L.F. Menezes

Three-dimensional numerical simulation of the deep-drawing process using solid finite elements

Abstract The main goal of this work is to present a three-dimensional mechanical model for the numerical simulation of the deep-drawing process. The model takes into account the large elastoplastic strains and rotations that occur in the deep-drawing process. Hill’s orthotropic yield criteria with isotropic and kinematics hardening describes the anisotropic plastic properties of the sheet. Coulomb’s classical law models the frictional contact problem treated with an augmented Lagrangian approach. This method yields a mixed system where the final unknowns of the problem are static (frictional contact forces) and kinematic (displacements) variables. To solve this problem use is made of a fully implicit algorithm of Newton–Raphson type. Three-dimensional isoparametric finite elements with a selective reduced integration are used for the spatial discretization of the deformed body. The geometry of the forming tools is modelled by Bezier surfaces. The numerical results of the deep-drawing of a square cup are presented to focus their good agreement with the results of experiment.

Ultra-microhardness testing procedure with Vickers indenter

Abstract Depth-sensing indentation equipment is widely used for evaluation of the hardness and Youngs modulus of materials. The depth resolution of this technique allows the use of ultra-low loads. However, aspects related to the determination of the contact area under indentation should be cautiously considered when using this equipment. These are related to the geometrical imperfections of the tip, the diamond pyramidal punch and the formation of pileup or the presence of sink-in, which alter the shape and size of the indent. These and other aspects, such as the thermal drift of the equipment and the scattering at the zero indentation depth position related to surface finishing, are discussed in this work. A study concerning the hardness and the Youngs modulus results determined by Vickers indentation on different materials was performed. Samples of fused silica, BK7 glass, aluminium, copper and mild steel (for which the values of Youngs modulus were previously known) were tested using indentation loads in the range 10–1000 mN. Moreover, two methods are proposed for performing the indentation geometrical calibration of the contact area; these are compared with a former method proposed by Oliver and Pharr (OP). The present methods are based on: (i) analysis of the punch profile using atomic force microscopy (AFM); and (ii) a linear penetration-depth function correction (LM), based on knowledge of the values of the Youngs modulus of several materials. By applying these methods to the indentation load/indentation depth results, it was possible to draw some conclusions about the benefit of the AFM and LM methods now under proposal.

Numerical study of the plastic behaviour in tension of welds in high strength steels

The influence of the mismatch between material properties and constraint on the plastic deformation behaviour of the heat affected zone of welds in high strength steels is investigated in this study, using finite element simulations. An elastoplastic implicit three-dimensional finite element code (EPIM3D) was used in the analysis. The paper presents the mechanical model of the code and the methodology used for the numerical simulation of the tensile test of welded joints. Numerical results of the tensile test of welded samples with different hypothetical widths for the Heat Affected Zone and various material mismatch levels are shown. The analysis concerns the overall strength and ductility of the joint and in relation to the plastic behaviour of the heat affected zone. The influence of the yield stress, tensile strength and constraint on the stress and plastic strain distribution in the soft heat affected zone is also discussed.

A modified swift law for prestrained materials

Abstract A modified Swift law to describe the evolution of the mechanical behaviour in reloading of prestrained materials is proposed in this work. This equation is deduced from the original Swift law by including a parameter that accounts for the effect of strain path change. This parameter depends on the value of the yield stress and the subsequent work-hardening behaviour in reloading. The new equation predicts well the general mechanical behaviour in the second path for copper and steel. In particular, it predicts accurately the strain value for which necking occurs during reloading and fits experimental stress-strain curves well. The flow equation formulated remains sufficiently simple to be applied in finite element modelling of prestrained materials. However, since the parameter, which is needed for the modified Swift law, must be previously known, the strain path change itself cannot be part of the simulation.

Thermal residual stresses in particle-reinforced viscoplastic metal matrix composites

Abstract A spherical symmetric thermoviscoplastic model is presented to calculate the thermal residual stresses in particle-reinforced metal matrix composites. It is based on the assumption that the particles behave elastically whereas the matrix exhibits an elastoviscoplastic behaviour. An internal-variable-type constitutive equation is used to predict the behaviour of the matrix, which is taken as Al-1100. The model can predict the change of the stress and displacement fields within the matrix and the particles during cooling of the material as well as the thermal residual stresses induced at room temperature. The effects of cooling rate and volume fraction of particles are emphasized. The stresses on reheating from room temperature and during thermal treatment are calculated. It is shown in particular that holding the composite at moderate temperature (≈ 200 °C) does not lead to substantial relaxation of the stresses. Aging treatment is thus usually carried out under a residual stress field which might influence the precipitation sequence and kinetics.

