During a tensile test a steel specimen was subjected to a tensile load of 180kN and gave the following results.
Gauge length = 50.000mm
Final length = 50.573
Original diameter = 10.000
final diameter = 10.0328
Determine;
Youngs modulus
Poissons ratio
bulk modulus
I cant figure this out so i would really appreciate your help!
Gauge length = 50.000mm
Final length = 50.573
Original diameter = 10.000
final diameter = 10.0328
Determine;
Youngs modulus
Poissons ratio
bulk modulus
I cant figure this out so i would really appreciate your help!
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We have to assume that the deformation was elastic. Let's start with Young's modulus, which is basically a spring constant, telling you how much the material stretches for a given amount of load. In order to make the Young's modulus an intensive property (that is, a property of the material itself, independent of the geometry), we use stress as the analogue of force, and strain as the analogue of distance.
Strain is equal to the change in length divided by the original length (this is technically engineering strain; true strain takes an integral form). The strain in the sample is
(50.573 mm - 50 mm) / 50 mm = 0.01146
The stress is equal to the load divided by the original cross-sectional area (again, this is engineering stress; true stress uses the actual cross section at the given load).
180 kN / [pi * (10.0000 mm)^2 / 4] = 2.2918 kN/mm^2 = 2.2918 GPa
The Young's modulus is equal to the engineering stress divided by the engineering strain,
E = 2.2918 GPa / 0.01146 = 200 GPa
The Poisson ratio measures how much a material "pulls itself in" in the direction perpendicular to a load. It's equal to the negative of the (engineering) strain in the perpendicular direction divided by the (engineering) strain in the loading direction. (Again, this is an engineering form, and it's more accurately expressed as a differential, d(strain perpendicular) / d(strain in loading direction).) Note that, because most materials contract perpendicular to the direction of a tensile load, the negative factor makes the Poisson ratio positive. But your sample increases in diameter, so it should have a negative Poisson ratio.
Strain is equal to the change in length divided by the original length (this is technically engineering strain; true strain takes an integral form). The strain in the sample is
(50.573 mm - 50 mm) / 50 mm = 0.01146
The stress is equal to the load divided by the original cross-sectional area (again, this is engineering stress; true stress uses the actual cross section at the given load).
180 kN / [pi * (10.0000 mm)^2 / 4] = 2.2918 kN/mm^2 = 2.2918 GPa
The Young's modulus is equal to the engineering stress divided by the engineering strain,
E = 2.2918 GPa / 0.01146 = 200 GPa
The Poisson ratio measures how much a material "pulls itself in" in the direction perpendicular to a load. It's equal to the negative of the (engineering) strain in the perpendicular direction divided by the (engineering) strain in the loading direction. (Again, this is an engineering form, and it's more accurately expressed as a differential, d(strain perpendicular) / d(strain in loading direction).) Note that, because most materials contract perpendicular to the direction of a tensile load, the negative factor makes the Poisson ratio positive. But your sample increases in diameter, so it should have a negative Poisson ratio.
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