RU2538414C2 - Device for determining modulus of elasticity of structural materials - Google Patents

Abstract

FIELD: testing technology.

SUBSTANCE: invention relates to the field of testing technology, namely to devices for determining the elastic characteristics of the material when bending, and can be used for determining the dependence of the modulus of elasticity of structural materials both on the temperature and the magnitude of bending stresses. The device comprises the support table with knife edges, placed in a muffle furnace equipped with the temperature control system, the loading mechanism. The loading mechanism from the side of the load application comprises a set of calibrated weights, and from the side of the support table the load bracket equipped with supporting prismatic projections, which are directly in contact with the test sample.

EFFECT: increase in accuracy of measurements of the modulus of elasticity, enhancement of the device and reduction of labour intensity of the testing process.

2 dwg

Description

The invention relates to the field of testing equipment, and in particular to devices for determining the elastic characteristics of materials under bending, and can be used to determine the dependence of the modulus of elasticity of structural materials both on temperature and on the magnitude of bending stresses.

Scope - mechanical engineering, metallurgy, etc.

The elastic modulus is a quantity characterizing the elastic properties of a material. The elastic modulus is established by experimental-mechanical testing of samples of the studied materials and is not a strictly constant value for the same material, its values vary depending on the chemical composition and crystal structure of the material, on its preliminary processing (heat treatment, rolling, forging, etc. ), as well as on the temperature of the material - Friedman Ya.B., Mechanical properties of metals, 2nd ed., Moscow, 1952 - therefore, when calculating the elastic characteristics of machine parts and their elements, It is necessary to know the value of the elastic modulus at various temperatures and the magnitude of bending stresses.

A known method of determining the modulus of elasticity of metallic materials and a device for its implementation [RF Patent 2169355 C1, G01N 3/20, 3/18, 06/20/2000].

In the specified device, the test sample is bent alternately with two loads of different sizes at normal and predetermined temperatures, the maximum deflection of the sample is measured, and the elastic modulus of the material at a given temperature is determined by calculation.

The disadvantages of this device include the complexity of the design and the presence of electrically dependent components (strain gauges), which introduce significant errors in the measurement, in addition, the measurement requires expensive test equipment.

Closest to the proposed invention is a device for determining the modulus of elasticity of structural materials at elevated temperatures [RF Patent 2308016 C2, G01N 3/20, 3/18, 01/20/2007]. In the indicated device, the test sample is placed in a muffle furnace and bent on 2 prismatic table supports with a fixed fixed value applied in the center by concentrated force at various temperatures, the deflection of the beam is recorded and according to it taking into account the geometric dimensions of the sample and the materials known from the resistance course formulas determine the magnitude of the modulus of elasticity at different temperatures.

This device also contains a number of disadvantages, namely: the impossibility of removing the dependences of elastic properties on the magnitude of bending stresses due to the static load; the absence of transverse forces in the sample, which introduces certain errors in the measurement results.

The objective of the present invention is to improve the accuracy of determining the modulus of elasticity of structural materials at elevated temperatures and expand the functionality of the device by measuring the modulus of elasticity in a wide range of bending stresses.

The technical result from the implementation of the present invention is expressed:

- to improve the accuracy of measurements of the elastic modulus by eliminating errors associated with the lack of consideration of the effect of the shear force diagram on the measurement result in the prototype and analogue;

- in expanding the functionality of the device in the direction of removing the dependence of the elastic modulus on the magnitude of bending stresses;

- in reducing the complexity of the test process.

The invention is illustrated by drawings: figure 1 shows a diagram of a device, figure 2 is a design diagram,

Where:

1 - supporting table;

2 - load bracket;

3 - loading mechanism;

4 - hollow bar;

5 - dial indicator;

6 - muffle furnace;

7 - test sample.

A device for determining the elastic modulus of structural materials in a wide range of temperatures and bending stresses consists of placed in a muffle furnace 6 equipped with a temperature control system (not shown in the drawing), a support table 1 with prismatic supports, a test sample 7 and a loading mechanism 3 equipped with a load bracket 2, transmitting the required force F, set by means of a set of calibrated weights, to the sample through the hollow rod 4 and the prismatic protrusions of the load bracket 2, directly GOVERNMENTAL contact with it, the measuring apparatus 5 as a dial gauge.

The device operates as follows: a sample from the test material 7 is mounted on the prismatic table legs that are fixed in the muffle furnace 6 and the required force P from the loading device through the hollow rod 4 to the load bracket 2 is transferred to the test sample 7, and the required temperature of the sample is set by the muffle furnace temperature controller . In this case, the dial gauge 5 measures the deflection of the sample in the zone of clean bending. The temperature of the sample is measured by thermocouples, and the registration is performed using a KSP-4 recorder.

