What is Measured?

During the fatigue test, the following quantities are observed:

• Applied force
• Bending stress developed in the specimen
• Number of loading cycles to failure
• Logarithm of the number of cycles

These observations are used to study the fatigue behaviour of the material.

Why are the Calculations Required?

The measured values are processed to

• determine the fatigue life,
• construct the S–N curve,
• understand the relationship between stress and fatigue life,
• compare fatigue performance under different loading conditions.

Live Observation Table (During Simulation)

The simulation page continuously updates the following values:

Number of Cycles (N)	Force (N)	Stress (MPa)
Running value	Running value	Running value

These values change as the specimen is subjected to cyclic loading.

Completion Summary Table (After Failure)

After failure, the simulation summary page shows a complete trial-wise table generated from the same dataset used in the animation.

Trial	Force (N)	Stress (MPa)	Cycles to Failure	log(N)	Result
1	140.0	295.40	133	4.89	Intermediate
2	130.0	275.50	176	5.17	Intermediate
3	120.0	253.60	200	5.30	Intermediate
4	110.0	233.60	280	5.63	Intermediate
5	94.5	199.40	350	5.86	Intermediate
6	86.6	182.80	380	5.94	Intermediate
7	83.9	177.00	444	6.10	Intermediate
8	76.4	121.00	876	6.78	Intermediate
9	67.9	112.80	907	6.81	Intermediate
10	72.4	117.30	1708	7.44	Intermediate
11	58.8	102.90	3000	8.01	Intermediate
12	46.1	86.66	6690	8.81	Intermediate
13	41.6	80.17	9750	9.18	Intermediate
14	39.4	76.68	15990	9.68	Intermediate
15	28.4	57.94	43560	10.68	Intermediate
16	37.1	73.07	60150	11.00	Intermediate
17	32.7	65.65	63300	11.06	Intermediate
18	19.8	41.41	141300	11.86	Intermediate
19	24.0	49.67	166560	12.02	Failed

Sequential Calculations

Step 1

Record the applied force.

Step 2

Determine the corresponding bending stress.

Step 3

Record the number of cycles at specimen failure.

Step 4

Calculate

$\log(N)$

Step 5

Plot the graph between Stress (MPa) and $\log(N)$ to study the fatigue behaviour.

Solved Numerical Example

Given

Force

$$F = 24\ \text{N}$$

Stress

$$S = 49.67\ \text{MPa}$$

Cycles

$$N = 166560$$

Therefore,

$$\log(N) = \log(166560) = 5.222$$

For the summary graph, the plotted point for this final stage is

$$(\log(N), S) = (5.222,\ 49.67)$$

which is plotted on the S-N curve.

Interpretation of Results

• Higher stress generally produces lower fatigue life.
• Lower stress generally increases the number of cycles to failure.
• The S–N curve is used to estimate the expected service life of engineering components subjected to cyclic loading.

Result

The fatigue behaviour of the given specimen is studied by determining the relationship between applied stress and number of cycles to failure using the S-N curve representation shown in the simulation.