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Beyond Strength of Materials

Strength of Materials, or Mechanics of Materials, is an engineering subject discussing the ultimate strength, yield stress, and stiffness of a material and the structure it forms. The subject of Mechanics of Materials generally presumes that the initially flawless material is ideally connected and perfectly assembled into the designed shapes. The failure criteria depend solely on the ultimate strength or yield stress of the material. Unfortunately, in reality, many other factors may shorten the service life of a structure. Some of these factors are:

  • Material defects: flaws, voids, dislocations.
  • Surface roughness and surface treatments: scratches, pits, machining marks, electroplating, stamping.
  • Assembling induced imperfection: press-fit,
  • Functionality requirements: sharp corners, grooves, nicks.
  • Size: everything being equal, the larger the size the more initial defects.
  • Loading types, e.g., tri-axial, bi-axial, axial, bending, torsion, combined loadings.
  • Harsh environments, e.g., thermal loadings (temperature changes), corrosion, UV light.
  • Damage in service, e.g., repeated loading, large dead loads, vibrations, impacts, other unexpected loadings.
  • Poor maintenance and improper repair, e.g., lack of lubrication, wear at joins or surfaces, not enough or unfit reinforcements in repair.

To overcome all these odds, safety factor is introduced in common industrial practices. Nevertheless, even with safety factors, it is estimated 80%+ structural failures occurs through a fatigue related mechanism.

Definition of Fatigue

There are many harmful factors to the materials beyond the scope of strength of materials as discussed in the previous section. The accumulation of one or several of these factors eventually shorten the service life of materials. The combined effect of these factors is called "fatigue mechanism". Some common fatigue mechanisms include

According to ASTM International (originally American Society for Testing and Materials), fatigue is "the process of progressive localized permanent structural change occurring in a material subjected to conditions which produce fluctuating stresses and strains at some point or points and which may culminate in cracks or complete fracture after a sufficient number of fluctuations."

Fatigue Failure upon Time-Varying Loading

Time-varying Loading Fatigue can be defined as a process caused by time-varying loads which never reach a high enough level to cause failure in a single application, and yet results in progressive localized permanent damages on the material. The damages, usually cracks, initiate and propagate in regions where the strain is most severe. When the local damages grow out of control, a sudden fracture/rupture ends the service life of the structure. Common categories and approaching methods include:

  • High-cycle fatigue, associated with low loads and long life (>103 cycles), is commonly analyzed with a "stress-life" method (the S-N curve), which predicts the number of cycles sustained before failure, or with a "total-life" method (endurance limit), which puts a cap stress that allows the material to have infinite life (>106 cycles).
  • Low-cycle fatigue, associated with higher loads (plastic deformation occurs) and shorter life (<103 cycles), is commonly used methods called "strain-life" to analyze or predict the fatigue life.
  • Crack-growth approach uses fracture mechanics to examine the propagation of a crack to predict its growth in length per cycle, and to determine the amount of loading that will result in true failure.
Fatigue Reduction

The effort of fatigue prevention/reduction and service life extension can be summarized as

  • Use stronger, more capable materials
  • Reduce the margin of errors in assembly and manufacture
  • Avoid, soften when inevitable, stress concentrations
  • Keep residual stress at surface, if any, in compression
  • Take service environment into account
  • Schedule routine maintenance, firm and thorough