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Experimental characterization and mechanical modeling of creep induced rafting in superalloys
(2012)
A constitutive model has been developed for the high temperature mechanical behavior of single crystal superalloys, including rafting and its consequences. The flow stress depends on the γ channel width via the Orowan stress. An evolution equation for channel widening during high temperature straining has been derived and calibrated with measurements. Therein, rafting is assumed to be driven by the relaxation of internal stresses. The model is able to represent the mechanical softening at high stresses consecutive to rafting. The model has been applied to simulate rafting during uniaxial creep in several crystal orientations, in notched specimens as well as in cyclically loaded specimens.
Constitutive modelling of creep degradation due to rafting in single-crystalline Ni-base superalloys
(2009)
A constitutive model for the mechanical behaviour of single-crystalline superalloys at high temperatures has been developed. The model relies on the slip system theory and is able to predict rafting and its influence on plastic flow. The kinetics of rafting are assumed to be driven by the reduction of the internal stresses represented by the macroscopic back-stress. The rafting effect is incorporated in the model through the dependence of the Orowan stress on the channel width. The model has been validated for the alloy CMSX-4 at 950 °C. The rafting part of the model has been calibrated by measurements of the channel widths after several levels of creep strains and for several loads.
The sound numerical prediction of welding-induced thermal stresses, residual stresses, and distortions strongly depends on the accurate description of a welded material’s thermomechanical deformation behaviour. In this work, we provide experimental data on the viscoplastic deformation behaviour of a grade-s960ql steel up to a temperature of 1000 ◦C. In addition, a multi-phase viscoplastic material model is proposed, which accounts for the experimentally observed isothermal deformation behaviour of grade-s960ql steel base and austenitised material, as well as for athermal contributions that originate from solid-state phase transformations. The multi-phase viscoplastic and a classic rateindependent isotropic hardening material model were applied in the numerical simulations of both-ends-fixed bar Satoh tests and a single-pass gas metal arc weld. The influence of material modelling choices on the agreement between numerical simulation and experimental results is discussed, and recommendations for further work are given.
A crystallographic constitutive model is developed, which accounts for both rate-sensitive and rate-insensitive flow. Single-crystal plasticity and viscoplasticity are the limiting cases of the model, so that it properly reflects the material response over a wide temperature range. A non-linear dynamic recovery is included to properly describe ratchetting. We provide a robust integration scheme based on generalization of the return-mapping algorithm and of the procedure for active set search.
The implicit integration and consistent tangent are implemented through the UMAT subroutine in the ABAQUS finite element program. The capability of the model to account for both high and low strain rates is demonstrated in numerical examples. Finally, the stability of integration scheme and quadratic convergence of the global NewtonRaphson equilibrium iterations are demonstrated on the example of a notched bar under tension.
A general concept for the consideration of the influence of strain gradients on elasto-viscoplastic material behaviour at finite deformation is presented that does not need to account for an additional flow rule for the plastic strain gradient. The balance of momentum including the representation of the stresses, the power of work at contact for the formulation of boundary conditions as well as the nonlocal form of the total power of deformation are derived via the dissipation inequality for the investigated nonpolar continuum model of second grade. In addition to the gradient of the elastic strain tensor, energy storage with gradients of different internal variables is considered: gradient of (i) the plastic strain Tensor itself, (ii) an internal strain tensor induced by viscoplastic straining, by which energy due to hardening is stored also with ist gradient, and (iii) scalar internal variables like the accumulated viscoplastic strain or an internal time variable of damage. Finally, for the simulation of the damage behaviour during a strain hold-time period at a crack tip the responses of a ratedependent and a quasi-rate-independent gradient-enhanced damage model are compared in finite element studies.
During aluminium extrusion, the die experience cyclic thermo-mechanical loads that can lead to materials degradation and failure. For a process optimization and a comparison of different hot work tool steels, the finite element method is an appropriate means. Local inelastic strains result from the interaction of the applied temperature and stress loading and can be computed by suitable inelastic constitutive equations. Stress amplitudes and dwell times during extrusion result in creep-fatigue damage. A lifetime consumption model sums increments of a damage variable over time and defines materials failure as the accumulation of the resulting damage variable to a critical value. The procedure for the identification of the material parameters for both the constitutive and the damage model is described in detail, including the material parameters for the description of time-effects, and applied to the hot work tool steel Böhler W300 ISOBLOC (EN 1.2343). The lifetime consumption for two different hot work tool steels is compared on the basis of an example in aluminium extrusion.