Chapter 12, Problem 12.103P

Interpretation Introduction

(a)

Interpretation:

The amount composition & hardness of material at ${\text{728}}^{\text{o}}\text{C}$ needs to be determined.

Concept Introduction:

Microstructure is a very small structure of any material. For a material, it describes the physical properties like hardness, strength, ductility, temperature behaviour and corrosion resistance of the material. The properties of any substance can be observed under optical microstructure. Materials such as metals, polymers, ceramics or composites show optimistic properties under microstructure.

Answer to Problem 12.103P

The composition, hardness and amount are $\text{0}\text{.77\%C}$, HRC65 and $96.9\%$ respectively.

Explanation of Solution

Given:

Graph showing $F_e{F}_{e3}C$ phase diagram:

  

Calculation:

As shown in the given diagram, at the line ${\text{728}}^{\text{o}}\text{C}$ the composition of martensite is $\text{0}\text{.77\%C}$. Extending the line at ${\text{728}}^{\text{o}}\text{C}$ with 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 $\text{0}\text{.77\%C}$ HRC65. Hence, hardness is HRC65. The lever rule is given by,

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

Where, %M=amount of martensite

  $6.67\%$ =b=Percentage of carbon in martensite

  $0.77\%$ =c=percentage of carbon in ferrite

  $0.95\%$ =x=percentage of carbon in steel

Put, the values in lever rule,

Therefore,

  $\begin{array}{l}\text{\%M=}\frac{\text{6}\text{.67\%-0}\text{.95\%}}{\text{6}\text{.67\%-0}\text{.77\%}}\times \text{100}\\ \\ \text{=}\frac{\text{5}\text{.72}}{\text{5}\text{.9}}\times \text{100}\\ \\ \text{=0}\text{.9694}\times \text{100}\\ \\ \text{=96}\text{.9\%}\end{array}$

Interpretation Introduction

(b)

Interpretation:

The amount composition & hardness of material at ${\text{750}}^{\text{o}}\text{C}$ needs to 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 12.103P

The composition, hardness and amount are $\text{0}\text{.82\%C}$, HRC65 and $97.8\%$ respectively.

Explanation of Solution

Given:

Graph showing $F_e{F}_{e3}C$ phase diagram.

  

Calculations:

As shown in the given diagram, at the line ${\text{750}}^{\text{o}}\text{C}$ the composition of martensite is $\text{0}\text{.82\%C}$. Extending the line at ${\text{750}}^{\text{o}}\text{C}$ with A3 curve at $\text{0}\text{.82\%C}$. Composition of ferrite is found. Therefore the composition of martensite is $\text{0}\text{.82\%C}$.

As from the figure, the effect of hardness of martensite in steel, the hardness of martensite at $\text{0}\text{.82\%C}$ HRC65. Hence, hardness is HRC65. The lever rule is given by,

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

Where, %M=amount of martensite

  $6.67\%$ =b=Percentage of carbon in martensite

  $0.82\%$ =c=percentage of carbon in ferrite

  $0.95\%$ =x=percentage of carbon in steel

Put, the values in lever rule,

Therefore,

  $\begin{array}{l}\text{\%M=}\frac{\text{6}\text{.67\%-0}\text{.95\%}}{\text{6}\text{.67\%-0}\text{.82\%}}\text{×100}\\ \\ \text{=}\frac{\text{5}\text{.72}}{\text{5}\text{.85}}\text{×100}\\ \\ \text{=0}\text{.9777×100}\\ \\ \text{=97}\text{.8\%}\end{array}$

Interpretation Introduction

(c)

Interpretation:

The amount composition & hardness of material at ${\text{780}}^{\text{o}}\text{C}$ needs to 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 12.103P

The composition, hardness and amount are $0.88\%$, HRC65 and $98.8\%$ respectively.

Explanation of Solution

Given:

Graph showing $F_e{F}_{e3}C$ phase diagram:

  

Calculations:

As shown in the given diagram, at the line ${\text{780}}^{\text{o}}\text{C}$ the composition of martensite is $0.88\%$. Extending the line at ${\text{780}}^{\text{o}}\text{C}$ with Acm curve at $0.88\%$. Composition of ferrite is found. Therefore the composition of martensite is $0.88\%$.

As from the figure, the effect of hardness of martensite in steel, the hardness of martensite at $0.88\%$ HRC65. Hence, hardness is HRC65. The lever rule is given by,

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

Where, %M=amount of martensite

  $6.67\%$ =b=Percentage of carbon in martensite

  $0.88\%$ =c=percentage of carbon in ferrite

  $0.95\%$ =x=percentage of carbon in steel

Put, the values in lever rule,

Therefore,

  $\begin{array}{l}\text{\%M=}\frac{\text{6}\text{.67\%-0}\text{.95\%}}{\text{6}\text{.67\%-0}\text{.88\%}}\text{×100}\\ \\ \text{=}\frac{\text{5}\text{.72}}{\text{5}\text{.79}}\text{×100}\\ \\ \text{=0}\text{.9879×100}\\ \\ =\text{98}\text{.8\%}\end{array}$

Interpretation Introduction

(d)

Interpretation:

The amount composition & hardness of material at ${\text{850}}^{\text{o}}\text{C}$ needs to 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 12.103P

The composition, hardness and amount are $\text{0}\text{.95\%C}$, HRC65 and 100% respectively.

Explanation of Solution

Given:

Graph showing $F_e{F}_{e3}C$ phase diagram.

  

Calculations:

As shown in the given diagram, at the line ${\text{850}}^{\text{o}}\text{C}$ the composition of martensite is $\text{0}\text{.95\%C}$. Extending the line at ${\text{850}}^{\text{o}}\text{C}$ with A3 curve at $\text{0}\text{.95\%C}$. Composition of ferrite is found. Therefore the composition of martensite is $\text{0}\text{.95\%C}$.

As from the figure, the effect of hardness of martensite in steel, the hardness of martensite at $\text{0}\text{.95\%C}$ HRC65. Hence, hardness is HRC65. The lever rule is given by,

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

Where, %M=amount of martensite

  $\text{6}\text{.67\%}$ =b=Percentage of carbon in martensite

  $0.95\%$ =c=percentage of carbon in ferrite

  $0.95\%$ =x=percentage of carbon in steel

Put, the values in lever rule,

Therefore,

  $\begin{array}{l}\text{\%M=}\frac{\text{6}\text{.67\%-0}\text{.95\%}}{\text{6}\text{.67\%-0}\text{.95\%}}\times \text{100}\\ \\ \text{=1}\times \text{100\%}\\ \\ \text{=100\%}\end{array}$