A photoelastic stress measurement system and method based on polarization gratings

Abstract

This invention discloses a photoelastic stress measurement system and method based on a polarization grating. The stress measurement system, along the optical path, includes a light source, a polarizer, a photoelastic sample to be measured, and a polarization grating. The light emitted from the light source is converted into linearly polarized light by the polarizer. The transmitted portion passes through the photoelastic sample, where the light vector is split into two components along the two principal stress directions. The polarization grating ensures that the diffraction distribution of the incident linearly polarized light is only at the ±1st and 0th orders. Since the photoelastic model has birefringence, the linearly polarized beam exiting the photoelastic model is diffracted to the ±1st and 0th orders under the action of the polarization grating. The vast majority of the beam is circularly polarized at the ±1st order, while a very small portion, with the same polarization state as the incident beam, is distributed at the 0th order. This invention solves the problems of traditional photoelastic stress measurement methods, such as complex equipment, inaccurate measurement results, and the inseparability of phase delay and the angle of the principal stress directions in the photoelastic model.

Description

Technical Field

[0001] This invention belongs to the field of photoelastic stress analysis. Specifically, it proposes a new method that measures the stress of anisotropic materials based on a photoelastic stress model and a liquid crystal polarization grating. Background Technology

[0002] With the development of modern industry, many fields such as aerospace, aviation, shipbuilding, and automobile manufacturing have higher requirements for the structural and mechanical precision of various components. This necessitates researchers to accurately grasp the internal stress and strain of materials. Photoelasticity is a full-field stress analysis technique that uses optical methods to measure the stress state at various points on a stress model. The photoelastic model is a transparent material with birefringence (or temporary birefringence). Brewster observed the birefringence phenomenon in 1816. Without external load, the photoelastic model is optically isotropic. When an external force is applied, the refractive index of the photoelastic model changes along the principal stress direction, exhibiting temporary birefringence. When the external force is removed, the material becomes isotropic again. Maxwell observed in 1853 that these changes in refractive index are linearly proportional to stress. By placing the model in a polarized light field, some fringes related to the stress state of the model can be observed. Counting and calibrating these stress-related fringes allows for the calculation of the stress distribution of the photoelastic model.

[0003] Specifically, a beam of polarized light is incident on a photoelastic model. The two emitted light vector components along the principal stress direction have a certain phase delay. The phase delay of the two beam components is proportional to the difference in principal stress at that point. Placing the photoelastic model in a polarized light field will produce equal-inclination and equal-arithmetic fringes. The equal-arithmetic fringes are related to the magnitude of the principal stress difference. By measuring and calibrating the equal-arithmetic fringes finally formed on the observation screen, stress can be measured non-contactly. There are two common methods for photoelastic stress measurement: plane polariscope and circular polariscope.

[0004] Generally, the experimental setup for plane-polarized light elastic stress measurement consists of a polarizer, a photoelastic stress model, an analyzer, and an observation screen. The measurement results of this method are related not only to the phase delay of the photoelastic model but also to the polarization angle of the incident beam, resulting in the difficulty of separating these two pieces of information. The experimental setup for circularly polarized light elastic stress measurement consists of a polarizer, a quarter-wave plate, a photoelastic stress model, a quarter-wave plate, an analyzer, and an observation screen. The optical axes of the polarizer and analyzer can be parallel or orthogonal, and the first and second quarter-wave plates can also be parallel or orthogonal. The function of the first quarter-wave plate is to convert the linearly polarized incident light into circularly polarized light. When circularly polarized light is incident on the stress model, its polarization direction is independent. This method reflects the intrinsic characteristics of the stress sample. However, in this method, due to the narrow bandwidth of the quarter-wave plate, it is usually impossible to achieve the required phase delay of the beam. Therefore, linear polarization cannot be completely converted into circular polarization, resulting in drawbacks such as inaccurate measurement results, complex experimental setup, and high cost. Summary of the Invention

[0005] In view of the shortcomings of existing photoelastic stress measurement methods, the purpose of this invention is to provide an accurate and simple method for measuring photoelastic stress distribution.

