The correlations between the properties of materials only refer to their atom structure. High magnetic permeability is not necessarily leads to high reactivity. There are mainly two types of stainless steel-- Austenite (ex. SUS 2 & 3 series) and Martensite (ex. SUS 4 series). Martensite is formed from Austenite with a series of special treatment. Having different atom structures, they are different in properties. Chemical properties, say reactivity, is what determining the resistivity to water and acids. Atom structures also determine the mechanical properties of a material. The strength and hardness is usually considered in this category. The level of response to magnets is base on the magnetic permeability, which is also determined by the atom structures of the material. If a material can be stuck by magnets, the material is magnetic. In magnetic materials, the atom structure is arranged in Body-Centered Lattice (BCC). Austenitic structures (FCC) are basically non-magnetic permeable while Martensite (BCC) is magnetic permeable. For motor shaft where magnetic is required for good performance, Martensitic stainless steel is preferred over Austenite.
So why do people think that if a block of steel is magnetic, it is not stainless steel? Stainless steel, containing chromium, can form a thin film of chromium oxide on the metal surface, preventing the rest of material from oxidation. Nickel, which forms the Austenite, helps the thin film to retain on the surface. There are two types of magnetic stainless steel-- Ferritic, martensitic. In these types, nickel is not used in the alloy recipe. Ferritic steel is the most basic stainless steel and is more susceptible to corrosion than all others. Because people cannot normally distinct between ferritic and martensitic stainless steel, they well just assume the if the material is magnetic, it is inferior. Furthermore, if Austenite (such as SUS 304, 316) is processed, especially forging and casting, its structure will reform and became magnetic.
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