ME 215 – Engineering Materials I

Dr. A. Tolga Bozdanawww.gantep.edu.tr/~bozdana

Mechanical EngineeringUniversity of Gaziantep

Chapter 6

Fatigue Properties (Part I)

1

Introduction Rather than simple tensile or torsional loading, machine parts in service are

often subjected to loads varying in magnitude or direction with varying time.The stresses due to such loading condition would cause “fatigue failure”.

Figure 1 For a shaft (Fig. 1) of radius R and rotating atspeed of w, a moment M is applied at its end.Stress element at point A (at distance c fromthe shaft center) is under compression. Whenit reaches to point O (shaft center), there isno stress acting on it. At point B, it is undertension. So, the stress state is changing fromcompressive to tensile due to the rotation.

Such repeated (cyclic) stresses are usuallylower than ultimate strength, so failure will nothappen in the first cycle. After certain rotation,material would fail, and the number of cyclesto the failure is called “life of the part”.

2

Definition of Fatigue According to ASTM E-206, fatigue is the process of progressive, localized

and permanent structural change occurring in the material subjected tofluctuating stresses at certain points, causing cracks or complete fractureafter sufficient number of fluctuations.

Fluctuations may occur in magnitude and direction of stresses as well aswith time (frequency). The failure starts at stress levels below elastic limitof material, and thus unexpected fracture occurs. For instance, breakinga piece of wire by bending back-and-forth is common way of fatigue failure.The number of times for cyclic bending depends upon extent of deformation.

Welded test piece Fatigue failure at welded partForward-backward bending

3

Fatigue Process Fatigue is a microscopic process through which its initiation and progress depend

upon the microscopic variables. This process consists of various stages (Fig. 2):1. Crack initiation: Fatigue is initiated due to microplasticity (the onset of plasticity at

microscopic level whilst the material is still nominally elastic). Due to “deformationby slip” (sliding blocks of crystal grains over each other), some crystals are distortedby shear stresses in the direction of 45°.

2. Stage I crack growth: A series of intrusions and extrusions are developed duringcyclic loading, and crack growth is oriented in the slip plane. The rate of crackpropagation in Stage I is very low as compared with that in Stage II.

3. Stage II crack growth: The crack propagates in a zigzag transgranular path alongthe slip planes in a perpendicular direction to maximum tensile stress.

4. Fracture: It will occur when Stage II crack has reached the sufficient length so thatthe remaining section cannot sustain the applied load.

Figure 2 Crack initiation Stage I Crack Growth Stage II Crack Growth

4

Fatigue Process

crack initiation

crack growth (stage I & II)

fracture

5

Photographs of Fatigue Failure

Fatigue failure on a crankshaft

Fatigue failure on a spring

Fatigue failure on an axle Fatigue failure on pipes Fatigue failure on bolts

6

Photographs of Fatigue Failure

Fatigue failure of a ship body

Fatigue failure on a road

Fatigue failure at Y-shape electrical power transmission tower

The tower The base

7

Basic Definitions Time-dependent stresses are classified into two groups: constant amplitude

and frequency stresses (Fig. 3a) and random stresses (Fig. 3b)

Maximum Stress (Smax): the stress having the highest algebraic value instress cycle (tensile or compressive being considered positive or negative).

Minimum Stress (Smin): the stress having the lowest algebraic value instress cycle (tensile or compressive being considered positive or negative).

Mean Stress (Sm): average of Smax and Smin (steady stress component).

Stress Range (Sr): algebraic difference between Smax and Smin in one cycle.

Stress Amplitude (Sa): one half of stress range (variable stress component).

Figure 3

(a) (b)

Sm = (Smax + Smin) / 2

Sr = Smax – Smin

Sa = (Smax – Smin) / 2

8

Constant amplitude and frequency stresses1. Alternating stress: the stress cycle is symmetrical about “zero” stress axis

(Sm = 0). Smax and Smin are equal in value, but of opposite sign. The stressvaries between ± Sa (Smax = Smin = Sa in absolute value). It is also called“completely reversed stress” in case of a rotating shaft.

2. Fluctuating stress: the stress varies between two arbitrary stress values ofSmax and Smin. Sm is different than zero, which can be positive or negative.The stress is represented by Sm and Sa: Smax = Sm + Sa and Smin = Sm – Sa

3. Repeated stress: the stress varies between zero and a peak value, whichcould be positive or negative. In other words: Sm = Sa

Figure 4

9

Random stresses The time variation of random stresses does not follow a definite pattern. So,

the amplitude of fluctuating stress changes together with its frequency.

A random stress is characterized by continuous change in amplitude andfrequency so that instantaneous values have no meaning. Thus, amplitudeof a random stress can only be expressed as the average of instantaneousamplitudes over a certain time period.

Classic examples of such loading conditions are: sea waves, atmosphericdisturbances, and road-induced vibrations in ground vehicles (Fig. 5)

Figure 5

Uniaxial fatigue testing under alternating stress Rotating bending test designed

by Wöhler (Fig. 6) was used todefine the strength of axles ofrailway cars. A specimen (withconstant diameter over gaugelength) is being rotated whilesubjected to constant bendingmoment over its entire length. Figure 6

Figure 7

During cantilever test (Fig. 7),the bending moment changeswhereas the bending stress isapproximately constant alonglength of a tapered specimenwith shape of cubic parabola.

11

Uniaxial fatigue testing under alternating stress Other testing methods are:

alternating bending test where bendingload alternates whilst the specimen isstationary (Schenk, Fig. 8) axial loading (push-pull) test obtained

by applying an alternating axial load onthe specimen (Amsler Vibrophore,Fig. 9a or Schenk, Fig. 9b)

Figure 8

Figure 9

(a)

(b)

The testers above can also be used toapply a mean stress whereas rotatingbending type testers are exclusively forapplying an alternating stress.

Axial loading testers with conversionattachments are capable of conductingbending and torsion fatigue testing.

12

Specimens for Fatigue Test Size and geometry of

fatigue specimens varyaccording to the tester.Various types of fatiguespecimens are given inFig. 10.

Extreme care must betaken during specimenpreparation in order toensure that the failuretakes place somewherealong the gauge length.

Figure 10

(a) Alternating bending tester(b) Rotating bending tester

(c, d) Push-pull tester (with bending attachment)(e, f) Push-pull tester (axial loading)

(g) Cantilever type rotating bending tester