Properties of MetalsDOE-HDBK-1017/1-93YOUNG'S MODULUSYOUNG'S MODULUSThis chapter discusses the mathematical method used to calculate the elongationof a material under tensile force and elasticity of a material.EO 1.7STATE Hooke's Law.EO 1.8DEFINE Young's Modulus (Elastic Modulus) as it relates tostress.EO 1.9Given the values of the associated material properties,CALCULATE the elongation of a material using Hooke's Law.If a metal is lightly stressed, a temporary deformation, presumably permitted by an elasticdisplacement of the atoms in the space lattice, takes place. Removal of the stress results in agradual return of the metal to its original shape and dimensions. In 1678 an English scientistnamed Robert Hooke ran experiments that provided data that showed that in the elastic range ofa material, strain is proportional to stress. The elongation of the bar is directly proportional tothe tensile force and the length of the bar and inversely proportional to the cross-sectional areaand the modulus of elasticity.Hooke's experimental law may be given by Equation (2-3).(2-3)d PAEThis simple linear relationship between the force (stress) and the elongation (strain) wasformulated using the following notation.P=force producing extension of bar (lbf)=length of bar (in.)A=cross-sectional area of bar (in.^{2})d=total elongation of bar (in.)E=elastic constant of the material, called the Modulus of Elasticity, orYoung's Modulus (lbf/in.^{2})The quantity E, the ratio of the unit stress to the unit strain, is the modulus of elasticity of thematerial in tension or compression and is often called Young's Modulus.Rev. 0Page 11MS-02

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