In metal forming operation, the true strain in the $$X$$-direction is $$0.3$$ and in the $$Y$$-direction is $$-0.1.$$ The true strain in the $$Z$$-direction is

A hemispherical cup of radius $$'R'$$ is formed in a press working operation. The radius of blank would be

Calculate the smallest punch diameter that can be designed for piercing sheet metal strip with the following data. Crushing strength of the punch material is $$1500$$ $$MPa.$$ Thickness of the sheet is $$2$$ $$mm,$$ factor of safety is $$3,$$ and shear strength of the sheet material $$500$$ $$MPa$$ is