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| Types of Modulus of Elasticity |
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| Corresponding to the three types of strains, there are three types of modulus. |
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| It is defined as the ratio of normal stress to the longitudinal strain within elastic limit. |
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| F is the normal force applied at the end of its wire, A is area of cross
section (= pr2), Dl
is the extension produced due to normal force, L is the original length of the wire. |
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| It is defined as the ratio of normal stress to the volumetric strain within the elastic limit. Thus, |
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Consider a spherical solid body of volume V and surface area a, when a force F is applied normally, the volume decreases by  |
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| It is defined as the ratio of tangential stress to the shearing strain within the elastic limit. |
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| Considering a solid metal cube whose lower face is fixed and its upper face is subjected to a tangential force F. The body suffers a change in its shape but not in its volume. If q is angle through which upper layer is sheared then, |
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  (Modulus of Rigidity) |
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| Stress - Strain Relationship in a wire |
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| AO = Elastic Range |
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| P = Yield point |
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| OD| = Breaking stress or tensile stress |
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| E = Breaking point |
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| OO1= Permanent set |
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| When the stress-strain relationship in a wire is studied, one finds that stress is directly proportional to the strain upto the point A (see the graph). The point 'A' is called the elastic limit and AO is called the elastic range. The Hooke's law is valid up till A. Beyond A, if the stress is removed, graph between stress and strain does not follow AO. BO| is followed when stress is zero, strain is not zero or a permanent deformation sets in the material. Therefore, OO| represents the permanent set. Notice that beyond 'A', the stress - strain graph is a curve and that for a small stress, large strain is produced in the material. The material beyond A and upto 'P' is partly elastic and partly plastic in behaviour. Beyond 'P', the behaviour of the wire is very erratic. There is a large increase in the strain but a very small change in the stress. |
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| At this stage, the wire flows down upto the point C. The point 'P', when the wire yields to the applied stress and begins to flow, is called the yield point. The region PC is called the plastic region. Materials used to make sheets or wires must have a longer plastic region and must be ductile. |
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| Beyond C, the graph has a hump at D. Even if the wire is loaded by a little amount, the wire becomes thin at weak portions of the wire and tends to break at E. The stress corresponding to the breaking point is called the breaking stress. Brittle substances generally have a small plastic region and the breaking stress lies closer to the elastic limit. |
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| The above graph is useful in classifying materials which serve different purposes. |
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