Robert Arrieux

Determination of the equivalent stress–equivalent strain relationship of a copper sample under tensile loading

Abstract In this paper, a new method is used to determine the true stress–true strain curve. As this method still makes use of a tensile test, the results are compared with the results obtained with an extensometer on a copper sample for which the strain between the grips is supposed to be homogeneous. In the present case, the deformation is determined using a correlation method applied to successive images of one randomly painted sample face. The calculated strain field brings into evidence an increasing heterogeneity at high deformations. Taking this heterogeneity into account allows a more precise computation of the equivalent stress–equivalent strain curve which is used in a finite element simulation of the tensile test. Comparing the results of the simulation with those of image analysis, it appears that a corrected equivalent stress–equivalent strain relationship is sufficient to obtain a correct behaviour up to necking. The simulation also shows that the necking in the material is obtained when a necking criterion (Considere’s criterion) is verified. It indicates that in this case only the datum of the σ eq = f ( e eq ) relationship is sufficient to obtain the whole behaviour of the material.

Analysis of a criterion of deep drawing operation capability for thin orthotropic sheets

This paper proposes a model which predicts the feasibility of deep drawing operations of thin plates for various directions of solicitation. The first part consists of a theoretical presentation and a comparison of experimental results. The influence of anisotropic parameters and their implications for the surface stress criteria are then analysed. It is possible to predict the optimal direction of solicitation (in direct or broken path) to increase the strains during deep drawing operations by using this approach. Finally, we propose a modification of the model to improve understanding of the influence of rate strain on forming limit stress and strain diagrams.

A Method to Predict the Onset of Necking in Numerical Simulation of Deep Drawing Operations

Abstract For an anisotropic material, the principal strain directions may not coincide with the orthotopic axes during a forming operation. In this paper we describe a numerical method to determine the forming limit stress surface of a sheet metal for off axes solicitations. This method is based on Marciniaks model. Experimental comparisons show the good accuracy of this theoretical model. Then the stress surface so determined is introduced in a finite element calculation software in order to detect numericaly the necking occurence during the simulation of the drawing of a square cup. The results so got are in good agreement with experimental data.

Off-axes forming-limit stress diagrams of an anisotropic steel sheet

Abstract In this study the off-axes forming-limit stress diagram is determined. First the experimental forming-limit diagrams at various directions of the sheet are drawn, after which the limit stress states are calculated by means of a step plastic calculation along the experimental strain paths. A reverse calculation allows the determination of the limit strains from the stress curves of various strain path shapes. Very good agreement with experimental results is observed, showing the great value interest of the forming-limit stress diagram, and its independence of the strain path shape.

Numerical study of the micro-formability of thin metallic materials: virtual micro-forming limit diagrams

This paper presents the determination of virtual micro-forming limit diagrams from two types of numerical simulations based on the finite element method: one with modelling of the full tool for microdeep drawing and a thin blank with geometric imperfections, based on a defined roughness; and a second called “reduced simulation” where different deformation paths were simulated with appropriate boundary conditions by introducing the same type of geometric imperfections on aluminium 1050A (99.5%). A new test for detecting the onset of necking, called the “change of slope” criterion has been defined. Several methods based on histograms to represent the distributions of major and minor strains, have been used to determine the strain at the onset of necking. The numerical micro-forming limit diagrams (MFLD) were then compared to one obtained experimentally.

Numerical determination of micro-forming limit diagrams: introduction of the effect of grain size heterogeneity

This paper presents the determination of virtual micro-forming limit diagrams by a behaviour law adapted to thin materials introducing the effect of microstructure heterogeneity. The observed size effect, i.e. the decrease in flow stress when the grain size increased, was modelled by a specific phenomenological behaviour law. A reduced numerical simulation by a finite element method rendered it possible to carry out very fast simulations of the different modes of deformation and to determine the virtual micro-forming limit diagrams from the onset of necking. This methodology was compared with experimental results on aluminium 1050A (99.5%) of thickness 0.2 mm. The comparison of the experimental and numerical data demonstrated good agreement between the real and virtual results obtained by such a methodology.

Numerical Optimization of an Industrial Multi-Steps Stamping Process by Using the Design of Experiment Method

The deep drawing process consists in realizing parts with complex shapes like different kind of boxes, cups, etc., from a metal sheet. These parts are obtained through one or several stamping steps. The tool setup motion of the stamping process is difficult to obtain. It requires practice and special knowledge on the process. The design is long and difficult to optimize. It is expensive in machining tool operations because it needs many trials and modifications on the tool before obtaining the right shape and the good working of the tool. The mains reasons of these difficulties come from the strain heterogeneity, the spring back after the tool removing and the decrease of thickness. There are many influent parameters for this kind of process. They modify directly the shape of the part. These parameters can be listed in three different categories: Firstly, the parameters linked to the tool geometry like the die enter radius, the punch diameter and the clearance between die and punch. Secondly, the parameters linked to the manufacturing conditions like the stamping speed, the lubricant and the blank holder force. And thirdly, the parameters linked to the flank geometry.