CLASS NOTES FOR MECHANICAL ENGINEERING
subjected to forces of one kind or the
other or combined forces. How the
materials behave under these forces is
explained in terms of mechanical
properties. Measure mechanical properties
by various destructive tests. Various worth
mentioning mechanical properties are
(iv) Yield strength
Ductile material deforms significantly before fracture under a tensile load. A tensile load draws a material into wires. All pure metals are ductile. Gold is most ductile among pure metals. Rubber and many polymers are also ductile materials. Measure ductility by the % elongation at fracture. (or % reduction in area at fracture also measures ductility. However % elongation and % reduction values are different for the same material. But either of two criterion’s is to compare the ductility of different materials. Tensile force lengthwise increases length and other dimensions decrease. Ductility is % elongation or % reduction in area.
Hence % elongation= [(final length – initial length)/initial length] x 100 = [(lf –li)/li] x 100
% reduction in area= ((Af – Ai)/Ai) x 100
Elasticity is the property. A body deforms under a force but regains original shape on the removal of force. Actually it applies to only ductile materials up to a certain limit. It is elastic limit. Hooke’s Law is applicable up to elastic limit.
Strain energy per unit volume is resilience. Its symbol is ‘u’. Its units are J/mm3. It is given by
u = σ2/2E
Resilience is an elastic property i.e. resilience is considered only within elastic limits. Its value at the elastic limit stress is called Proof resilience. Strain energy in the entire volume is called total strain energy and is represented by ‘U’.
U = Load x Extension/2 = P δL / 2
U=σ A (P L/AE)/2
Total strain energy U = σ (P/A) AL/2E = σ σ AL / 2E
= (σ2/ 2E) x Volume
Resilience u =U / V = σ2/ 2E
Yield stress a material is the maximum stress a material can bear without permanent deformation. It is an elastic property. It is possible only for ductile materials and its value is very near to the value of proportional limit stress. Upper yield point where the yielding starts i.e. change in micro-structure starts. Lower yield point where micro-structure change is complete. For example, at the upper yield point, BCC structure of Mild Steel start changing to FCC Structure. At the lower yield point, complete conversion mild steel to FCC takes place.
Stiffness of a material is the property of a material to resist deformation under an external load. Hence brittle materials are more stiff. Stiff materials are high carbon steels, tool steels and cast iron.
Toughness is also a mechanical property of a material to absorb impact loading up to the point of fracture. It is equal to area under the stress-strain curve. Thus toughness is the ability of a material to resist rupture under a moving (impact) load. In SI system, it is strain energy per unit volume i.e. (J/m3). Thus toughness is resilience in the plastic region. Toughness is the Modulus of Toughness. Measure toughness experimentally by Charpy test or Izod test. Perform these tests on a notched sample. Notch shape and size are standardized.
A brittle material shows no deformation under any type of load. However, if the load is increased, it will fail suddenly. Normally these materials fail due to small impact (moving) force. It has only one strength i.e. Ultimate strength. Brittle materials are cast iron, stone, brick etc.
Under this property, a material undergoes large deformation under a compressive force without fracture. Thus, it is a property similar but opposite to ductility. Materials, which are ductile under a tensile fore, are malleable under a compressive force. Malleable materials can be converted into thin sheets under a compressive force without fracture. Such materials are all pure metals.
Plasticity property of a material is to acquire permanent deformation even after the removal of the external applied force. This property is useful in the manufacture of various components. All ductile materials show this plastic property.
Hardness is a mechanical property. It is the resistance of a material to a localized plastic deformation under a point load. It is resistance to indentation, scratching, cutting or bending. Thus, less is the plastic deformation under a point load, harder will be the material. Hardness of a material is the quality control parameter. The difference between toughness and hardness is such that when toughness decreases, hardness increases and vice versa. Ductile materials are tougher and less hard. High toughness permits easy machining. High value of hardness does not permit easy machining.
There is a metal under a constant force at elevated temperature but below its yield stress. It undergoes a permanent deformation with respect to time. Even fracture occurs for a prolonged period of time. Creep exits in internal combustion engine, steam pipe and steam turbines. However, lead shows creep at room temperature.
Temperature effect on creep at constant stress
Creep strain increases with the increase of temperature and vice versa.
Stress effect at fixed elevated temperature
Strain due to creep increases with the increase of stress.
Effect of time
All other factors remaining constant, creep increases with increase of time and vice versa.
It is due to variable repeating loads. Fatigue failures occur due to the application of variable stresses. Lower value of stress causes fatigue failure during static loading. Fatigue contributes to approximately 90% of all mechanical service failures. Components in motion undergo fatigue. Automobiles on roads, aircraft wings and fuselages. Ships at sea, nuclear reactors, jet engines, and turbines undergo fatigue failures. Fatigue was initially recognized in early 1800. Investigators in Europe observed that bridge and railroad components were cracking when subjected to repeated loading. With passage of time, more fatigue failures under repeated loads were recorded.
Basic factors necessary to cause fatigue
Maximum tensile stress of sufficiently high value
Large variation in the applied stress
Sufficiently large number of cycles of the applied stress