Engineering Mechanics And Materials

Question 1

Mechanical properties’ definitions
- strength
- ductility
- toughness
- hardness

Answer 1

Strength - considered as the tensile strength (the maximum force required to fracture per unit cross sectional area in tension. Yield strength is the force at which the material begins to permanently deform.
Ductility - The capacity to undergo deformation (generally under tension) without rupture.
Toughness - Ability to withstand bending or deflection, or absorb energy, without fracture
Hardness - Ability to resist plastic deformation, indentation or abrasion.

Question 2

Engineering stress (tensile stress & Shear stress)

Answer 2

F/A, Fs/Ao

Question 3

Tensile strain, axial strain

Answer 3

Ez = change in L/Lo

Question 4

Lateral Strain

Answer 4

Ex = change in D/Do

Question 5

Poisson’s ratio

Answer 5

V = Ex/Ez (lateral strain/tensile strain)

Question 6

Hooke’s law

Answer 6

d = Ee (d - stress, E - constant proportionality, e - strain)

Question 7

Definition of the Ao - cross sectional area

Answer 7

An area of two dimensional shape in which we obtain when the same object is cut into two pieces. That area of that particular cross section is known as the cross sectional area

Question 8

Modulus of Elasticity (Young’s Modulus)

Answer 8

Hooke’s law ( d = Ee )

Question 9

Elastic bulk modulus, k

Answer 9

P = - k (change in V/V original)

Question 10

Elongation strain

Answer 10

Ez = change in length/original length

Question 11

Plastic (permanent) deformation

Answer 11

Cannot go back to its original form/shape after load is being removed

Question 12

Yield strength

Answer 12

The start of the plastic deformation where the stress is noticeable. (When Ep is 0.002)

Question 13

Tensile strength

Answer 13

Is the maximum stress on the engineering stress-strain curve

Question 14

Tensile strength for metal and polymers

Answer 14

Metal - occurs when noticeable necking starts
Polymers - occurs when polymers backbone chains are aligned and about to break

Question 15

Elastic region and plastic region

Answer 15

Elastic Region = stress is proportional to strain and material returns to its original form after load is being released

Plastic Region = Linear relationship between stress and strain disappears, the rate of increase falls away with strain

Question 16

tensile test
- Yield Point
- Proof stress
- tensile strength

Answer 16

Yield point = Load applied/Cross sectional area

Proof Stress = 0.2% = 0.2% PS/CSA

Tensile Strength = Maximum load/CSA

Question 17

% Reduction Area

Answer 17

Change in Area/Original Area x 100%

Question 18

Ductility. How to calculate?

Answer 18

Ductility is an important mechanical property and is a measure of the degree of plastic deformation that has been sustained at fracture.

%EL at fracture is a measure of ductility. It is an index quality of metal. If porosity or inclusions are present in metal or if damage due to overheating of metal occurred, %EL maybe decreased.

Calculate by using %EL and %RA

Question 19

What is the effect of temperature on yield strength, tensile strength and ductility?

Answer 19

When temperature is high, yield strength and tensile strength decreases while ductility increases. High temperature results in atom become active (move more), and becomes softer.

Question 20

Toughness and hardness

Answer 20

Toughness is the energy to break unit volume of material. Hardness is the resistance to permanently indenting the surface (small indent = large hardness)

Question 21

Hardness measurement

Answer 21

• Rockwell
• HB Brinell Hardness - Ts = 500 x HB (PSIA) & Ts = 3.45 x HB (MPa)

Question 22

Design factor. Factor of safety

Answer 22

Design Factor - stress d = N’d(stress)c

Factor of safety - stress d = stress y/N

Question 23

True Stress & True Strain

Answer 23

The engineering stress, is on the basis of the cross sectional area before any deformation and does not take into account this reduction in area at the neck.

True Stress is the force over initial area while true strain is the Ln x initial length over original area.

The conversion of engineering stress to true stress is by stress d = stress d (1 + e) and engineering strain to true strain is by true strain = Ln (1 + e)

Question 24

Ductile and brittle fracture

Answer 24

Fracture is the separation of a body into two or more pieces in response to an imposed stress. Ductile fracture occurs with plastic deformation while brittle fracture is the separation of a body into two or more pieces with little to no plastic deformation.

Question 25

Design against crack growth & formula

Answer 25

It is a relationship between critical stress for crack propagation to crack length.

Formula - Kc (fracture toughness; measure the material’s resistance to brittle fracture when crack is present) = Y (dimensionless parameter that depends on both crack and specimen sizes) stress d c (Square root of pie a)

Question 26

Principle of fracture mechanics

Answer 26

1) stress concentration - griffth crack = stress d m = 2 stress d o (a/Dt) 1/2. DT is the radius of curvature

Question 27

Crack propagation

Answer 27

Due to the sharpness of the crack tip. When? If applied stress is above critical stress.

Formula = stress do = 92Eys/pie a) 1/2

Question 28

Design example

Answer 28

The smaller the flow, the more ya dapat handle stress.
Example;

Material has Kc = 26 MPa. Theres 2 design but same material.

Design A - largest flaw; 9mm and failure stress = 112 MPa.

Design B - largest flaw, 4mm and failure stress - ? Unknown

So, we calculate using stress c = 112 square root pie x 9/ square root pie x 4

Question 29

Fatigue, fatigue failure

Answer 29

Fatigue is the failure under dynamics and fluctuating stress that critical stress (stress d max is bigger than stress d c)

Fatigue causes 90% of mechanical failures.