rus
Issue #2/2017
A. V.Kniazkov
Evaluation of Changes in the Stress State of Materials by Means of Light Reflection
Evaluation of Changes in the Stress State of Materials by Means of Light Reflection
The analysis of mechanical stress changes evaluation in elasto optic ferroelectric ceramics on reflection index variation of monochromic polarized light incident on medium surface is performed.
Теги: elasto optic ferroelectric ceramics mechanical stresses механические напряжения упругооптическая сегнетокерамика
INTRODUCTION
Under the influence of mechanical stress the isotropic substances become optically anisotropic substances. Occurring strains cause the guided double refraction. At that principal axes directions of material dielectric capacitance ellipsoid match the principal axes directions of stress ellipsoid. In case of one-sided compression this direction of compression becomes separated and acts as an optical axis. Optical characteristics of the body deformed this manner correspond to characteristics of uniaxial crystal. The refraction indexes difference for ordinary and extraordinary beams of Δn = no – ne is a measure of occurred anisotropy degree and is proportional to mechanical stress of σ:
. (1)
Optical methods of mechanical stress detection in transparent media are based on measurement of phase delay difference for ordinary and extraordinary polarized light waves passed through the stressed medium in interferometric arrangements (polarization-optical arrangements) [1–3]. For the absorbing media the intensity of passed waves with the measured phase can be insufficient for carrying out meaningful measurements. On the other hand, light waves incident on medium border always pass through reflection from border and its value is defined by nо,е refraction indexes. Reflection index R according to Fresnel laws in case of normal waves incidence and without regard to medium capacitance is as follows:
. (2)
The method of electrooptical indices measurement of guided double refraction of materials according to reflected light analysis was offered by us in the works [4, 5]. These works provide the basis for new reflective method development concerning changes evaluation of in the stress state of materials by means reflection indices difference of orthogonally polarized waves.
The light wave reflection index with parallel optical axis polarization is determined by n0 ordinary refraction index. The reflection index is determined by an unordinary refraction index of ne for polarization plane orthogonal orientation, in relation to medium optical axis. It necessary to use two orthogonally polarized waves or one circularly polarized wave in reflective geometry to measure ∆n on reflection indices difference of ΔR = Ro – Re. As a result the relation between ∆n and ∆R shall be defined by the following formula:
. (3)
EXPERIMENT PROCEDURE
Residual mechanical stresses in samples were caused by alternating electric field in course of repolarization and owing to micro break ups. Electrode planars were used to form an electric field (fig. 1). It is known that the optical indicatrix of residual double refraction and stress ellipsoid indicatrix should have the optical axes guided on the electric field generated during repolarization.
Two options of experimental assembly diagram performance to research residual materials stress state on light reflection at near-normal incidence are shown in figs.1a, b. In both arrangements the semiconductor laser 1 was a light source and its linear polarization had the smooth azimuth adjustment at the level of 45˚. Double beam arrangement of orthogonally polarized incident beams generation is shown in Fig. 1a. The laser emission was split by polarizing prism 2 into two orthogonally polarized beams of equal intensity. Nomarski prism creating two orthogonally polarized beams with the same direction can be used as polarizing prism. If Nomarski prism has not been used as polarizing prism, one of beams was deviated by a common prism 3 for intersection with the second one on the sample 4 in a gap between planar electrodes. Reflected beams were incident on photoelectric receiver 5 with preamplifiers. Photoelectric receivers’ signals were interfered and amplified with the instrumentation amplifier having modulated amplification factor 6. Further the signals difference was amplified with the help of selective lock-in amplifier 7. Amplification control for instrumentation and lock-in amplifiers was carried out by means of the low frequency driving oscillator 8. The resulting signal was registered by means of oscillograph 9. High-tension alternating voltage of a source 10 was applied on sample planar electrodes 4. A single beam arrangemeent with circularly polarized wave generated with a quarter wave plate 11 is provided in Fig. 1b. The reflected beam was split by a polarizing prism 2 into two orthogonally polarized beams. Remaining arrangement parts are similar to those used in the first diagram.
