An investigation of die profile effect on die wear of plane strain extrusion using incremental slab method and finite el
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ORIGINAL ARTICLE
An investigation of die profile effect on die wear of plane strain extrusion using incremental slab method and finite element analysis Hamed Farzad 1
&
Ramin Ebrahimi 2
Received: 24 February 2020 / Accepted: 20 September 2020 # Springer-Verlag London Ltd., part of Springer Nature 2020
Abstract In this research work, a new incremental slab method analysis has been derived to calculate extrusion force and its die pressure distribution during an extrusion process, while a die of arbitrary shape is used. In addition, a computational algorithm has been presented based on the proposed analysis method and Archard’s wear model to investigate the effect of die profile on its working life. Three different die profiles including optimum curved, optimum constant angle, and cylindrical shaped are numerically evaluated. The results revealed that the predicted extrusion loads and die pressure distributions through the implementation of the applied method are in an acceptable agreement with FEM analysis results. Moreover, it has been demonstrated that the maximum wear depth on all die profiles is located at the die exit area, which indicates the predominant effect of the material velocity profile. It is also found that the die life of the two optimum dies would be the same, but the least working life estimated is the working lifetime of the cylindrical die profile. Keywords Wear depth . Extrusion die profile . Incremental slab method . Finite element analysis . Die lifetime
Nomenclature c1, c2 Constants of integral (see Eq. (11) and Eq. (12)) dA, dt Differential form of contact area and sliding time dV, dp, dL Differential form of wear volume, contact load, and sliding length H, kw Local hardness and wear coefficient h Slope of the line that passes through the pseudo linear part of true stress–strain curve k Shear yield stress m Constant friction factor n Number of the considered constant angle elements (see Fig. 5) n nth element’s component (see Eq. (23) and Eq. (24)) * Hamed Farzad [email protected] 1
Department of Materials Science and Engineering, School of Engineering, Shiraz University, Shiraz, Iran
2
Department of Materials Science and Engineering, School of Engineering, Shiraz University, Shiraz, Iran
P Ph Pv rn ri, rf t t0, tf u(x) u˙rn , u˙rn V0 W WI(x) x z(x)
Extrusion pressure Normal stress acting on lateral die-material interface Normal stress acting on upper and lower die-material interface Radial distance of the point from the element’s origin Radial distance of the entry and the exit position of each element to the origin Sliding time Initial and final semi thickness of the billet Relative velocity of material and die (sliding velocity) Velocity of material on upper and lateral die-work piece interfaces The initial billet’s velocity Material’s constant width Wear depth in a time unit (wear index) Distance along die length of any point on die-material interface Wear depth at each point of die-material interface
Greek letters α Local die semi-angle αopt Optimum die semi-angle
Int
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