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Material Strength

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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Material Strength

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  1. Material Strength

  2. 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

  3. 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

  4. 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

  5. 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)

  6. 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

  7. 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)

  8. 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

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