Fatigue Physics

In this video, a fan blade on an engine that failed during a United Airlines flight showed damage consistent with “metal fatigue”, US air accident investigators said. United’s Boeing 777’s engine combusted on February 20, to the surprise and alarm of passengers, minutes after the plane took off from Denver.

During the past decades, numerous research programs on fatigue problems have been carried out, stimulated by catastrophic accidents due to fatigue failures.  Significant developments were possible by fundamental improvements of techniques for calculations, experiments and measurements.

The understandings of metal fatigue are characterized by 1) the variety of practical fatigue problems is large; 2) these different problems can be well defined in terms of relevant conditions; 3) from a physical point of view, the influences of the conditions on the fatigue behavior are reasonably well understood thanks to extensive tests and researches.

There are three stages of fatigue failure: 1) Crack initiation; 2) Crack propagation; 3) Final fracture.

The crack initiation usually takes place on the surface of the metal in the vicinity of a defect (a notch, a surface scratch or pit, or an inclusion of some other material, or nucleation site).  The mechanism is a slip band at a microscopic level driven by maximum shear stress.

The defect begins to grow and becomes a micro-crack.  After crack initiation has occurred within a few grains, subsequent microscopic growth will expand the crack to pass several grain boundaries.  When the crack front reaches over several grains, the crack will continue to grow in a direction perpendicular to the largest tensile principle stress.  After some number of cycles of loading, the crack will eventually grow and become a macro-crack.  At this point, the crack at its tip creates a tiny area of very high stress concentration, sometimes hundreds to thousands times more than in the bulk material.  This creates a runaway effect in that as the crack grows larger, the stress concentration in the material also increases, causing the crack to grow more and more rapidly.  The final fracture will take place when the crack becomes so large that the remaining ligament of the cross section is too small to transfer the peak of the load cycle, or when the local stresses and strains at the crack front inflict a local fracture .

The image below shows one half of a test specimen after fatigue fracture failure. The test specimen contained a typical aircraft fastener hole with countersink.  A fatigue test was performed on the specimen using a fatigue testing machine. During the fatigue test a fatigue crack grew until it reached a critical size, then the specimen rapidly broke into two halves, resulting in a fracture failure. The fatigue crack on the specimen is identified as the lighter gray area. The largest load cycles create distinctive markings on the surface, which are so called beach marks. By tracing these beach marks back in time, it can be determined that a fatigue crack grew from the fastener hole and the countersink intersection, where large stress concentration takes place.

The crack initiation stage consists of cyclic band slip, crack nucleation, and MICRO crack growth, driven by stress concentration factor.

The crack propagation stage is the MACRO crack growth stage driven by stress intensity factor.

The final fracture is a function of material fracture toughness.

There are three approaches for fatigue life analysis: 1) Stress-life analysis: it is stress-based, for high cycle fatigue, aims to prevent crack initiation; 2) Strain-life analysis: it is useful when yielding begins during crack initiation, for low cycle fatigue; 3) Fracture mechanics: it is best for crack propagation, for low cycle fatigue.  It is frequently used to evaluate remaining life of existing components that have cracks initiated, for example, fitnesses-for-service analysis.

crack_pic_1

crack_pic_2

Fatigue has the following characteristics:

  • In metal alloys, and for the simplifying case when there are no macroscopic or microscopic discontinuities, the process starts with dislocation movements at the microscopic level, which eventually form persistent slip bands that become the nucleus of short cracks.
  • Macroscopic and microscopic discontinuities (at the crystalline grain scale) as well as component design features which cause stress concentrations (holes, keyways, sharp changes of load direction etc.) are common locations at which the fatigue process begins.
  • Fatigue is a process that has a degree of randomness (stochastic), often showing considerable scatter even in seemingly identical sample in well controlled environments.
  • Fatigue is usually associated with tensile stresses but fatigue cracks have been reported due to compressive loads.
  • The greater the applied stress range, the shorter the life.
  • Fatigue life scatter tends to increase for longer fatigue lives.
  • Damage is cumulative. Materials do not recover when rested.
  • Fatigue life is influenced by a variety of factors, such as temperature, surface finish, metallurgical micro-structure, presence of oxidizing or inert chemicals, residual stresses, scuffing contact (fretting), etc.
  • Some materials (e.g., some steel and titanium alloys) exhibit a theoretical fatigue limit below which continued loading does not lead to fatigue failure.
  • High cycle fatigue strength (about 104 to 108 cycles) can be described by stress-based parameters. A load-controlled servo-hydraulic test rig is commonly used in these tests, with frequencies of around 20–50 Hz. Other sorts of machines—like resonant magnetic machines—can also be used, to achieve frequencies up to 250 Hz.
  • Low cycle fatigue (loading that typically causes failure in less than 104 cycles) is associated with localized plastic behavior in metals; thus, a strain-based parameter should be used for fatigue life prediction in metals. Testing is conducted with constant strain amplitudes typically at 0.01–5 Hz.

Engine_blade_fatigue_failure

The very day of the emergency landing in Philadelphia by Southwest Airlines Flight 1380, investigators were blaming a type of failure that spells alarm for materials engineers everywhere: metal fatigue.  That means one of the engine’s titanium fan blades, after vibrating or otherwise flexing many thousands of times over its lifetime, developed a series of microscopic cracks that suddenly “propagated” — tearing through the metal with violent speed.

Wing_fatigue_failure

Fatigue cracking in the wing carry-through spar was responsible for in-flight wing separation on a Cessna 210 near Mount Isa in Australia.

Gear_fatigue_failure

Fatigue failure of a gear tooth

 

fatigue_test

Fatigue testing

 

HAZ_fatigue_failure

Fatigue failure at heat-affected-zone (HAZ)

 

Hammer_peening

Hammer peening to improve fatigue life of welds