Chapter 8, Problem 8.70P

Interpretation Introduction

(a)

Interpretation:

The recovery, recrystallization and grain growth temperature needs to be estimated.

Concept Introduction:

Recovery takes place at the low annealing temperature. Recrystallization is a process of formation of new defect-free grains. In Recrystallization,grains of a crystal structure comes in a new structure or new crystal shape. Grain growth is the process of increasing the size of grains at high temperature. Grain growth occurs when recovery and recrystallization are complete.

Answer to Problem 8.70P

Recover temperature is ${\text{280}}^{\text{0}}\text{C}$

Recrystallization temperature is ${330}^0\text{C}$

Grain growth temperature is ${380}^0\text{C}$

Explanation of Solution

Given Information:

The following data shows the properties of cold worked material after annealing.

Annealing temperature ${(}^0\text{C})$	Residual stresses $(\text{Psi)}$	Tensile strength $\text{(Psi)}$	Grain size $\text{(in)}$
250	21000	52000	0.0030
275	21000	52000	0.0030
300	5000	52000	0.0030
325	0	52000	0.0030
350	0	34000	0.0010
375	0	30000	0.0010
400	0	27000	0.0035
425	0	25000	0.0072

From the above data, one can plot a graph of tensile strength, residual stress and grain size of cold worked metal at the given annealing temperature.

• Recover takes place at low annealing temperature and when there is no change in grain size thus, from figure recovery temperature should be near $280{}^{0}C$ .
• At recrystallization temperature, tensile strength is low and nucleation and growth of grain take place.
• From the figure, ${330}^{0}C$ is the temperature where grain growth and nucleation take place and tensile strength is minimum.
• Grain growth takes place a high annealing temperature from the figure, grain growth occurs at $380{}^{0}C$ the annealing temperature.

Interpretation Introduction

(b)

Interpretation:

The temperature at which high strength and conductivity occur needs to be determined.

Concept Introduction:

Recovery temperature increases high electrical conductivity. Conductivity is the measure of the ease at which an electric charge can pass through the material. The conductor gives very little resistance to the flow of thermal energy or an electric current. High Strength is the quality of material to be strong and also the capacity of a material or an object to withstand great force or pressure.

Answer to Problem 8.70P

High strength and high electrical conductivity occurs at ${320}^{0}C$.

Explanation of Solution

• Recovery temperature improves the high strength and high electrical conductivity.
• Strength is increased by heating material in recovery temperature.
• Thus, from figure high strength and high electrical conducting occurs at $320{}^{0}C$ .

Interpretation Introduction

(c)

Interpretation:

The temperature which is appropriate for hot working process should be determined.

Concept Introduction:

Hot working is carried out above the recrystallization temperature of a material.

Answer to Problem 8.70P

Hot working takes place at $375{}^{0}C$.

Explanation of Solution

• Hot working is a process carried out above recrystallization temperature of a given material
• Hot working improves strength.
• Hence, a suitable temperature for hot working is $375{}^{0}C$ .

Interpretation Introduction

(d)

Interpretation:

The melting temperature of the alloy should be determined.

Concept Introduction:

The relation between melting temperature and recrystallization temperature is as follows.

  $T_r=0.4T_m$

Where,

  $\begin{array}{l}{T}_r=Recrystalizationtemperature\hfill \\ T_m=Meltingtemperature\hfill \end{array}$

Answer to Problem 8.70P

Melting temperature of the alloy is $1235{}^{0}C$.

Explanation of Solution

The relation between melting temperature and recrystallization temperature is as follows.

  $T_r=0.4T_m$

Where,

  $\begin{array}{l}{T}_r=Recrystalizationtemperature={330}^{0}C\hfill \\ T_m=Meltingtemperature\hfill \end{array}$

Substituting the values:

  $\begin{array}{l}0.4T_m=330{}^{0}C\\ T_m=\frac{330+273}{0.4}\\ =1508{}^{0}K\\ T_m=1235{}^{0}C\end{array}$