37 (e). This may be justified using the Hall-Petch equation as thickness of layers is equivalent with the average grain size. Hardness decreases, however, with further decrease in thickness after the first peak. Non-compliance of the Hall-Petch equation in small thicknesses is attributed to ...
Decrease in thickness of layers in Ni/Cu nano-sized multilayer coatings leads to increase in hardness inFig. 37(e). This may be justified using the Hall-Petch equation as thickness of layers is equivalent with the average grain size. Hardness decreases, however, with further decrease in thickn...
However, importantly, the calculated fracture toughness values, which were derived using a newly developed semi-empirical equation, agreed well with the experimental results obtained by the authors, as well as with results obtained by other authors....
depending on the grain size and phases sampled by each indentation as shown inTable 5. Hardness decreased with increasing distance from the stir zone. The hardness of the stirzone and HAZ is found to be much higher than that of the base material, this may be due to grain refinement or du...
For example, an approximate equation connecting the two variables for steel is σUTS (psi) = 500 HB, where HB is the Brinell hardness. In addition, theory has shown that the hardness value (H) is related to the yield stress of metals through the formula H = 3σ0 and this relationship...
Notably, the simpler format of the equation and better prediction ability of the hardness model [4–9] has brought great attention and a broad application soon after its publication. Nevertheless, Chen et al. provided several remarks on the applications of their hardness model [10]: (1) The ...
From a theoretical point of view, Griffiths’ Fracture Theory [46], and the eponymous equation which shows the fracture tensile stress σF∝E, it is not surprising that Young’s modulus demonstrates a strong influence. Evidently though, the particle–particle powder friction, β, and onset of ...
for each temperature range: since the material model was built based on the range of 350°C to 450°C, the hardness predicted by the model increases exponentially with decreasing temperature due to the Arrhenius term in the constitutive equation (equation (3)), which is indeed observed in Fig...
The results show there is a good correlation between the dislocation density and the yield strength using the Taylor equation. The 伪 parameter in this equation is slightly lower for the higher Mo concentration in accordance with the less clustered dislocation structure....
In comparison, the hardness values obtained in this study for tungsten nanocrystals range from 24.73 to 54.7 GPa, with lower values associated with larger grain sizes. The relationship between grain size and hardness in nanocrystalline metals is typically described by the Hall–Petch equation, which ...