The experimental evaluation of materials stress state by means light reflection was carried out on transparent ferroelectric ceramics samples of solid plumbum lanthanum zirconate-titanate solution (PLZT‑8 ceramics) with 8/65/35 content having planar electrodes with 3 mm gap. Laser module KLM-F635-3-5 (l = 635 nm) with 3 mW beam output power was used as a source 1. Photodiodes with transimpedance amplifiers OPT101 were used as photoelectric receivers 5. Conversion of photosensors constant differential signal to a variable signal was carried out by instrumentation amplifier AD620 and its amplification factor was changed occasionally with the help of CD4066 key. The final amplification of variable signal was made by the selective nanovoltmeter Unipan 233. The driving oscillator 8 operated at 65 Hz frequency. Residual mechanical stress in samples was generated with a variable voltage of high-tension source 10 at a frequency of 85 Hz. The electric field in samples exceeded value of 5 kW/cm with which micro break up began. Before the subsequent series of measurements the ceramics samples were thermally depolarized.
RESULTS AND DISCUSSION
The proportionality factor k of mechanical stress to the guided double refraction (1) for PLZT-ceramics was calculated with the use of works results [6] according to dependence of phase delays difference of ordinary and extraordinary polarized light waves passed through the stressed medium from relative elongation of medium relating to elasticity coefficient value of 72 GPa [7] and amounted to 10–11 m2/N.
The typical dependence of residual stress state change of PLZT‑8 ceramics after removal of voltage applied to planar electrodes on reflective surface is shown in Fig. 2. The researched PLZT‑8 ceramics compositions had the partial ferro-rigid properties causing the possibility of samples polarization by alternating field. Residual polarization of ceramics caused residual double refraction and, respectively, residual stress state. Residual polarization led also to linearization of quadratic electro-optical effect observed earlier. Micro break ups causing microcracks also increased the stressed state.
CONCLUSION
Thus, the possibility of residual materials stress state measurement on change by means of light reflection from their surface caused by refraction index change is shown experimentally in the work for the first time. This method can be used for quick evaluation of nontransparent material stress state.
Under the influence of mechanical stress the isotropic substances become optically anisotropic substances. Occurring strains cause the guided double refraction. At that principal axes directions of material dielectric capacitance ellipsoid match the principal axes directions of stress ellipsoid. In case of one-sided compression this direction of compression becomes separated and acts as an optical axis. Optical characteristics of the body deformed this manner correspond to characteristics of uniaxial crystal. The refraction indexes difference for ordinary and extraordinary beams of Δn = no – ne is a measure of occurred anisotropy degree and is proportional to mechanical stress of σ:
. (1)
Optical methods of mechanical stress detection in transparent media are based on measurement of phase delay difference for ordinary and extraordinary polarized light waves passed through the stressed medium in interferometric arrangements (polarization-optical arrangements) [1–3]. For the absorbing media the intensity of passed waves with the measured phase can be insufficient for carrying out meaningful measurements. On the other hand, light waves incident on medium border always pass through reflection from border and its value is defined by nо,е refraction indexes. Reflection index R according to Fresnel laws in case of normal waves incidence and without regard to medium capacitance is as follows:
. (2)
The method of electrooptical indices measurement of guided double refraction of materials according to reflected light analysis was offered by us in the works [4, 5]. These works provide the basis for new reflective method development concerning changes evaluation of in the stress state of materials by means reflection indices difference of orthogonally polarized waves.
