experimental stress analysis-Chapter 7

Experimental Stress Analysis

Department of Mechanical Engineering Page 1

Unit 7: BRITTEL COATING METHODS Brittle coating methods: The principle of stress analysis involves the adherence of a thin coating brittle in nature on the surface of the specimen. When the specimen is subjected to external loads, the thin brittle coating cracks under tensile stress.

Strain produced in specimen is transmitted to the coating resulting in coating cracks. From the threshold strain of coating i,e. minimum strain required to cause the coating to

crack, determined through calibration of coating, the stresses in specimen are determined. The behavior of the coating is quite complicated as it depend on the number of

parameters influencing the behavior of the coating, such as 1) Coating thickness 2) Coating temperature 3) Creep in coating during testing 4) Moisture 5) Velocity of air flowing over coating 6) Curing time of the coating 7) Load time history The use of the coating is limited to identifying the regions of high stress and region of

low stresses. This technique is providing simple and direct approach for solving large class of

industrial problem such as pressure vessels. This technique has been used for

1) The determination of stress concentration in components subjected to various types of loads. 2) The measurement of thermal and residual strains in components 3) Providing whole field data for the magnitude and direction of principal stress. This method is based upon the perfect adhesion of a thin coasting , brittle in nature on the

surface of a components to be analyzed for stresses. When the specimen is stressed the surface strains of specimen are transmitted to the

coating and the coating cracks in a direction perpendicular to maximum tensile principle stresses.

Advantages of brittle coating 1) It is nearly a whole field stress analysis technique 2) The technique can be directly applied to a prototype of actual machine or machine

components in operation and there is no necessity for any model. 3) Analysis for converting the data into stress in component is not complicated



Disadvantages of brittle coating 1) Behavior of the coating is strongly dependent on temperature and humidity variations during

testing. 2) Number of variable affecting the sensitivity of coating therefore the behavior of coating has

to be properly understood. 3) This technique is more qualitative in nature than quantitative

Coating stresses Coating is sprayed over the surface of the specimen until a thickness of 0.1 to 0.25 mm is built up. Then, coating is dried either at room temperature or at an elevated temperature in a hot air oven. After the coating is completely dried or cured, loads are applied on the sample. Since the coating is very thin, it can be safely assumed that surface strain of the specimen are faithfully transmitted from specimen to coating without any magnification or attenuation. From the stresses in specimen, the stresses in the coating can be obtained.

Let us take

휎 , 휎 : Principal stress in the specimen

휀 , 휀 : Principal strains in the specimen

휎 ,휎 : Principal stress in the coating



휀 , 휀 : Principal strains in the specimen

휗 ,휗 : Poisons ratio of coating and specimen.

퐸 ,퐸 : Young’s modulus for coating and specimen respectively.

Consider the specimen and coating is as shown in fig

By Hooke’s law

휀 =휎 −휗 휎

퐸

휀 =휎 −휗 휎

퐸

휀 =휎 −휗 휎

퐸

휀 =휎 −휗 휎

퐸

since there is perfect adhesion between the coating and the surface of the specimen, hence

휀 = 휀

휀 = 휀

Thus, we get

휎 −휗 휎퐸 =

휎 −휗 휎퐸 … … … … … … . (1)

휎 −휗 휎퐸 =

휎 −휗 휎퐸 … … … … … … (2)

Thus on solving eq 1 and 2, we get

휎 =퐸

퐸 1− 휗[(1 − 휗 휗 )휎 − (휗 − 휗 )휎 ]

휎 =퐸

퐸 1− 휗[(1 − 휗 휗 )휎 − (휗 − 휗 )휎 ]



휎 − 휎 =퐸퐸

1 + 휗1 + 휗

[휎 − 휎 ] … … … … … … . (3)

From eq 3 we can say that 휎 − 휎 always has the same sign as 휎 − 휎 .

To calibrate the coating a cantilever calibration strip as shown in fig 2 . Calibration is used to determine the strain sensitivity. The strain at ‘A’ where the cracks start appearing is called the strain sensitivity of the coating or the threshold strain. The stresses at ‘a’ in the coating produced by the external load are found by setting 휎 = 0

Thus,

휎 =퐸

퐸 1− 휗[(1− 휗 휗 )휎 ]

휎 =퐸

퐸 1−휗[(휗 − 휗 )휎 ]

Crack Patterns The manner in which a brittle coating fails by cracking depends entirely upon the state of stresses in the specimen to which it adheres. The failure behavior of the coating is determined by the magnitudes of 휎 and휎 , the principal stress in the coating. Consider the following special cases when the specimen is subjected to direct loading.

