What Is Young's Modulus?

Young's modulus is a physical quantity that describes the resistance of a solid material to deformation. When a wire with a length of L and a cross-sectional area of S is stretched by L under the force of F, F / S is called stress, and its physical meaning is the force on the unit cross-sectional area of the wire; The physical meaning is the elongation corresponding to the unit length of the wire. The ratio of stress to strain is called elastic modulus. L is a small amount of change. Young's modulus, also known as tensile modulus, is the most common type of elastic modulus or modulus of elasticity. Young's modulus measures the stiffness of an isotropic elastomer and is defined as the ratio between uniaxial stress and uniaxial deformation within the range applicable to Hooke's law. It is related to the elastic modulus. In addition to the Young's modulus, the elastic modulus also includes a bulk modulus and a shear modulus. Young's modulus E, shear modulus G, bulk modulus K, and Poisson's ratio can be converted. The formula is: E = 2G (1 + v) = 3K (1-2v).
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According to different stress conditions, there are corresponding tensile elastic modulus (Young's modulus), shear elastic modulus (rigid modulus), bulk elastic modulus and so on. It is a material constant that characterizes the material's ability to resist elastic deformation. Its numerical value reflects the difficulty of the material's elastic deformation.

For general materials, this value is relatively stable, but for polymers, it is more dependent on conditions such as temperature and loading rate. For some materials

The solid will deform under the external force. If the corresponding deformation disappears after the external force is removed, this deformation is called

The factor of the Young's modulus is the same pressure. In the SI unit system, the unit of pressure is Pa, that is,

Young's modulus test methods generally include static and dynamic methods.

Dynamic methods include pulse excitation method, acoustic resonance method, and sound velocity method.

Pulse excitation method: The sample pulse excitation signal is given by a suitable external force. When a certain frequency in the excitation signal is consistent with the natural frequency of the sample, resonance occurs. At this time, the amplitude is the largest and the delay is the longest. This wave is converted into a signal by a test probe or a measuring microphone and sent to the instrument. The natural frequency of the sample is measured and the Young's modulus E is calculated by the formula.

Features: An international common temperature test method; Simple signal excitation and receiving structure, accurate test;

Accurate and intuitive.

Acoustic resonance method: refers to the audio electrical signal sent by the audio generator, which is converted by the transducer into a vibration signal to drive the sample, and then received by the transducer and converted into an electrical signal. Graphically, the natural frequency f of the sample is obtained, and the Young's modulus of the sample is obtained from the formula E = C1 · w · f.

Features:

--- Acoustic generator, amplifier and other exciters;

--- The transducer receives the signal and the oscilloscope displays the signal;

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Young's modulus experimental instrument

Fine wire, optical lever, telescope, ruler, bracket, tape measure, spiral micrometer, vernier caliper, etc.

Young's modulus experimental principle

Basic formula:

, Where L is the original length of the wire

Optical lever amplification principle

The two front toes of the optical lever are placed on the fixed platform of the elastic modulus tester, and the rear toes are placed on the measurement end face of the wire to be measured. When the metal wire is subjected to a slight elongation, the optical lever rotates a tiny angle around the front toe, thereby driving the optical lever mirror to rotate the corresponding micro angle, so that the image of the ruler is reflected between the optical lever mirror and the adjustment mirror. This small angular displacement is amplified into a larger linear displacement.

As shown on the right, when the length of the wire changes, the verticality of the optical lever mirror must change.

Then there must be an angle difference between the mirror surface after the change and the mirror surface before the change. Use to represent this angle difference. We can see from the figure below:

L = b · tan = b, where b is the distance between the front and back of the optical lever, which is called the optical lever constant.

Let the enlarged steel wire elongation be C, and the geometric relationship in the figure is:

= C / 4H

Therefore: L = bC / 4H

Substituting into the calculation formula, we can get the following formula:

Where D is the diameter of the wire, and the variables D (measured with a spiral micrometer), F (calculated by the mass of the added weight), H, C (direct reading), b (measured with a vernier caliper), and L are the targets to be measured Physical quantity. According to this formula, the Young's modulus can be calculated.