Select the correct limit strain value (ε1*, ε2*) in plane strain from the choices when a steel sheet reaches instability as per maximum tension line, ε1* + ε2* = 0.25. (0, 0.25) (0.25, 0) (-0.25, 0.5) (0.5, 0)

The correct limit strain value (ε1*, ε2*) in plane strain when a steel sheet reaches instability as per maximum tension line, ε1* + ε2* = 0.25, would be (0.25, 0).

Here's why:

The equation ε1* + ε2* = 0.25 represents a line on a strain graph where the sum of ε1* and ε2* is always 0.25.

The options given are (0, 0.25), (0.25, 0), (-0.25, 0.5), and (0.5, 0).

If we substitute these options into the equation, we get:

For (0, 0.25): 0 + 0.25 = 0.25. This satisfies the equation.

For (0.25, 0): 0.25 + 0 = 0.25. This also satisfies the equation.

For (-0.25, 0.5): -0.25 + 0.5 = 0.25. This satisfies the equation as well.

For (0.5, 0): 0.5 + 0 = 0.5. This does not satisfy the equation.

However, the question specifies that we are looking for the strain values when the steel sheet reaches instability. In the context of material science, instability often occurs when the material is under maximum tension. This would likely occur when ε1* is at its maximum value, which in this case is 0.25. Therefore, the correct answer is (0.25, 0).