Abstract: The flexural vibration equation of a beam under stress is set up. The solution of the equation indicates E=C (α)ω², where E stands for the apparent Young's modulus, C for a function of stress, and ω for the intrinsic frequency of sample. If the resonant frequencies of the first tone and the third one are measured at about same time, E and σ can be calculated.
The change of the apparent Young's modulus after charging with hydrogen is difined as ΔE=ΔE₁ (H) + ΔE₂, where ΔE₁ (H) has relation with the change of the perfect crystal interatomic cohesive force and ΔE₂ is induced by the change of stress. An artificially partial stress relaxation test was done to measure ΔE₂. The results show that during ageing after both charging with hydrogen and artificial stress releasing, the apparent modulus increased by 0.1-0.3%, i.e ₀ΔE=ΔE₂. Thus, the ΔE₁ (H) associated with the interatomic cohesive force does not evidently change during the ageing with evolving hydrogen of 7-8 wppm, i.e. hydrogen of 7-8 wppm does not significantly decrease the interatomic cohesive force of α-Fe.
The Forster's horizontal free-free bar apparatus was also used to measure the change of Young's modulus of a-Fe caused by hydrogen. The same conclusion was obtained.