True Stress-Strain & Strain Rate

Flashcards from lecture notes on True Stress-Strain & Strain Rate.

What happens to plastic deformation after reaching the UTS in a tensile test?

All plastic deformation is concentrated in the neck, where final fracture occurs.

Why is true stress higher than engineering stress during a tensile test?

Because the cross-sectional area of the test piece decreases, concentrating the force over a smaller area.

Define engineering stress and engineering strain.

Engineering stress is the applied load divided by the initial cross-sectional area (F/Ao), and engineering strain is the change in length divided by the initial length (Dl/lo).

Why are true stress and true strain considered 'true'?

Because they use the instantaneous cross-section area and length of the sample during deformation, reflecting real-time conditions.

How are true stress and engineering stress related?

True stress (σ) = Engineering stress (σo) * (1 + Engineering strain (e))

How are true strain and engineering strain related?

True strain (ε) = ln(1 + Engineering strain(e))

What is the relationship between volume, area, and length during plastic deformation?

During purely plastic deformation, the volume of metal remains approximately constant: A.l = Ao.lo

What is the equation for true stress involving engineering stress and strain based on volume constancy?

True stress (σ) = Engineering stress (σo) * (l/lo) = σo * (1+e)

Describe the power law relationship between true stress and true strain.

For many metals: σ = K * ε^n, where K is a constant and n is the strain-hardening exponent.

How can the constants K and n be found experimentally?

By calculating the true stress and true strain at the UTS from tensile tests where K can then be found, as at the UTS: sUTS = K. eUTS^n

What is the transverse (lateral) true strain?

et = ln (D/Do ) Where Do is the initial diameter and D is the final diameter.

Define Poisson's ratio.

Poisson's ratio (ν) is the ratio of -et /el, where et is transverse strain and el is longitudinal strain.

How does strain rate affect flow stress?

Flow stress generally increases with strain rate: σ ∝ (ε̇)^m where typically m < 0.025

Define flow stress.

The stress required to continue plastic deformation at any point during deformation and generally increases with strain.

What is work-hardening?

Work-hardening makes metals stronger during plastic deformation at near room temperature at T ≤ 0.3Tmelt (in Kelvin).

What is the effect of cold-working on metals?

Cold-working increases strength and hardness but decreases ductility.

How is ductility restored after cold-working?

By annealing, heating to a temperature typically above about 0.4Tm- 0.5Tm (in K) so that internal stresses disappear as new un-deformed grains form: called recrystallisation.

What happens to metals deformed at T > 0.5Tm?

All metals are relatively soft and don’t work harden. During this hot-working, the internal structure recrystallises simultaneously with deformation, and the metal stays soft and ductile.

Describe hot-forming in terms of recrystallization and stress approximation.

Recrystallization is simultaneous with plastic deformation, and it can be approximated by assuming a constant mean yield (flow-) stress Y, i.e. strue ≈ Y.

Describe cold-forming in terms of work-hardening.

Work-hardening occurs (flow stress increases with strain), and it is approximately shown by the equation: strue = K . etrue^n