Question

Spring back occurs due to

• A. grain growth
• B. plastic deformation
• C. elastic recovery
• D. diffusion

Hint:

To compensate for springback in industrial tooling:
- Overbending: Bend the sheet past the target angle so that it springs back exactly to the desired angle.
- Bottoming: Apply a high localized compressive force at the bend radius at the end of the stroke to force plastic flow in the neutral zone.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
This question asks for the underlying physical mechanism that causes "springback" in sheet metal forming processes.
Springback is a dimensional defect where the sheet metal attempts to recover its original shape slightly after the forming loads are released.

Step 2: Key Formula or Approach:
When a metal sheet is bent, the outer fibers experience tensile stress while the inner fibers experience compressive stress.
Both regions undergo plastic deformation at the surface, but near the neutral axis, the stress is low and remains strictly within the elastic limit.
The relationship between initial bend radius (\( R_i \)) and final bend radius (\( R_f \)) after springback can be estimated by:
\[ \frac{R_i}{R_f} = 4 \left(\frac{R_i Y}{E T}\right)^3 - 3 \left(\frac{R_i Y}{E T}\right) + 1 \]
where:
\( Y \) is the yield strength.
\( E \) is the elastic modulus (Young's modulus).
\( T \) is the sheet thickness.

Step 3: Detailed Explanation:

• Elastic Unloading: During any plastic deformation process, the total strain \( \epsilon_{\text{total}} \) is composed of both elastic and plastic components:
\[ \epsilon_{\text{total}} = \epsilon_{\text{elastic}} + \epsilon_{\text{plastic}} \]
- When the bending tool (punch and die) is retracted, the external load is reduced to zero.
- The material unloads elastically along a path parallel to the elastic modulus line on the stress-strain curve.
- The elastic portion of the strain (\( \epsilon_{\text{elastic}} \)) is fully recovered, while only the plastic strain remains permanent.
- This elastic recovery causes the bend angle to decrease and the bend radius to increase, which is called springback.

• Influencing Factors: Materials with high yield strength \( Y \) and low elastic modulus \( E \) (such as high-strength steels or aluminum) display the most significant springback.


Step 4: Final Answer:
Springback is caused entirely by the elastic recovery of the material upon the removal of the forming tool.
Thus, the correct option is (C).