Chapter 6: Mechanical Properties

Question 1

what is the formula σ = 𝐹/𝐴𝑜

Answer 1

σ = tensile stress,

Ft = force of tension

Ao = original cross-sectional area before loading

Question 2

what is the formula τ = Fs/Ao

Answer 2

τ = shear stress

Ft = force of shear

Ao = original cross-sectional area before loading

Question 3

what is the formula ε = δ/Lo

Answer 3

ε = tensile strian
δ = change in length
Lo = original length

Question 4

what is the formula εL = -δL/wo

Answer 4

εL = lateral strain
δL = lateral change
wo = original with

Question 5

what is the formula γ = Δx/y = tan θ

Answer 5

γ = Shear strain
Δx = change in direction
y = other direction
tan θ

Question 6

what are the units for stress?

Answer 6

N/m^2

Question 7

What is elastic deformation?

Answer 7

reversible strain

Question 8

what is the formula σ = E ε?

Answer 8

σ = tensile stress
E = Modulus of Elasticity (different for every substance)

Question 9

Do stronger or weaker bonds lead to a larger Young’s modulus?

Answer 9

Stronger

Question 10

Does elastic modulus vary with direction?

Answer 10

yes

Question 11

what is the formula 𝜈 =−𝜀𝑋/𝜀𝑍 =−𝜀𝑌/𝜀𝑍

Answer 11

ν = Poisson’s Ratio
𝜀𝑋 = strain perpendicular to stress
𝜀Z = strain parallel to stress

Question 12

what is the formula τ = G γ

Answer 12

τ = Shear stress
G = shear modulus
γ = shear strain

Question 13

when does noticeable plastic deformation occur?

Answer 13

when εp = 0.002

Question 14

what is uts?

Answer 14

the maximum stress on stress-strain curve

Question 15

list the relative strength of the common material groups

Answer 15

Metals > Ceramics > polymers> Composite/fibers

Question 16

what is the formula %EL = (Lf - Lo) / Lo x 100

Answer 16

%EL = percent elongation
Lf = Length final
Lo = Length initial

Question 17

What is the formula %RA = Ao - Af / Ao

Answer 17

RA% = percent reduction in area
Ao = Area initial
Af = Area final

Question 18

what is toughness?

Answer 18

The ability of a material to absorb energy and plastically deform before fracturing.

Question 19

What is resilience?

Answer 19

The ability of a material to store energy

Question 20

what is the formula σT = F/Ai?

Answer 20

σT = True Stress
F = Force
Ai = Area instantaneous

Question 21

what is the formula σT = σ(1+ε)?

Answer 21

σT = True Stress
σ = engineering stress
ε = engineering strain

Question 22

what is the formula εT = ln(1+ε)?

Answer 22

εT = True strain
ε = engineering strain

Question 23

what is the formula εT =ln( ℓi / ℓo)

Answer 23

εT = True strain
ℓi = instantaneous length
ℓo = original length

Question 24

what is the formula σT = k(εT)^n?

Answer 24

σT = True Stress
k and n (stain hardening exponent) are constants
εT = true strain

Question 25

What is hardness?

Answer 25

a measure of resistance to surface plastic deformation—dent or scratch.

Question 26

what is this formula 𝜎𝑑 =𝑁𝜎𝑐

Answer 26

𝜎𝑑 = design stress
𝑁 = safety factor
𝜎𝑐 = calculated stress

Question 27

how do you find the modulus of elasticity?

Answer 27

the slope of the linear curve

Question 28

How to find the proportional limit?

Answer 28

The end of the linear part of the stress curve

Question 29

How to find the yield strength on a graph

Answer 29

you take the 0.002 stress and take the slope of elasticity up to the point on the curve.

Question 30

How to find tensile straingth on a graph?

Answer 30

Maximum point