Strength

Question 1

What is linear elasticity?

Answer 1

Hooke’s law is obeyed
Stress versus strain for loading and unloading follow the same line

Question 2

What is Plastic behaviour?

Answer 2

Seen with many metals (linear elastic behaviour followed by permanent (plastic) deformation, yielding, unloading stress-strain curve is different from the loading stress-strain curve

Question 3

What is yield strength?

Answer 3

Strictly the stress corresponding to the onset of plasticity BUT difficult to determine where the curve deviates from linearity

Question 4

How do we determine the yield strength if it is difficult to determine where the curve deviates from linearity?

Answer 4

use a specified (small) permanent strain to define yield strength (0.1% or 0.2% may be used, need to make it clear which is being used). In either case this represents a small degree of plasticity

Question 5

How is yield strength denoted?

Answer 5

σ ys

Question 6

When does necking start?

Answer 6

Necking starts when maximum engineering stress is exceeded, complicated (triaxial) stress state

Question 7

What does the engineering stress-strain curve look like?

Question 8

What is true stress related to?

Answer 8

True stress is related to the instantaneous cross-sectional area, A
i.e σt = F/A

Question 9

How is true strain defined?

Answer 9

The true strain has to be defined incrementally δεt = δl/l
small incremental change in length
taking many small increments and integrating εt = ∫dl/l = ln(l/l0)

Question 10

What does the graph for true stress look like?

Question 11

What does the graph for true strain look like?

Question 12

What is the power law hardening equation?

Answer 12

Many metals can represent the plastic part of the curve by σt = Kε^n_t
n is known as the strain-hardening coefficient, perfectly plastic solid n = 0, perfectly elastic solid n = 1

Question 13

What is the ultimate tensile strength?

Answer 13

It can be shown that the true strain at the onset of necking is εu = n, the true uniform strain, hence the true stress at the onset of necking is σt = Kn^n

Question 14

What is the equation for the ultimate tensile strength?

Answer 14

The ultimate tensile strength is given by

Question 15

Given that low carbon steel has a true stress true strain curve given by, calculate the ultimate tensile strength and the true uniform strain

Question 16

What are the different types of strength?

Answer 16

Yeild strength σ ys
Ultimate tensile strength (UTS) σ UTS
Fracture strength σ f