Tensile Method for Measuring the Elastic Modulus of Metal (1)
The simplest form of deformation occurs when a linear or rod-like object is subjected to a tensile force along its length, resulting in elongation. Suppose a wire or rod has an original length L and a cross-sectional area S. When a tensile force F is applied within the elastic limit, the wire elongates by ΔL. The ratio F/S represents the force per unit area, known as stress, while the ratio ΔL/L is the relative elongation, referred to as strain. According to Hooke’s Law, stress is directly proportional to strain, expressed as:
(1)
The proportionality constant is called the elastic modulus, denoted as E. This value is independent of the object's shape, size, or length, and depends solely on the material's properties. It is a crucial physical quantity that reflects a material’s resistance to deformation and plays a vital role in mechanical design and engineering applications.
Any solid material undergoes deformation when subjected to external forces. If the force is removed within a certain limit, the object can return to its original shape, a phenomenon known as elastic deformation.
There are several methods for measuring Young’s modulus, including static measurement, resonance, and pulse transmission techniques. Among these, the resonance and pulse methods offer higher precision. The static method involves applying a load to the object, measuring the resulting stress and strain, and calculating E using a specific formula. Common approaches include the stretching method and the beam bending method.
When a force F is applied to the top of a cubic object while the bottom is fixed (as shown in Figure 1), the object deforms into an oblique parallelepiped, a process known as shearing. After shearing, the absolute deformation varies at different points (AA’ > BB’), but the relative deformation remains the same, given by equation (6-3).
In this formula, θ is the shear angle. For small angles, tanθ can be approximated as θ. Experiments show that the shear angle is proportional to the shear stress within a certain range. Here, S is the cross-sectional area parallel to the base. Thus, we have equation (6-4):
The proportionality constant G is known as the shear modulus.
Methods for measuring the shear modulus include the static torsion method and the swing method.
Purpose
1. Learn how to measure Young’s modulus of elasticity.
2. Understand the principle of the optical lever method for measuring small elongations and how to adjust and use the instruments.
3. Acquire knowledge of data processing techniques, such as the difference method.
Experimental Instruments: Young’s modulus meter, scale reading telescope, optical lever, level, micrometer, vernier caliper (0.02mm accuracy), and 9kg weights.
The experimental setup is illustrated in Figure 1. The scale reading telescope consists of a telescope and a scale frame, with adjustable elevation and focus. The Young’s modulus apparatus is a large tripod with two vertical columns. The upper beam allows the wire to be fixed, while the lower part supports the optical lever. The platform can be raised, adjusted, and secured along the column. Three leveling screws on the tripod’s feet help maintain the platform’s horizontal position.
The optical lever, shown in Figure 2, features a small mirror mounted on a tripod. Two legs are aligned with the mirror, while the third leg (or main pole) is vertical and adjustable in length.
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The simplest form of deformation occurs when a linear or rod-like object is subjected to a tensile force along its length, resulting in elongation. Suppose a wire or rod has an original length L and a cross-sectional area S. When a tensile force F is applied within the elastic limit, the wire elongates by ΔL. The ratio F/S represents the force per unit area, known as stress, while the ratio ΔL/L is the relative elongation, referred to as strain. According to Hooke’s Law, stress is directly proportional to strain, expressed as:
(1)
The proportionality constant is called the elastic modulus, denoted as E. This value is independent of the object's shape, size, or length, and depends solely on the material's properties. It is a crucial physical quantity that reflects a material’s resistance to deformation and plays a vital role in mechanical design and engineering applications.
Any solid material undergoes deformation when subjected to external forces. If the force is removed within a certain limit, the object can return to its original shape, a phenomenon known as elastic deformation.
There are several methods for measuring Young’s modulus, including static measurement, resonance, and pulse transmission techniques. Among these, the resonance and pulse methods offer higher precision. The static method involves applying a load to the object, measuring the resulting stress and strain, and calculating E using a specific formula. Common approaches include the stretching method and the beam bending method.
When a force F is applied to the top of a cubic object while the bottom is fixed (as shown in Figure 1), the object deforms into an oblique parallelepiped, a process known as shearing. After shearing, the absolute deformation varies at different points (AA’ > BB’), but the relative deformation remains the same, given by equation (6-3).
In this formula, θ is the shear angle. For small angles, tanθ can be approximated as θ. Experiments show that the shear angle is proportional to the shear stress within a certain range. Here, S is the cross-sectional area parallel to the base. Thus, we have equation (6-4):
The proportionality constant G is known as the shear modulus.
Methods for measuring the shear modulus include the static torsion method and the swing method.
Purpose
1. Learn how to measure Young’s modulus of elasticity.
2. Understand the principle of the optical lever method for measuring small elongations and how to adjust and use the instruments.
3. Acquire knowledge of data processing techniques, such as the difference method.
Experimental Instruments: Young’s modulus meter, scale reading telescope, optical lever, level, micrometer, vernier caliper (0.02mm accuracy), and 9kg weights.
The experimental setup is illustrated in Figure 1. The scale reading telescope consists of a telescope and a scale frame, with adjustable elevation and focus. The Young’s modulus apparatus is a large tripod with two vertical columns. The upper beam allows the wire to be fixed, while the lower part supports the optical lever. The platform can be raised, adjusted, and secured along the column. Three leveling screws on the tripod’s feet help maintain the platform’s horizontal position.
The optical lever, shown in Figure 2, features a small mirror mounted on a tripod. Two legs are aligned with the mirror, while the third leg (or main pole) is vertical and adjustable in length.
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