Elastic Stretch Comparison — How Far a Bar of Each MIL-HDBK-5 Material Stretches Under Load, and How the Modulus Changes With Temperature

A straight bar of length L and cross-section area A, pulled with a load P, carries a stress σ = P/A. While the material stays elastic the strain is ε = σ/E and the bar stretches δ = εL = PL/AE. The stress is the same in every material, so the stretch is simply inversely proportional to the modulus: aluminum (E about 10×10³ ksi) stretches roughly three times as far as steel (about 29×10³ ksi). The axial stiffness AE/L is the load per unit of stretch, the spring rate of the bar.

MIL-HDBK-5 gives the modulus as a percentage of its room-temperature value against temperature. Each curve here is multiplied by the material’s own tabulated E, so the stretch-vs-temperature chart is in real inches or millimetres. Where no modulus curve has been digitized, the material shows its room-temperature value only, marked ◇.

The formula is elastic only. The σ/F_ty column compares the stress with the tensile yield allowable at the same temperature. Above 100% the bar yields and stretches far more than shown. F_ty is a 0.2%-offset value, so the real curve already bends slightly from about 70% of it. Thermal growth from heating the bar (α ΔT L) is not included; the thermal expansion chart on the comparison page has α.

The room-temperature modulus and yield are transcribed from the MIL-HDBK-5J design mechanical and physical properties tables; the temperature curves are digitized from the handbook’s effect-of-temperature figures. E is a typical value, not an A- or B-basis allowable. MIL-HDBK-5 was superseded by MMPDS for new design work.