Abbott Aerospace – Analysis Method

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Taken from: Analysis and Design of Composite and Metallic Flight Vehicle Structures

Metal Materials, Stress Strain Curves

Abbott Aerospace – Analysis Method

XL-VIKINGDisplay Your Math in Excel

Taken from: Analysis and Design of Composite and Metallic Flight Vehicle Structures

Metal Materials, Stress Strain Curves

The two most common material types used in aircraft construction are steel and aluminum. With steel being used sparingly for specific high strength, high endurance or high-temperature applications because of its relatively high density (approx. 3 times that of aluminum).

Both steels and aluminum exhibit plastic behavior but in slightly different ways.

Stress-Strain Curve for a Typical Steel (MIL-HNDBK-5H, 1998)

Stress-Strain Curve for a Typical Aluminum (MIL-HNDBK-5H, 1998)

Abbott Aerospace – Analysis Method

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Taken from: Analysis and Design of Composite and Metallic Flight Vehicle Structures

Metal Materials, Stress Strain Curves

The Stress-Strain curve can be modeled with a simple close approximation, this is called the Ramberg-Osgood method and is defined in (NACA-TN-902, 1943). An adaptation of the Ramberg-Osgood approach is defined in section 1.6 of

(MIL-HNDBK-5H, 1998) and (NACA-TN-927, 1944). Having a simple method for modeling the stress-strain behavior of a material proves to be extremely useful when an accurate picture of how a feature may behave beyond the material yield point is required.

𝑒 = 𝑒𝑒 + 𝑒𝑝

The model of the stress-strain curve is predicated on the following relationship

Where: 𝑒𝑒 = Τ𝑓 𝐸 And: 𝑒𝑝 = 0.002𝑓

𝐹𝑦

𝑛

Abbott Aerospace – Analysis Method

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Taken from: Analysis and Design of Composite and Metallic Flight Vehicle Structures

Metal Materials, Stress Strain Curves

the total strain is the sum of the elastic and plastic strains. This can be re-written:

𝑒 =𝑓

𝐸+ 0.002

𝑓

𝐹𝑦

𝑛

Where:𝒏 Stress-strain curve shape factor (Ramberg Osgood Parameter)𝒇 Applied stress𝑭𝒚 Material yield strength

The lower the value of n, the more gradual the transition between the elastic and plastic regions of the curve. For higher values of n the transition is more abrupt. Metals with low values of n usually have a lower yield strength relative to their ultimate strength.

Abbott Aerospace – Analysis Method

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Taken from: Analysis and Design of Composite and Metallic Flight Vehicle Structures

Metal Materials, Stress Strain Curves

Full Range Ramberg-Osgood Approximate Stress-Strain Curve or a Sample Aluminum with a Low ‘n’ Value

Full Range Ramberg-Osgood Approximate Stress-Strain Curve or a Sample Aluminum with a High ‘n’ Value

Abbott Aerospace – Analysis Method

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Taken from: Analysis and Design of Composite and Metallic Flight Vehicle Structures

Metal Materials, Stress Strain Curves

Note that metal materials also will have small differences in strength and stiffnessproperties for compression and tension. They also usually have a different shapefactor ‘n’.

The shape factor and strength can also vary with grain direction.

(MIL-HNDBK-5H, 1998) notes this about theshape factor ‘n’:

“While this relationship may not be exact, it issufficiently accurate for use up to the yieldstrength for many materials, but cannot beemployed to compute full-range stress-straincurves.”

Abbott Aerospace – Analysis Method

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Taken from: Analysis and Design of Composite and Metallic Flight Vehicle Structures

Metal Materials, Stress Strain Curves

An approximate method for calculating the shape factor in the plastic region can bederived from the approach in (MIL-HNDBK-5H, 1998):

𝑛𝑢 =lo g

𝑒𝑓0.002

lo g𝑓𝑡𝑢𝑓𝑡𝑦

Where:𝒏𝒖 Stress-strain curve shape factor in the ultimate region𝒆𝒇 Elongation at failure

𝒇𝒕𝒖 Material ultimate tensile strength𝒇𝒕𝒚 Material yield strength

It is recommended that the ultimate shape factor is used above fty . When plotting fullrange stress train curves a smoothing function can be used to avoid an unnatural stepin the value of ‘n’.

Abbott Aerospace – Analysis Method

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Taken from: Analysis and Design of Composite and Metallic Flight Vehicle Structures

Metal Materials, Stress Strain Curves

Different measures of the nonlinear nature of the stress-strain curve are useful andused in the correction of buckling allowable stresses for plastic effects. The two mostcommonly used are the tangent modulus and the secant modulus

The tangent modulus is given by the following expression:

𝐸𝑡 =1

1𝐸 +

0.002 ∙ 𝑛𝑓𝑦

∙𝑓𝑓𝑦

𝑛−1

The secant modulus is given by the following expression:

𝐸𝑠 =𝑓

𝑓𝐸+ 0.002

𝑓𝑓𝑦

𝑛

Abbott Aerospace – Analysis Method

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Taken from: Analysis and Design of Composite and Metallic Flight Vehicle Structures

Metal Materials, Stress Strain Curves

A material property that is commonly missing from the certified, public domain material data is the shear yield strength. An approximation can be made for this value using the following expression:

𝑓𝑠𝑦 =൯𝑓𝑡𝑦(𝐿) + 𝑓𝑡𝑦(𝐿𝑇) + 𝑓𝑐𝑦(𝐿) + 𝑓𝑐𝑦(𝐿𝑇

4∙

2 ∙ 𝑓𝑠𝑢)𝑓𝑡𝑢(𝐿) + 𝑓𝑡𝑢(𝐿𝑇

An acceptable approximation for the shear shape factor is:

𝑛𝑠 =𝑛𝑐𝐿 + 𝑛𝑐𝐿𝑇 + 𝑛𝑡𝐿 + 𝑛𝑡𝐿𝑇

4

We have created a spreadsheet that constructs the elasto-plastic material curves from basic material properties.

AA-SM-000-001 Aluminum Material Data Basic Full Curves and Data