Effect of stress on the law of approach to saturation magnetization in carbon steels

In high fields where the magnetization is approaching saturation, the resolved magnetic polarization I can be expressed by a power series of the inverse of external field H as: I=I_s-b/H ²-c/H³ . . ., or alternatively in terms of the reversible permeability μ_rev=1+(2b/H³+3c/H⁴+ . . .)/μ₀ where I_s is the spontaneous magnetic polarization and b, c, are constants. These equations express the law of approach to saturation magnetization. The coefficient b for a cubic crystal has been deduced as b=0.0762/I_s[K+1.5(λ₁₀₀-λ ₁₁₁)σ]², where σ is the applied stress and others are magnetic constants. The values of reversible permeability μ_rev under biasing field H were measured for carbon steels with applied stresses. The results showed that the square root of 2b changed linearly with the applied stress, The values of magnetic constant K andλ₁₀₀ -λ₁₁₁ were calculated, They agreed with the standard values, but were affected by chemical composition and heat treatment of materials, especially in λ₁₀₀-λ₁₁₁