Which one of the following is true in which the sheet will thicken and for a strain-hardening material, the tension will never reach a maximum. β < −1 β > −1 β = 0 β = 1
Question
Which one of the following is true in which the sheet will thicken and for a strain-hardening material, the tension will never reach a maximum. β < −1 β > −1 β = 0 β = 1
Solution
The statement that is true in which the sheet will thicken and for a strain-hardening material, the tension will never reach a maximum is β > -1.
Here's why:
The parameter β is a measure of the strain path, and it is defined as the ratio of the width strain to the thickness strain during deformation.
If β > -1, it means that the width strain is greater than the thickness strain. This results in the sheet thickening during deformation.
For a strain-hardening material, the tension will continue to increase as the material deforms, and it will never reach a maximum as long as the strain continues to increase. This is consistent with the condition β > -1.
Therefore, β > -1 is the correct answer.
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