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Material Strength. Stress vs Strain. A graph of stress versus strain is linear for small stresses. The slope of stress versus strain is a modulus that depends on the type of material. For normal stress this is Young’s modulus Y . stiff material. Stress s. elastic material. Strain e.

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Presentation Transcript
stress vs strain
Stress vs Strain
  • A graph of stress versus strain is linear for small stresses.
  • The slope of stress versus strain is a modulus that depends on the type of material.
  • For normal stress this is Young’s modulus Y.

stiff material

Stress s

elastic material

Strain e

spring constant
Spring Constant
  • Young’s modulus is a from a linear relation like Hooke’s law.
    • Young’s modulus describes a type of material.
    • The spring constant describes an object.
  • Y and k are related.

F

DL

inelastic material
Inelastic Material
  • The linear behavior of materials only lasts up to a certain strength – the yield strength.
  • Materials can continue to deform but they won’t restore their shape.
  • For very high strain a material will break.

breaking strength

Stress s

yield strength

Strain e

shear modulus
Shear Modulus
  • Materials also have a modulus from shear forces.
  • Shear modulus S also matches with a spring constant.
  • The angle g = Dx/L is sometimes used for shear.

F

Dx

L

g

A (goes into screen)

twist a leg
One common fracture is a torsion fracture. A torque is applied to a bone causing a break.

The shear modulus of bone is 3.5 GPa.

The lower leg has a breaking angle of 3.

It requires 100 Nm of torque.

Torque and angle apply.

Angle is Dx/L = tang

Approximately Rf/L = g

Sheer is related to torque.

Twist a Leg

Rf

L

g

bulk modulus
Bulk Modulus
  • Pressure changes volume, not length.
  • Bulk modulus B relates changes in pressure and volume.
  • The negative sign represents the decrease in volume with increasing pressure.

P

DV

V

A (surface area)

under pressure
Steel has a bulk modulus of B = 60 GPa. A sphere with a volume of 0.50 m3 is constructed and lowered into the ocean where P = 20 MPa.

How much does the volume change?

Use the relation for bulk modulus.

B = -(DP) / (DV/V)

DV= -VDP / B

Substitute values:

(-0.50 m3)(2.0 x 107 Pa) / (6.0 x 1010 Pa)

DV = -1.6 x 104 m3

Under Pressure