19.10
Residual Stresses in Circular Shafts
In materials that exhibit elastic and plastic behavior, known as elastoplastic materials, residual stresses can accumulate when these materials experi…
In elastoplastic materials, residual stress can develop when the material undergoes plastic deformation due to high shearing stress or large strains.
When the external loading is removed, the internal stresses sustained within the shaft material are known as the Residual stresses.
Plotting the torque versus angle of twist diagram, it can be shown that the angle of twist does not return to zero when the torque is removed. A straight line represents the unloading of the shaft.
The residual stresses in elastoplastic material are obtained by applying the principle of superposition.
First, the stresses due to the applied torque are considered in the loading phase, and then the stresses due to the equal and opposite torque applied to unload the shaft are considered. The distribution of residual stresses in the shaft is obtained by adding these two groups of stresses.
Plotting stress versus the radial distance, it can be observed that some residual stresses share the same direction as the original stresses, while others are in the opposite direction.
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Q1: What are residual stresses and how do they form in circular shafts?
Residual stresses are internal stresses that persist within a shaft material after external loading is removed. They develop when elastoplastic materials undergo plastic deformation due to high shearing stress or large strains. These stresses remain trapped in the material even after the torque is removed, as evidenced by the shaft's angle of twist failing to return to zero.
Q2: How does the torque versus angle of twist diagram reveal residual stress?
The torque versus angle of twist diagram shows that when torque is removed, the shaft does not return to its original position. The unloading path appears as a straight line on the diagram, and the permanent angular displacement indicates residual stress. This permanent deformation demonstrates that the material has undergone plastic deformation and retains internal stresses.
Q3: What is the principle of superposition and how is it applied to calculate residual stresses?
The principle of superposition calculates residual stresses by combining two stress states: first, the stresses induced by the applied torque during loading, and second, the stresses from an equal and opposite torque applied during unloading. Adding these two stress distributions yields the final residual stress pattern within the shaft material.
Q4: What does the stress versus radial distance plot reveal about residual stress distribution?
Plotting stress against radial distance shows that residual stresses vary across the shaft's cross-section. Some residual stresses align with the original stress direction, while others oppose it. This non-uniform distribution is critical for understanding material resilience and structural integrity under stress conditions.
Q5: Why doesn't a shaft return to its original angle of twist after torque removal?
When a shaft experiences high shearing stress, elastoplastic materials undergo permanent plastic deformation. Upon torque removal, the elastic portion of the deformation recovers, but the plastic portion remains. This residual plastic deformation prevents the angle of twist from returning to zero, leaving the shaft permanently altered.
Q6: How do residual stresses affect the structural behavior of elastoplastic materials?
Residual stresses create internal stress fields that persist after external loading ceases, affecting how the material responds to future loads. These stresses can either enhance or reduce the material's load-carrying capacity depending on their direction and magnitude. Understanding residual stress distribution is essential for assessing long-term structural integrity and reliability.
Q7: What causes residual stresses to have opposite directions in different regions of the shaft?
During plastic deformation, outer regions of the shaft yield first while inner regions remain elastic. When unloading occurs, the elastic inner regions pull back against the plastically deformed outer regions, creating opposing stress directions. This mechanical incompatibility between regions generates residual stresses with different orientations across the radial distance.