Bifurcation analysis versus maximum force criteria in formability limit assessment of stretched metal sheets

The present contribution deals with the prediction of diffuse necking in the context of forming and stretching of metal sheets. For this purpose, two approaches are investigated, namely bifurcation and the maximum force principle, with a systematic comparison of their respective ability to predict necking. While the bifurcation approach is of quite general applicability, some restrictions are shown for the application of maximum force conditions. Although the predictions of the two approaches are identical for particular loading paths and constitutive models, they are generally different, which is even the case for elasticity, confirming the distinct nature of the two concepts. Closed-form expressions of the critical stress and strain states are derived for both criteria in elasto-plasticity and rigid-plasticity for a variety of hardening models. The resulting useful formulas in rigidplasticity are shown to also accurately represent the elasto-plastic critical states for small ratios of the hardening modulus with respect to Young's modulus. Finally, the well-known expression of Swift's diffuse necking criterion, whose foundations are attributed in the literature to the maximum force principle, is shown here to originate from the bifurcation approach instead, providing a sound justification for it

An elasto-viscoplastic constitutive model for the rate-dependent behavior of polyvinylidene fluoride

To model the engineering performance of components made of polyvinylidene fluoride (PVDF), the 3D elasto-viscoplastic Eindhoven glassy polymer (EGP) model is extended to describe the rate-dependent behavior of PVDF. Careful analysis of the intrinsic behavior of PVDF revealed that the postyield compressive response shows a strain rate-dependence that evolves with increasing deformation. The extension of the constitutive model captures the deformation-dependent evolution of the activation volume and the rate-factor, which describes the driving stress. Given the significant temperature-dependent behavior, the model has been characterized for different temperatures (23, 55 and 75 °C). The accuracy of the model has been validated by means of tension and creep experiments at these temperatures. The constitutive model is implemented in finite element simulations and the results are compared with the experiments. It is shown that the proposed model allows for an accurate prediction of the short- and long-term rate-dependent behavior of PVDF.</p

Non-local energetics of random heterogeneous lattices

In this paper, we study the mechanics of statistically non-uniform two-phase elastic discrete structures. In particular, following the methodology proposed in (Luciano and Willis, Journal of the Mechanics and Physics of Solids 53, 1505-1522, 2005), energetic bounds and estimates of the Hashin-Shtrikman-Willis type are developed for discrete systems with a heterogeneity distribution quantified by second-order spatial statistics. As illustrated by three numerical case studies, the resulting expressions for the ensemble average of the potential energy are fully explicit, computationally feasible and free of adjustable parameters. Moreover, the comparison with reference Monte-Carlo simulations confirms a notable improvement in accuracy with respect to approaches based solely on the first-order statistics.Comment: 32 pages, 8 figure

Spatially dependent kinetics of helium in tungsten under fusion conditions

Tungsten is the prime candidate material for divertor applications in future nuclear reactors (e.g. ITER and DEMO). In the present work, a spatially dependent cluster dynamics model is developed to investigate and understand the microstructure evolution of tungsten under low energy helium implantation and neutron irradiation varying over bulk length scales of millimetres and irradiation time scales of hours. The diffusion of helium, helium clusters and their trapping at neutron induced defects is simulated along the tungsten monoblock depth. The temperature gradient resulting from a steady state heat load of 10 MWm-2 along the monoblock depth is considered and its influence on the evolution of defects is discussed. The trapping of helium at vacancies and the associated formation of helium-vacancy clusters is found to be pronounced in the sub-surface layers. A significant influence of helium detrapping from grain boundaries and dislocations, along with its resolution from clusters, on the helium diffusion length scales is observed. Additionally, the effect of helium cluster mobility is investigated and overall lower retention in the monoblock bulk is observed through significant release of helium at the surface

Multi‑Scale Modeling of the Thermo‑Mechanical Behavior of Cast Iron

This work presents a multi-scale modelling framework for thermo-mechanical behaviour of Compacted Graphite Iron cast iron. A general thermo-elasto-visco-plastic model is developed to describe the matrix (pearlite) behavior under thermomechanical cyclic loading, for which the parameters are identified from tests on pearlitic steel. The pearlite model takes into account the temperature dependent rate-dependency and kinematic hardening. The importance of properly accounting for the graphite anisotropy is emphasised, for which a numerical procedure for estimating the local anisotropy directions from the graphite particle geometry and experimental observations is proposed. A high quality conforming finite element mesh is generated on a representative volume element using discrete voxelized microstructural data in combination with signed distance functions from the interfaces. For fully constraint thermal cyclic loading conditions with different holding times, the capabilities of the developed multi-scale model are demonstrated at both scales: the macroscale, where the simulation results are in very good agreement with the experimental data, and the microscale, providing the evolution of local fields