Strain Measurement
Prof. Yu Qiao Department of Structural Engineering, UCSD
Strain Measurement
• The design of load-carrying components for machines and structures requires information about the distribution of forces within the particular component. • Often we need to consider the deflection capacity. • This can be analyzed based on the measurement of physical displacements.
1 Strain Measurement
• A simple example is the slender rod that is placed in uniaxial tension. • Forcer per unit area is called stress. • Design criterion is often based on the stress levels. • The stress can be calculated through the measured deflection.
Stress and Strain
• The experimental measurement of stress is always accompanied with the determination of strain. • The ratio of the change in length of the rod to the original length is the axial strain: a = L/L • For most engineering materials, strain is a small quantity, usually in units of 10-6 in/in or 10-6 m/m.
2 Resistance Strain Gauge
• The measurement of the small displacements that occurs in a material or object under mechanical load determines the strain. • Strain can be measured by methods as simple as observing the change in the distance between two scribe marks, or as advanced as optical holograph. • In any case, the sensor would ; (1) have good spatial solution, i.e. the sensor should measure the strain at a “point”; (2) be unaffected by change in ambient conditions; and (3) have a high-frequency response for dynamic (time- based) strain measurement. • One of the most commonly used device is the bonded resistance strain gauge.
Resistance Strain Gauge
• There are metallic gauges. • Consider a conductor having a uniform cross- sectional area, Ac, and a length, L, made of a material having a resistivity, e. The overall resistance is given by R = e L/Ac • If the conductor is subject to a normal stress along the axis of the wire, the cross-sectional area and the length will change, which in turn affect R.
3 Resistance Strain Gauge
Hence, the changes in resistance are caused by two basic effects: the change in geometry as the length and cross- sectional area change, and the change in the value of the resistivity. The dependence of the resistivity on the strain is called piezoresistance and may be expressed in terms of a piezoresistance coefficient: Young’s modulus
Poisson’s ratio Gauge factor (GF)
Resistance Strain Gauge
• For example, consider a copper wire having a diameter of 1 mm and a length of 5 cm. The resistivity is 1.710-8 m.
4 Resistance Strain Gauge
• Another example. A very common material for the construction of strain gauge is the alloy constantan (55% copper with 45% nickel) having a resistivity of 4910-8 m. A typical strain gauge may have a resistance of 120 . What length of constantan wire of diameter 0.025 mm would yield this resistance?
Resistance Strain Gauge
• Through this example we can see that a single straight conductor is normally not practical for strain measurement. • A simple solution is to bend the wire conductor so that several lengths of wire are oriented along the axis of the strain gauge.
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5 Resistance Strain Gauge
• A typical metallic-foil bonded strain gauge consists of a metallic foil pattern that is formed in a manner similar to the process used to produced printed circuits. • The foil is mounted on a plastic backing material. • The gauge length is an important specification for a particular application.
Resistance Strain Gauge
• Since strain is usually measured at the location where the stress is a maximum and the stress gradients is high, the strain gauge averages the measured strain over the gauge length. • Usually the maximum strain is the quantity of interest. Thus, errors can result from improper choice of a gauge length. • Special mounting techniques and constructions are required for the variety of application conditions, including design variations in the backing material, the grid configuration, bonding techniques, and total gauge electrical resistance.
6 Resistance Strain Gauge
• The strain gauge backing serves several important functions. • It electrically isolates the metallic gauge from the test specimen and transmits the applied strain to the sensor. • The backing provides the surface used for bonding with an appropriate adhesive. • Backing materials are available that are useful over temperature ranging from -270 to 290oC.
Resistance Strain Gauge
• The adhesive bond serves as a mechanical and thermal coupling between the metallic gauge and the test specimen. • The strength of the adhesive should be sufficient to accurately transmit the strain. • It should have thermal conduction and thermal expansion characteristics suitable for the application. • A wide array of adhesives are available, e.g. epoxies, cellulose nitrate cement, and ceramic- based cement.
7 Resistance Strain Gauge
• If there are both normal and transverse components of strain, the total change in resistance of the gauge will be a result of both the axial and lateral components. • The goal of the strain gauge design is to create a sensor that is sensitive only to strain along one axis, and has negligible sensitivity to lateral and shear deformation. • Actual strain gauges are sensitive to lateral strains to some degree; while the sensitivity to shearing strains is often negligible.
