Viscoplastic self-consistent polycrystal modeling of texture evolution of ultra-low carbon steel during cold rolling (2019)

Abstract The viscoplastic self-consistent (VPSC) polycrystal model, where each grain is regarded as an ellipsoidal inclusion interacting with a homogeneous effective medium represented by the polycrystal has long been successful in explaining the mechanical response and crystallographic texture development during plastic deformation. VPSC has especially been used to model low-symmetry materials such as Mg-alloys, uranium, etc, which could not be addressed by the conventional Taylor model. Although there are several reports on the modeling of steel that successfully reproduce its measured crystallographic texture at specific reductions, few studies have been carried out to reproduce the evolution of the intensity of texture fibers at various rolling reductions. In this study the texture evolution of body-centered-cubic ultra-low carbon steel during cold rolling was calculated using the VPSC model and compared with textures measured at 40%, 60%, 70%, 80% and 90% reduction. The deformation by cold rolling was accommodated by <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mfenced close="}" open="{"> <mml:mrow> <mml:mn>110</mml:mn> </mml:mrow> </mml:mfenced> </mml:mrow> <mml:mo stretchy="false">〈</mml:mo> <mml:mn>111</mml:mn> <mml:mo stretchy="false">〉</mml:mo> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mfenced close="}" open="{"> <mml:mrow> <mml:mn>211</mml:mn> </mml:mrow> </mml:mfenced> </mml:mrow> <mml:mo stretchy="false">〈</mml:mo> <mml:mn>111</mml:mn> <mml:mo stretchy="false">〉</mml:mo> </mml:math> slip systems interacting via a Voce hardening law. Addressing a wide range of rolling reductions poses a more severe test on the modeling. It is found that accounting for grain shape, grain interaction with the surroundings, and their evolution with strain, is critical for explaining the experimentally observed evolution of texture intensities. Specifically, the mechanisms of grain-neighbor co-rotation and the role played by the relative plastic stiffness of grain and surrounding medium were explored in this work. The predicted evolution of the main texture components, namely, α fiber (RD// <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mo stretchy="false">〈</mml:mo> <mml:mn>011</mml:mn> <mml:mo stretchy="false">〉</mml:mo> </mml:math> ) and γ fiber (ND// <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mo stretchy="false">〈</mml:mo> <mml:mn>111</mml:mn> <mml:mo stretchy="false">〉</mml:mo> </mml:math> ) was compared with experimental data measured by x-ray Schultz method, resulting in that the calculated texture evolution using the above models captures well the experimental results which show a gentle ODF intensity increase in the γ fiber and a strong ODF increase near <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mfenced close="}" open="{"> <mml:mrow> <mml:mn>211</mml:mn> </mml:mrow> </mml:mfenced> </mml:mrow> <mml:mo stretchy="false">〈</mml:mo> <mml:mn>011</mml:mn> <mml:mo stretchy="false">〉</mml:mo> </mml:math> components in the α fiber during cold rolling.