UA146799U - METHOD OF DETERMINATION OF MECHANICAL CONSTANTS OF ISOTROPIC MATERIALS - Google Patents

Abstract

The method of determining the mechanical constants of isotropic materials includes tensile loading directed along the axis of the sample, and the measurement of deformations. The sample is suspended vertically at one end by a fixed rigid support, and at the other free end sequentially fastened loads with known masses and moments of inertia of these masses relative to the axis of the sample. Longitudinal deformations and periods of natural torsional oscillations of masses are measured, Young's modulus, shear and Poisson's ratio are calculated.

Description

A useful model belongs to the methods of studying the strength properties of solid materials by applying mechanical forces to them, specifically to tensile and torsional tests of material samples, the stiffness of which is relatively small in relation to these deformations (wire, thin strips, samples of elastic materials, etc.).

The well-known method of tensile testing of metals according to GOST 1497-84 does not apply to wire testing and the similar method of testing wire made of metals and alloys according to

GOST 10446-80 (analogues). In both cases, the sample fixed in the grips of the testing machine is pre-loaded with a force corresponding to the proportionality limit of 5-10 95, its axis is aligned, after which further loading is carried out under conditions of central tension, the forces and the corresponding deformations of the sample base are recorded, the stiffness characteristics are calculated (Young's modulus - E), strength and plasticity of the material.

The shear modulus Cx can also be determined according to GOST 3565-80 (analogue) by torsion testing of samples with a working part in the form of circular cylinders and pipes. Such a test requires the production of a batch of appropriate samples and additional equipment - a machine for torsional tests.

Having determined the Young's modulus E and the shear modulus C of an isotropic material, Poisson's ratio m is found from the expression connecting these three constants, any two of which are independent:

O-ED2 (I). (1)

Mechanical tensile tests of composite materials according to GOST 25.601-80 (the closest analogue) regulate the methods of determining the Young's modulus E and Poisson's ratio m, and therefore the shear modulus Si according to formula (1). To determine Poisson's ratio m, it is necessary to install mechanical or, technologically preferable, electrical deformation sensors along and across its axis on both sides of a flat sample. Installation of electrical resistance sensors requires preliminary preparation of surfaces, compliance with the technology of stickers and heat treatment, and therefore leads to a significant increase in the complexity of tests. The method cannot be applied to material samples with small cross-sectional dimensions (wire, narrow strips, etc.).

The useful model is based on the technical task of determining the mechanical constants of isotropic material of samples with relatively small cross-sectional dimensions (wire, narrow

From the strip, etc.), the tensile and torsional stiffnesses of which are also small.

The problem is solved by the fact that in the method of determining the mechanical constants of isotropic materials, which includes stretching by a load directed along the axis of the sample and measuring deformations, according to a useful model, the sample is suspended vertically by one end by a fixed rigid support, and the other free end is successively attached loads with known masses and moments of inertia of these masses relative to the axis of the sample, measure the longitudinal deformations and periods of their own torsional oscillations of the masses, calculate Young's moduli, shear and Poisson's ratio.

The set technical problem is solved in the following sequence: 1. The length of sample I with relatively small cross-sectional dimensions is chosen so that its tensile and torsional stiffnesses are sufficiently small. For this, it is necessary that the longitudinal load, which does not exceed the corresponding limit of proportionality, causes absolute longitudinal deformation, which is registered with acceptable accuracy by the displacement sensor. 2. The sample 1 (see the drawing) is fixed vertically with its upper end in a rigid support 2, which fixes it in terms of rotational and longitudinal movements, and to the other end with the help of a grip З, a platform 4 is attached, with a known mass and the moment of inertia of this mass relative to the longitudinal axis of the ОХ sample.

Z. Load bi with known mass t: and moment of inertia Ii relative to the axis of the sample is placed on the platform Z (pre-load for alignment of the axis) and the readings of the displacement sensor i) are recorded. 4. A series of i-2, 3 ... n consecutive loads are performed (c: with known masses t": and moments of inertia Ikh relative to the axis of the sample ОХ and the readings of the displacement sensor ци are recorded.

According to the obtained data, the shear modulus of longitudinal elasticity (Young) is determined at each load section:

EgDo/Dei, (2) where Doi-SaCtsA, De-(ini-y)L, A is the cross-sectional area of the sample. 5. In any variant of loading the platform with 4 loads C; excite small torsional oscillations of the total mass that are available for direct observation

(the platform is also taken into account) with the total moment of inertia Iz relative to the axis of the sample ОХ and record the period of these oscillations Тз.

To excite torsional oscillations, it is convenient to use a special device for one-time rotations of the axis of the rigid support 2 to a small angle in a time significantly shorter than the period of the self-oscillations Tv.

Since the moment of inertia of the mass of the sample is small in comparison with the moment of inertia of the mass of the cargo, the period of the natural torsional oscillations Tz in the system with one degree of freedom:

She

Tv is that in s, whence the torsional stiffness of the sample is s-4tpIv/T 82. (3)

On the other hand, for a sample in the form of a prismatic rod or cylinder: с-Сик/, (4) where Ik is the geometric characteristic of the cross-section of the sample with dimensions (unit length)", in particular, for round and in the form of a circular ring sections: tr? 4 a kA Their 32 r 20 .

Here O and a are the outer and inner diameters of the ring, respectively, for the circle a-0. For other forms of cross-sections, it is determined by the methods of the theory of elasticity, and a number of relevant solutions are given in the reference literature. Comparing (3) and (4), we obtain an expression for determining the shear modulus: 2 gly 5/ Kk, (5)

After performing measurements in accordance with points 4 and 5, for one installation of the sample in the device (Fig. 1) according to formulas (2) and (5), Young's modulus E and shear modulus C are calculated, then from formula (1)

Poisson's ratio is determined by: m-0.5E/5-1.

Technical results achieved by using the proposed method of determining the mechanical constants of isotropic materials: - the claimed method does not require the use of complex, expensive equipment and devices and can be used in laboratories that are not equipped with special equipment, for example educational ones; - measurements are performed for one sample setup.

Thus, in comparison with the known solutions, the declared method of determining the mechanical constants of isotropic materials has significant differences, and obtaining a positive effect is due to the whole set of methods of loading the sample and measurements.

Claims (1)

USEFUL MODEL FORMULA The method of determining the mechanical constants of isotropic materials, which includes stretching by a load directed along the axis of the sample, and the measurement of deformations, which is characterized by the fact that the sample is suspended vertically by one end by a fixed rigid support, and loads with known masses and moments of inertia are sequentially attached to the other free end of these masses relative to the axis of the sample, longitudinal deformations and periods of natural torsional oscillations of the masses are measured, Young's moduli, shear and Poisson's ratio are calculated.