[0006] A photoelastic stress measurement system based on a polarization grating comprises, in sequence along the optical path, a light source, a polarizer, a photoelastic sample to be measured, and a polarization grating. Light emitted from the light source is converted into linearly polarized light by the polarizer. The transmitted portion of the light vector is split into two components along the two principal stress directions after passing through the photoelastic sample. The polarization grating ensures that the diffraction distribution of the incident linearly polarized light is only at the ±1st and 0th orders, where the ±1st order is circularly polarized light and the 0th order is linearly polarized light with the same polarization as the incident light. The stress difference between the principal stress directions P1 and P2 is obtained using the system according to the following formula:

[0007]

[0008] In this test, the photoelastic sample has birefringence, so the two light vectors emitted from the two principal stress directions P1 and P2 have a phase delay δ; λ is the wavelength of the incident light; c is the relative stress optical coefficient; and h is the thickness of the photoelastic sample.

[0009] Furthermore, an analyzer is added to the optical path at the end. The measurement results after adding the analyzer are related to the polarization angle of the incident ray polarized light.

[0010] Furthermore, the light source is natural light.

[0011] Furthermore, the angle between the optical axis of the polarizer and the laboratory coordinate x-axis is... The light vector passing through the polarizer is A t .

[0012] Furthermore, the photoelastic sample to be tested is a transparent material with birefringence or temporary birefringence, with principal stress directions P1 and P2 respectively, and these two principal stress directions are perpendicular to each other. The angle between P2 and the laboratory coordinate x-axis is θ; the light vector components in the two principal stress directions P1 and P2 are A1 and A2.

[0013] Furthermore, the polarization grating is a liquid crystal polarization grating, in which liquid crystal molecules are periodically arranged, and the azimuth angle of the liquid crystal molecules changes linearly by 180° within one grating period; this polarization grating causes the diffraction distribution of the incident linearly polarized light to be only in the ±1st and 0th orders, the ±1st order being circularly polarized light, and the 0th order being linearly polarized light with the same polarization as the incident light, and mainly circularly polarized light distributed in the ±1st order.

[0014] A photoelastic stress measurement method based on a polarization grating comprises the following four steps:

[0015] Step 1: A beam of natural light is incident into a polarizer, which converts it into linearly polarized light. The transmitted light vector is A. t ;

[0016] Step 2: The light vector is A t Linearly polarized light is incident on the photoelastic sample to be tested. Due to the birefringence of the sample, the two light vectors A1 and A2 emitted in the two principal stress directions P1 and P2 have a certain phase delay δ.

[0017] Step 3: The light vectors A1 and A2 emitted from the photoelastic sample enter the polarization grating, and finally diffraction fringes are obtained;

[0018] Step 4: Count and calibrate the diffraction fringes, and obtain the stress difference between the principal stress directions P1 and P2 according to the following formula:

[0019]

[0020] In this test, the photoelastic sample has birefringence, so the two light vectors emitted from the two principal stress directions P1 and P2 have a phase delay δ; λ is the wavelength of the incident light; c is the relative stress optical coefficient; and h is the thickness of the photoelastic sample.

[0021] The system and method of the present invention have the following advantages over the two traditional photoelastic stress measurement methods:

[0022] 1. It is simpler than the plane polarized light elastic stress measurement method, and the relationship information between different parameters and stress can be separated (phase delay δ, angle θ between the photoelastic model and the x-axis);

[0023] 2. It is simpler, more accurate, and cheaper than the circularly polarized light elastic stress measurement method. Attached Figure Description

[0024] Figure 1 This is a schematic diagram of the experimental setup for measuring elastic stress of plane-polarized light.

[0025] Figure 2 This is a schematic diagram of the experimental setup for measuring elastic stress of circularly polarized light.

[0026] Figure 3 This is a schematic diagram of an experimental setup for measuring photoelastic stress using a polarization grating. LCPG represents a liquid crystal polarization grating.

[0027] The markings in the diagram are: 1-light source, 2-polarizer, 3-photoelastic sample, 4-analyzer, 5-first quarter-wave plate, 6-second quarter-wave plate; 7-liquid crystal polarization grating. Detailed Implementation

[0028] like Figure 1 The diagram shown is a schematic of an experimental setup for measuring elastic stress in plane-polarized light in the prior art, including a light source 1, a polarizer 2, a photoelastic sample 3, and an analyzer 4, wherein P axis Indicates the direction of the polarizer's optical axis, A axis The direction of the analyzer's optical axis is indicated. Theoretical analysis shows that the measurement results of this method are related to the polarization angle of the polarizer.

