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Experimental Stress Analysis

Strain Gauges

MEC 445

Mechanical Engineering

Amrita Vishwavidyapeetham

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Electrical Resistance Strain Gauges

The principle of electrical resistance strain gauge is that theelectrical resistance of a conductor changes proportionally to anystrain applied to it.

Lord Kelvin in 1856 first reported on the relationship between

strain and resistance of wire conductors.

During 1930s Simmons at California Institute of Tech and Rugeat MIT made practical use of it by bonding small diameter wires

to a structure to measure surface strain.

The strain gauges developed by them were known as SR-4Gauges.

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Strain Sensitivity of a Wire

Resistance of a conductor can be written as

Where is the specific resistanceL is the length of the conductor, and A is the cross

sectional area of the conductor

To find out the change in resistance we differentiate the above

If the wire diameter is D, the change in area can be calculated as

.

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Strain Sensitivity of a Wire

From the definition of Poissonsratio we can write

Hence

Strain sensitivity of metallic strain gauges 2

.

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Strain Gauge Construction

SR-4 measured 7000 with

Minimum resistance required from instrumentation point ofview is 100

For a dia of .025mm and R/L =1000 we need 100 mm ofwire.

Even for a reasonably thin wire we need very lengthy wire to

have a base resistance of 100

Scope study is measuring strain at a point. Its not possible tomeasure strain at a point using a long wire.

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Strain Gauge Construction

Gauges are formed by folded grids etched on metal foil.

We are measuring the strain along the gauge length

Strain gauges are available only at certain values

Thin metal foils are very fragile. Proper backing is

necessary.

The backing allows proper alignment and supports the leadwires

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Strain Gauge Construction

Different type of grid patterns are available for differentapplication

Standard resistances available are 120,350

Gauge factor must be measured experimentally

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Gauge Length

The gauge length of a strain gauge is the active or strain sensitive

length of the grid

The gauge measures the axial strain in the direction of the gauge

length.

The end loops and solder tabs are insensitive to strain because of

their relatively large cross-sectional area and low electrical

resistance.

Most common strain gauges have 3 mm gauge length and these

are good enough for a large verity of problems.

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Selection of Gauge Length

Thumb rule in selection of gauge length

Selection of gauge length is very important point in strain

measurement

The gauge length should be no grater than 0.1 times the radius

of a hole, fillet, or notch, or corresponding dimension of any

other stress raiser at which the strain measurement is to be

made.

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Commonly used strain gauge materials

The value of SAdepends upon the degree of cold working

imparted to the conductor during its formation, the impurities in

the alloy, and range of strain over which the measurement of

strain sensitivity is made

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Commonly used strain gauge materials

Most commonly used strain gauge material is an alloy of 55%Copper and 45% Nickel called Constantan/Advance.

SA2.1 for the Advance

SAis linear over a large range of strain ( 0 to 8%).

Constantan has excellent thermal capability

Has high specific resistance ( = 0.49 m)

Easy to develop self compensated strain gauges.(1 /0c)

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Commonly used strain gauge materials

Isoelastic alloy High sensitivity ( SA=3.6) : Advantageous in dynamic applications

where the strain gauge output must be amplified to a considerable

degree before recording.

High fatigue strength : Useful when the gauge is to operate in a

cyclic strain field where the alternative strains exceed 1500

Poor thermal stability : When mounted on steel a 10c wouldproduce a strain of 300 to 400

Useful for dynamic applications where temperature is stable

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Commonly used strain gauge materials

Karma alloy

Fatigue limit is higher than Advance but lower than Isoelastic.

Excellent stability with time: useful for strain measurements over

weeks or months.

Temperature compensation achievable in Karma is better over a widerange of temperature than advance alloy

Useful up to 260 0c in static strain measurements.

Difficult to solder the lead wires to the tabs.

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Commonly used strain gauge materials

Thermally induced apparent strains as a function of temperature