Grigolyuk and Kabanov (1978). The loads are assumed to be suf®ciently small that the instantaneous deformation is linear-elastic and can be determined by use of geometrically linear theory. In order to obtain the time-dependent response of shells ®nite de¯ections caused by small strain creep-damage material behaviour are considered. Numerical solutions of creep problems will be demonstrated ...

“…The calculation concept presented has been used for the analysis of creep bending shallow shells. Results of the numerical analysis are discussed in Altenbach et al (1997).…”

Section: Discussionmentioning

confidence: 99%

Creep bending of thin-walled shells and plates by consideration of finite deflections

Computational Mechanics

Naumenko

1997

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“…Further we include geometrical nonlinear terms for consideration ®nite de¯ection in the sense of the von Ka Ârma Ân plate theory. In Altenbach and Naumenko (1997) and Altenbach et al (1997a) we discussed the governing equations of the plate theory including creep strains and damage. The variational functional in the mixed form can be written as follows iY jY kY l 1Y 2…”

Section: Creep-damage Of Plates In Bendingmentioning

confidence: 99%

“…The solution method for the creep problem of a plate which is similar to the above discussed procedure for a beam is discussed in detail in Altenbach and Naumenko (1997) and Altenbach et al (1997a). On Fig.…”

Section: Creep-damage Of Plates In Bendingmentioning

confidence: 99%

On the accuracy of creep-damage predictions in thinwalled structures using the finite element method

Computational Mechanics

Kolarow²,

Morachkovsky

et al. 2000

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The constitutive model with a single damage parameter describing creep-damage behaviour of metals with respect to the different sensitivity of the damage process due to tension and compression is incorporated into the ANSYS ®nite element code by modifying the user de®ned creep material subroutine. The procedure is veri®ed by comparison with solutions for beams and rectangular plates in bending based on the Ritz method. Various numerical tests show the sensitivity of long-term predictions to the mesh sizes and element types available for the creep analysis of thinwalled structures. IntroductionEngineering structures operating at elevated temperatures such as fossil power plants, chemical plants, reactors, etc. are designed with respect to increased requirements of safety and assurance of long-term reliability. One of the main factors which must be considered in the long-term structural analysis is time-dependent material behaviour coupled with damage evolution (Roche et al., 1992). A powerful tool for the lifetime prediction is the continuum damage mechanics approach which is based on the formulation of constitutive and evolution equations for inelastic strains and material damage. Incorporating these material models into the ®nite element code predictions of time-dependent stress, strain and damage ®elds can be performed by numerical solution of nonlinear initialboundary value problems (e.g. . The ®rst problem arising by creep damage analysis is the formulation of a phenomenological material model that is able to describe the sensitivity of creep strain and damage rate to the stress level, stress state, temperature level, environmental effects, etc. Such a model must be able to extrapolate the experimental creep data usually available from uniaxial short-term creep tests and realised for narrow stress ranges to the in-service loading conditions in the real structure. The second problem can be related to the quality of the ®nite element predictions particularly by analysis of structures with complex shapes.The structural analysis of thinwalled components (pressure vessels, pipes, pipe bends, etc.) can be performed using the mechanical models of plane stress (strain) states or equations of shell theory. In the case of plane stress (strain) problems numerous ®nite element simulations considering creep damage effects has been made because of experimental data available for veri®ca-tion. Examples are discussed by Saanouni et al. Since these examples con®rm the ability of ®nite element simulations to predict stress redistributions and failure times with accuracy enough for engineering applications and can be used as benchmark tests by development of user de®ned material subroutines incorporating damage evolution a little effort has been made for the analysis of transversely loaded thinwalled structures. Numerical results for rupture times of rectangular plates in bending are given by Bodnar and Chrzanowski (1994), Bialkiewicz and Mika (1995) based on in-house ®nite element codes and Altenbach and Naumenko (1997) for re...

“…In addition, the shell theory allows to simplify the general geometrically nonlinear analysis, since the magnitude of the deformation can be estimated by the magnitude of the rotation of the normal to the midsurface, [17]. Since the creep behaviour of metals and alloys is usually characterised by small strain developing with time at moderate stresses, the simpli®ed shell equations (including the geometrically nonlinear terms in the sense of moderate rotations) can be applied, [2]. …”

mentioning

confidence: 99%

On the use of solid- and shell-type finite elements in creep-damage predictions of thinwalled structures

Archive of Applied Mechanics (Ingenieur Archiv)

Kushnevsky

Naumenko

2001

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Solid-and shell-type ®nite elements available for plasticity and creep analysis are applied to the creep-damage prediction of a thinwalled pipe bend under uniform internal pressure. Conventional creep-damage material model with scalar damage parameter is used. Based on the comparative numerical study, performed using solid and shell elements, the applicability frame of the shell concept is discussed. Particularly, if a dependence on the stress state is included in the material model, the cross-section assumptions of the ®rst-order shear deformation theory should be re®ned. The possibilities to modify the through-thickness approximations are demonstrated on the beam equations. The ®rst-order shear-deformation beam theory is discussed in detail. It is shown that if the damage evolution signi®cantly differs for tensile and compressive stresses, the classical parabolic transverse shear-stress distribution and the shear-correction coef®cient have to be modi®ed within time-step simulations.Key words Creep-damage analysis, pipe bend, ®nite element, beam IntroductionThe continuum damage mechanics (CDM) and the ®nite element (FE) method provide basic tools for the stress analysis and the life-time prediction of thinwalled structures exposed to elevated temperatures. Starting from the material science and the continuum mechanics, various models are proposed. They include physically based state variables and consider stressstate dependence, e.g., different sensitivity of the damage evolution to tension or compression stresses as well as damage-induced anisotropy, [27]. Since such models allow for more realistic predictions of the material behaviour at elevated temperatures, the question arises how accurate the available structural models of beams, plates or shells and the corresponding FE implementations represent the time-dependent stress redistributions. With respect to the analysis of thinwalled structures, two possibilities are available. The ®rst one is the use of general three-dimensional equations and solid FEs in the numerical analysis. The second one is the application of shell equations and shell-based FEs, usually of the Reissner±Mindlin type, [18]. The solid concept can be considered as general for structural analysis, particularly for studying damage effects. However, the numerical effort for the approximate solving of threedimensional equations is not comparable with that for the shell theory. In addition, the shell theory allows to simplify the general geometrically nonlinear analysis, since the magnitude of the deformation can be estimated by the magnitude of the rotation of the normal to the midsurface, [17]. Since the creep behaviour of metals and alloys is usually characterised by small strain developing with time at moderate stresses, the simpli®ed shell equations (including the geometrically nonlinear terms in the sense of moderate rotations) can be applied, [2].