Engineering Concepts: Strength of Tempered Martensite
One of the remarkable aspects of steel is that a wide range of strength properties can be obtained by quench hardening and subsequent tempering. The yield strength of AISI 8620 steel can be made equivalent to that of AISI 1045 steel by choosing the appropriate tempering temperatures for each. To fully explain this behavior, a short discussion of crystal dislocation mechanics is required.
Yielding is essentially a result of dislocation motion and in soft metals the dislocation can move long distances without interruption. The yield strength is dependent upon a combination of solid solution (or solute) strengthening and grain size. For single-phase alloys, such as brass and austenitic stainless steel, a decrease in the grain diameter will produce an increase in the yield strength. Thus, decreasing the mean free path of the dislocation produces strengthening.
Strengthening in Fe-C martensites is also a combination of solute strengthening and a refinement in the grain size. In general, the strength of martensite increases proportional to the square root of the carbon content. Upon tempering, the carbon in solid solution decreases rapidly as carbides are precipitated; and like age-hardening of copper-beryllium or aluminum alloys, these carbides contribute to the strengthening by decreasing the mean free path of the dislocations. The various strengthening contributions, as a function of the tempering temperature, are schematically shown in Figure 1.
Tempering usually decreases the strength of the as-quenched martensite; however, at tempering temperatures below (392F) 200C, hardening is observed in some steels with carbon contents less than 0.2 wt.%. Here, the increase in strength from carbide precipitation exceeds the loss in strength as the carbon solute is removed from solid solution. For carbon contents greater than 0.2 wt.%, the maximum strength is always obtained in the as-quenched, martensitic condition, i.e. the solute strengthening is greater than that obtained by carbide precipitation.
In the tempered condition, the microstructure consists of a matrix of iron with a uniform dispersion of carbides. The crystal structure of the matrix and carbides is dependent upon alloy content and tempering temperature. Yielding in the tempered condition is dependent upon the spacing between the carbide particles. This can be demonstrated by plotting the yield strength versus the reciprocal of the distance between the carbides, i.e. 1/L. Figure 2 shows a composite of four carbon steels; three of which were quenched and tempered and one was spheroidized. All four steels have different carbon contents. Various strength levels were obtained by a change in temperature (or time) during tempering or spheroidization.
A simple equation can be used to relate the yield strength to the carbide distribution in terms of the carbide spacing, L, the volume fraction, Vf, and the carbide radius, rcarbide. Here, k represents a materials constant and tsolute is the strengthening from carbon and alloy in the matrix. The carbide spacing, L, is based upon a simple cubic arrangement of carbides in the matrix. The carbide spacing can be decreased by either decreasing the size of the carbide particle by lowering the tempering temperature or by increasing the carbon content, which results in a higher volume fraction of the carbide.