The process of strip rolling is analyzed using the upper bound technique. Two triangular velocity fields, one with triangles in linear rigid body motion and the other with triangles in rotational rigid body motion, are developed. The total power is determined as a function of the four independent process parameters (relative thickness, reduction, friction and net front-back tension). The results of these two velocity fields are compared with the established solution from Avitzur’s velocity field of continuous deformation. Upon establishing the validity of the triangular velocity field as an approach to the strip rolling problem, recommendations are suggested on how this approach can be used to study the split end or alligatoring defect.
Based on the upper-bound theorem in limit analysis, a theoretical model for core fracture in bimetal rods during extrusion has been developed and a fracture criterion established. The variables affecting core fracture are: reduction in area (r%), die geometry, friction (m), relative size of the core and relative strength of the core. Within the wide range of possible combinations of these process variables, only a small range permits extrusion without fracture. With suitable modifications the present analysis can be extended to develop criteria for sleeve fracture during extrusion and for both core and sleeve fracture during drawing.
The process of core fracture in bimetals during extrusion was reexamined. The new analysis, based on the upper-bound theorem in limit analysis, eliminated the lengthy numerical computations employed in the previous work [1]. The criterion for core fracture was derived and discussed.
In conjunction with the previous analysis on core fracture [1, 2], a criterion for prevention of sleeve fracture in extrusion of bimetal rods is developed. The sleeve fracture is likewise affected by a set of independent process parameters, namely the reduction in area, die angle, friction, interfacial bonding, relative size, and relative strength of the sleeve. It is shown that the usage of the present criterion for sleeve fracture and the criterion previously described for core fracture can provide an effective path to a successful extrusion operation for bimetal rods and wires.
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