EXPERIMENTAL STRESS ANALYSIS

UNIT 1

Introduction

We make measurements everyday. For example, we routinely measure our body weight

on a scale or read the temperature of an outdoor thermometer. We put little thought into the selection of instruments for these routine measurements. But when the stakes become greater, the selection of measurement equipment and techniques, and the interpretation of

the measured data can demand considerable attention.

The objective in any test is to answer a question. So we take measurements to establish the value or the tendency of some variable, the results of which will help answerour question. But, how can a measurement system are used so that the engineer can easily interpret the measured data and be confident in their meaning? There are procedures that

address these measurement questions.

Reasons for Experimental Stress Analysis

Material characterization

Failure analysis

Residual or assembly stress measurement

Acceptance testing of parts prior to delivery or use General Measurement System

A measurement is an act of assigning a specific value to a physical variable. That

physical variable is the measured variable. A measurement system is a tool used for

quantifying the measured variable. As such, it is used to extend the abilities ofthe human senses that, while they can detect and recognize different degrees of roughness, length, sound, color, and smell, are limited and relative; they are not very adept at assigning specific to sensed variables. Basically such a system consists of part or all of four general stages: (1) Sensor-transducer stage; (2) Signal-conditioning stage; (3) Output stage; and (4) Feedback control stage. These stages form the bridge between the input to themeasurement system and the system output, a quantity that is used to infer the value of the physical variable measured. Sensor Transducer Stage:

The primary function of the first stage is to detect or to

sense the physical variable (Measurand) and performs either a mechanical or an electrical 1

transformation to convert the signal into a more usable form. The sensor is a physical element that employs some natural phenomenon by which it senses the variable being measured. The transducer converts this sensed information into a detectable signal form, which might be electrical, mechanical, optical, etc. In most cases, however, the physical variable is transformed into an electric signal because this is the form of signal that is

most easily measured.

Signal Conditioning Stage: The purpose of the second stage is to take the transducer

signal and modifies by amplification, filtering or other means so that a desirable output is

available.

Output Stage: Provides an indication of the value of the measurement. The output

equipment might be a simple readout display a marked scale or might contain devices that can record the signal for later analysis. Examples of these devices are taperecorders,

chart recorders and computer disk drives.

Feedback Control Stage: In those measurement systems involved in process control a

fourth stage the feedback control stage, contains a controller that interprets the measured signal and makes a decision regarding the control of the process. This decision results in a change in a process parameter that affects the magnitude of the sensed variable. It is very important to realize that the accuracy of control cannot be any better than the accuracy of the measurement of the control variable. Therefore one must be able to

measure a physical variable accurately before one can hope to control the variable.

Definition of Terms

The following terms are often employed to describe the quality of an instruments reading.

Range:The region between the limits within which a quantity is measured, received ortransmitted, expressed by starting the lower and upper range values. Span: The algebraic difference between the upper and lower range values. Measured Variable: A quantity property or condition that is measured. Sometimes will

be referred as the measurand. Example: Temperature, Pressure, rate of flow. Measured Signal:

The electrical, mechanical, pneumatic or other variable applied to the

input of a device. It is the analog of the Measured Variable produced by a transducer. Output Signal: A signal delivered by a device, element or system.2

Accuracy: The accuracy of an instrument indicates the deviation of the reading from a

known value.

Precision: The difference between the instruments reported values during repeated

measurements of the same quantity. Typically, this value is determined by statistical

analysis of repeated measurement.

Repeatability: Is the ability of an instrument to reproduce the same measurement each

time the same set of conditions is repeated. This does not imply that the measurement is

correct, but rather that the measurement is the same each time.

Sensitivity: The change of an instrument or transducer output per unit change in the

measured quantity. A more sensitive instrument reading changes significantly in response to smaller changes in the measured quantity. Typically an instrument with higher

sensitivity will also have better repeatability and higher accuracy.

Resolution: The smallest increment of change in the measured value that can be

determined from the instrument readout scale.

Hysteresis: An instrument is said to exhibit hysteresis when there is a difference in

readings depending an whether the value of the measured quantity is approached from above or below. Hysteresis results from the inelastic quantity of an element or device. In other word, it may be the result of mechanical friction, magnetic effects, elastic

deformation, or thermal effects. Hysteresis is expressed in percent of span.

Variables are entities that influence the test. A variable that can be changed

independently of other variables is known as an independent variable. A variable that is

affected by changes in one or more other variables is known as a dependent variable. Variables that are not or cannot be controlled during measurement, but that affect the value of the variable measured are called extraneous variables. A variable that can be held at constant value during the measurement process is called controlled variable. Noise

is a random variation of the value of the controller that interprets the measured

signal as a consequence of the variation of the variables. Noise increases data scatter. Interference imposes undesirable deterministic trends on the measured value. Any

different from its true behavior is interference. 3

Parameter

We define a parameter as a functional grouping of variables. For example, a Moment of Inertia, or a Reynolds number has its value determined from the values of a grouping of variables. A parameter that has an effect on the behavior of the measured variable is

called a control parameter.

