Different young modulus of rod - Need a proper explanation?

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SUMMARY

The discussion focuses on calculating the maximum tensile stress that can be applied to a composite rod made of two materials with different Young's moduli, specifically nylon and glass-reinforced plastic. The rod has a total extension limit of 3.0 mm before failure occurs. The calculated maximum tensile stress is 5.7 x 106 Pa. The key concept is that the combined strain of both materials must equal the total extension limit, regardless of which material fails first.

PREREQUISITES
  • Understanding of Young's modulus and its formula: Young modulus = stress / strain
  • Knowledge of tensile stress and strain in materials
  • Familiarity with composite materials and their mechanical properties
  • Basic principles of material failure and extension limits
NEXT STEPS
  • Study the calculation of tensile stress in composite materials
  • Learn about the properties of nylon and glass-reinforced plastic
  • Explore the concept of strain and its relationship to material deformation
  • Investigate failure modes in composite rods under tensile loads
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Students studying material science, engineers working with composite materials, and anyone interested in understanding the mechanical properties of different materials under stress.

PhysicStud01
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Homework Statement


A rod is made up as shown [pic attached]
pic.png

Both have same cross-sectional area. Ep and En are Young modulus.
The rod breaks when total extension = 3.0mm
Greatest tensile stress that can be applied before rod breaks?

Homework Equations


Young modulus = stress / strain

The Attempt at a Solution


Ans: 5.7 x 10^6 Pa.
Won't it break when the one of the 2 materials breaks? Can you please tell me the concepts to be used. How to solve?
Thanks
 
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PhysicStud01 said:

Homework Statement


A rod is made up as shown [pic attached]
View attachment 75901
Both have same cross-sectional area. Ep and En are Young modulus.
The rod breaks when total extension = 3.0mm
Greatest tensile stress that can be applied before rod breaks?

Homework Equations


Young modulus = stress / strain

The Attempt at a Solution


Ans: 5.7 x 10^6 Pa.
Won't it break when the one of the 2 materials breaks? Can you please tell me the concepts to be used. How to solve?
Thanks

The Young's modulus tells you how much the material stretches for a given applied tensile stress.

If you apply the same stress to the rod shown in the OP, which material is going to stretch more?

The problem is asking you to find how much stress can be applied to the rod so that the combined stretch of the nylon and the glass-reinforced plastic equals 3 mm. Remember, the strain is equal to the change in length of the material divided by the original length (unstretched).
 
PhysicStud01 said:
Won't it break when the one of the 2 materials breaks?
Sure, but you don't care which breaks, or even the fact that it breaks. What matters is that the max allowed extension of the rod as a whole is 3mm.
 

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