Assignment Sheet 4
Name : Omar Jubran
ID: 202111332
1 For an Fe–0.35%C alloy, determine (a) the temperature at which austenite first begins to
transform on cooling, (b) the primary microconstituent that forms, (c) the composition and
amount of each phase present at 728C, (d) the composition and amount of each phase present
at 726C, and (e) the composition and amount of each microconstituent present at 726C.
1. For an Fe–0.35%C alloy, the following can be determined:
(a) The temperature at which austenite first begins to transform on cooling:
The transformation begins at the upper critical temperature (Ac3), which is approximately 800°C.
(b) The primary microconstituent that forms:
The first microconstituent to form is ferrite (α), as the alloy is hypoeutectoid (i.e., it has less than
0.76% C).
(c) Composition and amount of each phase present at 728°C:
At 728°C, the phases present are ferrite (α) and austenite (γ). Using the lever rule:
Ferrite composition = 0.022% C
Austenite composition = 0.76% C
Thus, at 728°C, the phase distribution is:
Ferrite (α): 55.56%
Austenite (γ): 44.44%
(d) Composition and amount of each phase present at 726°C:
At 726°C, which is just below the eutectoid temperature, the phases present are ferrite (α) and
cementite (Fe₃C). The ferrite composition remains at 0.022% C, and the cementite composition is
6.7% C.
(e) Composition and amount of each microconstituent present at 726°C:
At 726°C, the microconstituents are primary ferrite and pearlite. Using the lever rule, the weight
fractions are as follows:
Primary ferrite: 95.09%
Pearlite: 4.91%
Thus, the microconstituents at 726°C are:
Primary Ferrite: 95.09%
Pearlite: 4.91%
2 For an Fe–1.15%C alloy, determine (a) the temperature at which austenite first begins to
transform on cooling, (b) the primary microconstituent that forms, (c) the composition and
amount of each phase present at 728C, (d) the composition and amount of each phase present
at 726C, and (e) the composition and amount of each microconstituent present at 726C.
For an Fe–1.15%C alloy, the following details can be determined:
(a) The temperature at which austenite first begins to transform on cooling:
For an Fe–1.15%C alloy, which is hypereutectoid, the transformation starts at the lower critical
temperature (Ac1), approximately 1130°C.
(b) The primary microconstituent that forms:
The primary microconstituent that forms is proeutectoid cementite (Fe₃C), as the alloy is
hypereutectoid (with more than 0.76% C).
(c) Composition and amount of each phase present at 728°C:
At 728°C, the phases present are austenite (γ) and cementite (Fe₃C). Using the lever rule:
Austenite composition = 0.76% C
Cementite composition = 6.7% C
The weight fractions of each phase are calculated as follows:
Thus, at 728°C, the phase distribution is:
Austenite (γ): 93.43%
Cementite (Fe₃C): 6.57%
(d) Composition and amount of each phase present at 726°C:
At 726°C, the composition of cementite remains at 6.7% C, and pearlite forms completely from
austenite. The pearlite composition is eutectoid, with 0.76% C. At this temperature, the phases
present are pearlite and proeutectoid cementite.
Thus, the phase distribution at 726°C is:
Pearlite: 93.43%
Proeutectoid Cementite: 6.57%
(e) Composition and amount of each microconstituent present at 726°C:
At 726°C, the microconstituents are:
Proeutectoid cementite: 6.57%
Pearlite: 93.43%
3- A steel contains 8% cementite and 92% ferrite at room temperature. Estimate the carbon
content of the steel. Is the steel hypoeutectoid or hypereutectoid?
Given the following information:
8% cementite (Fe₃C) and 92% ferrite (α) at room temperature.
The composition of cementite is 6.7% carbon.
The composition of ferrite is 0.022% carbon.
To estimate the carbon content of the steel, we can calculate the overall carbon content using the
weight fractions of cementite and ferrite:
Since the carbon content of the steel (0.556%) is less than the eutectoid composition of 0.76%, the
steel is hypoeutectoid.
