Name: torsional failure and plastic strain in shafts
Uploaded: 2024-05-23T12:59:41.000Z
Duration: 1 min 20 s
Channel: JoVE

When materials are subjected to stresses exceeding their yield strength, plastic deformation occurs, causing a permanent strain. In the case of circular shafts, plastic deformation changes its configuration.
An accurate assessment of plastic deformation necessitates the determination of stress distribution within the circular shaft.
If the maximum shearing stress in the material is known, then plotting a shearing-stress-strain diagram gives the corresponding maximum shearing strain.
Recall that the shearing strain varies linearly with the distance from the axis of the shaft. The relationship between shearing strain and radial distance is established by substituting the maximum shearing strain value. Further, the relationship between shearing stress and radial distance is obtained.
Using the integral relation and substituting for the elemental area and the polar moment of inertia in terms of shaft radius, the ultimate torque that causes shaft failure can be determined by maximizing the value of the material&#39;s ultimate shearing stress.
The corresponding fictitious stress is called the modulus of rupture in the torsion of the given material.

plastic deformation in circular shafts

When materials are subjected to forces that surpass their yield strength, they undergo a process known as plastic deformation. This results in a permanent alteration or strain in their structure. This concept can be specifically applied to circular shafts, where the deformation leads to a change in its shape. The precise evaluation of this plastic deformation requires understanding the stress distribution within the circular shaft, which is achieved by calculating the maximum shearing stress in the material. Once identified, a shearing-stress-strain diagram can be plotted to reveal the maximum shearing strain. It is crucial to remember that the shearing strain has a linear relationship with the distance from the axis of the shaft.
The relationship between shearing strain and radial distance can be determined by substituting the maximum shearing strain value into this equation. Similarly, the relationship between shearing stress and radial distance can also be derived. By using the integral relation and replacing the elemental area and polar moment of inertia with the shaft radius, the ultimate torque that leads to the shaft's failure can be calculated by maximizing the material's ultimate shearing stress value. The equivalent stress derived from this calculation is often referred to as the modulus of rupture in the torsion of the given material. This term represents the maximum stress to endure before the material fails under torsion.
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Plastic Deformation in Circular Shafts

When materials are subjected to stresses exceeding their yield strength, plastic deformation occurs, causing a permanent strain. In the case of circular ...

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Torsion

KEY TERMS AND CONCEPTS

torsional failure and plastic strain in shafts

Plastic deformation in circular shafts happens when torsional force pushes the material past its yield strength. At that point, the shaft does not return to its original shape. Instead, it keeps a permanent strain.

To measure this change, the stress pattern inside the shaft must be understood. The maximum shearing stress is calculated first. Then a shearing-stress-strain diagram can be drawn to find the maximum shearing strain.

Shearing strain changes linearly with the distance from the shaft axis. The value at the outer radius can be used to write the strain relationship for the rest of the shaft. The same idea is used to derive the relationship between shearing stress and radial distance.

The final step is to use the integral relation to find the torque that causes failure. In this calculation, the elemental area and polar moment of inertia are replaced with the shaft radius. The ultimate torque is found by using the material's ultimate shearing stress. The equivalent stress from this result is called the modulus of rupture in torsion, and it marks the maximum stress the material can withstand before failure.

Torsional Failure and Plastic Strain in Shafts

torsional-failure-and-plastic-strain-in-shafts

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Plastic deformation in circular shafts happens when torsional force pushes the material past its yield strength. At that point, the shaft does not return to its original shape. Instead, it keeps a permanent strain. To measure this change, the stress pattern inside the shaft must be understood. The maximum shearing stress is calculated first. Then a shearing-stress-strain diagram can be drawn to find the maximum shearing strain. Shearing strain changes linearly with the distance from the shaft...

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key terms and concepts

Learn how circular shafts deform under torsion, how shear stress and strain vary with radius, and how ultimate torque and modulus of rupture are found.

Torsional Failure and Plastic Strain in Shafts | JoVE K12

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Torsional Failure and Plastic Strain in Shafts

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