Chapter 12, Problem 12.102P

Interpretation Introduction

(a)

Interpretation:

The amount, composition and hardness of material at $\text{728° C}$ should be determined.

Concept Introduction:

Material hardness is the property of a metal due to which material resist the plastic deformation. Plastic deformation means material deformation which undergoes non-reversible change. Hardness is the property of any material which process stiffness resistance to bending, scratching or cutting. Hardness is not constant or fixed for all material, but it depends upon strength and plasticity of metal. Material hardness is expressed in terms of hardness number.

Answer to Problem 12.102P

The composition, hardness and amount are $\text{0}\text{.77\%C, HRC65}$ and $\text{37}\text{.2\%}$ respectively.

Explanation of Solution

Given:

Graph showing ${\text{Fe-Fe}}_{\text{3}}\text{C}$ the phase diagram.

As shown in the given diagram, at the line $\text{728°C}$ the composition of martensite is $\text{0}\text{.77\%C}$. Extending the line at $\text{728°C}$ with $\text{A3}$ curve at $\text{0}\text{.77\%C}$. Composition of ferrite is found. Therefore, the composition of martensite is $\text{0}\text{.77\%C}$.

As from the figure, the effect of hardness of martensite in steel, the hardness of martensite at $\text{0}\text{.77\%C}$

  $\text{HRC65}$. Hence, hardness is $\text{HRC65}$. The lever rule is given by,

  $\text{\%M=}\frac{\text{x-c}}{\text{x-c}}\times \text{100\%}$

Where, $\text{\%M=}$ amount of martensite

  $\text{0}\text{.077\%=b=}$ Percentage of carbon in martensite

  $\text{0}\text{.0218\%=c=}$ Percentage of carbon in ferrite

  $\text{0}\text{.3\%=x=}$ Percentage of carbon in steel

Put, the values in lever rule,

  $\text{\%M=}$

  $\begin{array}{l}\frac{0.3\%-0.0218\%}{0.77\%-0.0218\%}\times 100\%\\ =\frac{0.2782}{0.7482}\times 100\\ =0.3718\times 100\\ =37.2\%\end{array}$

Interpretation Introduction

(b)

Interpretation:

The amount, composition and hardness of material at $\text{750° C}$ should be determined.

Concept Introduction:

Material hardness is the property of a metal due to which material resist the plastic deformation. Plastic deformation means material deformation which undergoes non-reversible change. Hardness is the property of any material which process stiffness resistance to bending, scratching or cutting. Hardness is not constant or fixed for all material, but it depends upon strength and plasticity of metal. Material hardness is expressed in terms of hardness number.

Answer to Problem 12.102P

The composition, hardness and amount are $\text{0}\text{.60\%C, HRC65}$ and $\text{48}\text{.3\%}$ respectively.

Explanation of Solution

From the given figure, draw a line at $\text{750°C}$ intersecting $\text{A3}$ the curve at $\text{0}\text{.60\%}$. Hence from this, the composition of martensite is $\text{0}\text{.60\%}$. Now from the effect of the carbon content of hardness of martensite in steel, the hardness of martensite is $\text{HRC65}$ at $\text{0}\text{.60\%C}$.

The lever rule is given by,

  $\text{\%M=}\frac{\text{x-c}}{\text{x-c}}\times \text{100\%}$

Where,

  $\begin{array}{l}\text{b= 0}\text{.60\%}\hfill \\ \text{c=0}\text{.02\%}\hfill \\ \text{x=0}\text{.3\%}\hfill \end{array}$

Put the values in lever rule

  $\begin{array}{l}\text{\%M=}\frac{\text{0}\text{.3\%-0}\text{.02\%}}{\text{0}\text{.6\%-0}\text{.02\%}}\times \text{100\%}\\ \text{=}\frac{\text{0}\text{.28}}{\text{0}\text{.58}}\times \text{100}\\ \text{=0}\text{.4827}\times \text{100}\\ \text{=48}\text{.3\%}\end{array}$

Interpretation Introduction

(c)

Interpretation:

The amount, composition and hardness of material at $\text{790° C}$ should be determined.

Concept Introduction:

Material hardness is the property of a metal due to which material resist the plastic deformation. Plastic deformation means material deformation which undergoes non-reversible change. Hardness is the property of any material which process stiffness resistance to bending, scratching or cutting. Hardness is not constant or fixed for all material, but it depends upon strength and plasticity of metal. Material hardness is expressed in terms of hardness number.

Answer to Problem 12.102P

The composition, hardness and amount are $\text{0}\text{.35\%C, HRC58}$ and $\text{84}\text{.8\%}$ respectively.

Explanation of Solution

Calculate the amount of martensite from the heating temperature $\text{790°C}$, the figure is the eutectoid portion of the $\text{Fe-Fe3c}$ phase diagram at temperature $\text{790°C}$.

Therefore at $\text{790°C}$ ,

  $\text{γ = 0}\text{.35\%C}$

Applying lever rule at a heating temperature $\text{790°C}$

  $\text{\%M=}\frac{\text{co-ca}}{\text{cr-ca}}\times \text{100\%}$

Put,

  $\begin{array}{l}\text{co=0}\text{.3}\\ \text{ca=0}\text{.02}\\ \text{cγ=0}\text{.35}\end{array}$

Therefore,

  $\text{\%M=}\frac{\text{0}\text{.3-0}\text{.02}}{\text{0}\text{.35-0}\text{.02}}\times \text{100\%}$

The effect of carbon content on the hardness of martensite in steel, the amount of hardness for martensite composition $\text{γ= 0}\text{.35\%C}$ is as follows for weight percent of $\text{0}\text{.35\%C}$, the corresponding hardness is $\text{HRC58}$.

Interpretation Introduction

(d)

Interpretation:

The amount, composition and hardness of material at $\text{850° C}$ should be determined.

Concept Introduction:

Material hardness is the property of a metal due to which material resist the plastic deformation. Plastic deformation means material deformation which undergoes non-reversible change. Hardness is the property of any material which process stiffness resistance to bending, scratching or cutting. Hardness is not constant or fixed for all material, but it depends upon strength and plasticity of metal. Material hardness is expressed in terms of hardness number.

Answer to Problem 12.102P

The composition, hardness and amount are $\text{0}\text{.30\%C}$, $\text{HRC55}$ and $\text{84}\text{.8\%}$ respectively.

Explanation of Solution

From the diagram, the eutectoid portion of $\text{Fe-Fe3c}$ the phase diagram, the heating temperature is 850⁰c. The corresponding weight percent of carbon is less than $\text{0}\text{.3\%}$ .Thus the minimum amount of martensite at a temperature at $\text{850°C}$ is $\text{0}\text{.30\%C}$. Thus at temperature $\text{850°C}$.

r =0.30%c

Applying lever rule, calculate the composition of martensite at them $\text{850°C}$. As the temperature is $\text{850°C}$ %M equal to 100%.

Calculate the amount of hardness at temperature $\text{850°C}$.

From the figure, the effect of carbon content hardness at $\text{γ = 0}\text{.3\%C}$ for weight percentage $\text{0}\text{.3}$ hardness is $\text{HRC55}$.