Resistance Strain Gauge
• Semiconductor strain gauges are also commonly used. • Silicon crystals are the basic material. The crystals are sliced into very thin sections. • Due to the high piezoresistance coefficient, the semiconductor strain gauge exhibits a very high gauge factor, as high as 200 for some gauges! • They also have higher resistance, longer fatigue life, and lower hysteresis. • However, the output is nonlinear with strain, and the strain sensitivity or gauge factor may be remarkably dependent on temperature.
8 Resistance Strain Gauge
• Semiconductors with high charge carrier density (~1020 carriers/cm3) exhibit little variation of their gauge factor with strain or temperature. • If the charge carrier density is low (<1017 carriers/cm3),
Resistance Strain Gauge
• Due to the capability for producing small gauge length, silicon semiconductor strain gauge is usually very small. • It allows the measurement of the strains with high frequencies. • However, special treatment is required if the environment is corrosive (e.g. in a liquid pressure measurement). • The maximum strain can be measured is usually below 0.005 (in compression ~0.05).
9 Strain Gauge Electrical Circuit
•A Wheatstone bridge is generally used to detect the small changes in resistance that are the output of a strain gauge measurement circuit. • A typical sensitivity is ~10-6 /kNm2 • Commercially available equipment can measure changes in gauge resistance of less than 0.0005 ( ~ 0.0001%).
Strain Gauge Electrical Circuit
E is very sensitive to • The bridge output (voltage) Eo+Eo is o small change in R1 Voltagemeasurement
• If all the fixed resistors and the strain gauge resistance are initially equal, and the bridge is balanced such that
Eo = 0,
• This equation is valid for all the circuits as long as R/R <<1.
GF / 4 DC power source
(voltage = Ei)
10 Strain Gauge Electrical Circuit
• This bridge can be balanced by changing the resistance of one arm, and thus the bridge can be balanced without touching the gauge.
Multiple gauges can be used to increase the bridge output and cancel out ambient effects.
Strain Gauge Electrical Circuit
• For example, consider a strain gauge with a gauge factor of 2 mounted on a rectangular steel bar (Em = 200 GPa). The bar is 3 cm wide and 1 cm high, and is subjected to a tensile force of 30 kN. Determine the resistance change of the strain gauge, if the resistance of the gauge was 120 in the absence of the axial load.
11 Strain Gauge Electrical Circuit
The Multiple Gauge Bridge
• The output from a bridge circuit can be increased by the appropriate use of more than one active strain gauge. • In addition, the use of multiple gauges can be used to compensate unwanted effects, such as temperature or specific strain components. • If all four resistances in the bridge circuit represent active strain gauges, the bridge output becomes
12 The Multiple Gauge Bridge
• The four strain gauges are assumed initially to be in a state of zero strain. • If these gauges are now subjected to strains such that
the resistances change by dRi, then
• Evaluating the appropriate partial derivatives yields
The Multiple Gauge Bridge
If Ri is not a strain gauge but a constant resistor, it is eq’t to set i = 0 in this eq. Thus, for a bridge containing one or more active strain gauges, equal strains on opposite bridge arms sum, whereas equal strains on adjacent arms of the bridge cancel. These characteristics can be used to increase the output of the bridge, to provide temperature compensation, or to cancel unwanted components of strain.
13 Bridge Constant
• Commonly used strain gauge bridge arrangements may be characterized by a bridge constant, , defined as the ratio of the actual bridge output to that output of a single
gauge sensing the maximum strain, max (assuming the remaining bridge resistances remain fixed). • The output for a single gauge experiencing the maximum strain is is the ratio of the actual output to this value. Valid for all the systems if R/R << 1
Bridge Constant
• For example, consider the bridge constant for two strain gauges mounted on a member. The member is subject to uniaxial tension, which produces an axial strain a and a lateral strain L = -pa. Assume that all the resistances are initially equal, and therefore the bridge is initially balanced. Let (GF)1 = (GF)2.
GF GF 0 0 1 4 4 > 1
14 Apparent Strain and Temperature Compensation • Apparent strain is manifested as any change in gauge resistance that is not due to the component of strain being measured. • Techniques for accomplishing temperature compensation, eliminating certain components of strains, and increasing the value of the bridge constant have been well established. • The bridge constant is influenced by (1) the location of the strain gauges on the test specimen and (2) the gauge connection position in the bridge circuit.
Apparent Strain and Temperature Compensation • We can remove (compensate) a component of strain. • Consider a beam having a rectangular cross section
and subject to the external loadings FN and M. The stress distribution in the cross section is
15 Apparent Strain and Temperature Compensation • To remove the effects of bending strain, identical strain gauges are mounted to the top and bottom of the beam, and they are connected to bridge locations 1 and 4 (opposite bridge arms). • The gauges experience equal but opposite bending strains, and both strain gauges are subject to the same axial strain caused by FN.
