Correlations Between XRD Peak Broadening and Elastic and Plastic Deformation for Mild Steel Sheets Under Tensile Loading


  • Sarra KHELIFI Université Mohammed Seddik Benyahia-Jijel
  • Abdelhak AYAD Univeristé Frères Mentouri Constantine 1 / Université Salah Boubnider Constantine 3
  • Ahcène BOUMAIZA Université Mohammed Seddik Benyahia-Jijel
  • Nadjet ROUAG Univeristé Frères Mentouri Constantine 1
  • Francis WAGNER Université de Lorraine
  • Vincent JI Université Paris-Saclay



XRD peak broadening, strain gauge, In-situ tensile loading, strain measurement, Young’s modulus, anisotropy, mild steel


The polycrystalline nature of steel sheets plays a fundamental role in their plastic behavior during forming, especially under complex stresses, such as the deep drawing process. Heterogeneous microstructures cause variable internal stress levels, which strongly impact the material’s macroscopic mechanical properties. X-ray diffraction (XRD) technique can be applied to determine microscopic internal stresses by peaks broadening analysis, which can be related to the degree of cold work at the microscopic level. As deep drawing is a complex deformation mode, an important motivating factor to perform such a study is to find the correlation between anisotropy and XRD peak broadening through tensile deformation tests. Therefore, the initial mechanical state and different deformed states were analysed by in-situ XRD peak broadening under tensile tests in various directions in the rolling plane of mild steel sheet, for both the elastic and plastic deformation domains. The results showed that the XRD peak broadening gives accurate estimations of deformation degrees. In the elastic domain, under realistic assumptions, a relation between the relative variation of peak broadening and the applied stress σ, like Hooke’s law, was obtained by exploiting the linearity between the peak broadening and the elongation measured by the strain gauge. This formula may be used to deduce The Young’s modulus. Interesting empirical relations between peak broadenings, macro deformations and hardness have been also established for the studied sheet in the plastic deformation region. Moreover, XRD peak broadenings were able to characterize the anisotropy of deformation in the rolling plane of the sheet. They are like the anisotropy coefficients in indicating the expected behavior under complex processes such as deep drawing by using ordinary tensile tests.