Keywords: shock waves, shell theory, viscoplasticity, material damage.

In recent years a rapid development of innovative materials for structural components at high temperatures can be observed. This is due to the fact that in many fields of modern technology challenging problems of thermally and mechanically loaded structures arise in the high temperature regime. Examples include novel material solutions for combustion chambers, steam turbine components and gas turbine blades, elements of aircraft fuselages, and heat exchangers for solar power stations, among many others. Many of these structural components are exposed to dynamic, impulsive loading conditions. In this context the transient analysis of structures accounting for the material and structural non-linear effects is of outmost importance.

Numerical simulation of the inelastic response of structures to impulsive loading has been performed in literature based on a large variety of assumptions concerning the structural and material behaviour. As to the structural hypotheses, the theories adopted range from the linear bending theory to non-linear membrane theory. Likewise, the material models adopted for the simulation of the inelastic material behaviour range from rigid-perfectly plastic theory to elastic-plastic models including hardening and strain rate effects. Very different approaches can be also observed concerning the prediction of yield initiation. For a detailed review of the literature we refer to our papers [5,6]. In the present paper the geometrically non-linear first-order shear deformation theory of layered shells given by Schmidt and Reddy [4] is adopted. The kinematical hypothesis accounts for transverse shear deformations, rotary inertia and structural non-linearity due to large deflections and large amplitude vibrations, respectively. The material non-linearity is taken into consideration by means of constitutive equations that account for elastic-plastic material, isotropic and kinematic hardening, and strain rate dependent behaviour in the framework of the Chaboche model [1]. The evolution of the material characteristics during impulsive, shock-type loading of structures is traced in the framework of a layered shell model. The transient response is simulated by a structural dynamics FE code described in our paper [5] using the isoparametric Lagrangian nine node shell finite element with selective reduced integration and the central difference method for the time integration of both the constitutive equations and the equations of motion, respectively. In order to verify the accuracy of the modelling technique, experiments are performed on conventional thin clamped circular aluminium and steel plates in a shock tube at room temperature. A very good correlation between the numerically simulated and experimentally observed inelastic dynamic response is achieved for various loading histories and plate diameters.

Uni-axial tension tests for the nickel based superalloy DS CM 186 at 1000^oC reported in [2] are used as a basis for the identification of the material parameters required by the Chaboche viscoplastic model. Finite element simulations are performed subjecting plates made out of this material to impulsive distributed pressure loading with different time histories. In these simulations the focus is on the detailed analysis of the evolution of deflections, bending moments, membrane forces, and equivalent plastic strain rates. The results reveal the complexity of the dynamic deformation under impulsive loading, which consists in an interaction of flexural waves travelling at different speed with the developing membrane and transverse shear forces. Consequently, the evolution of the material characteristics is very involved as can be seen by the time history of the equivalent plastic strain rates. The results of the simulations show significant differences of the structural and material response of DS CM 186 plates at elevated temperatures, if compared to the response of conventional steel and aluminium plates at room temperature.

1

J.L. Chaboche, "Constitutive equations for cyclic plasticity and cyclic viscoplasticity", Int. J. of Plast., 5, 247-302, 1989. doi:10.1016/0749-6419(89)90015-6

2

J.J. Klabbers-Heimann, "Anwendungsgrenzen von modernen Nickelbasis - Superlegierungen in effusionsgekühlten Bauteilen zukünftiger Gasturbinen", PhD Thesis, RWTH Aachen University, 2002.

3

J. Lemaitre, J.L. Chaboche, "Mechanics of Solid Materials", Mechanics of Solid Materials, Cambridge University Press, 1994.

4

R. Schmidt, J.N. Reddy, "A refined small strain moderate rotation theory of elastic anisotropic shells", ASME J. Appl. Mech., 55, 611-617, 1988.

5

M. Stoffel, R. Schmidt, D. Weichert, "Shock wave-loaded plates", Int. J. Solids Structures, 38, 7659-7680, 2001. doi:10.1016/S0020-7683(01)00038-5

6

M. Stoffel, "Evolution of plastic zones in dynamically loaded plates using different elastic-viscoplastic laws", Int. J. Solids Structures, 41, 6813-6830, 2004. doi:10.1016/j.ijsolstr.2004.05.060

7

A.J. Wang, "The permanent deflection of a plastic plate under blast loading", J. Appl. Mech., 22, 375-376, 1955.

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