Formula Sheet: Manufacturing Engineering | Formula Sheets of Mechanical Engineering PDF Download

 Page 1


Short Notes for Engineering Materials 
Crystal Structure of Materials 
• When metals solidify from molten state, the atoms arrange themselves into various crderly 
configurations called crystal. 
• There are seven basic crystal structures, they are  
 
 
Simple Cubric Cell (SCC) 
• The total number of atoms present in crystal structure, 
 
• Atomic Packing Factor (APF) 
 
 
• Percentage APF = 52% 
• Percentage of voids = 100 – 52 = 48% 
Body Centered Cubic (BCC) Structure 
Page 2


Short Notes for Engineering Materials 
Crystal Structure of Materials 
• When metals solidify from molten state, the atoms arrange themselves into various crderly 
configurations called crystal. 
• There are seven basic crystal structures, they are  
 
 
Simple Cubric Cell (SCC) 
• The total number of atoms present in crystal structure, 
 
• Atomic Packing Factor (APF) 
 
 
• Percentage APF = 52% 
• Percentage of voids = 100 – 52 = 48% 
Body Centered Cubic (BCC) Structure 
• Total effective number of atoms present in the crystal 
 
 
• Atomic Packing Factor (APF) 
 
• Percentage APF = 68% 
• Percentage of voids = 100 – 68 = 32% 
Face Centred Crystal (FCC) 
In this arrangement, each face has an atom and corners are also occupied by atoms. 
Total effective number of atoms in cell. 
• Atomic Packing Factor (APF) 
 
 
• Percentage APF = 74% 
• Percentage of voids = 100 – 74 = 26% 
 
Gibbs phase rule : 
• F = C – P + 2 
• Number of external factors = 2 (pressure and temperature). 
• For metallurgical system, pressure has no appreciable effect on phase equilibrium and 
hence, 
• F = C – P + 1 
 
 
Page 3


Short Notes for Engineering Materials 
Crystal Structure of Materials 
• When metals solidify from molten state, the atoms arrange themselves into various crderly 
configurations called crystal. 
• There are seven basic crystal structures, they are  
 
 
Simple Cubric Cell (SCC) 
• The total number of atoms present in crystal structure, 
 
• Atomic Packing Factor (APF) 
 
 
• Percentage APF = 52% 
• Percentage of voids = 100 – 52 = 48% 
Body Centered Cubic (BCC) Structure 
• Total effective number of atoms present in the crystal 
 
 
• Atomic Packing Factor (APF) 
 
• Percentage APF = 68% 
• Percentage of voids = 100 – 68 = 32% 
Face Centred Crystal (FCC) 
In this arrangement, each face has an atom and corners are also occupied by atoms. 
Total effective number of atoms in cell. 
• Atomic Packing Factor (APF) 
 
 
• Percentage APF = 74% 
• Percentage of voids = 100 – 74 = 26% 
 
Gibbs phase rule : 
• F = C – P + 2 
• Number of external factors = 2 (pressure and temperature). 
• For metallurgical system, pressure has no appreciable effect on phase equilibrium and 
hence, 
• F = C – P + 1 
 
 
 
Engineering and True Stress-Strain Diagrams: 
• When we calculate the stress on the basis of the original area, it is called the engineering or 
nominal stress. 
• If we calculate the stress based upon the instantaneous area at any instant of load it is then 
termed as true stress. 
• If we use the original length to calculate the strain, then it is called the engineering strain. 
 
Brittleness: 
• It may be defined as the property of a metal by virtue of which it will fracture without any 
appreciable deformation. 
• This property is just opposite to the ductility of a metal. 
Toughness: 
• It may be defined as the property of a metal by virtue of which it can absorb maximum 
energy before fracture takes place. 
• Toughness is also calculated in terms of area under stress-strain curve. 
• Toughness is the property of materials which enables a material to be twisted, bent or 
stretched under a high stress before rupture. 
Resilience: 
• This may be defined as the property of a metal by virtue of which it stores energy and resists 
shocks or impacts. 
• It is measured by the amount of energy absorbed per unit volume, in stressing a material up 
to elastic limit. 
Endurance: 
• This is defined as the property of a metal by virtue of which it can withstand varying stresses 
(same or opposite nature). 
• The maximum value of stress, which can be applied for indefinite times without causing its 
failure, is termed as its endurance limit. 
Anelastic Behaviour: 
• Recoverable deformation that takes place as a function of time is termed an-elastic 
deformation. 
• Due to some relaxation process within the material, the elastic deformation of the material 
continues even after the application of the load 
 
 
Page 4


Short Notes for Engineering Materials 
Crystal Structure of Materials 
• When metals solidify from molten state, the atoms arrange themselves into various crderly 
configurations called crystal. 
• There are seven basic crystal structures, they are  
 
 
Simple Cubric Cell (SCC) 
• The total number of atoms present in crystal structure, 
 
• Atomic Packing Factor (APF) 
 
