Finding Engineering Strain Just Before Yield for Wire w/ Modulus of Elasticity

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SUMMARY

The discussion focuses on calculating engineering strain just before yield for a wire, utilizing parameters such as yield strength, modulus of elasticity, and wire diameters. It establishes that engineering strain closely approximates true strain until necking occurs. The conversation highlights the application of Hooke's Law and Young's Modulus in determining lateral strain, while also addressing the lack of specific measurements for original and final lengths, which complicates the comparison to true strain. The participants confirm that Hooke's Law is applicable in longitudinal cases, clarifying its relevance in this context.

PREREQUISITES
  • Understanding of engineering strain and true strain concepts
  • Familiarity with Young's Modulus and its application in material science
  • Knowledge of Hooke's Law and its implications for longitudinal and lateral strain
  • Basic principles of yield strength and yield stress in materials
NEXT STEPS
  • Research the relationship between engineering strain and true strain in materials under tension
  • Study the application of Hooke's Law in both longitudinal and lateral strain scenarios
  • Explore methods for measuring original and final lengths of materials during tensile testing
  • Investigate the concept of necking and its effects on strain measurements
USEFUL FOR

Mechanical engineers, materials scientists, and students studying material mechanics who are interested in understanding strain behavior in wires and other materials under stress.

jabers
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The engineering yield strength, the modulus of elasticity, the original diameter and final diameter of a wire are given. That wire is stretched and it diameter decreases. I am trying to find the engineering strain just before yield and the corresponding true strain.

So I assume I will find that the engineering strain is equal to or very close to the true strain because their curves don't diverge, in my experience, until necking occurs but I have to show that is the case. I believe that the yield strength is at the yield stress so a good approximation would be the proportionality limit.

My problem is that there are no specifics about the modulus elasticity. If it is young's modulus then I can find the lateral strain from hooke's law but then because I don't know the original or final lengths I don't know how to compare it to the true strain. Is there another law that I am forgetting about? Is hooke's law applicable for the longitudinal case?
 
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Young's modulus is another name for the modulus of elasticity. Hooke's law applies longitudinally, in addition to other axes.
 
What do you mean by the "longitudinal case"?
 

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