Calculate Elastic Modulus of Iron Single Crystal: E=207.9GPa

[erichling]

Homework Statement

Based on the data in Table 1.3 of Hertzberg, estimate the elastic modulus of an iron single crystal along the [2 1 -3] direction. Express your answer in GPa in the form yyy.y

S11=0.80, S12=-0.28, S44=0.86 (10^-11Pa^-1)

Homework Equations

1/E=S11-2((S11-S12)-.5*S44)(l1^2*l2^2+l2^2*l3^2+l1^2l3^2)

The Attempt at a Solution

1/E=0.80-2((0.80-(-.28)-.5(0.86))(.25)

 

[KataKoniK]

1/E=0.80-2(1.08)(.25)
1/E=0.80-0.54
1/E=0.26
E=1/0.26
E=3.846 GPa

Thank you for your post. Based on the data provided in Table 1.3 of Hertzberg, the elastic modulus of an iron single crystal along the [2 1 -3] direction can be estimated using the following formula:

1/E = S11 - 2((S11 - S12) - 0.5*S44)*(l1^2*l2^2 + l2^2*l3^2 + l1^2*l3^2)

Where S11 = 0.80, S12 = -0.28, and S44 = 0.86 (all in 10^-11 Pa^-1).

Plugging in the values, we get:

1/E = 0.80 - 2((0.80 - (-0.28)) - 0.5*0.86)*(0.25)

1/E = 0.80 - 2*(1.08 - 0.43)*(0.25)

1/E = 0.80 - 0.65*0.25

1/E = 0.80 - 0.1625

1/E = 0.6375

E = 1/0.6375

E = 1.57 GPa

Therefore, the estimated elastic modulus of an iron single crystal along the [2 1 -3] direction is approximately 1.57 GPa. Please note that this is an approximation and may vary depending on the specific crystal structure and conditions.

I hope this helps. Let me know if you have any further questions.
Scientist