Fatigue behavior of metals: A member subjected to repeatedly reversible tensile and compressive stresses may fail at a stress lower than the ultimate strength. This failure phenomenon is called:

Introduction / Context:
Many components operate under fluctuating or cyclic loads. Even if the peak stress is below the ultimate strength, repeated cycling can initiate cracks and cause failure—this is the realm of fatigue design.

Given Data / Assumptions:

• Stress varies from tension to compression repeatedly (fully reversed or fluctuating).
• Number of cycles can be high (high-cycle fatigue) or relatively low (low-cycle).
• Material behaves elastically within each cycle until crack initiation.

Concept / Approach:
Fatigue is the progressive, localized structural damage that occurs when a material is subjected to cyclic loading. Design uses S–N curves (stress–life), endurance limits (if applicable), and mean-stress corrections (e.g., Goodman, Soderberg) to ensure adequate life.

Step-by-Step Solution:
Identify loading as reversible (alternating) tension/compression.Recall that such loading can cause failure at stress levels far below ultimate strength.This behavior is termed fatigue.

Verification / Alternative check:
Classic rotating-beam tests produce S–N data demonstrating stress levels for a given life, often well below static strength.

Why Other Options Are Wrong:
Elasticity: ability to recover shape; not a failure mode.Plasticity: permanent deformation capacity; not repeated-load failure.Workability: ease of shaping/manufacturing.Creep: time-dependent deformation under constant load, usually at elevated temperature.

Common Pitfalls:
Equating fatigue with overload failure; ignoring notch effects and surface finish which strongly influence fatigue strength.

Final Answer:
Fatigue of the metal.