Abstract: A linear integration of strain rate vector is developed.First, effective strain rate for slab forging with bulge is expressed in terms of two-dimensional strain rate vector.Its inner-product is integrated term by term.Second, sum of the integrated results is obtained, and an analytical solution to the stress factor obtained from a bulge formula.It turns out that the expression of power by the above inner-product integration is the same as that of the traditional immediate integration.Also, the calculated result of total forging pressure by formula in the present paper is in general agreement with that by Avitzur's formula, both 4.2% higher than the measured value in a press test.

Key words: slab forging, strain rate vector, inner-product, bulge, linear integration