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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.
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.
The material and damage behaviour of additively manufactured polyamide 12 (PA12) under dynamic loading was characterized by cyclic tests and microstructure analysis. The results were used to develop a numerical material and damage model. In a recent study, it was shown that the material and damage behaviour of 3D printed PA12 under quasistatic loading is simulated in a realistic way by coupling the
material model by Chaboche and the damage model by Gurson-Tvergaard-Needleman (GTN).
Using microscopy, X-ray refraction, and computed tomography, a porosity of about 5% was evaluated. These results served as a starting point for the present work. For the dynamic load, both the previously used Chaboche model and the GTN model were extended. Furthermore, the temperature was measured during the experiment and the self-heating effect was observed. Therefore, a temperaturedependent material parameters for the simulation were introduced. Considering the results of mechanical experiments, microstructural investigations, and self-heating effects, a good agreement between Experiment and numerical simulation could be achieved.
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.
The essence of dynamic failure is closely linked to the formation of adiabatic shear bands (ASB), which result from the localization of shear strain under high deformation speeds accompanied by a rapid temperature increase. Understanding this phenomenon is crucial in view of safety issues when impacts of fast rotating machine components (i.e. aircraft turbine blades) may occur. Our contribution addresses both the experimental evidence and characterization of ASBs due to high-speed impact tests at the Split HOPKINSON pressure bar (SHPB) setup and the finite element analysis to determine the parameters of the underlying constitutive model, which is closely related to JOHNSON-COOK (JC) material model.
Experimental investigations were performed on notched shear specimens made of the fine -grained structural steel S690QL and the displacements in the regions affected by shear localization were measured with subset-based local Digital Image Correlation (DIC). The displacement fields, obtained in the SHPB tests, were considered as an objective to validate and to identify the constitutive parameters with. The JC model could reasonably reproduce the displacement distribution. In order to overcome the issues with mesh dependency we provide a nonlocal extension based on the implicit gradient model approach.
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.
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.