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

Abstract

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].

Analysis of Inelastic Behavior for High Temperature Materials and Structures

“…This result agrees well with the data presented in May et al (1994), where the creep failure has been detected at the same position. The processes of time dependent deformation, stress relaxation and redistribution have been illustrated in the literature based on different examples for beams, plates and shells Altenbach et al 2000bAltenbach et al , 2001Altenbach et al 2004). One feature of the example considered here is that the final creep stage is not only the result of the local material deterioration but is additionally governed by the flattening (ovalisation) of the pipe bend cross section.…”

“…Results of studies on elastic and elasto-plastic deformation and stability are reviewed in Bielski and Skrzypek (1989); Libai and Simmonds (1998). Creep and damage processes in curved tubes were discussed in Altenbach et al (2001); Boyle and Spence (1983); Hyde et al (2002). These studies were concerned with the analysis of a single pipe bend subjected to special loading conditions, i.e.…”

On the Time-Dependent Behavior of FGM Plates

“…Such a model can be accepted in the case of plates with constant or slow changing thickness. For the linear variant the identification of the elastic and viscoelastic stiffness tensors considering changing properties was proposed in [18,19,20]. Using the techniques presented in these articles the static boundary-value problems for FGM plates made of metal foams which behave elastically are solved in [21].…”

A phenomenological model for anisotropic creep in a multipass weld metal

“…One possibility for studying the creep behavior in structures is the use of continuum damage mechanics, e.g., [3,4,16]. The application of this approach to welded joints is discussed in [15,17,21], for example.…”

“…4) where a and n are material constants. For the longitudinal direction from (4.1) and (4.4) followṡ ε cr L ≡ m m m · · ·ε ε ε cr m m m = a L σ n 0 , a L…”