Case 1: 흈ퟏ > 0,흈ퟐ < 0,흈ퟑ = ퟎ



In this case, only one set of cracks forms, and they are perpendicular to 휎 . These cracks indicate the principal stress direction of 휎 , and, as a consequence, the cracks represent stress trajectories, or isostatics.

Case 2: 흈ퟏ > 흈ퟐ > 0,흈ퟑ = ퟎ

For this two families of cracks can form. The first set of cracks due to 휎 forms perpendicular to 휎 and parallel to 휎 . When the stress level of 휎 becomes sufficiently high, a second family of crack will form perpendicular to 휎 and parallel to 휎 .

Crack patterns of this type are often encountered in testing the cylindrical portion of pressure vessels. Where 휎 ( the hoop stress) is twice as large as 휎 ( the axial stress). If the pressure is increases slowly, the first crack will appear in the coating along the axis of the cylinder and will be due to hoop stress. Later, after the hydrostatic pressure acting on the cylindrical vessel has more than doubled, a second set of crack will form in the hoop direction because of the axial stress.

Case 3: 흈ퟏ = 흈ퟐ > 0,흈ퟑ = ퟎ



When 휎 = 휎 at any point on the body, the stress system is said to be isotropic and every direction is a principal direction. If the values of σ and σ are sufficiently high, the coating will fail; however, the crack pattern produced will be random in character. Crack pattern of this form are often referred to as craze patterns since the crack have no preferential direction.

Case 4: 흈ퟐ < 흈ퟏ < 0,흈ퟑ = ퟎ

In this instance, the coating is subjected to a state of biaxial compressive stress and will not crack under direct load.

However, if the compressive stresses are sufficiently large the coating will fail by flecking from the surface of the specimen. Brittle coating have failed by flecking are not common in elastic analysis, where loads are limited to maintain stresses in the specimen below the yield strength of the specimen.

Refrigeration technique It is possible to obtain coating cracks in low stressed regions by employing refrigeration

technique with brittle coating. First, the specimen is loaded until the stress in the critical region is just below the yield

stress; then, the coating is subjected to a rapid temperature drop while under load. The rapid temperature drop produces a state of hydrostatic tension in the coating which is

superimposed upon the existing stress in the coating due to load. The combined load and thermal stress are used sufficient to produce coating failure and

crack pattern. The direction of resulting cracks is coincident with one of the principal stress due to the

load since the isotropic thermal stresses have no preferential direction.



This technique is simple to apply and the results are accurate provided the coating stress due to the loads is sufficiently large.

In order to reduce the temperature of coating two methods are employed.

Ice water is sponged over the area of the coating which has not previously responded. This method is not very much successful.

A stream of compressed air is passed through a box containing dry ice and it is directed into the surface of the coated model. The stream of much cooled air can be accurately directed and the resulting crack patterns can be closely controlled.

Load relaxation for compressive stress A brittle coating does not respond to compressive loads. In order to overcome this

difficulty, a relaxation technique is applied. A load is applied to coated specimen before it had opportunity to dry. This load is maintained on the coated specimen until drying is complete. Under this condition the coating is stress free, while the specimen is highly stressed in

compression. When load is released, the specimen will stretch, since it was previously compressed and

tensile stress will develop in the coating caused the coating cracks.

Crack detection methods When the coating fails, very fine V-shaped cracks with a depth equal to the coating thickness and a width of approximately 0.05 mm to 0.075mm appear. These cracks are generally not visible to the naked eye. In order to observe these cracks the following methods may be used



1. Oblique incidence method: in order to visually observe these fine cracks, a focused light source must be directed at oblique incidence to the surface and normal to the cracks. For observing small areas this is a good method. However, this method is a very much time consuming.

2. Statiflux method: this is a form of electrified particle inspection method. This method consists in applying a special Statiflux penentrant to the coated test piece, the surface is then superficially dried, leaving the penentrant in the in the coating cracks and finally an ionized Statiflux powder is blown over the part. The powder particles, which have obtained an electrostatic charge in being blown from a special gun, are electrically attracted to the cracks. When dynamic strains are being studied or when coatings with high threshold strains are used, it will often be necessary to apply the Statiflux penentrant before initiating the test and to keep the coating wet with the penetrate during the test. Upon completion of the test, the part is dried and the Statiflux powder applied in the normal manner. Statiflux does not destroy the sensitivity of the coating for further testing. The powder forms small, white mounds over the cracks and provides an excellent means of locating the crack pattern and recording the crack patterns for a permanent record. The disadvantage of this method is that the non-uniform application of the Statiflux penentrant will probably result in a temperature gradient due to different evaporation rates.

