S. He

Residual stress determination in cold drawn steel wire by FEM simulation and X-ray diffraction

Abstract This paper presents a study on residual stress in cold drawn wire of low carbon steel by means of finite-element method (FEM) simulation and X-ray diffraction. A thick wire with a diameter of 17.9 mm drawn from an annealed wire with a diameter of 20.1 mm was investigated. First, FEM simulations were performed based on a suitable model describing the boundary conditions and the exact material behavior. Due to the initial texture in the original material, the anisotropy of the material plastic behavior was taken into account on the basis of the texture measurement of the wire. Instead of the isotropic von Mises yield criterion, a texture-based anisotropic yield locus was incorporated into the model to simulate the wire drawing process and calculate residual stresses. Next, X-ray diffraction measurements were carried out at the surface of the wire to obtain the distribution of the lattice spacing versus sin 2 ψ , from which the macroscopic residual stresses at the wire surface were calculated. The comparison between the results from the simulations and the measurements shows that a good agreement has been reached.

Forming Limit Predictions for the Serrated Strain Paths in Single Point Incremental Sheet Forming

The forming limits of sheets subjected to the Single Point Incremental Forming process (SPIF) is generally several times higher than those found in the Forming Limit Curve (FLC). In this paper it is shown that the non‐monotonic, serrated strain paths to which the material is subjected to during the SPIF process, play a role in the high formability, compared to the monotonic loading in the traditional FLC. The deformation history of an aluminium alloy truncated cone formed with the SPIF process is retrieved through a finite element (FE) model, and discussed. Subsequently, the strain paths at three different depths in the sheet are used as input into a Marciniak‐Kuczynski (MK) forming limit model. The usage of different constitutive models in this analysis shows that anisotropic hardening contributes to the delay of the onset of necking in the SPIF process. The large difference in the predicted forming limits that were obtained from the different layers indicates that an interaction between these layers sho...

Finite element modeling of incremental forming of aluminium sheets

Incremental forming is an innovative and flexible sheet metal forming technology for small batch production and prototyping, which does not require any dedicated die or punch to form a complex shape. This paper investigates the process of single point incremental forming of an aluminum cone with a 50-degree wall angle both experimentally and numerically. Finite element models are established to simulate the process. The output of the simulation is given in terms of final geometry, the thickness distribution of the product, the strain history and distribution during the deformation as well as the reaction forces. Comparison between the simulation results and the experimental data is made.

Comparison of FEM simulations for the incremental forming process

Incremental forming is an innovative and highly flexible sheet metal forming technology for small batch production and prototyping that does not require any adapted dies or punches to form a complex shape. The purpose of this article is to perform FEM simulations of the forming of a cone with a 50-degree wall angle by incremental forming and to investigate the influence of some crucial computational parameters on the simulation. The influence of several parameters will be discussed: the FEM code used (Abaqus or Lagamine, a code developed at the University of Liège), the mesh size, the potential simplification due to the symmetry of the part and the friction coefficient. The output is given in terms of final geometry (which depends on the springback), strain history and distribution during the deformation, as well as reaction forces. It will be shown that the deformation is localized around the tool and that the deformations constantly remain close to a plane strain state for this geometry. Moreover, the tool reaction clearly depends on the way the contact is taken into account.

Forming Limit Predictions for Single-Point Incremental Sheet Metal Forming

A characteristic of incremental sheet metal forming is that much higher deformations can be achieved than conventional forming limits. In this paper it is investigated to which extent the highly non‐monotonic strain paths during such a process may be responsible for this high formability. A Marciniak‐Kuczynski (MK) model is used to predict the onset of necking of a sheet subjected to the strain paths obtained by finite‐element simulations. The predicted forming limits are considerably higher than for monotonic loading, but still lower than the experimental ones. This discrepancy is attributed to the strain gradient over the sheet thickness, which is not taken into account in the currently used MK model.

Strain rate effect in high-speed wire drawing process

This paper presents a study on the strain rate effect during high-speed wire drawing process by means of finite element simulation. Based on the quasistatic stresses obtained by normal tensile tests and dynamic stresses at high strain rates by split Hopkinson pressure bar tests, the wire drawing process was simulated for low carbon steel and high carbon steel. The results show that both the deformation process and the final properties of drawn wires are influenced by the strain rate.

Determination of Strain in Incremental Sheet Forming Process

A simplified method to determine the strain distribution during incremental forming of a cone is proposed in this paper. Because of the symmetry of the deformed part, the strain can be derived using the results obtained from a limited number of consecutive tool contours instead of going through the whole process. Comparisons made between the measured and simulated results show that the proposed method can be applied to determine the strain encountered in such kind of incremental forming process where axi-symmetric parts are formed.

Anisotropy and Formability in Sheet Metal Forming

Two types of anisotropy have been introduced in the Marciniak model for the prediction of forming limit diagrams (FLDs) of sheet material. One type is due to crystallographic texture, the other is due to dislocation substructure. First, an anisotropic plastic potential is derived from a measured crystallographic texture using a multilevel model. The yield locus can be derived from this plastic potential. In addition to this, a model is used to simulate microstructure‐induced work hardening and softening. This model can take effects of strain path changes into account. Both the texture‐based and microstructure‐based anisotropic model are then implemented in the Marciniak model and used for FLD calculation. Examples of application are given for IOF steel and for aluminium alloys. Recent research has focused on the physical basis of the microstructure‐induced work hardening and softening. The principles of this model will be elucidated.

Texture-Based Explicit Finite-Element Analysis of Sheet Metal Forming

An explicit integration algorithm using a texture-based plastic potential and isotropic hardening has been developed and implemented into a commercial explicit finite-element software program through a user material subroutine (VUMAT in ABAQUS/Explicit). Simulations of cup drawing of an IF-steel are presented and compared to both experimental data and calculation results obtained with a previously developed fully implicit approach (UMAT in ABAQUS/Standard). The explicit formulation has the advantage of being more stable, but local sheet thickness variations cannot be reproduced with the same accuracy.

Model identification and FE simulations: Effect of different yield loci and hardening laws in sheet forming

The bi‐axial experimental equipment developed by Flores enables to perform Baushinger shear tests and successive or simultaneous simple shear tests and plane‐strain tests. Such experiments and classical tensile tests investigate the material behavior in order to identify the yield locus and the hardening models. With tests performed on two steel grades, the methods applied to identify classical yield surfaces such as Hill or Hosford ones as well as isotropic Swift type hardening or kinematic Armstrong‐Frederick hardening models are explained. Comparison with the Taylor‐Bishop‐Hill yield locus is also provided. The effect of both yield locus and hardening model choice will be presented for two applications: Single Point Incremental Forming (SPIF) and a cup deep drawing.