Behaviour of Elastic Materials & Direct and Shear Strain

Question 1

If we have a force extension graph, what is the cause of the wobbly plateau after the limit of proportionality?

Answer 1

Strain Hardening

Question 2

What is Elongation proportional and inversely proportional to?

Answer 2

Proportional to:
* Load
* Initial Length

Inversely Proportional to:
* Cross-Sectional Area

Question 3

What is the equation for direct strain?

Answer 3

Elongation / Original Length

Question 4

What is the equation for elongation considering the Elastic Modulus, Force, Initial Length and Cross-Sectional Area?

Answer 4

Elongation = (1 / Elastic Modulus) * (Force / Initial Length) / Cross-Sectional Area

Question 5

What is the elastic modulus for uniaxial tension / compression?

Answer 5

Elastic Modulus = Stress / Strain

Question 6

What is an isotropic material?

Answer 6

A material where the modulus of elasticity or other properties are the same in all directions. This is in all directions, not in all locations

Question 7

What is an anisotropic material?

i

Answer 7

A material where the modulus of elasticity or other properties are different according to direction

Question 8

What is the factor of safety of a material?

Answer 8

f.o.s. = Actual Strength / Required Strength

Question 8

What must the factor of safety be greater than?

Answer 8

1

Question 9

For parts made of ductile materials and when permanent deformation is unacceptable, what do we assume the actual strength to be?

Answer 9

The Yield Stress

Question 9

For a brittle material, what do we use instead of the yield stress which would be present in ductile materials?

Answer 9

We use the Ultimate Stress

Question 9

What is Poisson’s Ratio?

Answer 9

v = - Lateral Strain / Axial Strain

The minus is present as the ratio falls

Question 10

What is necking?

Answer 10

It’s when there is a point on the sample where the diameter decreases

Question 11

How can we calculate the shear strain of a sample?

Answer 11

If one of the corners on a square sample is pulled, the sample deforms and becomes more like a rhombus.
We can say that once we rotate the rhombus onto its side, we can see an angle called gamma which appears due to the deformation.
We can say due to trigonometry, that tan gamma = Elongation / Length of the original sides of the sample
Therefore, using small angle approximations, we can then say that gamma = Elongation / Length of the original sides of the sample

Finally, we then know that gamma is the shear strain of the sample, and that gamma is also equal to the change of a right angle (measured in radians)