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# Stress strain curve for ductile and brittle materials

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Machanics Of Structures

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### Stress strain curve for ductile and brittle materials

1. 1. Mechanics Of Structures-1
2. 2.  Hooke’s law states that: “ When a body is loaded within elastic limit, the stress is proportional to strain developed” or “Within the elastic limit the ratio of stress applied to strain developed is a constant”  The constant is known as Modulus of elasticity or Elastic modulus or Young’s modulus  Mathematically within elastic limit Stress/Strain=σ/e=E σ= P/A; e =ΔL/L E=PL/A Δ L
3. 3.  Young's modulus (E) is generally assumed to be the same in tension or compression and for most of engineering applications has a high numerical value. Typically, E=210 x 10^9 N/m² (=210 GPa) for steel  Modulus of rigidity, G= τ/φ= Shear stress/ shear strain  Factor of safety= Ultimate stress/Permissible stress  In most engineering applications strains do not often exceed 0.003 so that the assumption that deformations are small in relation to orginal dimensions is generally valid
4. 4. stress is a physical quantity that expresses the internal forces that neighboring particles of a continuous material exert on each other strain is the measure of the deformation of the material.
5. 5. The relationship between the stress and strain that a particular material displays is known as that particular material's stress–strain curve. It is unique for each material and is found by recording the amount of deformation (strain) at distinct intervals of tensile or compressive loading (stress).
6. 6. Ductile Materials: >Ductile materials will withstand large strains before the specimen ruptures. >Ductile materials often have relatively small Young’s moduli and ultimate stresses. >Ductile materials exhibit large strains and yielding before they fail. >Steel and aluminum usually fall in the class of Ductile Materials Brittle Materials: >Brittle materials fracture at much lower strains. >Brittle materials often have relatively large Young’s moduli and ultimate stresses. >Brittle materials fail suddenly and without much warning. >Glass and cast iron fall in the class of Brittle Materials.
7. 7. Steel generally exhibits a very linear stress-strain relationship up to a well defined yield point
8. 8. Typical regions that can be observed in a stress- strain curve are:  Elastic region,  Yielding,  Strain Hardening,  Necking and Failure
9. 9.  If the specimen returns to its original length when the load acting on it is removed, it is said to response elastically
10. 10.  A slight increase in stress above the elastic limit will result in permanent deformation. This behavior is called yielding  The stress that causes yielding is called yield stress σy.  The deformation that occurs is called plastic deformation
11. 11.  When yielding has ended, a further load can be applied to the specimen, resulting in a cure that rises continuously but becomes flatter until it reaches a maximum stress referred to as ultimate stress, σu.  The rise in the curve is called Strain Hardening
12. 12.  After the ultimate stress, the cross- sectional area begins to decrease in a localized region of the specimen, instead of over its entire length. The load (and stress) keeps dropping until the specimen reaches the fracture point.