Numerical characterization of residual stresses in a four-point-bending experiment of textured duplex stainless steel

Abstract

The resulting shapes in production processes of metal components are strongly influenced by deformation induced residual stresses. Dual-phase steels are commonly used for industrial application of, e.g., forged or deep-drawn structural parts. This is due to their ability to handle high plastic deformations, while retaining desired stiffness for the products. In order to influence the resulting shape as well as component characteristics positively it is important to predict the distribution of phase-specific residual stresses which occur on the microscale of the material. In this contribution a comparative study is presented, where two approaches for the numerical simulation of residual stresses are applied. On the one hand a numerically efficient mean field theory is used to estimate on the grain level the total strain, the plastic strains and the eigenstrains based on macroscopic stress, strain and stiffness data. An alternative ansatz relies on a Taylor approximation for the grain level strains. Both approaches are applied to the corrosion-resistant duplex steel X2CrNiMoN22-5-3 (1.4462), which consists of a ferritic and an austenitic phase with the same volume fraction. Mean field and Taylor approximation strategies are implemented for usage in three dimensional solid finite element analysis and a geometrically exact Euler–Bernoulli beam for the simulation of a four-point-bending test. The predicted residual stresses are compared to experimental data from bending experiments for the phase-specific residual stresses/strains which have been determined by neutron diffraction over the bending height of the specimen.

Residual stresses in deep-drawn cups made of duplex stainless steel X2CrNiN23-4

“…The phase-specific crystallographic texture was determined by means of X-ray diffraction, as described in [11]. Three incomplete pole figures were analyzed at the sheet surface for both phases, respectively.…”

“…15 tilt angles equally distributed over sin 2 were set, with limitation of j j Ä 50 ıı , to avoid shadowing effects from the curved wall of the sectioned deep drawn cup. For stress evaluation, lattice plane specific diffraction elastic constants for ferrite 1 2 s f211g 2 = 5.7006 10 -6 MPa -1 and austenite 1 2 s f220g 2 = 5.9613 10 -6 MPa -1 were used [11]. For all measuring points, the residual stress components in circumferential direction (CD) and drawing direction (DD) were analyzed for both phases h CD,DD i˛; .…”

“…The material parameters for the mean-field modeling of the duplex stainless steel X2CrNiN23-4, listed in Table 3, are chosen based on the experimental results of Simon et al [11]. Note that for simplicity the phase-specific behavior is modeled statistically isotropic.…”

“…In [10] an incremental two-scale simulation K approach is presented, which allows for the consideration of the history of phase-specific micro residual stress evolution for complex forming processes. With the phase-specific and anisotropic strain hardening of the duplex stainless steel X2CrNiN23-4 investigated in [11], the mean field approach can now be applied for sheet metal forming simulation considering the anisotropic and phase-specific material behaviour. In this work, the influence of the drawing depth of circular deep drawn cups made of duplex stainless steel X2CrNiN23-4 on the residual stress distribution is investigated.…”

“…Material parameters of austenite and ferrite for mean-field modeling based on experimental results of Simon et al[11] …”