Non-proportional loads

Fig. 9.2 Non-proportional loads in an axle subjected to cyclic traction F and torque T out-of-phase that a generate out-of-phase stress components, b principal directions are continuousiy...

OP loadings at the same equivalent strain amplitudes suggest that the von Mises criterion underestimates the fatigue damage under non-proportional loadings. 

Itoh, T., Kameoka, M., Obataya, Y. A new model for describing a stable cyclic stress-strain relationship under non-proportional loading based on activation state of slip systems. Fatigue Fract. Eng. Mater. Struct. 27, 957-966 (2004)... 

Sao and Smo are the initial acid and metal site densities. The AT, A, and A, are the adsorption equilibrium constants and initiation rate constants discussed in [8]. Equation (8) says that the prodigious coke producers are methylcyclopetadienes and methylclopentenes. The latter predominate at high Ph with r /Ph, while the former predominate at low Ph with to MPh). Equation (9) is consistent with the non-proportional increase in 1/a with increased Pt loading in Table 1. 

Loads, deformations and forces are already nonlinearly interdependent in the two-dimensional case. Therefore, the nonlinear equations to calculate the forces can only be solved iteratively. This non-proportional relation between loads, deformations and forces characterises the positive but complex load-bearing behaviour of ETFE-foil structures. 

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