Improving Computational Performance through HPC Techniques: case study using DD3IMP in‐house code

The computational efficiency of the FEA is strongly dependent on the algorithmic and numerical efficiency of the FE solver. This is particularly important in case of implicit FE codes, such as DD3IMP, the in‐house static implicit FE solver under analysis in this work. This study describes the procedure adopted to identify the main computational bottlenecks of the FE solver in order to introduce the OpenMP directives and, consequently, to achieve a major speedup of the whole algorithm. The different parallelized branches of the code are tested using the well‐known square cup deep drawing example, considering different FE discretizations. The analysis of the preliminary results, concerning the CPU wall time, allows to demonstrate that the adoption of HPC techniques, such as the abovementioned OpenMP directives, enables to: (i) achieve a speedup factor close to the number of cores (in a single computer); (ii) solve a problem in a shorter time; (iii) solve a bigger problem in the same amount of time and, thus...

Numerical determination of the influence of the cooling rate and reinforcement volume fraction on the levels of residual stresses in Al–SiC composites

Abstract It is natural to suppose that some of the technological factors associated to the processes used in the fabrication of metal matrix composite (MMC) materials can and will influence in some extent the performance of these materials when in service. This is often true due to the levels of residual stresses that may be induced in the MMC after the cooling down phase during the fabrication process. In the present work, the authors propose a complete three-dimensional constitutive model and numerical implementation procedure that allows the determination of residual stress fields in metal matrix composites. The model is based in a thermoelastic reinforcement behaviour and a thermoelastic–viscoplastic matrix behaviour. The role of the reinforcement volume fraction and cooling rate on the levels of residual stresses at room temperature is investigated with the proposed model. For this purpose, a large set of simulations is performed with Al–SiC metal matrix composites. Two different unit cells are used, representative of continuous and short fiber reinforcement MMCs. The tested reinforcement volume fractions range from 5% to 35% and cooling rates from 0.1 to 500 K s−1. The influence of these parameters is evaluated in terms of the resulting stress fields at room temperature. It is shown that the levels of equivalent stress can reach values above the yield limit of the aluminium matrix, leading to plastic straining near the matrix/reinforcement interface.

Numerical simulation of tensile tests of prestrained sheets

Abstract The effect of cross section variation on formability of prestrained samples has been investigated using finite element simulations of a standard sheet tensile test. The mechanical model takes into account large elastoplastic strains and rotations that occur during deformation. Hill’s orthotropic yield criterion with isotropic hardening describes the anisotropic plastic properties of the sheet. The isotropic hardening is modelled by a modified Swift law that describes the response of prestrained materials in reloading. Two different situations were simulated: reloading in tension of samples with constant cross sectional area and reloading in tension of samples with two zones of slightly different cross sectional areas. The results show that the strain distribution along the tensile axis of a prestrained sample depends on the level of the prestrain and also on the presence and size of geometrical fluctuations in the cross section, which always occur in experimental samples. This dependence is higher for materials with lower work-hardening rates.

Improving Nagata patch interpolation applied for tool surface description in sheet metal forming simulation

The contact surface description is a very important field in the numerical simulation of problems involving frictional contact, which are among the most difficult ones in continuum mechanics, as is the case of sheet metal forming simulation. In this paper, a methodology to control the Nagata patch interpolation of piecewise linear meshes is proposed, in order to improve its applicability for tool surface description used in the numerical simulation of sheet metal forming processes. The interpolation can be applied either to triangular and quadrilateral Nagata patches, as well as structured and unstructured patches. The normal vectors needed for the Nagata interpolation are obtained through two distinct strategies. The first uses the information available in the CAD surface model, while the second resorts only to the piecewise linear mesh model information. In order to evaluate the interpolation accuracy, the Nagata patch is applied to describe a sheet metal forming complex shape part tool geometry. The results obtained show that, regardless of the strategy used to evaluate the surface normal vectors, the use of the proposed Nagata patch interpolation enables a large improvement in the geometric accuracy when compared with the models composed by piecewise linear elements. The use of CAD surface geometry to evaluate the surface normal vectors leads to the best Nagata patch interpolation in terms of shape and normal vector field accuracy.

A model for coated surface hardness

Abstract The authors present a model that predicts the hardness of a film deposited on the surface of a substrate. The model is based on a simple mathematical relationship involving the hardness of the film and the hardness of the substrate, together with the hardness of the composite film/substrate at a given film thickness/penetration depth ratio. The parameters of the present model depend on the mechanical properties of the film/substrate pair and can be experimentally determined by using depth-sensing hardness instruments. In the models found in the literature, the equation parameters are constants typical for each model. The present model is proposed and validated for the case of a film (W–C–Co coating) harder than the substrate (various metallic materials) and it allows determination of the film hardness without the need to determine either the film thickness or the substrate hardness.