Key Engineering Materials Vols. 651-653

Abstract: This work consists of determining the plastic strain value undergone by a material during a forming process using the instrumented indentation technique (IIT). A deep drawing steel DC01 is characterized using tensile, shear and indentation tests. The plastic strain value undergone by this steel during uniaxial tensile tests is determined by indentation. The results show that, the identification from IIT doesn’t lead to an accurate value of the plastic strain if the assumption that the hardening law follows Hollomon law is used. By using a F.E. method, it is shown that using a Voce hardening law improves significantly the identification of the hardening law of a pre-deformed material. Using this type of hardening law coupled to a methodology based on the IIT leads to an accurate determination of the hardening law of a pre-deformed material. Consequently, this will allow determining the plastic strain value and the springback elastic strain value of a material after a mechanical forming operation.

Abstract: The roll levelling is a forming process used to remove the residual stresses and imperfections of metal strips by means of plastic deformations. The process is especially important to avoid final geometrical errors when coils are cold formed or when thick plates are cut by laser. In the last years, and due to the appearance of high strength materials such as Ultra High Strength Steels, machine design engineers are demanding a reliable tool for the dimensioning of the levelling facilities. In response to this demand, Finite Element Analysis is becoming an important technique able to lead engineers towards facilities optimization through a deeper understanding of the process.In this scenario, the accuracy and quality of the simulation results are highly dependent on the accuracy of the implemented material model. During roll levelling process, the sheet metal is subjected to cyclic tensile-compressive deformations, therefore a proper constitutive. model which considers the phenomena that occurs during cyclic loadings, such as the Bauschinger effec, work hardeningt and the transient behaviour, is needed. The prediction of all these phenomena which affect the final shape of the product are linked to the hardening rule.In the present paper, the roll levelling simulation of a DP1000 steel is performed using a combined isotropic-kinematic hardening formulation introduced by Chaboche and Lemaitre since its simplicity and its ability to predict the Bauschinger effect. The model has been fitted to the experimental curves obtained from a cyclic tension-compression test, which has been performed by means of a special tool developed to avoid the buckling of the specimen during compressive loadings. The model has been fitted using three different material hardening parameter identification methodologies which have been compared.

Abstract: We consider a variational formulation of gradient elasto-plasticity, as they arise in the incremental formulation of the plastic evolution problem, subject to a class of single-slip side conditions. Such side conditions typically render the associated boundary-value problems non-convex. We first show that, for a large class of plastic deformations, a given single-slip condition (specification of Burgers' vectors and slip planes) can be relaxed by introducing a lamination microstructure. This yields a relaxed side condition which allows for arbitrary slip in a prescribed family of slip planes. This relaxed model can be thought of as an aid to simulating macroscopic plastic behavior without the need to resolve arbitrarily fine spatial scales. We also discuss issues of existence of solutions for the relaxed model.

Abstract: Lightweighting materials (e.g., advanced high strength steels, aluminum alloys etc.) are increasingly being used by automotive companies as sheet metal components. However, accurate material models are needed for wider adoption. These constitutive material data are often developed by applying biaxial strain paths with cross-shaped (cruciform) specimens. Optimizing the design of specimens is a major goal in which finite element (FE) analysis can play a major role. However, verification of FE models is necessary. Calibrating models against uniaxial tensile tests is a logical first step. In the present study, reliable stress-strain data up to failure are developed by using digital image correlation (DIC) technique for strain measurement and X-ray techniques and/or force data for stress measurement. Such data are used to model the deformation behavior in uniaxial and biaxial tensile specimens. Model predictions of strains and displacements are compared with experimental data. The role of imperfections on necking behavior in FE modeling results of uniaxial tests is discussed. Computed results of deformation, strain profile, and von Mises plastic strain agree with measured values along critical paths in the cruciform specimens. Such a calibrated FE model can be used to obtain an optimum cruciform specimen design.