The elastic modulus is determined by the following formula:

, где: $$E\left(\sigma ,t\right)=\frac{\mathrm{eleven}\cdot P\cdot a^3}{12\cdot J\cdot \Delta }$$

where:

E is the modulus of elasticity of the material;

σ is the value of bending stresses;

t is the temperature, ° C;

P is the magnitude of the load;

J is the moment of inertia of the beam section;

Δ - the value of the deflection of the beam.

This formula is obtained on the basis of the following assumptions (figure 2).

Assuming that P / 2 = F, the adopted design scheme is presented in figure 2. It is obvious that the support reactions on the left and right supports, due to the symmetry of the applied load, will also be equal to F.

According to the presented design scheme, the equation of bending moments for section II has the following form:

$$M=F\cdot z-F\cdot \left(z-a\right)\left(2\right)$$

As you know from the course of resistance of materials, the differential equation of the elastic line of the beam has the following form:

$$E\cdot J\cdot {\Delta }^{"}=M\left(3\right)$$

Integrating equation (3), we obtain the equation of the angles of inclination of the tangent to the elastic line of the beam, and integrating it twice, the equation of the elastic line of the beam (equation of deflections).

In our case, integrating equation (3) twice, taking into account (2), we obtain:

$$E\cdot J\cdot \Delta =\frac{F\cdot z^3}{6}-\frac{F\cdot {\left(z-a\right)}^3}{6}+C_{\mathrm{one}}\cdot z+C_2,gde\left(\mathrm{four}\right)$$

C ₁ and C ₂ are the constants of the first and second integration, respectively.

Since the left end of the beam is pivotally supported on a prism, C ₂ = 0.

C ₁ we define based on the equality of 0 the angle of inclination of the tangent to the elastic axis of the beam in its center (coordinate z = 2a). Differentiating (3) once, we obtain:

$$E\cdot J\cdot \Theta =E\cdot J\cdot 0=0=\frac{F\cdot z^2}{2}-\frac{F\cdot {\left(z-a\right)}^2}{2}+C_{\mathrm{one}}\left(5\right)$$

Whence for z = 2a we define C ₁ :

$$C_{\mathrm{one}}=-\frac{3\cdot F\cdot a^2}{2}\left(6\right)$$

Then finally the equation of the elastic line takes the form:

$$\Delta =\frac{F\cdot z^3-F\cdot {\left(z-a\right)}^3-9F\cdot a^2\cdot z}{6E\cdot J}\left(7\right)$$

Since in the proposed device the watch-type indicator actually measures the difference of the deflections at points with coordinates z = 2a and z = a, we define these deflections in the notation according to the diagram shown in figure 2.

$${\Delta }_I=-\frac{\mathrm{four}\cdot F\cdot a^3}{3\cdot E\cdot J}\left(8\right)$$

$${\Delta }_{II}=-\frac{\mathrm{eleven}\cdot F\cdot a^3}{6\cdot E\cdot J}\left(9\right)$$

The minus sign before the deflection means that it is directed in the direction opposite to the direction of the Y axis that we have chosen, i.e. way down. In further calculations, we will use the absolute values of the deflections.

Then the deflection Δ, fixed by the dial indicator, will be:

$$\Delta ={\Delta }_{II}-{\Delta }_I=\frac{\mathrm{eleven}\cdot F\cdot a^3}{6\cdot E\cdot J}\left(10\right)$$

Given that the temperature t of the sample is set by the researcher, bending stresses in the test zone of the sample, taking into account (11), are determined by the formula (12),

$$M_{\mathrm{and}sg}=F\cdot a\left(\mathrm{eleven}\right)$$

$$\sigma =\frac{M_{\mathrm{and}sg}}{W},gde:\left(12\right)$$

W is the moment of resistance of the cross section of the beam,

and the deflection of the sample is known from the indications of a dial indicator, the elastic modulus depending on temperature and the magnitude of bending stresses is determined by the following relationship:

$$E\left(\sigma ,t\right)=\frac{\mathrm{eleven}\cdot P\cdot a^3}{12\cdot J\cdot \Delta }\left(\mathrm{one}\right)$$

This device allows you to determine the dependence of the modulus of elasticity of structural materials in a wide range of temperatures and values of bending stresses, increase the accuracy of measurements, reduce the complexity and costs of test equipment. Thus, the object of the invention was achieved.

Claims (1)

A device for determining the modulus of elasticity of structural materials, comprising, placed in a muffle furnace equipped with a temperature control system, a support table with prismatic supports, a loading mechanism, characterized in that the loading mechanism on the load side contains a set of calibrated weights, and on the side of the supporting table a load bracket equipped with supporting prismatic protrusions directly in contact with the test sample.

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