Measurement error of Young's modulus considering the gravity and thermal expansion of thin specimens for in situ tensile testing

Most miniature in situ tensile devices compatible with scanning/transmission electron microscopes or optical microscopes adopt a horizontal layout. In order to analyze and calculate the measurement error of the tensile Young's modulus, the effects of gravity and temperature changes, which would respectively lead to and intensify the bending deformation of thin specimens, are considered as influencing factors. On the basis of a decomposition method of static indeterminacy, equations of simplified deflection curves are obtained and, accordingly, the actual gage length is confirmed. By comparing the effects of uniaxial tensile load on the change of the deflection curve with gravity, the relation between the actual and directly measured tensile Young's modulus is obtained. Furthermore, the quantitative effects of ideal gage length l(o), temperature change Delta T and the density rho of the specimen on the modulus difference and modulus ratio are calculated. Specimens with larger l(o) and rho present more obvious measurement errors for Young's modulus, but the effect of Delta T is not significant. The calculation method of Young's modulus is particularly suitable for thin specimens.