The light wave reflection index with parallel optical axis polarization is determined by n0 ordinary refraction index. The reflection index is determined by an unordinary refraction index of ne for polarization plane orthogonal orientation, in relation to medium optical axis. It necessary to use two orthogonally polarized waves or one circularly polarized wave in reflective geometry to measure ∆n on reflection indices difference of ΔR = Ro – Re. As a result the relation between ∆n and ∆R shall be defined by the following formula:
. (3)
EXPERIMENT PROCEDURE
Residual mechanical stresses in samples were caused by alternating electric field in course of repolarization and owing to micro break ups. Electrode planars were used to form an electric field (fig. 1). It is known that the optical indicatrix of residual double refraction and stress ellipsoid indicatrix should have the optical axes guided on the electric field generated during repolarization.
Two options of experimental assembly diagram performance to research residual materials stress state on light reflection at near-normal incidence are shown in figs.1a, b. In both arrangements the semiconductor laser 1 was a light source and its linear polarization had the smooth azimuth adjustment at the level of 45˚. Double beam arrangement of orthogonally polarized incident beams generation is shown in Fig. 1a. The laser emission was split by polarizing prism 2 into two orthogonally polarized beams of equal intensity. Nomarski prism creating two orthogonally polarized beams with the same direction can be used as polarizing prism. If Nomarski prism has not been used as polarizing prism, one of beams was deviated by a common prism 3 for intersection with the second one on the sample 4 in a gap between planar electrodes. Reflected beams were incident on photoelectric receiver 5 with preamplifiers. Photoelectric receivers’ signals were interfered and amplified with the instrumentation amplifier having modulated amplification factor 6. Further the signals difference was amplified with the help of selective lock-in amplifier 7. Amplification control for instrumentation and lock-in amplifiers was carried out by means of the low frequency driving oscillator 8. The resulting signal was registered by means of oscillograph 9. High-tension alternating voltage of a source 10 was applied on sample planar electrodes 4. A single beam arrangemeent with circularly polarized wave generated with a quarter wave plate 11 is provided in Fig. 1b. The reflected beam was split by a polarizing prism 2 into two orthogonally polarized beams. Remaining arrangement parts are similar to those used in the first diagram.
The experimental evaluation of materials stress state by means light reflection was carried out on transparent ferroelectric ceramics samples of solid plumbum lanthanum zirconate-titanate solution (PLZT‑8 ceramics) with 8/65/35 content having planar electrodes with 3 mm gap. Laser module KLM-F635-3-5 (l = 635 nm) with 3 mW beam output power was used as a source 1. Photodiodes with transimpedance amplifiers OPT101 were used as photoelectric receivers 5. Conversion of photosensors constant differential signal to a variable signal was carried out by instrumentation amplifier AD620 and its amplification factor was changed occasionally with the help of CD4066 key. The final amplification of variable signal was made by the selective nanovoltmeter Unipan 233. The driving oscillator 8 operated at 65 Hz frequency. Residual mechanical stress in samples was generated with a variable voltage of high-tension source 10 at a frequency of 85 Hz. The electric field in samples exceeded value of 5 kW/cm with which micro break up began. Before the subsequent series of measurements the ceramics samples were thermally depolarized.
RESULTS AND DISCUSSION
The proportionality factor k of mechanical stress to the guided double refraction (1) for PLZT-ceramics was calculated with the use of works results [6] according to dependence of phase delays difference of ordinary and extraordinary polarized light waves passed through the stressed medium from relative elongation of medium relating to elasticity coefficient value of 72 GPa [7] and amounted to 10–11 m2/N.
The typical dependence of residual stress state change of PLZT‑8 ceramics after removal of voltage applied to planar electrodes on reflective surface is shown in Fig. 2. The researched PLZT‑8 ceramics compositions had the partial ferro-rigid properties causing the possibility of samples polarization by alternating field. Residual polarization of ceramics caused residual double refraction and, respectively, residual stress state. Residual polarization led also to linearization of quadratic electro-optical effect observed earlier. Micro break ups causing microcracks also increased the stressed state.
CONCLUSION
Thus, the possibility of residual materials stress state measurement on change by means of light reflection from their surface caused by refraction index change is shown experimentally in the work for the first time. This method can be used for quick evaluation of nontransparent material stress state.
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