RU2806404C1 - Method for determining elastic constants of material of different moduli - Google Patents

Abstract

FIELD: measuring technology.

SUBSTANCE: invention relates to the methods for determining the elastic constants of a material of different moduli. The method consists in loading the sample with a bending moment according to the four-point bending scheme. In this case, a sample of equal cross-section along the length is made, two pairs of fibre-optic strain sensors on Bragg gratings are installed on opposite surfaces symmetrically and parallel to each other, each pair is glued with an intersection at a right angle in the centre of the sample surface. Using an interrogator, strain values are taken from each sensor on the tensile and compressed surfaces of the sample along the length of the sample and along the width of the sample. Based on the obtained strain values, Poisson's ratios and elastic moduli on the tensile and compressed surfaces of the sample are determined using the formulas.

EFFECT: increasing the accuracy of measuring deformations and expanding the functionality of the method.

1 cl, 1 dwg, 2 tbl

Description

The invention relates to measuring technology, in particular to methods for determining the elastic constants of a material of different moduli.

The closest known analogue of the proposed method, chosen as a prototype, is a method for determining the strength characteristics of a multi-module material (SU 1583732 A1, G01B 5/30 dated 08/07/1990) which consists of measuring displacements using a pair of equal-base displacement meters installed in the middle of the sample symmetrically and parallel each other on opposite surfaces and an additional measurement of deflection on a tensile or compressed surface at each level of loading from a sample that has an equal cross-section along its length, when subjected to a bending moment. Based on the totality of the measurements obtained, using relationships and dependencies, the actual radius of curvature and the position of the neutral line of the sample are determined, and then the deformations and stresses on the tensile and compressed surfaces. As a result of sequential loading until failure of the sample, the bending strength, tensile and compression diagrams, as well as the elastic moduli of the material on the tensile and compressed surfaces, determined by Hooke's law, are obtained.

The disadvantages of this method are:

1. insufficient accuracy of measuring strains during tension and compression, due to the indirect nature of measurements;

2. the impossibility of using the method to determine Poisson's ratios under tension and compression of a material, due to insufficient experimental data.

The technical results of the proposed method are:

1. increasing the accuracy of strain measurement through the use of fiber-optic strain sensors on Bragg gratings;

2. expansion of the functionality of the method - the ability to determine Poisson's ratios under tension and compression through the use of two pairs of sensors, each of which intersects at a right angle, making it possible to measure deformations on the tensile and compressed surfaces of the sample in two directions.

To achieve this result, a method is proposed for determining the elastic constants of a material of different moduli, which consists in making a sample of equal cross-section along the length, installing mechanical quantity meters on opposite surfaces symmetrically and parallel to each other, loading the sample with a bending moment in the plane of location of the meters, recording the readings of the meters at each fixed level of loading and determine the deformation and elastic modulus of the material under tension and compression, while loading the sample with a bending moment is carried out according to the four-point bending scheme, two pairs of fiber-optic strain sensors on Bragg gratings are used as mechanical measurers, each pair is glued with an intersection at a right angle in the center of the opposite surfaces of the sample, using an interrogator, the strain values on the tensile and compressed surfaces of the sample along the length of the sample are taken from each sensor: , and along the width of the sample: , and based on the obtained values of deformations, the coefficients are determined

Poisson on the tensile and compressed surfaces of the sample according to the formulas, respectively:

and the modulus of elasticity in tension and compression is determined by the formulas, respectively:

where M is the applied bending moment, b is the width of the sample, h is the height of the sample.

A distinctive feature of the proposed method is that the sample is loaded with a bending moment according to a four-point bending scheme; two pairs of fiber-optic strain sensors on Bragg gratings are used as mechanical measurers; each pair is glued with a right-angle intersection in the center of the opposite surfaces of the sample, with using an interrogator, the strain values on the tensile and compressed surfaces of the sample along the length of the sample are taken from each sensor: , and along the width of the sample: , , and based on the obtained strain values, Poisson’s ratios are determined on the tensile and compressed surfaces of the sample using the formulas, respectively:

and the modulus of elasticity in tension and compression is determined by the formulas, respectively:

where M is the applied bending moment, b is the width of the sample, h is the height of the sample.

The proposed method is carried out as follows. A sample of equal cross-section along the length is made.

On its opposite surfaces, two pairs of fiber-optic strain sensors on Bragg gratings are installed symmetrically and parallel to each other, each pair is glued with an intersection in the center of the sample surface at a right angle.

Then the sample is loaded with a bending moment according to a four-point bending scheme in the plane of the fiber-optic sensors.

At each fixed level of loading, using an interrogator, the strain values on the tensile and compressed surfaces of the sample along the length of the sample are taken from each sensor: , and along the width of the sample: , .

Based on the obtained strain values, Poisson's ratios are determined on the tensile and compressed surfaces of the sample using the formulas, respectively:

and elastic moduli in tension and compression are determined by the formulas, respectively:

The proposed method is illustrated in Fig. 1, which shows a diagram of a four-point bending of a sample with glued fiber-optic strain sensors on Bragg gratings, where 1 is a sample of width b, height h and length L; 2, 3 - the first pair of fiber-optic strain sensors on Bragg gratings, located on the upper surface (compressed during bending moment loading); 4, 5 - the second pair of fiber-optic strain sensors on Bragg gratings, located on the bottom (stretched during bending moment loading) surface; 6 - upper supports; 7 - lower supports.

Execution example.

To determine the elastic constants (Poisson's ratios and elastic moduli) of a material of different moduli, a four-point bending experiment was carried out. Foam concrete was chosen as a multi-module material, from which a sample was made with dimensions: h=58 mm, b=72 mm, L=300 mm.

Then, two pairs of fiber-optic strain sensors on Bragg gratings with a right-angle intersection at the center of each surface were glued onto the opposite surfaces of the sample using cyanoacrylate glue.

The sample with glued sensors was loaded with a bending moment according to a four-point bending scheme in the plane of location of fiber-optic strain sensors on Bragg gratings.

During loading, the strain values on the tensile and compressed surfaces of the sample along the length of the sample were taken from each sensor using an interrogator: , and along the width of the sample: ,

Table 1 shows the strain values corresponding to the applied moment.

Based on the obtained strain values, the Poisson's ratios and elastic moduli on the tensile and compressed surfaces of the sample were determined using the formulas presented above.

Table 2 shows the obtained elastic constants of the material - Poisson's ratios and elastic moduli on tensile and compressed surfaces.

Claims (7)

A method for determining the elastic constants of a material of different moduli, which consists in making a sample of equal cross-section along the length, installing meters of mechanical quantities on opposite surfaces symmetrically and parallel to each other, loading the sample with a bending moment in the plane of location of the meters, recording the readings of the meters at each fixed level of loading and determine the deformation and elastic moduli of the material under tension and compression, characterized in that the loading of the sample with a bending moment is carried out according to the four-point bending scheme, two pairs of fiber-optic strain sensors on Bragg gratings are used as mechanical measurers, each pair is glued with an intersection at a right angle in the center of the opposite surfaces of the sample, using an interrogator, the strain values on the tensile and compressed surfaces of the sample along the length of the sample are taken from each sensor: , and along the width of the sample: , and based on the obtained strain values, Poisson’s ratios are determined on the tensile and compressed surfaces of the sample using the formulas, respectively: , , and the modulus of elasticity in tension and compression is determined by the formulas, respectively: , , Where - applied bending moment, - sample width, - sample height.