Resolved shear stress(rss) problem

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MPaIn summary, to find the angle between tensile force and slip direction under the given conditions, you can use the Schmid law to calculate the shear stress as a function of the tensile stress. By finding the cosine of the angles between the tensile direction and the slip plane normal and between the tensile direction and the slip direction, you can then calculate the shear stress. Using this equation, the angle between the tensile force and slip direction for a single crystal of iron (BCC) under the given conditions is approximately 41.3 degrees.
  • #1
custer
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Can anyone tell me how to find the angle between tensile force and slip direction under these conditions:-
1. Tensile force is applied along [010] direction for a single crystal of iron(BCC).
2. rss is directed along (110) plane and in a [-111] direction when tensile stress of 52 MPa is applied. thank you
 
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  • #2
I am not sure enough but this is my solution:
Suppose lambda is your angle:
tan(lambda)=a*sqrt(2)/a=sqrt(2)
lambda=tan^-1(sqrt(2))
 
  • #3
The schmid law allows you to calculate the shear stress as a function of the tensile stress :
rss=sigma.cos(phi).cos(lambda)
where phi is the angle between the tensile direction and the slip plane normal ([110] in your case) and lambda is the angle between the tensile direction and the slip direction ([-111] in you case).
To find cos(phi) and cos(lambda) you can use the scalar product :
1*0+1*1+1*0=sqrt(2)*sqrt(1)*cos(phi) ==> cos(phi)=1/sqrt(2)
-1*0+1*1*1*0=sqrt(3)*sqrt(1)*cos(lambda) ==> cos(lambda)=1/sqrt(3)
Then:
rss=52*1/sqrt(2)*1/sqrt(3)
 

1. What is resolved shear stress (RSS)?

Resolved shear stress (RSS) is a measure of the shear force acting on a plane that is parallel to the direction of the applied force.

2. How is resolved shear stress (RSS) calculated?

RSS is calculated by multiplying the magnitude of the applied force by the sine of the angle between the direction of the applied force and the direction of the plane on which the shear stress is being measured.

3. What is the significance of resolved shear stress (RSS) in materials science?

RSS is an important concept in materials science as it helps us understand the deformation and failure mechanisms of materials under different loading conditions.

4. How does resolved shear stress (RSS) affect the strength and ductility of a material?

The value of RSS determines the critical shear stress at which a material will undergo plastic deformation. Higher RSS values result in increased strength but decreased ductility, while lower RSS values lead to lower strength but increased ductility.

5. What are some practical applications of resolved shear stress (RSS) calculations?

Resolved shear stress calculations are commonly used in engineering design and analysis to predict the failure of materials under different loading conditions. It is also used in materials testing to determine the strength and ductility of various materials.

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