A revised Johnson–Cook model comprised of acoustic plasticity for non-oriented silicon steel under transverse ultrasonic vibration

Establishing a constitutive model that can accurately describe material plastic flow behavior in the ultrasonic energy field is the foundation that finite element simulation guides the design of ultrasonic vibration-assisted (UVA) forming dies and optimizes the process. Based on the original Johnson–Cook (JC) model and experimental results, a transverse ultrasonic vibration-assisted (TUVA) uniaxial tensile constitutive model for non-oriented silicon steel 50WW70 was developed by introducing an acoustic softening function. The influence of ultrasonic energy field density on strain energy and sheet elongation was quantitatively analyzed. The results show that the effect of the ultrasonic energy field on strain energy has a saturation effect. The ultrasonic energy field can improve the elongation of non-oriented silicon steel 50WW70 . However, the effects on elongation have an inflection point. In this work, the maximum elongation of non-oriented silicon steel 50WW70 can reach 41.12%. When the ultrasonic energy field density is greater than 2618.45 J/m 3 , the elongation is suppressed. The constitutive model proposed in this study can describe the tensile deformation behaviors under TUVA forming.