Abstract: Multiscale tools are important for the development of multiphase steel grades within Tata Steel R&D. The spatial distribution and morphology of the hard and soft phases in the microstructure as well as their micromechanical properties influences strongly the macroscopic behaviour. To be able to predict the macroscopic response and be of use in an industrial research environment accurate modelling on microscale has to be coupled to efficient homogenization principles. A new algorithm, which extends the capabilities of voronoi tessellations has been developed capturing relevant microstructure parameters. In this paper we show the versatility of the algorithm in simulating many microstructure features in 2 and 3 dimensions and how it is used for micromechanical simulations.

Abstract: Ni-based superalloys comprising of elastic particles embedded in a single crystal elastic-plastic matrix are usually subject to loading at elevated service temperatures. In order to enhance the understanding of high temperature deformation mechanisms a two dimensional discrete dislocation plasticity framework wherein the dislocations movement that incorporates both glide and climb is formulated. The climbing dislocations are modelled as point sources/sinks of vacancies and the vacancy diffusion boundary value problem is solved by superposition of the vacancy concentration fields of the point sources/sinks in an infinite medium and a complementary non-singular solution that enforces the relevant boundary conditions. The vacancy concentration field along with the Peach-Kohler force provides the climb rate of the dislocations.

Abstract: We report quantitative measurement of plasticity in confined Cu thin films with a new micro-pillar testing protocol. Polycrystalline Cu and CrN thin films were sequentially sputter deposited onto Si (100) substrates, forming thin film assemblies in which polycrystalline Cu thin films of various thicknesses were confined between non-deforming Si and CrN. Cylindrical micro-pillars of CrN/Cu/Si were fabricated through scripted focused Ga⁺ ion beam milling, with the interfaces either normal to the axial direction or at a 45° inclination. The CrN/Cu/Si micro-pillars were compression loaded in the axial direction with a flat diamond punch on an instrumented nanoindenter. The axial compression loading caused extensive plasticity within the thin Cu interlayers with the interfaces in both the normal and inclined orientations, but with distinctly different responses. We show that significant plastic flow occurs within the confined Cu thin films in both normal compression and shear loading. The flow stress of the confined Cu films is dependent on the Cu layer thickness and the deformation geometry. The presently described micro-pillar testing protocol offers quantitative evaluation of the plastic response of thin metal films under different deformation geometries. The present results offer new experimental examples of scale-dependent plasticity in thin metal films, and new experimental test cases for non-local plasticity theories.

Abstract: This paper addresses a physics based derivation of mode-I and mode-II traction separation relations in the context of cohesive zone modeling of ductile fracture of metallic materials. The formulation is based on the growth of an array of pores idealized as cylinders which are considered as therepresentative volume elements. An upper bound solution is applied for the deformation of the representative volume element and different traction-separation relations are obtained through different assumptions.

Abstract: The present study addresses the difficulties in heating thermoplastic sheets for ther-moforming applications. In industrial environments, the sheets are heated in a contact free method by means of convective hot air ovens and infrared radiation. In this study the temperature evolution at the outer surface as well as the core of thermoplastic sheets as a function of time is measured by means of thermocouples. These measurements reveal significant through thickness temperature dif-ferences which need to be resolved before high quality products can be made. The temperature dif-ferences can be decreased by decreasing the radiative power. This is however not acceptable in in-dustry since it lowers the number of produced parts per unit of time.In order to gain insight in the time-temperature relationship during the heating phase, a finite differ-ence model is developed. The model clearly shows the constantly changing through thickness tem-perature distribution and can be used as a tool by the thermoforming industry to optimize the pro-duction process.

Abstract: To assess the crashworthiness of simple wrought magnesium structures, the axial deformation behaviour of different square tubes produced from magnesium alloys AZ31 and ZE10 were numerically investigated under quasi-static compressive loading conditions. Finite-element simulations were conducted to predict and assess the plastic buckling and crush behaviour. The necessary data to determine parameters for the plastic potential were taken from compression tests conducted along different orientations. The yield function Hill48 was selected, despite its inability to capture the strength differential effect. The modelling approach pursued is justified by considering the mechanical loading conditions, the fabrication process of the profiles and its implication on strain anisotropy, balancing achievable accuracy and computational efforts. The simulation results revealed that the material work hardening rates evidenced in uniaxial compression tests influenced the buckling modes as well as the energy dissipation.