Bulk Modulus - Ppt 71r22

BULK MODULUS:

Volume elasticity

Bulk modulus - The bulk modulus (K) of a substance measures the substance's resistance to uniform compression. It is defined as the pressure increase needed to cause a given relative decrease in volume. Its base unit is the Pascal. Its the ratio of the stress on the body to the body's fractional decrease in volume.

The modulus of elasticity for a material subjected to compression on all surfaces—that is, volume stress. Bulk modulus is the relationship of volume stress to volume strain, expressed as the ratio between F/A and dV/Vo, where dV is the change in volume and Vo is the original volume.

Definition The bulk modulus K can be formally defined by the equation: K= -V ∂P/∂V where P is pressure, V is volume, and ∂P/∂V denotes the partial derivative of pressure with respect to volume. The inverse of the bulk modulus gives a substance's compressibility. Other moduli describe the material's response (strain) to other kinds of stress: the shear modulus describes the response to shear, and Young's modulus describes the response to linear strain. For a fluid, only the bulk modulus is meaningful. For an anisotropic solid such as wood or paper, these three moduli do not contain enough information to describe its behavior, and one must use the full generalized Hooke's law.

When forces are applied to each surface of a cube, the cube experiences a strain on its volume. The volume will be reduced. In this case the volume stress is force per unit area (F/A). The volume strain is change in volume per unit volume ( V/V) K=volume stress/volume strain B= F/A / V/V Volume elasticity applies both to liquids and solids .

Gases are easily compressed and have very small coefficients and vary with pressure and temperature. Characteristics of materials which are closely related to the elastic properties are ductility, malleability, compressibility and hardness.

Ductility 

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Ductility is a mechanical property that describes the extent in which solid materials can be plastically deformed without fracture. Ductility is especially important in metalworking, as materials that crack or break under stress cannot be manipulated using metal forming processes, such as hammering, rolling, and drawing.

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Malleability 

Malleability, a similar concept, refers to a material's ability to deform under compressive stress; this is often characterized by the material's ability to form a thin sheet by hammering or rolling .

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Compressibility 

Compressibility is a measure of the relative volume change of a fluid or solid as a response to a pressure (or mean ”stress”) change.

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Hardness 

Hardness is dependent on ductility, elasticity, plasticity, strain, strengt h, toughness, viscoelasticity, and viscosity.

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Common examples of hard matter are ceramics, concrete, certain metals, and super hard materials, which can be contrasted with soft matter.

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