20.12
Residual Stresses in Bending
View the full transcript and gain access to JoVE Core videos
Q1: What happens to stress during the unloading phase of an elastoplastic member?
During unloading, stress does not return to zero and may differ in sign from the loading phase, creating residual stress. The stress-strain relationship becomes linear during unloading, allowing elastic flexure formulas to apply. This contrasts with purely elastic materials, where stress retraces its original path.
Q2: How are residual stresses calculated in bent elastoplastic members?
Residual stresses are calculated using the superposition principle by combining two components: stresses from elastoplastic loading and stresses from elastic unloading with an opposite bending moment. Adding these stress distributions yields the final residual stress state at any point in the member.
Q3: Why do plastic zones develop when bending moments are applied to elastoplastic members?
When a sufficiently large bending moment exceeds the material's yield strength, the outer fibers undergo permanent deformation. This creates zones where material no longer obeys Hooke's Law, resulting in irreversible strain that persists after load removal. Understanding plastic deformations is essential for predicting member behavior.
Q4: What is the difference between the loading phase and unloading phase in elastoplastic bending?
The loading phase increases the bending moment from zero to maximum, causing elastic then plastic deformation. The unloading phase decreases the moment back to zero, following a linear stress-strain path that differs from the loading path, leaving residual stresses in the member.
Q5: Why does stress not retrace its original path during unloading of elastoplastic members?
Irreversible plastic strains induced during loading prevent the stress from retracing the original loading path. Instead, unloading follows a new linear path determined by elastic behavior, reflecting the permanent deformation that remains in the material after the load is removed.
Q6: How do residual stresses affect structural behavior under repeated loading?
Residual stresses persist in the member after unloading and can influence how structures respond to repeated loads. These stresses may lead to unexpected failures or altered structural performance, making accurate prediction and management critical for designing safer, more reliable structures.
Q7: When can elastic flexure formulas be applied to elastoplastic members in bending?
Elastic flexure formulas apply during the unloading phase because the stress-strain relationship becomes linear again as the bending moment decreases. This linear behavior allows engineers to use standard elastic analysis methods to calculate stresses during unloading, simplifying residual stress determination.