Fatigue failure is a crucial concern in mechanical design. S-N diagrams help engineers predict how long parts can last under repeated stress. These graphs show the relationship between stress levels and the number of cycles a material can withstand before breaking.

Endurance limits are key for designing parts that need to last forever. They represent the stress level below which a material won't fail, no matter how many cycles it goes through. Understanding these concepts is vital for creating safe, long-lasting mechanical components.

S-N Curve Components

Stress-Life Relationship

• S-N curve plots the relationship between stress amplitude and the number of cycles to failure for a material
• Stress amplitude ($\sigma_a$) represents the magnitude of the alternating stress applied to the material during each cycle
• Number of cycles ($N$) indicates how many stress cycles the material can withstand before failure occurs
• S-N curve is typically plotted on a log-log scale to accommodate the wide range of stress amplitudes and cycle counts

Fatigue Life Regions

• Finite life region of the S-N curve corresponds to the portion where the material fails after a specific number of cycles at a given stress amplitude
• Finite life region is characterized by a downward sloping curve, indicating that as the stress amplitude increases, the number of cycles to failure decreases
• Infinite life region of the S-N curve represents the portion where the material can withstand an infinite number of cycles without failure
• Infinite life region is characterized by a horizontal line, known as the endurance limit, below which the material has an infinite fatigue life
• Transition point between the finite and infinite life regions is determined by the material's properties and loading conditions

Endurance Limit and Fatigue Strength

Fatigue Resistance Parameters

• Endurance limit ($\sigma_e$) is the stress amplitude below which a material can withstand an infinite number of cycles without failure
• Endurance limit is a critical parameter in designing components subjected to cyclic loading, as it defines the safe operating stress range
• Fatigue strength is the stress amplitude at which a material fails after a specified number of cycles (typically $10^6$ or $10^7$ cycles)
• Fatigue strength provides a measure of the material's resistance to fatigue failure at a given cycle count

Notch Effects on Fatigue

• Fatigue notch factor ($K_f$) quantifies the reduction in fatigue strength due to the presence of notches, holes, or other stress concentrations
• Notches act as stress raisers, increasing the local stress and making the material more susceptible to fatigue failure
• Fatigue notch factor is defined as the ratio of the fatigue strength of an unnotched specimen to the fatigue strength of a notched specimen
• Higher fatigue notch factors indicate a greater sensitivity to notches and a lower resistance to fatigue failure in the presence of stress concentrations

Stress Considerations

Mean Stress Effects

• Stress ratio ($R$) is the ratio of the minimum stress to the maximum stress in a cyclic loading scenario
• Stress ratio affects the mean stress, which is the average of the maximum and minimum stresses
• Mean stress can have a significant impact on the fatigue life of a material
• Tensile mean stresses reduce the fatigue life by increasing the overall stress level and promoting crack growth
• Compressive mean stresses can improve the fatigue life by reducing the effective stress range and retarding crack growth

Stress-Life Modification Factors

• Various factors can modify the stress-life relationship and affect the fatigue behavior of a material
• Surface finish, size, temperature, and loading type are common factors that influence fatigue life
• Surface finish effects are accounted for by applying a surface factor ($k_a$) to the endurance limit
• Size effects are considered using a size factor ($k_b$) to adjust the endurance limit based on the component's dimensions
• Temperature effects are incorporated through a temperature factor ($k_c$) that modifies the endurance limit based on the operating temperature
• Loading type (axial, bending, or torsion) is accounted for by applying a loading factor ($k_d$) to the endurance limit