2.StrainGauges

2.StrainGauges - 2. Strain Gages 2.1 Strain Sensitivity and...

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2. Strain Gages 2.1 Strain Sensitivity and Gage Factor For most common materials, there is a constant ratio between stress and strain. The relationship is then expressed by Hooke's law : E = σ ε , (12) where: E = the modulus of elasticity or Young's modulus σ = stress ε = strain All electrically conductive materials possess a strain sensitivity , which is defined as the ratio of the relative change in electrical resistance of a conductor to the applied relative change in conductor length, or F = RR LL s o o (13) where: F s = strain sensitivity factor R = resistance change (ohms) R o = initial conductor resistance (ohms) L = change in length (mm) L o = initial conductor length (mm) Note that F s is a dimensionless quantity, as are both the numerator and the denominator. The term ( L / L o ) = ε , the strain. The electrical resistance of a conductor of uniform cross section behaves according to the equation : RL A = ρ (/) (14) where: R = resistance (ohms) L = length of conductor A = cross-sectional area of conductor ρ = resistivity constant , a property of the specific conductor material If a straight wire is stretched elastically, the length will increase and the cross-section will decrease by Poisson's ratio, ν = ( D / D )/( L / L ) ( D is the diameter of the wire), which is about 30% for most metals used in electrical resistance wire. From eq.(14), one can see that, provided ρ remains constant, the two effects are additive in causing the resistance to increase. Also notice that R R L L A A L L D D =+ 2 (15)
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The overall effect is that the percentage change in the electrical resistance of the conductor will be 1.6 times greater than the applied strain percentage. This also means that F s will be about 1.6 for an elastically stretched wire. For most alloys, the specific resistivity ρ , is not constant. It is affected by the applied strain. More precisely, resistivity changes occur when a conductor is strained because of an elastic distortion of the lattice structure which influences electron flow through the conductor. It can be said then that the resistance change in a conductor is made up of a geometrical effect plus a resistivity change due to the internal state of stress of the conductor. In order for the overall resistance change of a conductor to be a linear function of the applied strain, the resistivity change must be proportional to the internal stress level. This requirement is met by most, but not all metals.
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This note was uploaded on 07/20/2009 for the course AME 341BL taught by Professor Spedding during the Spring '08 term at USC.

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2.StrainGauges - 2. Strain Gages 2.1 Strain Sensitivity and...

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