By Pierre-Antoine Bois and Agnes Kubicki

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Rocks, Paris August 1999, p. 792-794; II. Elastoviscoplasticity with aging in aluminium alloys G. Cailletaud***, C. Depoid*, D. Massinon**, E. fr Abstract: After two decades of intense activity on constitutive equations and integration algorithms in the research laboratories, news methods are now available for engineers who need numerical tools for the design of critical components working at high temperature. Due to the increase of computer power, this approach (computation of the actual stress-strain state, then creep–fatigue damage modeling) should progressively replace the classical design method, based on elastic computations followed by plastic corrections, and reduce the number of prototypes, thus the duration of the development.

A better description of the triple point zone may be possible with more elaborate models (non linear elasticity, second gradient theory of fluid/solid interaction). But it is difficult to know a priori what kind of model to use for a better modeling of specific quantities encountered in the coupled systems fluid-solid. 1 The moving triple point A more elaborate model of the triple point has been provided in [Seppecher, 1989] where the second gradient theory is used. The theory introduces a third order stress tensor s, symmetric in its first two indices, generalizing the power of internal forces in a fluid domain as follows By relaxing the incompressibility condition, he succeeded in analysing the structure of the density field in the vicinity of the stationary triple point.

The fluid is separated from the crack tip by a lag (a vacuum), with the surface tension the contact angle The boundary condition at the section AA’ is given by a parabolic profile velocity, with a vanishing total flow rate and the velocity at the wall equal to –V. The equations of the fluid-solid system are summarized below: • Navier-Stokes equations : 71 (where is the kinematic viscosity, p the pressure, the constant density) • Capillary force: • In-flow velocity (2h is the crack opening at A’A) • Boundary conditions at the wall: • Parabolic crack profile: • Global equilibrium equation : Equation (11) expresses the global relation between the stress-intensity factor in the symmetric mode I, the applied loads on the cracked body and the pressure p on the crack, without the point force at FSV.