development of a modified relationship between the constant friction factor and the coefficient of friction in extrusion using upper bound analysis

This study evaluates friction in bulk metal forming processes, where frictional shear stress is commonly described by either coulomb’s friction law or the constant friction factor law. despite their widespread use, establishing a precise correlation between the constant friction factor (m) and the coefficient of friction (μ) remains challenging. building on previous work, a modified relationship between these parameters is proposed to improve consistency across practical friction ranges. the new equation is based on upper bound analysis, incorporating both the constant friction factor and coulomb’s hypothesis. using regression on the extrusion process results, the equation was obtained and validated. the proposed equation satisfies the required boundary conditions and offers simplified implementation in forming simulations. comparative analysis shows strong agreement, particularly under low-friction conditions typical of metal forming. the findings enhance the reliability of frictional behavior modeling in engineering applications.