Engineering Materials

Mass friction of proeutectoid cementite \mathrm{W}_{\mathrm{Fe}_{3}} C^{\prime}=\frac{1.5-0.8}{6.7-0.8}=0.1186

Mass fraction of total cementite
\mathrm{W}_{\mathrm{Fe}_{3}} \mathrm{C}=\frac{1.5-0.035}{6.7-0.035}=0.2197

So, \quad \frac{W_{F_{3}} C^{\prime}}{W_{F_{e 3}} C}=\frac{0.1186}{0.2197}=0.54

Data given:
\begin{aligned} r & =\frac{\sqrt{2}}{10} \mathrm{~nm} \\ M & =24.092 \mathrm{~kg} / \mathrm{mol} \\ \mathrm{A} & =6.023 \times 10^{13} \end{aligned}
For FCC structure a=2 \sqrt{2} r=2 \sqrt{2} \times \frac{\sqrt{2}}{10}=\frac{4}{10}
So,volume of unit cell =a^{3}=\left(\frac{4}{10}\right)^{3}=0.064 \mathrm{~nm}^{3}
\mathrm{Ne}=4 for \mathrm{FCC}
\begin{aligned} \rho & =\frac{N_{e} \times M}{A \times \text { Volume of unit cell }} \\ & =\frac{4 \times \frac{24.092}{1000}}{6.023 \times 10^{3} \times \frac{0.064}{\left(10^{-9}\right)^{3}}} \\ & =2500 \mathrm{~kg} / \mathrm{m}^{3} \end{aligned}

Solidification range =A'B
\triangle ABC \text{ and } \triangle MB'C is similar
\begin{aligned} \frac{MA}{MB'}&=\frac{BC}{BC'}\\ \frac{700-T_A}{700-400}&=\frac{15}{30}\\ 700-T_A&=\frac{1}{2} \times 300\\ T_A&=550^{\circ}C \end{aligned}
Solidification range =T_A-T_B=550-400=150 ^{\circ}C

Fraction of pro eutectoid \alpha- Ferrite
=\frac{0.8-0.5}{0.8-0.025}=0.387

Surface Treatments:
During machining operations,small scratches and grooves are invariably introduced into the workpiece surface by cutting tool action. These surface markings can limit the fatigue life. It has been observed that improving the surface finish by polishing will enhance fatigue life significantly.
One of the most effective methods of increasing fatigue performance is by imposing residual compressive stresses within a thin outer surface layer. Thus, a surface tensile stress of external origin will be partially nullified and reduced in magnitude by the residual compressive stress. The net effect is that the likelihood of crack formation and therefore of fatigue failure is reduced.
Residual compressive stresses are commonly introduced into ductile metals mechanically by localized plastic deformation within the outer surface region. Commercially, this is often accomplished by a process termed shot peening. Small, hard particles (shot) having diameters within the range of 0.1 to 1.0 mm are projected at high velocities onto the surface to be treated. The resulting deformation induces compressive stresses to a depth of between one-quarter and one-half of the shot diameter.