Fatigue of Metals: Part Three

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Understanding Stress-Life Relationships in Metal Fatigue

Fatigue strength determination involves applying varying levels of cyclic stress to test specimens until failure occurs. Modern laboratory testing employs multiple methods, including rotating bend, cantilever bend, axial push-pull, and torsion testing. Engineers typically present this data through stress-number of cycles to failure (S-N) curves, plotted on logarithmic scales. Due to the statistical nature of fatigue failure, multiple specimens undergo testing at each stress level to ensure reliable results.

Figure 1: Typical S-N curves with both continuous and limiting behavior

Endurance Limits and Material Behavior

Materials exhibit two distinct patterns in fatigue behavior. Some materials, particularly low-carbon steels, demonstrate a fatigue limit - a stress level below which failure theoretically never occurs. This limit typically approximates 40% of the material's tensile strength. However, most materials show a continuously declining stress-life curve, necessitating the specification of an endurance limit for a predetermined number of cycles.

Fatigue Strength Characteristics in Stainless Steels

Test Sensitivity and Variability

Fatigue strength measurements exhibit significant sensitivity to both testing methodology and specimen surface finish. Results frequently display scatter patterns, reflecting the complex nature of fatigue failure mechanisms in metals. This variability necessitates careful consideration in experimental design and data interpretation.

Research Findings on Fatigue Limits

Recent research provides valuable insights into stainless steel fatigue behavior. According to Avesta researchers, austenitic and duplex stainless steels typically demonstrate fatigue limits in air approximating their 0.2% proof strength levels. Their studies also revealed an important correlation between fatigue strength and stress fluctuation frequency, with higher frequencies generally resulting in decreased fatigue strength values.

Alternative research by Alan Haynes (NiDI) presents a more conservative assessment, suggesting that duplex stainless steels exhibit fatigue limits at approximately 50% of their ultimate tensile strength (Rm/UTS). This finding is further supported by INCO data (NiDI publication No. 2978), which provides comprehensive endurance limit data from reverse bending fatigue tests.

Table 1. Endurance Limit Data for Common AISI Stainless Steels

AISI Type	Endurance Limit, MPa
301	240
303	240
304	240
310	215
316	270
321	260
347	270

This table presents endurance limits for various AISI stainless steel grades, with values converted to MPa and rounded to the nearest 5 MPa.

Relationship Between Fatigue Strength and Material Properties

The fatigue strength, characterized by the fatigue limit So (stress amplitude) in Wöhler curves at 106 – 107 load cycles, demonstrates a clear relationship with tensile strength (Rm).

Table 2. Fatigue properties of stainless steel

Steel type	So/Rm		Uncertainty	Limitations
Stress ratio	R=-1	R=0
Austenitic 1.4301, 1.4310 (304, 301)	0.45	0.35	0.04	< Rp0.2
Austenitic 1.4362, 1.4462 (2304, 2205)	0.60	0.35	0.04	< Rp0.2

This table illustrates the relationship between fatigue strength and material properties for different steel types, including stress ratios and their associated limitations.

Analysis of Fatigue Ratios

The relationship between fatigue limit (So) and yield strength (Rp) reveals interesting patterns across different steel types. While the So/Rp ratio shows considerable variation with strength, the So/Rm ratio remains relatively constant within each steel category. Notably, austenitic steels exhibit lower fatigue ratios compared to duplex varieties, primarily due to their lower yield-to-tensile strength ratio. The stress ratio (R = S_min/S_max) follows expected patterns, with fatigue limits decreasing as mean load increases.

Figure 2. The fatigue limit related to yield and tensile strength

This figure illustrates the relationship between fatigue limits and both yield and tensile strength across different steel types.

Practical Applications and Design Considerations

Engineers must consider that endurance limits aren't absolute values, but statistical measures derived from multiple tests. Surface finish, testing methodology, and environmental conditions significantly influence fatigue behavior. For design purposes, particularly in critical applications like nuclear vessels and turbines, these variations require careful consideration and appropriate safety factors.