Calibration

A calibration applies a known input value to a measurement system for the purposeof observing the system output value. It establishes the relationship between the input and output values. The known value used for the calibration is called the standard. The most common type of calibration is known as a static calibration. The term static implies that the values of the values of the variables involved remain constant, that is, theydo not vary with time or space. When the variables of interest are time (or space) dependent and such varying information is sought, we need dynamic information. In a broad sense, dynamic variables are time (or space) dependent in both their magnitude and frequency content. A dynamic calibration determines the relationship between an input of known

dynamic behavior and the measurement system output.

Random and Systematic Errors

Random error is a measure of the random variation found during repeated measurements of a variable. A system that repeatedly indicates the same wrong value upon repeated application of a particular input would be considered to have small random error

contributions regardless of its accuracy.

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Strain, Force, and Pressure Measurements

The most popular electrical elements used in force measurements include the resistance strain gage, the semiconductor strain gage, and piezoelectric transducers. The strain gage measures force indirectly by measuring the deflection it produces in a calibratedcarrier. Pressure can be converted into a force using an appropriate transducer, and strain gage techniques can then be used to measure pressure. Flow rates can be measured using

differential pressure measurements which also make use of strain gage technology.

Strain Gauge Basics A strain gauge is a device used to measure the mechanical strain on an object or structure. When an object is under a lot of pressure, the material can slowly fatigue and begin to subtly bend. These bends, nearly impossible to see with the naked eye, can be early indicators that a building is aging or beginning to buckle. Strain gauges constantly measure these minute changes, giving engineers an easy way to monitor a structure's condition. Factors to be considered before selecting a Strain Gauge: Readability Ease of mounting 5

Required operation skill

Weight

Cost

Range and accuracy required

Types of Strain Gauges

Depending upon its magnification system, the strain gauges may be classified as under:

1. Mechanical

(a) Wedge and screw

(b) Lever Simple and compound

(c) Rack and pinion

(d) Combination of lever and rack & pinion

2. Optical

3. Electrical

(a) Inductance

(b) Capacitance

(c) Resistance

(d) Piezo-electric and Piezo-resistive

5. Magnetic

6. Acoustical

7. Pneumatic

8. Scratch type

9. Photo-stress gauge

Types of Mechanical strain gauge Wedge and Screw type: The wedge gauge is simply a triangular plate with its longer sides related by a 1:10 slope. When inserted between two shoulders clipped to the test specimens, extensions could be detected to nearest 0.05 mm. A single screw extensometer is the other type and used for measurement of strain in actual structure. The magnification in this instrument is accomplished solely by screw manometer, which measures the relative motion between two coaxial tubes each provided with a conical point. The contact points are inserted in prepared holes marking aknown

gauge length on the structure. In this device, extensions could be measured to nearest 0.0025 mm with a probable accuracy of 0.005 mm under normal operating conditions.

Lever Simple and compound

Simple lever magnification

The simple lever strain gauge gains its magnification factor by a suitable positioning of the fulcrum. The magnification of this type is unlimited. However, the magnification ratio is limited to 10 to 20. The gauge length is generally 50 mm and the strain is

magnified 10:1 on the graduated scale.

Compound lever magnification

Berry strain gauge comes under this type. These gauges use a lever magnification with a

dial indicator to show the magnified motion. It consists of a frame with two conically pointed contact points. One point is rigidly fixed to the frame, while the other is pivoted from the frame and is integral with a lever arm, which alone magnifies the strainabout 5:1. A screw micrometer or dial indicator is used to measure the motion of arm. The

strain measurements could be done to the nearest 0.005 mm.

Huggenberger Extensometer It consists of a frame, which supports the lever system including the fixed contact point a and movable point b which serves dually as part of the lever system andas a contact point. Movable point is integral with arm h. Its rotation, resulting from themotion l, magnifies the motion and transmits it, through linkd in a knife edges m and n to the pointer e, where further magnification occurs. The reading taken from the scale f are

converted to actual strain values by application of multiplication factor (= l1l2/a1a2),

which is established for each instrument by calibration. Mounting may be accomplished with a clamp, spring or screw pressure as the frame to hold points a and b in contact with the test piece. The magnification may vary from 300 to 2000 depending on the

odel. The gauge length varies from 12.5 mm to 25 mm. m

Johansson Extensometer

These extensometers use tension tape or twisted metal strip between two knife edges. Half of the strip is twisted to one direction and remaining half is twisted to other direction and a pointer is fixed at the center of the strip. On application of load, displacement in the movable knife edge takes place with high amplification due to stretching of twisted metal

strip.

