165

100 h

aLoss of strength will not exceed 5% at these times.

aLoss of strength will not exceed 5% at these times.

elements according to their proportion in the alloy, although magnesium and lithium tend to have a disproportionate effect. An approximate value of 10,000 ksi (69,000 MPa) is sometimes used, but moduli range from 10,000 ksi for pure aluminum (1xxx series), manganese (3xxx series), and magnesium-silicon alloys (6xxx series) to 10,800 ksi (75,000 MPa) for the aluminum-copper alloys and 11,200 ksi (77,200 MPa) for 8090, an aluminum-lithium alloy. Moduli of elasticity for various alloys are given in Table 9.14. This compares to 29,000 ksi (200,000 MPa) for steel alloys (about three times that of aluminum) and to 6500 ksi (45,000 MPa) for magnesium.

For aluminum, the tensile modulus is about 2% less than the compressive modulus. An average of tensile and compressive moduli is used to calculate bending deflections; the compressive modulus is used to calculate buckling strength.

Aluminum's modulus of elasticity is a function of temperature, increasing about 10% around -300°F(-200°C) and decreasing about 30% at 600°F (300°C).

At strains beyond yield, the slope of the stress-strain curve is called the tangent modulus and is a function of stress, decreasing as the stress increases. Values for the tangent modulus or the Ramberg-Osgood parameter n define the shape of the stress-strain curve in this inelastic region and are given in the U.S. Military Handbook on Metallic Materials and Elements for Aerospace Structures (MIL HDBK 5) [23] for many aluminum alloys. The Ramberg-Osgood equation is a (a s = -+0.002 (where e = strain a = stress Fy = yield strength

The modulus of rigidity (G) is the ratio of shear stress in a torsion test to shear strain in the elastic range. The modulus of rigidity is also called the shear modulus. An average value for aluminum alloys is 3800 ksi (26,000 MPa).

Poisson's ratio (v) is the negative of the ratio of transverse strain that accompanies longitudinal strain caused by axial load in the elastic range. Poisson's ratio is approximately 0.33 for aluminum alloys, similar to the ratio for steel. While the ratio varies slightly by alloy and decreases slightly as temperature decreases, such variations are insignificant for most applications. Poisson's ratio can be used to relate the modulus of rigidity (G) and the modulus of elasticity (E) through the formula

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