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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 hot extrusion of copper alloys, extrusion tools have to withstand cyclic thermal and mechanical loads. To enhance the service life of the tools, materials with high temperature strength are designed as well as an optimised process control is performed. To characterise the tool damage evolution during service and to improve process guiding, modelling and simulation are appropriate means. The extrusion process of copper billets at three different temperatures was simulated by an FE-program to obtain the temporal boundary conditions, i.e. stress and temperature distributions at the interface billet-liner. Those boundary conditions were used to simulate the elastic–viscoplastic behaviour of the tool steel Böhler W750 in service by means of Abaqus Standard v.6.8-3 software in conjunction with Z-Mat package. A lifetime rule was added in order to compute the lifetime consumption and the cycles to failure.
The uniaxial, torsional and axial-torsional thermomechanical fatigue (TMF) behavior of the near-γ TiAl-alloy TNB-V5 was investigated. TMF tests were performed at 400-800 °C with mechanical strain amplitudes ranging from 0.15% to 0.7%. The tests were conducted thermomechanically in-phase (IP) and out-of-phase (OP).
For the same lifetimes, uniaxial IP tests required the highest strain amplitudes, while OP test conditions were most damaging and needed the lowest strain amplitudes. The Mises equivalent mechanical strain amplitudes of pure torsional tests were found in between uniaxial in-phase and out-of-phase tests for the same lifetimes. The non-proportional multiaxial out-of-phase test showed a lower lifetime at the same equivalent mechanical strain amplitude compared to the other types of tests.
The microstructure has been characterized applying electron microscopy and microstructural parameters such as fraction of twinned grains, grain size, lamellar distance and dislocation density have been quantified.
A material family to replace the current superalloys in aeronautical gas turbine engines is
considered to be that of gamma Titanium Aluminide (γ-TiAl) alloys. Structural components in
aeronautical gas turbine engines typically experience large variations in temperatures and multiaxial
states of stress under non-isothermal conditions. The uniaxial, torsional and bi-axial thermomechanical
fatigue (TMF) behaviour of this γ-TiAl alloy have been examined at 400 800°C with
strain amplitudes from 0.15% to 0.7%. The tests were conducted at both in-phase (IP) and out-ofphase
(OP). The effects of TMF on the microstructure were also investigated. For the same
equivalent mechanical strain amplitude uniaxial IP tests showed significantly longer lifetimes than
pure torsional TMF tests. The non-proportional multiaxial OP test showed the lowest lifetimes at
the same equivalent mechanical strain amplitude compared to the other types of tests.
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.
During hot extrusion of aluminium alloys, extrusion dies experience cyclic temperature changes as well as multiaxial loadings. To improve the service life of the dies, cleaner and high hot strength materials are designed as well as an optimised process control is performed. For the improvement of the process guiding and a comparison of lifetime behaviour of different hot work tool steels, modelling and simulation are appropriate means. The extrusion process has been simulated using the FE-program Deform to find the stress and temperature history at the inner diameter of the liner, i.e. the boundary conditions for the subsequent cyclic simulation of the container during service. Inelastic constitutive equations have been implemented into Abaqus Standard to describe strain hardening and time recovery effects. They include the Norton viscoplastic flow rule, thermo-mechanical isotropic hardening and two non-linear kinematic hardening laws. A damage-rate model predicts failure and thus the lifetime of the container. The procedure for the identification of material parameters for both the constitutive and the damage model is described in detail for the hot work tool steel Böhler W400 VMR (EN 1.2343).
A hierarchy of higher order continua is presented that introduces additional degrees of freedom accounting for volume changes, rotation and straining of an underlying microstructure. An increase in the number of degrees of freedom represents a refinement of the material description. In addition to available nonlinear Cosserat and micromorphic theories, general formulations of elastoviscoplastic behaviour are proposed for microdilatation and microstretch continua. A microstrain theory is introduced that is based on six additional degrees of freedom describing the pure straining of the microstructural element. In each case, balance equations and boundary conditions are derived, decompositions of the finite strain measures into elastic and plastic parts are provided. The formulation of finite deformation elastoviscoplastic constitutive equations relies on the introduction of the free energy and dissipation potentials, thus complying with requirements of continuum thermodynamics. Some guidelines for the selection of a suitable higher order model for a given material close the discussion.
This work deals with the formulation of a three-dimensional crystallographic time-incremental lifetime rule for face-centered cubic (fcc) single crystals used for gas-turbine blade applications. The damage contribution rate of each slip system to the total damage is governed by the current values of the resolved shear stress and the slip rate on the corresponding slip system. The damage rule is combined with a crystallographic viscoplastic deformation model. For the nickel-base single-crystal superalloy CMSX4 at 950 °C, various strain- and stress-controlled uniaxial cyclic tests with and without hold-times can be described for different crystal orientations by one set of material parameters. For verification, simulation results for a single-crystal specimen with a notch have been compared with corresponding experimental results. The predicted lifetime is within the factor of two of the measured one.