[0029] like Figure 2 The diagram shown is a schematic of an experimental device for measuring the elastic stress of circularly polarized light in the prior art. It includes a light source 1, a polarizer 2, a first quarter-wave plate 5, a photoelastic sample 3, a second quarter-wave plate 6, and an analyzer 4. Here, F and S represent the fast axis and slow axis of the quarter-wave plate. This device is obviously complicated and cannot be accurately measured due to the narrow bandwidth of the quarter-wave plate.

[0030] Figure 3 This is a schematic diagram of a photoelastic stress measurement system based on a polarization grating according to the present invention. In this system, after passing through the polarizer 2, the natural light emitted by the light source 1 is converted into light with an angle of θ to the x-axis. Linearly polarized light, partially transmitted through a photoelastic sample 3 of thickness h, is split into two components, A1 and A2, along the two principal stress directions P1 and P2. n0 is the refractive index of the stress-free material; n1 and n2 are the refractive indices of the photoelastic sample under stress in the P1 and P2 directions, respectively, and are related to the directions of the principal stresses P1 and P2; c1 and c2 are stress optical coefficients. The phase difference between A1 and A2 is δ. Assuming the wavelength of the incident light is λ, the following is a theoretical analysis of the isochromatic fringes of the light beam passing through the photoelastic sample.

[0031] The relationship between refractive index change and stress is as follows:

[0032] n1-n0=c1P1+c2P2

[0033] n2-n0=c1P2+c2P1

[0034] After sorting, we get:

[0035] n2-n1=(c2-c1)(P1-P2)=c(P1-P2);

[0036] Where c2-c1=c, and c is the relative stress optical coefficient, the following formula represents the phase delay δ between the two components of the light vector along the two directions:

[0037]

[0038] Where h is the thickness of the photoelastic model and λ is the wavelength of the incident light, the stress difference becomes:

[0039]

[0040] σ f These are stress fringe values, calculated using the Jones matrix algorithm for light propagation in a medium, with an angle of [value missing] with the x-axis. The Jones vector of the linearly polarized light is

[0041]

[0042] The Jones matrix of the photoelastic sample is...

[0043] M = R(-θ)M0R(θ);

[0044] in but

[0045]

[0046] Simplifying M, we get:

[0047]

[0048] When linearly polarized light passes through this photoelastic sample, the emitted polarized light is...

[0049] E out =M*E0;

[0050] Calculations show that:

[0051]

[0052] It is believed that any beam of polarized light can be represented as a superposition of left-handed and right-handed circularly polarized light, i.e.

[0053]

[0054] The size of the left-handed component was calculated:

[0055]

[0056] Size of the right-handed portion:

[0057]

[0058] Preferably, the linear polarization angle is used respectively. and At incidence, the intensity difference of the left-handed portion:

[0059]

[0060] When I1 = 0, there are two cases:

[0061] 1.sin(δ)=0, that is, δ=nπ, n=1, 2, 3, 4, 5...;

[0062] or:

[0063]

[0064] or:

[0065] Where n = 1, 2, 3, 4, 5...;

[0066] σ f Here, λ represents the stress fringe value, λ is the wavelength of the incident light, c is the relative stress optical coefficient, and h is the thickness of the photoelastic model. The extinction order is controlled by the magnitude of the principal stress difference, and the fringe pattern related to the principal stress difference is called an equidistant fringe. The stress of the test object can be calculated by combining separation techniques.

[0067] 2.sin(2θ)=0, that is, θ=nπ, n=1, 2, 3, 4, 5...;

[0068] This extinction occurs when the principal stress is along the optical axis of the polarizer, and the fringes observed from this extinction are equal-inclination fringes.

[0069] Preferably, with and The intensity difference of the right-handed portion at incidence:

[0070]

[0071] Regarding the separation of δ and θ, the following proof is provided:

[0072]

[0073]

[0074] The above describes an invention that provides a simple experimental setup, accurate measurement, and a photoelastic stress measurement method that allows for the separation of two pieces of information: phase delay and the angle of the photoelastic model.

