Elastic Constants
The elastic region will always be linear because any deformation caused by the applied load can be instantly reversed if the applied load is taken away. Stress-Strain equations are always represented in the
The "y" or dependent variable will always represent the stress value. The "M" will always represent the slope of the stress/strain curve. The slope of the elastic region is known as the elastic modulus. The "X" or the independent variable will always represent the value of strain
In all three elastic constants, the value of stress follows the same units.
Young's Modulus
It is used to explain the relationship between stress and strain when referring the Hooke's Law in the elastic region of the stress-strain curve. Since the elastic region is linear in the stress-strain curve it has a defined slope. Youngs Modulus can also be defined as the slope of the elastic region.
Young's Modulus can be used to determine how stiff a material is. The higher the value of Young's Modulus the stiffer the material. This also means it will have smaller elastic deformations. (The closer to the y-axis the line is the stiffer it is)
The value of Young's Modulus is relative to the strength of the interatomic bonds. The elastic strain causes the space between atoms to stretch apart. The interatomic bonds resist this which causes the material to resist failure. This is also why different materials have different values for Young's Modulus.
Hooke's law equation is used to describe, explain, and represent the elastic region in the stress-strain diagram
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The region denotes that when a material is put under a tensile load it will return to its original dimensions when the load is undone
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Hooke's Law Equation for the elastic region:
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It is written in slope-intercept form because when graphed it is strictly linear
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The E represents the ratio between stress and strain when referring to the elastic region (Young's Modulus)
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The value is represented as Psi (Pressure) in American units and PA (Pascals) every else
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This is because Young's Modulus is measured the same way as stress
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