Combination of Two X‐Ray Diffraction Settings for Determining the Texture of Small Sheared Samples

Abstract

We developed a method to perform accurate texture determination on small size sample. Limitations occur when samples having a small gauge area are investigated by classical XRay diffraction. As the irradiated surface increases with the tilt angle, it becomes larger than the gauge area. The measured pole figures are then reduced to low values of the tilt angle and do not allow an accurate texture analyze. To enlarge the measurement range of pole figures and perform measurements on small samples, we have used two complementary methods. The first one is the Bragg-Brentano geometry which is used for small tilt angles. In the second one, used for larger tilt angles, the size of the irradiated surface by the incident XRay beam remains lower than the sample surface thanks to a specific diffraction setting developed for thin film measurement. The diffraction experiment is conducted so that the incidence angle between the incident beam and the sample surface is kept constant. Consequently, the irradiated area is constant during the measurement. The choice of the convenient incidence angle, which permits to extend the pole figure measurements for high tilt angles is then an important parameter. The pole figures are reconstructed from the intensities obtained by these different measurements. In this contribution, we present in details these combined techniques applied to the texture measurement of a high strength FeMnC austenitic TWIP steel during simple and reverse shear testing. INTRODUCTION In the field of the development of high strength alloy for automotive industry, the quantitative texture analyze during the deformation of the material is essential for the understanding of it behavior. As the metal sheet undergoes complex deformation during the forming process, several devices were developed in the recent year to reproduce these conditions by the combinations of several mechanical tests, like the reverse shear or the strain path change (plane-strain / simple shear). Most of the time, the gauge area of these samples is limited to a few millimeters width (3.5mm in our study) with a sheet thickness of nearly 1mm. This small size conducts to the decrease of the accuracy of the texture analyze. In fact, texture measurement limitations occur when small size samples (ie samples having a small gauge area) are investigated by classical X-Ray diffraction. The dimension of the irradiated surface increases with the goniometer tilt angle (ψ) and can become larger than the gauge surface. The analyzed PFs (PF) are then reduced to low values of the tilt angle ψ and do not allow an accurate texture analyze. In our study for example, the PF measurement is limited to ψ =60° for the {111} PF. Moreover deformation by shear conducts to PFs having intensity at their border, ie at χ>50° . This information will not be accessible by using classical X-Ray diffraction geometry. Therefore, to accurately study the texture evolutions of small samples submitted to shear tests, the use of adapted X-Ray techniques is necessary. EXPERIMENTAL TECHNIQUE A classical method to measure PFs with X-ray diffraction is the Schultz one, with the Bragg-Brentano (BB) geometry. One of the consequences of this geometry is that the size of the irradiated surface increases with the goniometer tilt angle ψ. With a cylindrical collimator, the irradiated surface has an ellipsoidal shape, characterized by the length L of it major axis (figure 1). Figure 1. Irradiated surface geometry (collimator diameter d; greatest size of the irradiated surface L; real incidence angle i). The greatest size L of the ellipse depends on the measurement conditions, ie the real incidence angle i itself related to θinc and ψ by the following relation (1): sin i = sin θinc cos ψ (1) During a classical PF measurement (θinc constant), when the goniometer tilt angle ψ increases, the real incidence angle i decreases, resulting in an augmentation of the length L. On the figure 2, the evolution of L is plotted with i for a collimator diameter of 0.8mm. For low values of i, ie high values ψ, L becomes very large. For a {111} PF, L becomes larger than the smallest dimension of the sample gauge area (L>3.5 mm) from i=13°, ie ψ=60°. Figure 2. Evolution of the size L of the irradiated surface with the real incidence angle i, for the {111} PF with a collimator diameter of 0.8 mm. In the present case, when L is larger than the sheared zone (L>3.5 mm), the beam will overlap both the clamping and the gauge areas. The analyzed surface will not be representative from the deformed one. Moreover the homogeneity of the deformation is limited to a restricted part of the gauge area. To increase the analyzed surface over 3.5 mm in width, and go through the problem link to the Bragg-Brentano geometry, the sample is classically cut into two pieces L d