[0075] In summary, this invention provides a photoelastic stress measurement system and method based on a polarization grating. The stress measurement system sequentially includes a light source, a polarizer, a photoelastic model, a polarization grating, and an observation screen. The light source is natural light; the polarizer converts the natural light into linearly polarized light; the photoelastic model exhibits birefringence, meaning that when a light vector passes through a point on the sample, the two components of the light vector in the two principal stress directions have a certain phase delay; the linearly polarized beam emitted from the photoelastic model is diffracted to ±1st and 0th orders under the action of the polarization grating, with the vast majority being circularly polarized beams in the ±1st order, and a very small portion of light with the same polarization state as the incident polarization state distributed in the 0th order. This invention solves the problems of traditional photoelastic stress measurement methods, such as complex equipment, inaccurate measurement results, and the inseparability of phase delay and the angle of the principal stress directions of the photoelastic model.

[0076] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A photoelastic stress measurement system based on a polarization grating, characterized in that, The system comprises, sequentially along the optical path, a light source, a polarizer, a photoelastic sample under test, and a polarization grating. Light emitted from the light source is converted into linearly polarized light by the polarizer. The transmitted portion, after passing through the photoelastic sample, is split into two components along the two principal stress directions. The polarization grating ensures that the diffraction distribution of the incident linearly polarized light occurs only at the ±1st and 0th orders. The ±1st order represents circularly polarized light, and the 0th order represents linearly polarized light with the same polarization as the incident light. The stress difference between the principal stress directions P1 and P2 is obtained using the system according to the following formula: In this test, the photoelastic sample has birefringence, so the two light vectors emitted from the two principal stress directions P1 and P2 have a phase delay δ; λ is the wavelength of the incident light; c is the relative stress optical coefficient; and h is the thickness of the photoelastic sample.

2. The photoelastic stress measurement system based on a polarization grating according to claim 1, characterized in that, A polarizer is added at the end of the optical path. The measurement result after adding the polarizer is related to the polarization angle of the incident linearly polarized light.

3. The photoelastic stress measurement system based on a polarization grating according to claim 1, characterized in that, The light source is natural light.

4. The photoelastic stress measurement system based on a polarization grating according to claim 1, characterized in that, The angle between the optical axis of the polarizer and the laboratory coordinate x-axis is: The light vector passing through the polarizer is A t .

5. The photoelastic stress measurement system based on a polarization grating according to claim 1, characterized in that, The photoelastic sample to be tested is a transparent material with birefringence or temporary birefringence. Its principal stress directions are P1 and P2, which are perpendicular to each other. The angle between P2 and the laboratory coordinate x-axis is θ. The light vector components in the two principal stress directions P1 and P2 are A1 and A2.

6. The photoelastic stress measurement system based on a polarization grating according to claim 1, characterized in that, The polarization grating is a liquid crystal polarization grating, in which liquid crystal molecules are periodically arranged, and the azimuth angle of the liquid crystal molecules changes linearly by 180° within one grating period. This polarization grating causes the diffraction distribution of the incident linearly polarized light to be only in the ±1st and 0th orders. The ±1st order is circularly polarized light, and the 0th order is linearly polarized light with the same polarization as the incident light, and mainly circularly polarized light is distributed in the ±1st order.

7. A method for measuring photoelastic stress based on a polarization grating, characterized in that, It has the following four steps: Step 1: A beam of natural light is incident into a polarizer, which converts it into linearly polarized light. The transmitted light vector is A. t ; Step 2: The light vector is A t Linearly polarized light is incident on the photoelastic sample to be tested. Due to the birefringence of the sample, the two light vectors A1 and A2 emitted in the two principal stress directions P1 and P2 have a certain phase delay δ. Step 3: The light vectors A1 and A2 emitted from the photoelastic sample enter the polarization grating, and finally diffraction fringes are obtained; Step 4: Count and calibrate the diffraction fringes, and obtain the stress difference between the principal stress directions P1 and P2 according to the following formula: In this test, the photoelastic sample has birefringence, so the two light vectors emitted from the two principal stress directions P1 and P2 have a phase delay δ; λ is the wavelength of the incident light; c is the relative stress optical coefficient; and h is the thickness of the photoelastic sample.

Images