MAT-35

Endurance-limit estimate

Se ≈ 0.5 Sut · ka kb kc. Marin factors on a rotating-beam limit.

Reading speed

FatigueMarin

Governing equation

S_e=0.5 S_{ut} k_a k_b k_c

$S_{ut} \in \left[200, 1400\right]$

where

S_{ut}: Ultimate tensile (MPa)
k_a: Surface factor (—)
k_b: Size factor (—)
k_c: Load factor (—)
S_e: Endurance limit (MPa)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

S_e=0.5 S_{ut} k_a k_b k_c

$S_{ut} \in \left[200, 1400\right]$

$S_{ut} = 200$ $S_e = 72$

Along the curve

②

Domain of the variable — blue

S_{ut}_{\min} = 200,\quad S_{ut}_{\max} = 1400

$S_{ut} \in \left[200, 1400\right]$

$S_{ut} = 200$ $S_{ut} = 200$

Along the curve

③

Response curve — green

S_e=0.5 S_{ut} k_a k_b k_c

$S_{ut} \in \left[200, 1400\right]$

$S_{ut} = 200$ $S_e = 72$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}S_e}{\mathrm{d}S_{ut}}

$S_{ut} \in \left[200, 1400\right]$

$S_{ut} = 207.5$ $S_e^{\prime} = 0.36$

Along the curve

Lecture brief

Historical brief

Hooke (1678), Hall–Petch grain size, Arrhenius activation and Paris fatigue-crack growth are the spine of materials selection. The sheets relate stress, microstructure and life. This sheet (MAT-35 — Endurance-limit estimate) is the form associated with Marin. Working symbols: $S_{ut}$ , $k_a$ , $k_b$ , $k_c$ $\rightarrow$ $S_e$ . For steels the rotating-beam endurance is about half the ultimate. Surface, size and load factors knock it down.

Purpose

Purpose: compute

S_e

from

S_{ut}

k_a

k_b

k_c

in Materials via

S_e=0.5 S_{ut} k_a k_b k_c

Se ≈ 0.5 Sut · ka kb kc. Marin factors on a rotating-beam limit. Use it when a real materials question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

S_{ut} = 600.000\,\mathrm{MPa}

k_a = 0.800\,\mathrm{—}

k_b = 0.900\,\mathrm{—}

k_c = 1.000\,\mathrm{—}

, the governing relation

S_e=0.5 S_{ut} k_a k_b k_c

yields

S_e = 216.0\,\mathrm{MPa}

. An S–N floor, three reduction ticks. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Ultimate tensile S_{ut}600 MPaSurface factor k_a0.8 —Size factor k_b0.9 —Load factor k_c1 —

Outputs

Endurance limit S_e216.0 MPa

Reading speed

Watch on YouTube

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Narration of this film

An S–N floor, three reduction ticks.

For steels the rotating-beam endurance is about half the ultimate. Surface, size and load factors knock it down.

Reading speed

Watch on YouTube