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You do a series of tensile tests on plates of a magnesium alloy that have been subjected to prior cold rolling to true plastic strains of 0.1, 0.2 and 0.3. The resulting true stress-true strain curves are shown below (including a zoomed in version expanding on the small strain region). It is reasonable to approximate the the 0.2% offset yield strength of the magnesium as ✓ MPa for 0.2 and ✓ MPa for 0.3. Assuming the yield strength is proportional to the square root of the prior true plastic strain results in a hardening coefficient of approximately k ✓ MPa. Hence, we can predict that we need a prior plastic strain of approximately MPa for 0.1 plastic strain, to obtain a gth of 120 MPa. 85

You do a series of tensile tests on plates of a magnesium alloy that have been subjected to prior cold rolling to true plastic strains of 0.1, 0.2 and 0.3. The resulting true stress-true strain curves are shown below (including a zoomed in version expanding on the small strain region). It is reasonable to approximate the the 0.2% offset yield strength of the magnesium as ✓ MPa for 0.2 and ✓ MPa for 0.3. Assuming the yield strength is proportional to the square root of the prior true plastic strain results in a hardening coefficient of approximately k ✓ MPa. Hence, we can predict that we need a prior plastic strain of approximately MPa for 0.1 plastic strain, to obtain a gth of 120 MPa. 85

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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True Stress (MPa) True Stress (MPa) True Stress (MPa) 250 200 150 100 50 0 0.00 250 200 150 100 50 0 0.00 250 200 150 100 50 0 0.00 Ep=0.1 0.01 Ep = 0.2 0.01 Ep = 0.3 0.01 0.02 True Strain 0.02 0.03 0.02 0.03 True Strain 0.03 True Strain 0.04 0.04 0.04 True Stress (MPa) 0.05 0.000 0.001 True Stress (MPa) Ep = 0.1 True Stress (MPa) Ep = 0.2 0.05 0.000 0.001 Ep = 0.3 Zoomed version of left plot 0.002 0.003 0.004 0.005 0.006 True Strain Zoomed version of left plot 0.002 0.003 0.004 0.005 0.006 True Strain Zoomed version of left plot 0.05 0.000 0.001 0.002 0.003 0.004 0.005 0.006 True Strain
Transcribed Image Text:True Stress (MPa) True Stress (MPa) True Stress (MPa) 250 200 150 100 50 0 0.00 250 200 150 100 50 0 0.00 250 200 150 100 50 0 0.00 Ep=0.1 0.01 Ep = 0.2 0.01 Ep = 0.3 0.01 0.02 True Strain 0.02 0.03 0.02 0.03 True Strain 0.03 True Strain 0.04 0.04 0.04 True Stress (MPa) 0.05 0.000 0.001 True Stress (MPa) Ep = 0.1 True Stress (MPa) Ep = 0.2 0.05 0.000 0.001 Ep = 0.3 Zoomed version of left plot 0.002 0.003 0.004 0.005 0.006 True Strain Zoomed version of left plot 0.002 0.003 0.004 0.005 0.006 True Strain Zoomed version of left plot 0.05 0.000 0.001 0.002 0.003 0.004 0.005 0.006 True Strain
Question 4 You do a series of tensile tests on plates of a magnesium alloy that have been subjected to prior cold rolling to true plastic strains of 0.1, 0.2 and 0.3. The resulting true stress-true strain curves are shown below (including a zoomed in version expanding on the small strain region). It is reasonable to approximate the the 0.2% offset yield strength of the magnesium as ✓ MPa for 0.1 plastic strain, ✓ MPa for 0.2 and ✓ MPa for 0.3. Assuming the yield strength is proportional to the square root of the prior true plastic strain results in a hardening coefficient of approximately k= ✓ MPa. Hence, we can predict that we need a prior plastic strain of approximately ✓to obtain a hgth of 120 MPa True Stress (MPa) 250 200 100 85 95 50 105 115 125 135 145 300 350 0.12 0.14 150 0.16 0.18 155 165 175 200 250 0.1 True Stress (MPa) Ep = 0.1 Zoomed version of left plot
Transcribed Image Text:Question 4 You do a series of tensile tests on plates of a magnesium alloy that have been subjected to prior cold rolling to true plastic strains of 0.1, 0.2 and 0.3. The resulting true stress-true strain curves are shown below (including a zoomed in version expanding on the small strain region). It is reasonable to approximate the the 0.2% offset yield strength of the magnesium as ✓ MPa for 0.1 plastic strain, ✓ MPa for 0.2 and ✓ MPa for 0.3. Assuming the yield strength is proportional to the square root of the prior true plastic strain results in a hardening coefficient of approximately k= ✓ MPa. Hence, we can predict that we need a prior plastic strain of approximately ✓to obtain a hgth of 120 MPa True Stress (MPa) 250 200 100 85 95 50 105 115 125 135 145 300 350 0.12 0.14 150 0.16 0.18 155 165 175 200 250 0.1 True Stress (MPa) Ep = 0.1 Zoomed version of left plot
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