Strain Gauges

Historical development• Lord kelvin in 1856 first reported on the relationship b/w strain

and the resistance of wire conductors.• It took 80 years to find commercial application.• Simmons at california institute of technology and ruge at MIT

independently discovered in 1938 that small diameter wires could be adhesivly bonded to a structure to measure surface strain.

• Strain gauges developed by them were known as SR-4 gauges.• Metal foil strain gauges were first developed by sanders and roe

in england in 1952.• These gauges have replaced the wire grid SR-4 gauges except for a

very few special applications.• Semi conductor gauges were developed in 1960 by bell labs.• Present focus is towards better instrumentation and data

reduction. • System 5000/system 6200/system 7000

Strain sensitivity of a wire Resistance of a conductor can be written as R = ϼL/A (1) Where ϼ-specific resistance of a material, L-length of a

conductor, A-c/s area of the conductor. Differentiating eqn 1 and dividing it by R gives dR/R=d ϼ/ ϼ+dL/L-dA/A (2) If the wire diameter is D, the change in area can be calculated

as A = pi/4 (D2) dA/A = 2 dD/D From the defn of poisson’s ratio one can write, dD/D = -(poisson ratio) dL/LHence, dA/A = -2(poisson ratio) dL/L (3)(stress as well as temperature changes the resistance)

Strain sensitivity of the conductor SA is defined as

SA = (dR/R)/(dL/L) (4) In terms of specific resistance and poisson’s ratio

of the strain gauge material, SA = (dϼ/ϼ)/(dL/L) +(1+2(poison ratio)) (5)

strain sensitivity approaches too when the gauge experiences plastic deformation.

Gauge construction

Gauge construction Minimum resistance required from instrumentation point of view

is 100 ohms. If for example, diameter of the conductor is 0.0025mm and the

resistance per meter is 1000 ohms. To have a minimum resistance of 100 ohms, one requires 100mm

length of wire---this is too long. Obviously one cannot measure strain at a point using a long wire. Hence the gauge is formed by folded grids etched on metal foil. If the area of c/s is large, resistance is small and vice versa. Gauge factor needs to be found experimentally in strain gauge. Standard resistance are 120 and 350 ohms, whereas 500,1000 and

3000 ohms are for special purpose gauges.

Gauge length – defnition Gauge length of a strain gauge is the active or

strain sensitive length of the grid. gauge measures the axial strain in the direction

of the gauge length. End-loops and solder tabs are considered

insensitive to strain because of their relativly large c/s area and low electrical resistance.

Gauge length ranges from 0.2mm to 100mm.

Error in measurement ( when gauge length is not choosen appropriate)

Thumb rule in selection of gauge length As a rule of thumb, when practicable, the gauge

length should be no greater than 0.1 times the radius of a hole, fillet, or notch, or the corresponding dimension of any other stress raiser at which the strain measurement is to made.

Gauge location

Commonly used SG material Most commonly used SG material is an alloy of 55% cu and

45% ni called constantan/advance.• Advantages- • SA =2.1 for the above alloy.

• SA is linear over a large range of strain (0 to 8%)

• SA is not altered even when the material is subjected to plastic strain.

• Excellent thermal stability.• Has high specific resistance of 0.49µ-ohm-meter- only 50mm

wire for 100ohm resistance using a 0.025mm wire dia.• Useful to construct a small gauge with high resistance lower

current, hence I2R loss is less.Note: both temp and load affects the resistance.

Metallic alloys commonly employed in commercial strain gauges

The value of strain sensitivity depends upon degree of cold working imparted to the conductor in its formation, impurities in the alloy and range of strain over which the measurement of strain sensitivity is made.

Advance or constantan alloy• The value of strain sensitivity is linear over wide range of strain,

and hysteresis of bonding filaments is extremely small.• The value of strain sensitivity does not change significantly as the

material is subjected to plastic strain.

• The alloy has a high specific resistance ( 0.49 micro-ohm-meter)o Useful when constructing small gauges with relatively a high

resistance.

• The alloy has excellent thermal stability.o When mounted on common structural materials,small

temperature changes don’t influence.