 
• Percentage APF = 52% 
• Percentage of voids = 100 – 52 = 48% 
Body Centered Cubic (BCC) Structure 
• Total effective number of atoms present in the crystal 
 
 
• Atomic Packing Factor (APF) 
 
• Percentage APF = 68% 
• Percentage of voids = 100 – 68 = 32% 
Face Centred Crystal (FCC) 
In this arrangement, each face has an atom and corners are also occupied by atoms. 
Total effective number of atoms in cell. 
• Atomic Packing Factor (APF) 
 
 
• Percentage APF = 74% 
• Percentage of voids = 100 – 74 = 26% 
 
Gibbs phase rule : 
• F = C – P + 2 
• Number of external factors = 2 (pressure and temperature). 
• For metallurgical system, pressure has no appreciable effect on phase equilibrium and 
hence, 
• F = C – P + 1 
 
 
 
Engineering and True Stress-Strain Diagrams: 
• When we calculate the stress on the basis of the original area, it is called the engineering or 
nominal stress. 
• If we calculate the stress based upon the instantaneous area at any instant of load it is then 
termed as true stress. 
• If we use the original length to calculate the strain, then it is called the engineering strain. 
 
Brittleness: 
• It may be defined as the property of a metal by virtue of which it will fracture without any 
appreciable deformation. 
• This property is just opposite to the ductility of a metal. 
Toughness: 
• It may be defined as the property of a metal by virtue of which it can absorb maximum 
energy before fracture takes place. 
• Toughness is also calculated in terms of area under stress-strain curve. 
• Toughness is the property of materials which enables a material to be twisted, bent or 
stretched under a high stress before rupture. 
Resilience: 
• This may be defined as the property of a metal by virtue of which it stores energy and resists 
shocks or impacts. 
• It is measured by the amount of energy absorbed per unit volume, in stressing a material up 
to elastic limit. 
Endurance: 
• This is defined as the property of a metal by virtue of which it can withstand varying stresses 
(same or opposite nature). 
• The maximum value of stress, which can be applied for indefinite times without causing its 
failure, is termed as its endurance limit. 
Anelastic Behaviour: 
• Recoverable deformation that takes place as a function of time is termed an-elastic 
deformation. 
• Due to some relaxation process within the material, the elastic deformation of the material 
continues even after the application of the load 
 
 
Isomorphous  system. 
• There are 5 invariant reactions occurring in binary phase system: 
• Eutectic reaction: When a liquid phase changes into two different solid phases during 
cooling or two solid phases change into a single liquid phase during heating, this point is 
known as eutectic point 
• Eutectoid reaction: When a solid phase changes into two solid phases during cooling and 
vice-versa that point is known as eutectoid point 
• Peritectic reaction: A binary system when solid and liquid phases changes solid phase on 
cooling and vice-versa on heating, then state of system is known as peritectic point 
• Peritectoid reaction: If a binary phase diagram when two solid phases changes to one solid 
phase, then state of system is known as peritectoid point. 
Normalising 
• For this process, the metal is placed in the furnace and heated to just above its ‘Upper 
Critical Temperature’. 
• When the new grain structure is formed it is then removed from the furnace and allowed to 
cool in air as it cools new grains will be formed. 
• These grains, although similar to the original ones, will in fact be smaller and more evenly 
spaced. 
• Normalising is used to relieve stresses and to restore the grain structure to normal. 
Quenching 
• It is a heat treatment when metal at a high temperature is rapidly cooled by immersion in 
water or oil. 
• Quenching makes steel harder and more brittle, with small grains structure 
Annealing (Softening) 
• Annealing is a heat treatment procedure involving heating the alloy and holding it at a 
certain temperature (annealing temperature), followed by controlled cooling. 
• Annealing results in relief of internal stresses, softening, chemical homogenising and 
transformation of the grain structure into more stable state. 
• The annealing process is carried out in the same way as normalising, except that the 
component is cooled very slowly. This is usually done by leaving the component to cool 
down in the furnace for up to 48 hours 
Hardening 
• Hardening also requires the steel to be heated to its upper critical temperature (plus 50°C) 
and then quenched. 
• The quenching is to hold the grains in their solid solution state called Austenite; cooling at 
such a rate (called the critical cooling rate) is to prevent the grains forming into ferrite and 
pearlite. 
• Hardening is a process of increasing the metal hardness, strength, toughness, fatigue 
resistance. 
Tempering 
Page 5


Short Notes for Engineering Materials 
Crystal Structure of Materials 
• When metals solidify from molten state, the atoms arrange themselves into various crderly 
configurations called crystal. 
• There are seven basic crystal structures, they are  
 
 
Simple Cubric Cell (SCC) 
• The total number of atoms present in crystal structure, 
 
• Atomic Packing Factor (APF) 
 
 
• Percentage APF = 52% 
• Percentage of voids = 100 – 52 = 48% 
Body Centered Cubic (BCC) Structure 
• Total effective number of atoms present in the crystal 
 
 
• Atomic Packing Factor (APF) 
 
