Stress Measurement Using Gauges and Photoelectric - Book Report/Review Example

 Stress Measurement Using Gauges and Photoelectric Summary This paper provides a report on the principles of stress measurement while using the photoelastic technique and strain gauges. As such, the report identifies the technology used in each principle, as well as the procedure for utilization of the technique in stress measurement. Finally, the report provides an example of typical industrial application of the identified techniques in the measurement of stress in different test specimen. Both strain gauges and photoelastic measurement methods for stress are regarded as non-destructive methods. This is because these methods do not tamper with the physical properties or natural states of the samples under investigation for strain and stress. Photoelastic Photoelastic depicts a method, which is commonly used in the process of determining stress distribution in a given material (Aben 1993). Such a method is useful in cases where it is complex to use mathematical methods. Photoelastic aids in the determination of stress in irregular geometries and abrupt material discontinuities (Vishay 2011). The light speed in a polycarbonate material tends to vary with respect to a function of the magnitude and direction of the residual or applied stress. Hence, polarization of such a light results in a split that forms two independent wave fronts, which travel in unique velocities and parallel to the principal stress direction, but normal to each other. As such, the material gets two independent refraction indices, which is the birefringence property. Principle The stress measurement method is founded on the birefringence property, which is depicted by some transparent materials. The property of birefringence involves a light ray that passes via birefringent material and it encounters two refractive indices (Ramesh 2000). Such a property is often regarded as double refraction and can be seen in several optical crystals. In measurement of the stresses, photoelastic materials indicate birefringence property whereby the magnitude of the obtained refractive indices is directly proportional to the stress state at the given point (Frocht 1965). Additional information, which includes orientation and maximum shear stress, is obtained through the analysis of birefringence using the polariscope. Figure 1 is a clear illustration of the principle stress directions while using the technique of photoelastic. Figure 1: principal stress directions For birefringence induced stress, the normal induced light is split into 2 components on its principal stress direction on the plane, which is perpendicular to the light propagation direction (Asundi 2002). Figure 1 indicates how a polariscope facilitates in determining the principal directions of the fringes. The light that is transmitted in these directions has velocities, which are proportional to the intensities of the principal stresses. Such results in the deduction of the stress optic law as: S1-S2 = Nfs/d Where N= a/2p the fringe order Fs= 1/C the fringe value of the material with a wavelength of 1 and stress optic coefficient of C d= the distance under which the light traverses Figure 2: Schematic representation of the polariscope in action Process In photostress method, the procedure begins with the bonding of a strain-sensitive plastic coat on the surface of the test specimen. The service or test loads are applied of the specimen surface whereby the coating receives illumination from the polarized light of polariscope reflection. This is illustrated in figure 3, which shows the process of polarization of light in a test specimen (Fernandez et al. 2010). Observation occurs on the coating of test specimen surface, which reveals strains of informative and colorful pattern (see figure 4). Such indicates the strain distribution points of the specimen, as well as the areas where there is a high concentration of the strain. Quantitative stress analysis occurs when an optical transducer is linked to the polariscope. Such aids in the measurement of the stress distribution on the different surface areas of the test specimen. The procedure aids in identification of the critical areas that are understressed and overstressed. Such includes accurate measurement of the peak stresses and stress concentrations in fillets, notches, holes, as well as other potential areas of fracture for the material. It is also possible to determine principal stresses and test load conditions in different locations (Humphreys, & Bahrani 1990). These include the detection of the yielding abilities for the strain redistribution on the surface of a material, which may result in plastic deformation. Figure 3: Polarization of light Figure 4: polariscope schematic representation Industrial application Photoelastic stress measurement is widely used in the testing of stresses in PC sheets. Figure 5 illustrates such an example where the technique is used in the process of testing the stresses in the PC sheet. In this, a spacer is inserted to ensure that the two vertical legs spread effectively, which results in the development of a fringe pattern observed in between polarizing filters. Prior to the application of the stresses, the sample did not indicate any signs of the fringe pattern. Thus, the generated fringe pattern, which results from the applied deformation in the test specimen, provides a clear example of the stress distribution in the PC sheet. Figure 5: PC sheet under photoelastic testing Fringes on the specimen inner edge depict tensile stress while those on the outer edge illustrate the compressive stresses. For the sample, stresses orientation is with reference to the sample deformation (Bayer 2010). Compressive and tensile stresses cross on the black fringe in the middle of the led. Hence, tracking the sequence of the fringe from the black band towards the higher fringe region adjacent to the corner or part edge creates room for retardation estimation, as well as calculation of the level of stress in the sample. Strain Gauges Strain gauges are used widely in the process of physical force measurement in medical science, automobiles, architecture, civil engineering, aircraft, marine and different mechanical scenarios (Patterson 2002). As such, strain is determined, which indicate