The mechanism of coining is analyzed and several approximate solutions are given. The solutions were based on the strip, slip-line, and upper-bound methods of analysis. Comparison of the solutions for the local stress distribution could only be made for the strip and slip-line methods of analysis and it was found that the particular solutions obtained agreed reasonably well with each other in predicting coining pressures as functions of degree of coining. A comparison of the strip and upper-bound method of solution revealed that the predicted average coining pressures for a single central square groove are nearly identical for blanks having thicknesses of h0 = 1/16 in. for all values of b/b0 (degree of coining) except when b/b0 approaches unity. At b/b0 = 1 (deg of coining = 100 per cent), the modified strip method of analysis, using a cylindrical state of stress in the square corner of the groove, gave the highest average coining pressures. The upper-bound solution seems to overestimate the forging pressures for h0 > 1/16 in. for all values of b/b0, except when b/b0 is unity. A comparison of experimental average pressures, for coining 1-in-diameter blanks of commercially pure lead and aluminum, with the theoretical solutions, revealed that the modified strip method appears to be the best method for predicting the pressures when the ratio of b/b0 approaches unity. However, the exact pressure at b/b0 = 1 is indeterminable by use of this method. The analyses presented in the paper and comparisons of the solutions with experimental data reveal that a lowering of the coefficient of friction has a profound influence on decreasing the required coining pressures. The analyses further show that for high friction the pressure required for getting exact definition rises rapidly as the ratio b/b0 approaches unity.

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