• Percentage APF = 68% 
• Percentage of voids = 100 – 68 = 32% 
Face Centred Crystal (FCC) 
In this arrangement, each face has an atom and corners are also occupied by atoms. 
Total effective number of atoms in cell. 
• Atomic Packing Factor (APF) 
 
 
• Percentage APF = 74% 
• Percentage of voids = 100 – 74 = 26% 
 
Gibbs phase rule : 
• F = C – P + 2 
• Number of external factors = 2 (pressure and temperature). 
• For metallurgical system, pressure has no appreciable effect on phase equilibrium and 
hence, 
• F = C – P + 1 
 
 
 
Engineering and True Stress-Strain Diagrams: 
• When we calculate the stress on the basis of the original area, it is called the engineering or 
nominal stress. 
• If we calculate the stress based upon the instantaneous area at any instant of load it is then 
termed as true stress. 
• If we use the original length to calculate the strain, then it is called the engineering strain. 
 
Brittleness: 
• It may be defined as the property of a metal by virtue of which it will fracture without any 
appreciable deformation. 
• This property is just opposite to the ductility of a metal. 
Toughness: 
• It may be defined as the property of a metal by virtue of which it can absorb maximum 
energy before fracture takes place. 
• Toughness is also calculated in terms of area under stress-strain curve. 
• Toughness is the property of materials which enables a material to be twisted, bent or 
stretched under a high stress before rupture. 
Resilience: 
• This may be defined as the property of a metal by virtue of which it stores energy and resists 
shocks or impacts. 
• It is measured by the amount of energy absorbed per unit volume, in stressing a material up 
to elastic limit. 
Endurance: 
• This is defined as the property of a metal by virtue of which it can withstand varying stresses 
(same or opposite nature). 
• The maximum value of stress, which can be applied for indefinite times without causing its 
failure, is termed as its endurance limit. 
Anelastic Behaviour: 
• Recoverable deformation that takes place as a function of time is termed an-elastic 
deformation. 
• Due to some relaxation process within the material, the elastic deformation of the material 
continues even after the application of the load 
 
 
Isomorphous  system. 
• There are 5 invariant reactions occurring in binary phase system: 
• Eutectic reaction: When a liquid phase changes into two different solid phases during 
cooling or two solid phases change into a single liquid phase during heating, this point is 
known as eutectic point 
• Eutectoid reaction: When a solid phase changes into two solid phases during cooling and 
vice-versa that point is known as eutectoid point 
• Peritectic reaction: A binary system when solid and liquid phases changes solid phase on 
cooling and vice-versa on heating, then state of system is known as peritectic point 
• Peritectoid reaction: If a binary phase diagram when two solid phases changes to one solid 
phase, then state of system is known as peritectoid point. 
Normalising 
• For this process, the metal is placed in the furnace and heated to just above its ‘Upper 
Critical Temperature’. 
• When the new grain structure is formed it is then removed from the furnace and allowed to 
cool in air as it cools new grains will be formed. 
• These grains, although similar to the original ones, will in fact be smaller and more evenly 
spaced. 
• Normalising is used to relieve stresses and to restore the grain structure to normal. 
Quenching 
• It is a heat treatment when metal at a high temperature is rapidly cooled by immersion in 
water or oil. 
• Quenching makes steel harder and more brittle, with small grains structure 
Annealing (Softening) 
• Annealing is a heat treatment procedure involving heating the alloy and holding it at a 
certain temperature (annealing temperature), followed by controlled cooling. 
• Annealing results in relief of internal stresses, softening, chemical homogenising and 
transformation of the grain structure into more stable state. 
• The annealing process is carried out in the same way as normalising, except that the 
component is cooled very slowly. This is usually done by leaving the component to cool 
down in the furnace for up to 48 hours 
Hardening 
• Hardening also requires the steel to be heated to its upper critical temperature (plus 50°C) 
and then quenched. 
• The quenching is to hold the grains in their solid solution state called Austenite; cooling at 
such a rate (called the critical cooling rate) is to prevent the grains forming into ferrite and 
pearlite. 
• Hardening is a process of increasing the metal hardness, strength, toughness, fatigue 
resistance. 
Tempering 
• As there are very few applications for very hard and brittle steel, the hardness and 
brittleness needs to be reduced. The process for reducing hardness and brittleness is called 
tempering. 
• Tempering consists of reheating the previously hardened steel. 
• During this heating, small flakes of carbon begin to appear in the needle like structure. (See 
below) This has the effect of reducing the hardness and brittleness. 
Stress Relieving 
• When a metal is heated, expansion oc-curs which is more or less proportional to the 
temperature rise. Upon cooling a metal, the reverse reaction takes place. That is, a 
contraction is observed. 
• When a steel bar or plate is heated at one point more than at another, as in welding or 
during forging, internal stresses are set up. 
• During heating, expansion of the heated area cannot take place unhindered, and it tends to 
deform.  
• On cooling, contraction is prevented from taking place by the unyield-ing cold metal 
surrounding the heated area.