An holistic view is attempted towards prediction of the effect of residual stresses induced by full-forward extrusion on fatigue life of workpieces during operation. To study the effect of constitutive model on the accuracy of forming simulations, a combined nonlinear isotropic/kinematic hardening model as well as the isotropic hardening part of the same model are calibrated based on five compression-tension-compression uniaxial stress experiments. A full-forward extrusion finite element model is developed adapting both the aforementioned hardening plasticity models and the predicted residual stress states at the surface of the workpiece are compared against that of a corresponding forming experiment. Results show residual stress predictions of remarkable accuracy by the FE-models with the isotropic hardening model. The effect of residual stresses on fatigue life of the workpiece is qualitatively studied by uncoupled multiscale simulations featuring gradient crystal plasticity at the microscale. While the effective (homogenized) macroscale response indicates elastic response during a macroscopically cyclic loading, plasticity accompanying reduction of residual stresses is still present at the microscale within, e.g. grain boundaries.
In this paper we discuss how configurational forces can be computed in an efficient and robust manner when a constitutive continuum model of gradient-enhanced viscoplasticity is adopted, whereby a suitably tailored mixed variational formulation in terms of displacements and microstresses is used. It is demonstrated that such a formulation produces sufficient regularity to overcome numerical difficulties that are notorious for a local constitutive model. In particular, no nodal smoothing of the internal variable fields is required. Moreover, the pathological mesh sensitivity that has been reported in the literature for a standard local model is no longer present. Numerical results in terms of configurational forces are shown for (1) a smooth interface and (2) a discrete edge crack. The corresponding configurational forces are computed for different values of the intrinsic length parameter. It is concluded that the convergence of the computed configurational forces with mesh refinement depends strongly on this parameter value. Moreover, the convergence behavior for the limit situation of rate-independent plasticity is unaffected by the relaxation time parameter.
The forward rod extrusion of ferritic stainless steel X6Cr17 (DIN 1.4016) is here investigated with the objectives to experimentally identify and numerically verify the effect of the lubrication system and die opening angle on residual stresses. Three lubricants – MoS2, soap and polymer – are considered whose tribological properties are characterized via double cup extrusion tests. The effect of material flow is also studied by forming in conical dies featuring three different opening angles. The extrusion experiments revealed a decrease in the near-surface tensile stresses with decreasing friction for all the considered opening angles. An opening angle of 2α = 90° led to the highest tensile residual stresses. Both an increase to 2α = 120° and a decrease to 60° resulted in reduced tensile stresses and even a shift to compressive stresses.Furthermore, a previously developed numerical model of forward rod extrusion is optimized and validated against the experimentally measured residual stresses. The effect of the spatial and temporal discretizations of the model on the predicted residual stresses is investigated. Based on the experimental and numerically verified results, the recommendation to reduce friction in forward rod extrusion is derived as a means to obtain a less detrimental to the lifecycle of extruded parts residual stress state.
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