EngArc - L - Endurance Limit and Ultimate Strength

Endurance Limit and Ultimate Strength

Quick

The endurance limit, also known as fatigue limit, is a stress level below which a material has an "infinite" life. Infinite life is commonly considered to be 1 million cycles. Ultimate strength alone is explained here, its purpose on this page is to show how it is related to the endurance limit.

Nomenclature

symbol	description
S_e, σ_N	endurance limit
S_u, σ_u	ultimate strength, or ultimate stress, respectively
S₁₀₀₀	alternating stress for life of 1000 cycles
BHN	Brinell hardness number

Details

The endurance limit is due to interstitial elements, such as carbon or nitrogen in iron, which pin dislocations. This prevents the slip mechanism that leads to the formation of microcracks. Care must be taken when using the endurance limit since it can disappear due to:
•   Periodic overloads (which unpin dislocations)
•   Corrosive environments (due to fatigue corrosion interaction)
•   High Temperatures (which mobilize dislocations)

Note: the effect of periodic overloads mentioned above relates to smooth specimens. Notched components may have completely different behavior, due to the residual stresses set up by overloads.

Most nonferrous alloys have no endurance limit and the S-N line has a continuous slope. A pseudo-endurance limit or fatigue strength for these materials is taken as the stress value corresponding to a life of 5×10⁸ cycles.

There are some correlations that are used to approximate ultimate strength and endurance limit:

S_u(ksi) ≈ 0.5*BHN

S_e(ksi) ≈ 0.25*BHN	for BHN ≤ 400
S_e ≈ 100 ksi	for BHN > 400

S_e ≈ 0.5*S_u	for S_u ≤ 200 ksi
S_e ≈ 100 ksi	for S_u > 200 ksi

S₁₀₀₀ ≈ 0.9*S_u

A stress-life curve may be used to approximate life for different amplitude stresses. Because S₁₀₀₀ corresponds to 10³ cycles and typically, S_e corresponds to 10⁶ cycles, the two points can be connected and the line used to estimate life for different amplitude stresses.

When the load on a member is constantly varying in value, is repeated at relatively high frequency, or constitutes a complete reversal of stresses with each operating cycle, the material's endurance limit must be substituted for the ultimate strength where called for by the design formulas.

Under high load values, the variable or fatigue mode of loading reduces the material's effective ultimate strength as the number of cycles increases. At a given high stress value, the material has a definite service or fatigue life, expressed as "N" cycles of operation.

A series of identical specimens are tested, each under a specific load value expressible as a unit stress. The unit stress is plotted for each specimen against the number of cycles before failure. The result is a σ-N diagram.

The endurance limit is the maximum stress to which the material can be subjected for an indefinite service life. Although the standards vary for various types of members and different industries, it is a common practice to accept the assumption that carrying a certain load for several million cycles of stress reversals indicates that load can be carried for an indefinite time.

Theoretically the load on the test specimens should be of the same nature as the load on the proposed machine member, i.e. tensile, torsional, etc.

Since the geometry of the member, the presence of local areas of high stress concentration, and the condition of the material have considerable influence on the real endurance limit, prototypes of the member would give the most reliable information as test specimens. This is not always practical however, because building one-of-a-kind, fatigue tests are seldom possible.