• Easy to develop self temperature compensated gauges. This is achieved by introducing trace impurities or by heat treatment.

o With temperature compensated strain gauges, the temperature induced change in resistance/unit resistance on a material can be maintained at less than 10-6/oc

Percentage change in resistance as a function of percent strain for advance alloy

Isoelastic alloy• High sensitivity ( strain sensitivity = 3.6)o Advantages in dynamic applications where the strain gauge

output must be amplified to a considerable degree before recording.

• High fatigue strengtho Useful when the gauge is to operate in cyclic strain field where

the alternating strains exceed 1500 micro strains.

• Poor thermal stabilityo When mounted on steel a 1 deg celcius would produce a strain

of 300 to 400 micro strains.• Useful for dynamic applications where temperature is stable.

Karma alloy• Fatigue limit is higher than advance but lower than

isoelastic.• Excellent stability with time.o Useful for strain measurements over weeks or months.• Temperature compensation achievable in karma is

better over wide range of temperature than advance alloy.

• Useful upto 260 deg celcius for static strain measurements.(advance is limited to 204 deg celcius)

• Difficult to solder the lead wires to the tabs.

Thermally induced strain vs temperature

Strain gauge carriers – its need.• The etched metal film grids are very fragile.• Easy to distort, wrinkle or tear.• Metal film is usually bonded to a thin plastic sheet,

which serves as a backing or carrier before photoetching.

• Carrier material provides electrical insulation between the component and the gauge.

• Markings for the centerline of gauge length and width are also displayed on the carrier.

• Very thin paper was the first carrier material.

Types of carriers• Polyamide sheet of 0.025 mm has replaced paper.o Its tough and flexible.• Very thin high modulus epoxy is used for transducer

applications.o Has high precision and linearity.o Not suitable for general purpose as it is brittle and can

be broken during installation.• Glass fibre reinforced epoxies and or phenolics.o High level cyclic strains and fatigue life.o Useful for temperature upto 400 deg celcius.

1) The grid is encapsulated by the carrier for high level cyclic strain applications.

2) For very high temperature applications strippable carrier is used.

Carrier is removed during application of a gauge and ceramic adhesives serves to maintain the grid configuration.

Cements used for bonding• CynoacrylateFor quick curing and short term applications.• Epoxies For long term-transducer applications.• PolyesterRecommended for low temperature applications.• CeramicFor high temperature applications.

Cynoacrylate cement• Ideal for general purpose strain gauge applications.• Thin film of adhesive is placed between the gauge and the

specimen and gentle pressure is applied for 1 to 2 mins for inducing polymerization.

• Poymerization continues at room temperature without maintaining the pressure.

• Strain gauge can be employed approximatly 10 mins after bonding.

• Not suitable for extended life applications.• Coatings such as polyurethane, microcyrstalline wax or

silicon rubber can be used to protect from moisture and marginally extend the life of installation.

Epoxy cements• Exhibit Higher bond strength and higher level of strain at failure.• Epoxy is mixed with hardener to induce polymerization.o Amine-type curing agents produce exothermic reaction and cure

at room temperature.o Anhydride type of curing agents require application of heat of the

order of 120 deg celcius for several hours.• The relative proportion of hardener used has to be maintained as

per manufacturers recommendation.o Small deviations can affect the curing temperature and the

residual stresses during polymerization.• Bonding strength can be increased by adding micro-sized

particles of pure silica ( of 5 to 10% by weight)o However, temperature coefficient expansion of epoxy is reduced.

• Thin bond lines tends to minimize creep hysteresis and linearity problems.

o Clamping pressure of 35 to 140 kpa is recommended to ensure a thin adhesive layer.

• In transducer applications dilutent-thinned epoxies are used to get extremely thin void free bond lines(0.005mm)

o Clamping pressure of 350kpa is recommended.• The use of hardware-store variety two-tube epoxy systems is

discouraged.o Usually incorporate modifiers or plastisizers to improve the

toughness.o These cause large amount of creep and hysteresis and hence

undesirable.• A properly cured installation exhibit a resistance to ground

exceeding 10000 micro ohms.