Chapter 18: Stress and Strain – Axial Loading

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18.7:

Plastic Behavior

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Mechanical Engineering

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JoVE Core Mechanical Engineering

Plastic Behavior

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18.6: Hooke’s Law

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18.8: Fatigue

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Materials under stress due to tensile loading exhibit elastic and linear behavior until the yield point. Removing the load at the yield point, stress and strain decrease linearly. The strain does not return to zero, indicating plastic deformation. Plastic deformation is influenced by the maximum stress value and the time elapsed before load removal. Upon re-loading, the specimen follows the previous unloading curve until near the yield point, then aligns with the original stress-strain curve, implying a higher yield point than the initial strain-hardening. However, the rupture point remains unchanged, suggesting reduced ductility. If the initial loading is large enough to cause strain-hardening of the material at C', unloading occurs along line C'D'. If a compressive load is applied, yield strength decreases to a maximum point H' via a curved path, yielding the material along H'J'. While the compressive stress is less than the yield stress, the total change in stress between the maximum tensile and the compressive stress equals twice the yield stress.

18.7:

Plastic Behavior

A material's elastic behavior is characterized by the disappearance of stress once the load is removed, allowing the material to return to its original state. However, when stress surpasses the yield point, yielding commences, marking the onset of plastic deformation or permanent set. This change from elastic to plastic behavior is influenced by the peak stress value and the duration before the load is removed. An intriguing observation occurs when a specimen is loaded, unloaded, and reloaded. The new loading curve mirrors the previous unloading curve near the yield point, which veers towards the original stress-strain curve. This shift indicates an increase in proportional and elastic limits, a consequence of initial strain-hardening.

Despite these increases, the rupture point remains constant, implying a reduction in ductility.

The Bauschinger effect is observed when a second load is applied in the direction that is opposite to the first. This phenomenon results in a decrease in yield strength following the change in the load's path, and the stress-strain diagram becomes curved without a distinct yield point. If substantial initial loading leads to strain-hardening, the total stress change between the highest tensile and maximum compressive stress will be twice the yield stress, illustrating the material's response to significant stress and strain variations.