the intensity of deformation because of forces that include load or stress. This facilitates in evaluation of the safety level of the structural element or material for it to be used in a given specific area. Figure 5 shows how strain is generated in a material when such a material is subjected to a given load condition. Figure 6: Strain generation in a material The principle of strain gauges In a test specimen, a strain gauge is attached. A strain is generated, which is transferred through a gauge base, which is an electrical insulation to a resistance foil or wire in the gauge. This results in the development of different variations of electrical resistances in the foil or wire (Timoshenko 2001). Such a variation is proportion to the generated strain of the test specimen. Such is indicated in the equation below: ε= ⊿L/L = (⊿R/R)/K Where ε: the measured strain R: resistance of the gauge ⊿R: change of the gauge resistance because of the strain K: gauge factor Configuration of strain gauge The construction process of the strain gauge involves bonding of fine electric resistance foil or wire to a base that is electrically insulated using gauge leads and bonding materials. These are clearly demonstrated in figure 7. Figure 7: Strain gauge configuration As such, strain gauges have different features and limitations. The limitations include the amount of strain, fatigue, temperature and environmental measurements. Thus, there is a need to conduct a thorough examination of these limitations prior to the use of the strain gauge (Patterson 2002). The key features of the strain gauge include electrical output, which ensures quick data processing, simple construction, the least distance in measuring points, good frequency response and simultaneous measurement of points. Procedure The strain gauge has to be mounted on the specimen body surface in which stress is to be determined. Such occurs through the use of special bonding glues or agents. Stress in two dimension of the specimen surface is expressed in the form of the three components of Cartesian strain while considering the Hooke’s law (Li 2010). This indicates a necessity of measuring three strains in a given point to have a complete definition of the strain in the field. However, there are special cases under which it becomes easy to determine strain state while using just a single strain gauge. Uniaxial stress state For uniaxial stress, it is only σ Xx , which is present. Thus, a single strain gauge element is positioned such that its axis is coincident with the x-axis. Hence, σxx = Eεxx. Such a condition of uniaxial stress state is illustrated in figure 8. Figure 8: Uniaxial stress state Isotropic stress state For the isotropic stress, the stress state in any point is obtained asσxx = σyy = σ1 = σ2 = σ and τxy =0. Figure 9 depicts a schematic representation of isotropic stress state. Thus, to determine the state of stress in a single element, the strain gauge can be placed in any direction, which makes it easy to determine the stress magnitude from the equation below: Figure 9: Isotropic stress state Pure torsion For pure torsion, (σxx = σyy = 0 and only τxy is present (see figure 10). Thus, the placement of the single strain gauge occurs on the axis that coincides with principal direction of the stress, which is 450 on the x-axis (ME 410, 2010). Hence, the maximum shearing stress is determined from: Where γxy = 2 ε Figure 10: Pure torsion shearing strain and loading Biaxial stress state In cases where there is less information on stress state, but directions exist, a two-element rectangular rosette facilitates in the determination of the state of stress (see figure 11). The rosette is fixed on the specimen such that its axes coincide with principal directions (Flavenot 1996). This result in obtaining two strains ε1 and ε 2 where the principal stresses are determined from the equations below: and . Figure 11: Biaxial stress state and 2-element strain gauge Such is also applicable in a 3-element strain gauge rosette (see figure 12) where the principal stresses are obtained from the equation Figure 12: Three-element rosette Industrial application An industrial application of the strain gauges is the household spray pressure pack stress measurement. In this case, the pack is mounted on three strain gauges, which are to measure longitudinal and hoop stress in the hemispherical and cylindrical parts (Omega 2013). The gauges are temperature compensated and linked to a static strainmeter, which acts as the balancing unit. As such, the gauges provide readings that aids in determination of the pressure of the specimen, as well as the stresses on all the points of interest. References Aben, H, 1993. "Photoelasticity of Glass", Berlin ; New York : Springer-Verlag. Asundi, A, 2002. Recent advances in photoelastic applications. Available online at < http://www.ntu.edu.sg/home/masundi/optical-methods/photoelasticity/recent_advances.html> Bayer, 2010. Photoelastic stress analysis of polycarbonate medical plants. Available online at Fernandez, M, et al., 2010. Digital photoelasticity - A comprehensive review. The Journal of Strain Analysis for Engineering Design May 1, 2011 46: 245-266 Flavenot, E, 1996. “Handbook of measurement of residual stresses”, Society for Experimental Mechanics ,35 – 48. Frocht, M, 1965. Photoelasticity. J. Wiley and Sons, London. Humphreys, J, & Bahrani, A, 1990. The application of photoelastic techniques in orthopaedic engineering. Applied stress analysis. 1 (1). Li, F, 2010. Study of stress measurement using polariscope. Available online at < https://smartech.gatech.edu/bitstream/handle/1853/34762/li_fang_201008_phd.pdf;jsessionid=144839F7F8FAE39A8B1876A0B05D08AA.smart2?sequence=1> ME 410, 2010. Stress analysis by using strain gauges. Available online at < http://www.me.metu.edu.tr/courses/me410/exp5/ME410_exp5_theory.pdf> Omega, 2013. Practical strain gage measurements. Available online at < http://www.omega.com/techref/pdf/StrainGage_Measurement.pdf> Patterson, E, 2002. Digital photoelasticity: principles, practices and potential. Strain, 38:27–39. Ramesh, K, 2000. Digital Photoelasticity, Springer. Timoshenko, S, 2001. Strength of Materials. United States: University Press. Vishay, 2011. Photostress instruments. Available online at < http://www.vishaypg.com/docs/11212/11212_tn.pdf> Read More