volume fraction should be as large as possible (to minimize λ) without exceeding the percolation limit (approximately 18 volume percent) at which particle-particle contact becomes highly probable. Precipitation hardening, solid solution hardening, grain size minimization, and deformation each may promote secondary hardening. The cohesive strength of the particle interface should be high. Impurities and large inclusions should be avoided.
Many of these guidelines have been demonstrated in rapid solidification technology alloys.82 In such alloys, segregation is minimized and overaging of particles formed during solidification and cooling is suppressed. Thus, the fine dispersoids desirable for strength can be formed.
The constant σ0 in Equation (1) is not well understood theoretically.
Pileup-pileup interactions can modify Equation (1).82 Therefore, three-dimensional calculations are needed.
Refinements needed in the interpretation of Equation (2) include consideration of screening effects caused by different elastic properties of obstacles; statistical averaging or computer simulation for finite-size obstacles and those with long-range strain fields; and further work on the weak, dilute solute case.
Experimentally derived values of cohesive energies of particles, which would be valuable in providing a guideline for alloy design, are sparse.
A detailed estimate of the decohesion probability for a dispersoid is required.
Three-dimensional models of dislocations would be beneficial in understanding particle decohesion and crack-void interactions.
More experiments are needed to test the statistical models for the DBTT.
With the complications of multicomponent systems, adsorption, absorption, and diffusion, the roles of solute and environment cannot be discussed completely. However, several advances in the past 25 years are relevant to this discussion. Although there had been suggestions of such effects earlier, the role of impurities in enhancing embrittlement, specifically intergranular fracture, is now well established.83 The key was the development of Auger electron microscopy. Such microscopy showed, for example, that elements in Groups V and VI of the periodic table adsorb to prior austenite grain boundaries to cause temper embrittlement of nickel-chromium steels. Coad-