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An analytical approach to prediction of internal defects during the flat rolling process of strain-hardening materials

Amjadian P., Haghighat H.

Journal of Theoretical and Applied Mechanics

2017

Vol. 55 nr 4

1341--1353

In this paper, the upper bound method has been used in analysis of the flat rolling process and prediction of internal defects for a strain-hardening material. The arc of contact has been replaced by a chord. The inlet shear boundary of the deformation zone has been assumed as an exponential curve and the boundary at the exit has been assumed as a cylindrical surface. A kinematically admissible velocity field has been proposed and internal, shear and frictional power terms have been derived. By minimizing the total power with respect to the neutral point position and the shape of the inlet shear boundary, the rolling torque has been determined. A criterion has been presented to predict the occurrence of the internal defects for given rolling conditions. Comparison of the analytically developed approach for rolling torque and internal defects with published theoretical and experimental data shows generally good agreement.

A generalized upper bound solution for extrusion of bi-metallic rectangular cross-section bars through dies of any shape

Haghighat H., Amjadian P.

Journal of Theoretical and Applied Mechanics

2013

Vol. 51 nr 1

105--116

In this paper, a generalized upper bound solution is developed for extrusion of bi-metallic rectangular cross-section bars through dies of any shape. The internal, shearing and frictional power terms are derived and they are used in the upper bound model. By using the developed upper bound model, the extrusion pressures for two types of die shapes, an optimum wedge shaped die as a linear die profile and an optimum streamlined die shape as a curved die profile, are determined. The corresponding results for those two die shapes are also determined by using the finite element code and compared with the upper bound results. These comparisons show a good agreement.

W pracy wyprowadzono uogólnione rozwiązanie ograniczenia górnego problemu wytłaczania bimetalowych belek o przekroju prostokątnym za pomocą tłoczników o dowolnym kształcie. Wyznaczono wyrażenia potęgowe opisujące wewnętrzne, ścinające oraz tarciowe obciążenia i zastosowano je w modelu matematycznym omawianego zagadnienia. Zaproponowana metoda badań pozwoliła na określenie nacisku podczas wytłaczania elementów przy użyciu dwóch typów tłocznika – optymalnego klinowego o profilu liniowym oraz tłocznika o zarysie krzywoliniowym, opływowym. W obydwu przypadkach obliczenia porównano z wynikami uzyskanymi z metody elementów skończonych. Porównanie to wykazało dobrą zgodność rozwiązania ograniczenia górnego z rezultatami MES.