Francisco M. Andrade Pires

Prediction of Forming Limit Diagrams for Materials with HCP Structure

The forming limit diagram (FLD) is an important tool to be used when characterizing the formability of metallic sheets used in metal forming processes. Experimental measurement and determination of the FLD is time-consuming and therefore the analytical prediction based on theory of plasticity and instability criteria allows a direct and efficient methodology to obtain critical values at different loading paths, thus carrying significant practical importance. However, the accuracy of the plastic instability prediction is strongly dependent on the choice of the material constitutive model [1–3]. Particularly for materials with hexagonal close packed (HCP) crystallographic structure, they have a very limited number of active slip systems at room temperature and demonstrate a strong asymmetry between yielding in tension and compression [4, 5]. Not only the magnitude of the yield locus changes, but also the shape of the yield surface is evolving during the plastic deformation [4]. Conventional phenomenological constitutive models of plasticity fail to capture this unconventional mechanical behavior [4, 6]. Cazacu and Plunkett [6] have proposed generic yield criteria, by using the transformed principal stress, to account for the initial plastic anisotropy and strength differential (SD) effect simultaneously. In this contribution, a generic FLD MATLAB script was developed based on Marciniak–Kuczynski analytical theory and applied to predict the localized necking. The influence of asymmetrical effect on the FLD was evaluated. Several yield functions such as von Mises, Hill, Barlat89, and Cazacu06 were incorporated into analysis. The paper also presents and discusses the influence of different hardening laws on the formability of materials with HCP crystal structures. The findings indicate that the plastic instability theory coupled with Cazacu model can adequately predict the onset of localized necking for HCP materials under different strain paths.

Constitutive modelling of mechanically induced martensitic transformations: Prediction of transformation surfaces

Purpose The purpose of this work is to apply a recently proposed constitutive model for mechanically induced martensitic transformations to the prediction of transformation loci. Additionally, this study aims to elucidate if a stress-assisted criterion can account for transformations in the so-called strain-induced regime. Design/methodology/approach The model is derived by generalising the stress-based criterion of Patel and Cohen (1953), relying on lattice information obtained using the Phenomenological Theory of Martensite Crystallography. Transformation multipliers (cf. plastic multipliers) are introduced, from which the martensite volume fraction evolution ensues. The associated transformation functions provide a variant selection mechanism. Austenite plasticity follows a classical single crystal formulation, to account for transformations in the strain-induced regime. The resulting model is incorporated into a fully implicit RVE-based computational homogenisation finite element code. Findings Results show good agreement with experimental data for a meta-stable austenitic stainless steel. In particular, the transformation locus is well reproduced, even in a material with considerable slip plasticity at the martensite onset, corroborating the hypothesis that an energy-based criterion can account for transformations in both stress-assisted and strain-induced regimes. Originality/value A recently developed constitutive model for mechanically induced martensitic transformations is further assessed and validated. Its formulation is fundamentally based on a physical metallurgical mechanism and derived in a thermodynamically consistent way, inheriting a consistent mechanical dissipation. This model draws on a reduced number of phenomenological elements and is a step towards the fully predictive modelling of materials that exhibit such phenomena.

Prediction of the yielding behaviour of ductile porous materials through computational homogenization

Purpose The purpose of this paper is to predict the yield locus of porous ductile materials, evaluate the impact of void geometry and compare the computational results with existing analytical models. Design/methodology/approach A computational homogenization strategy for the definition of the elasto-plastic transition is proposed. Representative volume elements (RVEs) containing single-centred ellipsoidal voids are analysed using three-dimensional finite element models under the geometrically non-linear hypothesis of finite strains. Yield curves are obtained by means of systematic analysis of RVEs considering different kinematical models: linear boundary displacements (upper bound), boundary displacement fluctuation periodicity and uniform boundary traction (lower bound). Findings The influence of void geometry is captured and the reduction in the material strength is observed. Analytical models usually overestimate the impact of void geometry on the yield locus. Originality/value This paper proposes an alternative criterion for porous ductile materials and assesses the accuracy of analytical models through the simulation of three-dimensional finite element models under geometrically non-linear hypothesis.

A framework for product architecture and technology selection in competitive environment

Product positioning is a key marketing activity that defines the profitability of the company. In turn, product position is characterised by product architecture and underlying manufacturing technologies. Thus, the problem of product positioning can be reduced to the selection of appropriate product architecture. The paper presents a framework aiding on product architecture and technologies selection decision at the early stage of product development process. The model integrates utility analysis and appropriate market segmentation with competitive reactions and has been applied to business environment with competitive tendering. The framework is thought to enhance the communication between product development and marketing teams and general management within SME while making product positioning decisions.

Thermodynamical Framework for Ductile Damage and Plasticity

Many models employed for the prediction of plastic deformation rely exclusively on elastoplastic theories, disregarding significant effects of internal degradation [1]. Constitutive models based on the Continuum Damage Mechanics theory provide more realistic predictions since damage is taken into account as an internal variable. In the present contribution, Lemaire’s model for ductile damage [2] is questioned under the assumption of the principle of maximum inelastic dissipation [3]. The model is enhanced with a nonlocal formulation where the damage variable is spatially averaged by means of an integral operator [4]. Thermodynamical admissibility of the nonlocal model is checked by applying the global version of the Clausius‐Duhem inequality [5]. Results from numerical analysis show that the constitutive model is insensitive to spatial discretization.

Classical and Thermodynamically Consistent Non‐local Formulations for Ductile Damage: Comparison of Approaches

Non‐local theories have been commonly used as suitable localisation limiters for plasticity and damage in finite element analysis. Within the non‐local framework, two competitive formulations have emerged: the first one is the classical approach, where a previous local model is directly enhanced with a non‐local variable; the other one is fully supported on thermodynamical requirements. In this paper, we present two distinct classical non‐formulations for elasto‐plasticity coupled with damage where we chose damage and the energy release rate as non‐local variables. Within the thermodynamically motivated framework, a simultaneous averaging of both damage and its conjugated thermodynamic force is implied from the Clausius‐Duhem inequality. The three resulting models are assessed through numerical simulation with finite elements. The results show that the classical non‐local model with averaging of the energy release rate may not regularise the solution under certain circumstances. On the other hand, the other two formulations are able to effectively eliminate the pathological mesh dependency.