QB_AE_STRUC_NEW_021
Section Question Bank
MSQ · 2 Marks
Aerospace Structures • Aerospace Materials - S-N Curve Fatigue and Goodman Diagram
Which of the following statements regarding fatigue design and cyclic loading of aerospace metals are **CORRECT**?
(A) The modified Goodman relationship for fatigue life under fluctuating stresses is $\frac{\sigma_a}{\sigma_e} + \frac{\sigma_m}{\sigma_u} = 1$, where $\sigma_a$ is stress amplitude, $\sigma_m$ is mean stress, $\sigma_e$ is endurance limit, and $\sigma_u$ is ultimate tensile strength
(B) A compressive mean stress $(\sigma_m < 0)$ generally increases the fatigue life of an aircraft structural component by delaying microcrack initiation and closure
(C) According to Miner's linear damage accumulation rule, fatigue failure occurs when the cumulative cycle ratio $\sum \frac{n_i}{N_i} \ge 1$
(D) Aluminum aerospace alloys (such as Al 2024-T3 and Al 7075-T6) exhibit a well-defined asymptotic fatigue endurance limit below which fatigue life is infinite
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Step-by-Step Verified Solution
### 1. Strategy & Theoretical Principles 1. **Goodman Line:** The modified Goodman criterion accounts for non-zero mean stress: $$\frac{\sigma_a}{\sigma_e} + \frac{\sigma_m}{\sigma_u} = 1$$ 2. **Effect of Mean Stress:** Tensile mean stress promotes crack opening and accelerates fatigue damage. Conversely, compressive mean stress holds microcracks closed (crack closure effect), extending fatigue life significantly (the basis of shot peening and cold working of fastener holes in aircraft structures). 3. **Miner's Rule:** Palmgren-Miner linear cumulative damage law states failure occurs when damage index $D = \sum_{i=1}^k \frac{n_i}{N_i} = 1$. 4. **Endurance Limit in Non-Ferrous Alloys:** Ferrous alloys (steels) and titanium typically exhibit a true asymptotic fatigue endurance limit (horizontal S-N asymptote). Non-ferrous alloys like aluminum and copper do **NOT** have an endurance limit; their S-N curves continuously slope downward, meaning fatigue strength is always specified at an arbitrary benchmark life (typically $10^7$ or $5 \times 10^8$ cycles). ### 2. Statement Evaluation - **Statement A:** **CORRECT.** Standard modified Goodman relation. - **Statement B:** **CORRECT.** Compressive mean stress inhibits crack propagation. - **Statement C:** **CORRECT.** Formulation of Miner's linear cumulative damage rule. - **Statement D:** **INCORRECT.** Aluminum alloys do NOT exhibit a true endurance limit. ### 3. Exam Trap & Standard Reference - **Trap Alert:** A well-known classic GATE question: Aluminum alloys lack a distinct fatigue endurance limit. - **Standard Reference:** Megson, T.H.G., *Aircraft Structures for Engineering Students*, Chapter 13.