Stress: When a material in subjected to an external force, a resisting force is set up within the component. The internal resistance force per unit area acting on a material is called the stress at a point. It is a scalar quantity having unit.
Types of Stresses:
Normal stress
Shear Stress
Bulk Stress
Strain: It is the deformation produced in the material due to simple stress. It usually represents the displacement between particles in the body relative to a reference length.
F is expressed in Newton (N) and A, original area, in square meters (m2), the stress σ will be expresses in N/ m2. This unit is called Pascal (Pa).
• As Pascal is a small quantity, in practice, multiples of this unit is used.
Types of Strains:
Normal Strain
Since strain is m/m it is dimensionless.
Shear strain
Note 1: The angle is radians, not degrees. The volume of the solid is not changed by shear strain.
Note: the angle is radians, not degrees
Bulk Strain
True Stress and True StrainThe true stress is defined as the ratio of the load to the cross section area at any instant.
Where σ and ε is the engineering stress and engineering strain respectively.
The true strain is defined as
The volume of the specimen is assumed to be constant during plastic deformation.
Stress-Strain Relationship
The stress-strain diagram is shown in the figure. In brittle materials there is no appreciable change in rate of strain. There is no yield point and no necking takes place.
Graph between stress-strain
In figure (a), the specimen is loaded only upto point A, is gradually removed the curve follows the same path AO and strain completely disappears. Such a behavior is known as the elsastic behavior.
In figure (b), the specimen is loaded upto point B beyond the elastic limit E. When the specimen is gradually loaded the curve follows path BC, resulting in a residual strain OC or permanent strain.
Comparison of engineering stress and the true stress-strain curves shown below:
The true stress-strain curve is also known as the flow curve.
• True stress-strain curve gives a true indication of deformation characteristics because it is based on the instantaneous dimension of the specimen.
• In engineering stress-strain curve, stress drops down after necking since it is based on the original area.
• In true stress-strain curve, the stress however increases after necking since the cross sectional area of the specimen decreases rapidly after necking.
• The flow curve of many metals in the region of uniform plastic deformation can be expressed by the simple power law.
σT = K(εT)n
Where K is the strength coefficient
n is the strain hardening exponent
n = 0 perfectly plastic solid
n = 1 elastic solid For most metals, 0.1< n < 0.5
Properties of Materials
Some properties of materials which judge the strength of materials are given below:
Elasticity: Elasticity is the property by virtue of which a material is deformed under the load and is enabled to return to it original dimension when the load is removed.
Plasticity: Plasticity is the converse of elasticity. A material in plastic state is permanently deformed by the application of load and it has no tendency to recover. The characteristic of the material by which it undergoes inelastic strains beyond those at elastic limit is known as plasticity.
Ductility: Ducitility is the characteristic which permits a material to be drawn out longitudinally to a reducd section, under the action of a tensile force (large deformation).
Brittleness: Brittleness implies lack of ductility. A material is said to be brittle when it cannot be drawn out by tension to smaller section.
Malleability
Malleability is a property of a material which permits the material to be extended in all directions without rapture. A malleable material possess a high degree of plasticity, but not necessarily great strength.
Toughness
Toughness is the property of a material which enable it to absorb energy without fracture.
Hardness
Hardness is the ability of a material to resist indentation or surface abrasion. Brinell hardness test is used to check hardness.
Brinell Hardness Number (BHN)
where, P = Standard load, D = Diameter of steel ball
d = Diameter of the indent.
Strength
The strength of a material enables it to resist fracture under load.
Engineering Stress-Strain Curve
The stress-strain diagram is shown in figure. The curve start from origin. Showing thereby that there is no initial stress of strain in the specimen.
The stress-strain curve diagram for a ductile material like mild steel is shown in figure below.
* Upto point A, Hooke's Law is obeyed and stress is proportional to strain. Point A is called limit of proportionality.
* Point B is called the elastic limit point.
* At point B the cross-sectional area of the material starts decreasing and the stress decreases to a lower value to point D, called the lower yield point.
* The apparent stress decreases but the actual or true stress goes on increasing until the specimen breaks at point C, called the point of fracture.
* From point E ownward, the strain hardening phenomena becomes predominant and the strength of the material increases thereby requiring more stress for deformation, until point F is reached. Point F is called the ultimate point.
Rigidity modulus
Bulk modulus
Free expansion of 1 due to temperature rise
Free expansion of 2 due to temperature rise
Expansion of 1 due to temperature stress (tensile)
Compression of 2 due to temperature stress (compression)
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