4- A steel contains 18% cementite and 82% ferrite at room temperature. Estimate the
carbon content of the steel. Is the steel hypoeutectoid or hypereutectoid?
Given the following information:
18% cementite (Fe₃C) and 82% ferrite (α) at room temperature.
The composition of cementite is 6.7% carbon.
The composition of ferrite is 0.022% carbon.
To estimate the overall carbon content of the steel, we use the weight fractions of cementite and
ferrite:
Since the carbon content of the steel (1.224%) is greater than the eutectoid composition of 0.76%,
the steel is hypereutectoid.
5- A steel contains 18% pearlite and 82% primary ferrite at room temperature. Estimate the
carbon content of the steel. Is the steel hypoeutectoid or hypereutectoid?
Given the following information:
18% pearlite and 82% primary ferrite at room temperature.
The composition of pearlite is 0.76% carbon.
The composition of ferrite is 0.022% carbon.
To estimate the overall carbon content of the steel, we use the weight fractions of pearlite and
ferrite:
Since the carbon content of the steel (0.155%) is less than the eutectoid composition of 0.76%, the
steel is hypoeutectoid.
6- In eutectic alloys, the eutectic microconstituent is generally the continuous one, but in the
eutectoid structures, the primary microconstituent is normally continuous. By describing the
changes that occur with decreasing temperature in each reaction, explain why this difference
is expected.
Eutectic Alloys:
In eutectic alloys, the eutectic reaction occurs when a liquid phase transforms into two solid
phases upon cooling: L → α + β.
This transformation happens from a single liquid phase, and both solid phases (α and β)
nucleate and grow simultaneously as the alloy solidifies.
Because both phases nucleate at the same time, they form a fine, interlocking, or lamellar
structure.
The eutectic microconstituent is continuous because the transformation directly from the
liquid phase ensures both phases uniformly fill the volume as the alloy cools and solidifies.
Eutectoid Structures:
In eutectoid structures, the reaction occurs when a single solid phase transforms into two
different solid phases upon cooling: γ → α + β.
The eutectoid transformation happens in the solid state, where the initial phase (γ, typically
austenite in steels) first undergoes nucleation of one phase (α) at grain boundaries or within
the grains.
As cooling continues, the second phase (β) forms adjacent to the first, often leading to a
lamellar structure (e.g., pearlite in steel).
The primary microconstituent is continuous because it forms first as discrete grains that
grow and fill the matrix before the eutectoid structure is fully developed.
7- The microstructure of an iron–carbon alloy consists of proeutectoid ferrite and pearlite;
the mass fractions of these two microconstituents are 0.174 and 0.826, respectively.
Determine the concentration of carbon in this alloy.
The microstructure of an iron-carbon alloy consists of proeutectoid ferrite and pearlite, with mass
fractions of these phases being 0.174 and 0.826, respectively. To determine the carbon content of
the alloy:
1. Composition of Carbon:
o Ferrite: 0.022% carbon
o Pearlite: 0.76% carbon
Since the carbon content of the alloy is 0.631%, which is less than the eutectoid composition of
0.76%, the alloy is classified as hypoeutectoid.
8- The mass fractions of total ferrite and total cementite in an iron–carbon alloy are 0.91
and 0.09, respectively. Is this a hypoeutectoid or hypereutectoid alloy? Why?
The mass fractions of total ferrite and total cementite in an iron-carbon alloy are 0.91 and 0.09,
respectively. To determine whether this is a hypoeutectoid or hypereutectoid alloy, we can
calculate the carbon content as follows:
1. Composition of Carbon:
o Ferrite: 0.022% carbon
o Cementite: 6.7% carbon
Since the carbon content of the alloy is 0.623%, which is less than the eutectoid composition of
0.76%, the alloy is classified as hypoeutectoid.