Apparent Strain and Temperature Compensation
•The bridge output is
Differs by a factor of 2, which is the bridge constant of the two-gauge bridge.
16 Apparent Strain and Temperature Compensation • Differential thermal expansion between the gauge and the specimen creates an apparent strain. • Thus, temperature sensitivity of strain gauges is a result of both the changes in resistance caused by temperature changes and the strain experimenced by the differential expansion. • Using gauges of identical alloy composition as the specimen would minimize this error. • Even under this condition, heating of the strain gauge as a result of current flow from the measuring device may be a source of significant error, since usually the gauge is temperature-sensitive.
Apparent Strain and Temperature Compensation • We can use a compensating gauge that experiences resistance change caused only by the temperature variation the same as that of the specimen.
17 Apparent Strain and Temperature Compensation • Consider the case when all the bridge resistances are initially equal, and the bridge is therefore balanced. • If the temperature of the gauges now changes, their resistances will change as a result of thermal expansion, creating an apparent thermal strain. Thus,
• Under this condition, the output value will not be affected by thermal effects. • Actually, any two active gauges mounted on adjacent bridge arms will compensate for temperature.
Construction and Installation
• There are a variety of strain gauge configurations. • Practical construction of gauges is accomplished by techniques similar to those used in printed circuit board technology, resulting in a thin-film metallic grid on conductors.
18 Construction and Installation
• The first metallic foil gauge were developed around 1950. • Standard gauge resistances are 120 and 350 . • Because of the accuracy of the process that produces the metal foil, a variety of patterns for the metal film are possible. • The operating assumption is that the change in resistance is linear with applied strain. • But the nonlinearity error always exists. • In loading and unloading, there will also be some degree of hysteresis and a shift in the resistance for a state of zero strain.
19 Construction and Installation
• The strain gauge will typically indicate lower values during unloading. • This behavior is determined not only by the gauge characteristics but also by the adhesive and the strain history. • For properly installed gauge the nonlinearity error should be below 0.1%, after the first “break-in” cycle. • The first cycle hysteresis and zero shift are difficult to predict. Its effect can be minimized by cycling the gauge between zero strain and a value of strain above the maximum value to be measured.
Analysis of Strain Gauge Data
Single-plane type strain gauge rosettes
Stacked type strain gauge rosettes
20 Optical Strain Measuring Techniques
• Optical method of stress/strain field measurement can provide information concerning directions and magnitude. • Optical techniques have been developed either in models made of materials having appropriate optical properties or through coating techniques for existing specimens. • Photoelasticity takes advantage of the changes in optical properties of certain materials that occur when strained.
Optical Strain Measuring Techniques
• E.g., some plastics display a change in optical properties when strained that causes an incident beam of polarized light to be split into two polarized beams that travel with different speeds and that vibrate along the principal axes of stress. • Since the two light beams are out of phase, they can be made to interfere, leading to the insight into the stress. • The implement this method we need to either make a model of the real parts or apply coatings on the real specimens.
21 Photoelastic Measurement
Optical Strain Measuring Techniques
• Moiré method is also widely applied. • Moiré pattern is an optical effect resulting from the transmission or reflection of light from two overlaid grid patterns. • The fringes that result from relative displacement of the two grid patterns can be used to measure strain. • Each fringe corresponds to the locus of points of euqal displacement. • Recent development include the use of lasers and holography to very accurately determine whole field displacement for complex geometries.
22 Moiré Methods • Enhanced visual inspection, aided by Moiré pattern that results from two overlaid, relatively dense patterns that are displaced relative to each other. • This observable optical effect occurs, e.g., in color printing, where patterns of dots form an image when the printing is slightly out of register. • Another common example is the striking shimmering effect that occurs with some patterned clothing on television. This effect results when the size of the pattern in the fabric is essentially the same as the resolution of the television image.
Moiré Methods
US Patent 7341348 B2 (2008)
23 Moiré Methods
• Recently, the Moiré-fringe multiplication have greatly increased the sensitivity to 2400 lines/mm. • Moiré interferometry is an extension of Moiré-fringe multiplication that uses coherent light and has sensitivities of 0.4 m/fringe. • A reflective grating is applied to the specimen, which experience deformation under load conditions. • The technique provides whole field readings of in-plane strain. • If more than one master gratings are used, 3D displacement field including the out-of-plane component can be obtained.
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