Cup Drawing (Sheet Metal) — Identify the Stress States During the deep drawing of a cylindrical cup from a flat blank, which stress states are present in the flange and in the drawn wall?

Introduction / Context:
Deep drawing transforms a flat sheet into a cup by forcing material to flow radially inward and then vertically along the punch. Stress states vary by region and dictate failure modes such as wrinkling, tearing, or earing.

Given Data / Assumptions:

• Standard cylindrical cup drawing with blank holder pressure applied.
• Negligible bending effects compared to membrane stresses for the conceptual analysis.
• Isotropic sheet assumption for baseline reasoning.

Concept / Approach:
In the flange, material flows radially into the die; the circumferential (hoop) direction experiences compression, which can cause wrinkling if the blank holder force is insufficient. In the cup wall, the material is stretched longitudinally along the punch direction, creating tensile stress that can lead to wall thinning or tearing if excessive.

Step-by-Step Solution:
Analyze flange: radial inflow induces hoop compression → wrinkling tendency.Analyze wall: drawn over the die radius and along the punch → axial/longitudinal tension.Combine insights: compressive in flange and tensile in wall simultaneously.Therefore, both (a) and (b) are correct.

Verification / Alternative check:
Forming limit diagrams and draw ratio limits correlate failures with these respective stress states.

Why Other Options Are Wrong:
Only compression or only tension fails to represent the full mechanics of drawing.Shear-only description ignores dominant membrane stresses governing defects.

Common Pitfalls:
Confusing flange compression with wall compression; the wall is primarily in tension.

Final Answer:
both (a) and (b)