This paper presents (i) the formulation that calculates an applied uniaxial load on an absolute precision load gauge (APLG) by using the finite deformation theory1,2 of an elastic solid, which was initially isotropic at strain-free state, (ii) design and construction of the APLG, and (iii) validity of the APLG by testing it under a compression machine with maximum capacity of 300 imperial tons. The load-carrying member of the APLG is a cylindrically shaped 7075 aluminum alloy with 122.61mm diameter, which can carry more than 480 metric tons of load in the elastic range without inducing plastic deformation. The vertically applied load is calculated using four measured data: a lateral dimensional change of a specimen in the horizontal direction and three travel times of horizontally propagating longitudinal, vertically polarized shear (SV) and horizontally polarized shear (SH) waves. These data can be easily measured in experiments with a great accuracy. The lateral dimensional change of the specimen is measured with a resolution of 50 nm and travel times of the sound waves are measured with accuracy better than a few parts in 100,000. The theory takes care of the linear and nonlinear elastic contributions of material behavior under finite deformation, contributing to great precision for the calculation of the applied load. The accuracy of the calculated load is better than 0.1 %. The APLG directly calculates the applied load in units of force or mass, and thus precludes the need for its calibration, providing advantages over the conventional load cells.
In the finite deformation theory the thermodynamic stress τ33 is calculated using the complex formulae and measured data. Dimensional changes are measured in the isothermal condition. The applied Cauchy stress σ33 is obtained from τ33 and fractional dimensional changes in lateral and vertical directions. Wave propagation is an adiabatic process that yields adiabatic second order elastic constants. Third order elastic constants obtained from the wave speed data and the dimensional change are mixed elastic constants. These adiabatic and mixed elastic constants are converted into isothermal values using the thermodynamics of finite deformation of elastic solids developed by this author. Then the isothermal second order elastic compliance constant and the isothermal third order elastic compliance constant are calculated. Finally applied load P is expressed Several APLG applied loads are obtained under several compressive loads up to 300 imperial tons at the Test Bay of Cornell University.