Rack and pinion The rack and pinion principle along with various types of gear trains is employedin gauges in which the magnification system is incorporated in dial indicator. The dial indicator consists of an encased gear train actuated by a rack cut in the spindle, which follows the motion to be measured. A spring imposes sufficient spindle force to maintain

8a reasonably uniform and positive contact with the moving part. The gear train terminates

ch contact points are

predetermined gauge length. Motion between two

with a light weight pointer which indicates the spindle travel on a graduated dial.

Combined lever, rack & pinion magnification

The Whittmore strain gauge is an important gauge of this type. This gauge is a self contained instrument consisting essentially of two frame members A bound together by two elastic hinges B for parallel frictionless motion. One 45 conical contacts point C

is attached to each frame member. For strain measurements ea

inserted into drilled holes of defining

frame members or strain is measured directly with a dial indicator.

Electrical resistance strain gauge:

In electrical resistance strain gauge the displacement or strain is measured as afunction

of resistance change produced by the displacement in the gauging circuit.

When the conductor is stretched, its length will increase and area of cress section will decrease this will result in change in resistance. Change in resistance per unit strain is

defined as Gauge Factor.

Gauge factor indiuge.

Characterics ofauges

l

atic and dynamic strain nable cost

cates the sensitivity of the strain ga

ist Electrical resistance strain g

- should be of extremely small size

- should have significant mass

- should be easily attached with materia

- higher degree of sensitivity and accuracy

- should be unaffected by temperature

- should be capable of measuring both st- should\ld exhibit linear response to strain - should be available at reaso- should be used both as sensing element and also in transducer systems Types of electrical resistance strain gauges

Elec metallic sensing element may be broadly classified ctrial resistance strain gauge within to four groups. a. Un-bonded wire strain gauge b. Bonded wire strain gauge 9

c. Foil strain gauge

d. Weldable strain gauge

Un-bonded wire strain gauge:

The principal of the un-bonded metallic strain gauge is based on the change in electrical resistance of a metallic wire due to the change in the tension of the wire. This type consists of a stationary frame and a movable platform. Fine wire loops are wounded around the insulated pins with pretension. Relative motion between the platform and the frame increases the tension in two loops, while decreasing tension in the other two loops. These four elements are connected approximately to a four arm Wheat stone bridge.

These type strain gauges are used for measurement of acceleration, pressure, force etc.

Bonded Wire Strain Gauge:

The bonded metallic type of strain gauge consists of a strain sensitive conductor(wire) mounted on a small piece of paper or plastic backing. In us this gauge is cemented to the surface of the structural member to be tested. The wire grid may be & flat type or wrap-around. In the flat type after attaching the lead wires to the ends of the grids,a second piece of paper is cemented over the wire as cover. in the wrap-around type, the wire is wound around a cylindrical core in the form of a close wound helix. This core is then flattened & cemented between layers of paper for the purpose of protection and insulation. Formerly only wrap-around gauges were available, but generally

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flat grid gauges are preferred as they are superior to wrap-around gauge in terms of hysterisis,

creep, elevated temperature, performance, stability & current carrying capacity. 10

il grid made up of thin strain sensitive foil. The

mpared to the thickness (microns) so that larger area

ng

strain sensitive

Tungsten, housed within a small diameter

ent is insulated from the tube with highly compacted

ic insulation. This gauge is subsequently spot welded to structure under test and

in. The test specimen which is put into tension or

itted through the weld to mounting flange and in to for static or dynamic applications.

Foil Strain Gauges:

The foil type of strain gauges has a fo

width of the foil is very large as co

of the gauge is for cementi

Weldable Strain gauge:

Weldable strain gauges are easy to install in minutes in any environment comparedto

bonded type strain gauge. The weldable strain gauge consists of a

element, the nickel Chromium or platinum

stainless steel tube. The strain elem

ceram

provides bonding to transfer the stra

compression, the stress is transmstrain tube. These gauges can be used

ACOUSTICAL STRAIN GAUGES

This gauge essentially consists of a steel wire tensioned between two supports a

predetermined distance apart. Vibration of the distance alerts the natural frequency of vibration of the wire and this change in frequency may be correlated with the change in strains causing it. An electromagnet adjacent to the wire may be used to set the wire in vibration and this wire movement will then generate an oscillating electric signal. The signal may be compared with, the pitch of an adjustable standard wire, the degreeof which adjustment necessary to match the two signal frequencies being provided by a tension screw on the standard wire. Calibration of the screw allows a direct determination of the change of length of a measuring gauge to be made once the standard gauge has been tuned to match the frequency of the measuring wire. The visual display produced or

CRO renders adjustment easier.

Strain Gage based measurements

Strain: Strain Gage, Piezoelectric Transducers

Force: Load Cell

Pressure: Diaphragm to Force to Strain Gage

Flow: Differential Pressure Techniques

The resistance strain gage is a resistive element which changes in length, hence

resistance, as the force applied to the base on which it is mounted causes stretching or compression. It is perhaps the most well known transducer for converting force into an

electrical variable.