3. Dye Etching method: red dye etchant, can be used with some of the resin-based coatings to increase the visibility of the crack patterns for photographic purposes. The dye etchant is a mixture containing turpentine, machine oil, and red dye. The enchant is applied to the surface of a cracked brittle coating for approximately 1 min. During this time the enchant begins to attack the coating in the neighborhood of the coating too long, it will attack the coating in the neighborhood of the cracks, thus making them wider. If the enchant is left contact with coating too long, it will attack the surface of the coating. After the etchant is wiped, the surface of the coating, the coating is cleaned with an etchant emulsifier (soap and water). The dye which has penetrated the cracks is not removed during the cleaning process’s thus cracks appears as fine red lines on a yellow background.



Types of brittle coatings

Resin based coating/ stress coat: this consists of about one third zinc resinate as a base dissolved in about two-third carbon disulphide with a small amount of plasticizer. Dibutyl phthalate is used as a polarizer to vary the degree of brittleness of the coating, which increases with its increase. The strain sensitivity of this coating, varies from 0.0003 to 0.0030. it can be applied to the test specimen by a spraying method. This coating can be used upon 60 deg C and absorbs water and oil. The thickness of this coating can be made varying from 0.1 to .15mm and can be used for macro and micro applications. Stress coat has been employed widely and can be applied to all materials . synthetic resin dissolved in trichloroethylene or benzene and phenolic resin mixed with titanic white and dissolved in a mixture of benzene, toluene and xylene have also been used as brittle lacquers.

Ceramic based coating: It consists of finely ground ceramic particles suspended in a solvent. It can be sprayed by conventional means onto the specimen. Upon drying at room temperature the coating presents a chalklike appearance and is not suitable for use. In order to make the coating effective, it must be fired at about 540 deg C until the ceramic particles melt and coalesce. When fired, the coating is glasslike in appearance and brown in color. These coatings are relatively insensitive to minor changes in temperature. They can be used upon 370 deg C and are not influenced by the presence of oil and water. Their disadvantages include the high temperature of 537 deg C required to fire the coating which produces detrimental effect on components fabricated from aluminum, magnesium, plastics and highly heat treated steel. Their visual inspection for cracks is not possible and Statiflux method must be resorted to. Strain sensitivity of these coatings range from 0.0002 to 0.002.



Calibration Method To determine the strain sensitivity or threshold strain for the coating, the coating has to be calibrated. The static method may be adopted to calibrate the coating.

For calibration of the stress coat a cantilever calibrating strip is used. The calibrating strip consists of a bar of aluminum 300 mm long, 2.54 mm wide and 6 mm thick. The calibrating strip after having been sprayed with the same lacquer as the test specimen and dried, is mounted in a special loading fixture as a cantilever beam and subjected to a fixed deformation at its free end. The lacquer should be scraped from the calibrating strip at the end which is to be clamped in the loading fixture and at the point of contact with the cam. When clamping the strip in the calibrating fixture, the locking screw should be tightened until the strip just touches the bottom of the loading cam to ensure consistency of strain between the calibrating fixture and the calibrating scale. The load is applied to the calibrating strip in the same length of time as that used in loading the test specimen. The point on the strip at which the crack commences is marked and represents the section where the strains are equal to the strain sensitivity of the lacquer.



The calibrating strip can then be removed from the loading fixture and placed alongside a calibrated scale, from which the incipient cracking strain can read. Fig shows the Tens-Lac calibrator which is used to measure the threshold crack sensitivity of the brittle coating. In this case a calibration bar is coated at the same time as the test part. After drying, the bar is placed in the calibrator and simply loaded with thumb pressure at its free end. Cracks will appear in the coating and threshold strain value is read directly from a scale built in the calibrator. The Tens-Lac calibrator is available with twelve calibration bars.

For a biaxial state of stress two strain gages are mounted on an isoentatic line, the first perpendicular to the isostatics and the second parallel to the isostatics and readings are taken. Then

휎 =퐸

1 − 휗(휖 + 휗 휖 )

휎 =퐸

1 − 휗(휖 + 휗 휖 )

The threshold strains are computed from

(휖 ) =휎퐸

(휖 ) =휎퐸

For the first and second family of isoentatics respectively.



In actual practice 10 to 15 strips are tested so that a number of 휖 values are obtained. Then the estimated mean value of the threshold strain becomes

휖 =1푁

(휖 )

Where N=total number of calibration values used

(휖 ) = ith value of the threshold strain

Standard deviation of threshold strain is computed from

푆 =1

푁− 1(휖 ) − (휖 )

푆 =1

푁 − 1(휖 ) −

1푁

(휖 )