**Fatigue Testing**

**EXPERIMENT # 4**

*Safety first!*

*Proper protective eyewear must be worn while operating the fatigue tester.**Place the guard shield in place before starting a fatigue test.**Never touch the sample while it is rotating.**Caution: the sample may be hot after the test.*

**Objectives**

- To determine how surface finish affects fatigue life.
- To determine how fillet radius affects fatigue life.
- To observe fatigue fracture surface markings and be able to differentiate fatigue from fast fracture markings.
- To generate a Wöhler diagram (an S-N curve) and extract information relating to fatigue limit, fatigue strength, and fatigue life.

**Background**

Material fatigue is a well-known situation whereby rupture can be caused by a large number of stress variations at a point, even though the maximum stress in the material is less than its yield stress. As the number of load cycles increases, the permissible stress level declines. Fracture is initiated by tensile stress at a flaw in the material (the flaw may be microscopic or macroscopic). Once started, the edge of the crack acts as a stress raiser and assists in propagation of the crack until the reduced section can no longer carry the applied load, and the part fails.

While it appears that fatigue failure may occur in all materials, there are differences in the incidence of fatigue. For example, mild steel is known to have an ‘endurance limit stress’ below which fatigue fracture does not occur, no matter how many loads cycles the material experiences, which is known as the fatigue limit. With non-ferrous materials, such as aluminum alloys, however, there is no such limit. As a consequence of these differences, there are two design methods. With a material like mild steel, the stress range can be kept below the endurance limit to ensure failure will not occur. Alternatively, one can design for a specified number of stress variations, on condition that the part will be replaced at that stage. The latter method is quite common with aircraft where the use of aluminum is widespread.

Fatigue strength is also significant in machine design. When designing a part for fatigue strength, an engineer uses results from a fatigue test. However, when designing for infinite life (millions of cycles), such results may not exist and will take too long to determine. In such a case, interpolation from the measured fatigue data will be used instead. To introduce this very complex subject in a simple way, the apparatus demonstrates the classical fatigue experiments carried out by Wöhler. He selected the method of reversing the stress on a part by employing a cantilever beam rotated about its longitudinal axis, therefore the stress at any point on the surface of the beam varies sinusoidally. A Wöhler diagram (stress-number (S-N) curve) can be created by repeating the experiment at many different loads and recording the number of cycles until failure occurs.

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**Fatigue Testing Machine**

The Gunt Fatigue Testing Machine provides a simple way of observing the effect of fillet radius and surface smoothness on a material subjected to fluctuating flexural stresses. The fatigue tester is driven by an induction motor, which is connected on one side to a counter mechanism. The tapered test piece is attached to a very stable shaft in between two spherical ball bearings. The loading fixture is attached to the shaft at the other end. The loading device consists of a spherical ball bearing and a micro switch that automatically switches off the motor when the fracture occurs. The loading on the test piece can be increased by turning the loading wheel clockwise. The force applied to the test piece by a spring can be varied from 0-300 N. A load cell measures the applied force. The number of load changes and the applied force are read directly from the LCD.

**Basic Principles**

In the fatigue apparatus, the specimen acts as a clamped beam (left end) under a concentrated force F (right end). This induces a triangular bending moment along the length of the specimen, with a maximum bending moment of . As shown in the figure, *a* is the length of the specimen. The bending moment is largest at the clamped end and drops to zero at the free end. We expect the specimen to fail where the loading is highest, i.e., at the clamped end.

Under pure bending, the normal stress varies in the cross-section as well, going from zero at the neutral axis (the center of a circular cross-section) to a maximum/minimum value at the outermost surface of the specimen. One side of the beam is in tension while the other is in compression. The maximum normal stress in a beam, s, is:

Where Mb is the applied moment, *c* is the distance from the centroid to the outermost surface (in this case, *r*), and* I* is the moment of inertia about the centroid, which for a circular cross-section, is:

The cyclic stress experienced by a specimen during a fatigue test is composed of a constant part, the mean stress, which is caused by an initial load, and a superimposed cyclic part with an alternating stress amplitude. In this experiment, the bending moment is fixed and the specimen is rotating, which results in an alternating, sine-shaped bending stress, with a mean value () of zero. The alternating stress amplitude in the specimen is a function of the applied bending moment (described above), and the geometry (described below).

In this experiment, the alternating stress amplitude, , is equivalent to the maximum normal stress in the beam. Combining all equations, the alternating stress amplitude is given by:

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**Test Procedure**

You will run the fatigue experiment on three different specimens of heat-treated steel, details of which are shown in the table below:

Specimen | Fillet radius (mm) | Surface roughness Rt (μm) | Notes |

1 | 0.5 | 4 | Sharp corner, smooth |

2 | 2 | 4 | Curved corner, smooth |

3 | 2 | 25 | Curved corner, rough |

As the time required for a fatigue experiment is prohibitively long for small loads, all three specimens will be loaded with a relatively high force of **200 N** in this lab.

- Measure the diameter of the specimen and inspect the surface roughness.
- Insert the specimen into the equipment.
- Measure the distance from the neck to the specimen’s contact surface with the bearing.
- Refer to the PDF “Fatigue Testing User Manual – For Students” for specific instructions on setting up and running the experiment.
- Once the experiment is complete, record the number of load cycles to failure (N) and calculate the maximum normal stress in the specimen.

It takes much longer to create a complete S-N curve given the nonlinear nature of the response. Data were taken on five **#3 specimens**, and the results are shown in the table below:

Number | Load (N) | Stress (N/mm2) | Cycles to failure, N | Duration (min) |

1 | 200 | 14030 | 5 | |

2 | 170 | 48800 | 17 | |

3 | 150 | 167000 | 60 | |

4 | 130 | 455000 | 162 | |

5 | 120 | 1280800 | 457 |

For these specimens, the length was *a*=100.5 mm, and the diameter *d*=8 mm

- Calculate the alternating stress amplitude (equal to the maximum normal stress) for each load, and plot this on a graph as a function of logl0 number of cycles N. (Should be a semi-log plot.)

**Report**

A full lab report is to be submitted. The lab report should include the following:

- Explanations of the fatigue limit, fatigue strength, and fatigue life.
- Maximum normal stress calculation for each load.
- Discussion about the fractured surface cross-section and identification of the cause of the rupture.
- How was the lifespan affected by fillet radius? Compare specimens #1 and #2.
- How was the lifespan affected by the surface smoothness? Compare specimens #2 and #3.
- An S-N curve (Wöhler diagram) for the experimental data provided for specimen #3.