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A 1.5 mm thick sheet is subject to unequal biaxial stretching and the true strains in the directions of stretching are 0.05 and 0.09. The fh'1al thickness of the sheet in mm is
- a)1.414
- b)1.304
- c)1 362
- d)289
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
A 1.5 mm thick sheet is subject to unequal biaxial stretching and the ...
To find the final thickness of the sheet after unequal biaxial stretching, we can use the formula for true strain in the direction of stretching:
ε = ln(l_f/l_i)
Where ε is the true strain, l_f is the final length, and l_i is the initial length.
Given that the initial thickness of the sheet is 1.5 mm, we can find the final thickness by rearranging the formula:
l_f = l_i * e^ε
First, let's calculate the final length in the first direction of stretching:
l_f1 = 1.5 mm * e^0.05 = 1.577 mm
Now, let's calculate the final length in the second direction of stretching:
l_f2 = 1.5 mm * e^0.09 = 1.638 mm
Since the sheet is subject to unequal biaxial stretching, the final thickness will be the average of the final lengths in the two directions:
l_f_avg = (l_f1 + l_f2) / 2 = (1.577 mm + 1.638 mm) / 2 = 1.6075 mm
Therefore, the final thickness of the sheet is approximately 1.6075 mm.
However, none of the given answer options match this value exactly. The closest option is option 'B' with a value of 1.304 mm. It seems like there might be a mistake in the answer options provided, as option 'B' does not match the calculated value.
ε = ln(l_f/l_i)
Where ε is the true strain, l_f is the final length, and l_i is the initial length.
Given that the initial thickness of the sheet is 1.5 mm, we can find the final thickness by rearranging the formula:
l_f = l_i * e^ε
First, let's calculate the final length in the first direction of stretching:
l_f1 = 1.5 mm * e^0.05 = 1.577 mm
Now, let's calculate the final length in the second direction of stretching:
l_f2 = 1.5 mm * e^0.09 = 1.638 mm
Since the sheet is subject to unequal biaxial stretching, the final thickness will be the average of the final lengths in the two directions:
l_f_avg = (l_f1 + l_f2) / 2 = (1.577 mm + 1.638 mm) / 2 = 1.6075 mm
Therefore, the final thickness of the sheet is approximately 1.6075 mm.
However, none of the given answer options match this value exactly. The closest option is option 'B' with a value of 1.304 mm. It seems like there might be a mistake in the answer options provided, as option 'B' does not match the calculated value.
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A 1.5 mm thick sheet is subject to unequal biaxial stretching and the ...
Final thickness=initial thickness/e€1*e€2
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A 1.5 mm thick sheet is subject to unequal biaxial stretching and the true strains in the directions of stretching are 0.05 and 0.09. The fh'1al thickness of the sheet in mm isa)1.414b)1.304c)1 362d)289Correct answer is option 'B'. Can you explain this answer?
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