Engineering Mechanics And Materials Flashcards
Mechanical properties’ definitions
- strength
- ductility
- toughness
- hardness
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.
Engineering stress (tensile stress & Shear stress)
F/A, Fs/Ao
Tensile strain, axial strain
Ez = change in L/Lo
Lateral Strain
Ex = change in D/Do
Poisson’s ratio
V = Ex/Ez (lateral strain/tensile strain)
Hooke’s law
d = Ee (d - stress, E - constant proportionality, e - strain)
Definition of the Ao - cross sectional area
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
Modulus of Elasticity (Young’s Modulus)
Hooke’s law ( d = Ee )
Elastic bulk modulus, k
P = - k (change in V/V original)
Elongation strain
Ez = change in length/original length
Plastic (permanent) deformation
Cannot go back to its original form/shape after load is being removed
Yield strength
The start of the plastic deformation where the stress is noticeable. (When Ep is 0.002)
Tensile strength
Is the maximum stress on the engineering stress-strain curve
Tensile strength for metal and polymers
Metal - occurs when noticeable necking starts
Polymers - occurs when polymers backbone chains are aligned and about to break
Elastic region and plastic region
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
tensile test
- Yield Point
- Proof stress
- tensile strength
Yield point = Load applied/Cross sectional area
Proof Stress = 0.2% = 0.2% PS/CSA
Tensile Strength = Maximum load/CSA
% Reduction Area
Change in Area/Original Area x 100%
Ductility. How to calculate?
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
What is the effect of temperature on yield strength, tensile strength and ductility?
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.
Toughness and hardness
Toughness is the energy to break unit volume of material. Hardness is the resistance to permanently indenting the surface (small indent = large hardness)
Hardness measurement
- Rockwell
- HB Brinell Hardness - Ts = 500 x HB (PSIA) & Ts = 3.45 x HB (MPa)
Design factor. Factor of safety
Design Factor - stress d = N’d(stress)c
Factor of safety - stress d = stress y/N
True Stress & True Strain
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)
Ductile and brittle fracture
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.
Design against crack growth & formula
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)
Principle of fracture mechanics
1) stress concentration - griffth crack = stress d m = 2 stress d o (a/Dt) 1/2. DT is the radius of curvature
Crack propagation
Due to the sharpness of the crack tip. When? If applied stress is above critical stress.
Formula = stress do = 92Eys/pie a) 1/2
Design example
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
Fatigue, fatigue failure
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.
