Failure theories

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Failure theories

Lecture 7 – Stress controlled fatigue

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Introduction

• Metals and alloys subjected to repeated loads over time may experience rupture for stress values much lower than those that would cause the fracture with a single application of the stress. This fracture mode is indicated as FATIGUE

• When fatigue damage takes place, rupture occurs for stress values much lower than the macroscopic yield stress.

• Fatigue is considered responsible for 90% of failures in operation of metal structures

(machine components, aircraft, bridges, etc.)

• Fatigue fracture is BRITTLE, in the sense that it is characterized by small deformations

(global), it occurs suddenly with catastrophic

consequences even for ductile materials.

Tendi-cinghia di distribuzione Porsche 928 Mechanical Engineering Design - N. Bonora 2018

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• de Havilland DH 106 Comet was the first jet for civil transportation: high altitude flight with pressurized cabin.

• First commercial flight in 1952. Same year, one Comet experienced fracture of fuselage at the take off at Ciampino Rome Airport.

• 1953: three accidents consequence of fuselage fracture

• 1954: explosion in flight over the Elba island (Tuscany) due to rapid decompression 20’’

after take off.

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deHavilland Comet Aircraft disaster

• To understand the cause of failure, a full-scale experimental investigation - aimed to

simulate the pressurizing cycle - was carried out: 3,057 pressurization cycles over an

aircraft in a water-tank

• Test revealed that fracture started at the

upper corner of the window of the main door

• Subsequent tests confirmed the results:

rupture was expected to occur between 1000 and 9000 pressurization cycles.

• The aircraft that exploded in air over Elba undergo 1290 pressurization cycles

Mechanical Engineering Design - N. Bonora 2018

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• Fatigue resistance is

expressed by a curve where S (stress amplitude) is given as a function the number of cycles N for a given

probability of failure (P)

• 1837 – Albert first publication on fatigue

• 1870 Woheler introduced the term «endurance»

• 1910 Basquin proposed the linear relationship on the log-log diagram

S′

_e

′

VITA A TERMINE VITA INFINITA

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Stress cycle and quantities

Mean stress 

_m

= (

_max

+ 

_min

) / 2

Range of stress 

_r

= (

_max

- 

_min

)

Stress amplitude 

_a

= 

_r

/2 = (

_max

- 

_min

) / 2

Stress ratio R = 

_min

/ 

_max

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• Fatigue: is a specific mode of failure

• It is the result of two processes:

flaw initiation and propagation.

• It takes place in three stages:

• Crack initiation

• Crack propagation

• Fracture

DEVELOP OF PROGRESSIVE DAMAGE IN FATIGUE 1. Substructural and microstructural changes

cause irreversible damage nucleation.

2. This initial damage leads to the formation of microscopic crack like flaws.

3. Microdefects grow and coalesce resulting in dominant macroscopic cracks

4. Stable crack propagation

5. Structural instability or complete fracture

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Fatigue: mechanisms

• Damage at microscale occurs in form of persistent slip and

formation (PSB)

• PBS volume increases with shear deformation on the shear planes

• This results in the formation of intrusion/extrusion of the slip planes at the free surface

(a) Persistent slip bands in vein structure.

Polycrystalline copper fatigued at a total strain amplitude of 6.4 × 10−4 for 3 × 105 cycles. Fatiguing carried out in reverse bending at room temperature and at a frequency of 17 Hz. The thin foil was taken 73 μm below the surface. (Courtesy of J. R.

Weertman and H. Shirai.) (b) Cyclic shear stress, τ , vs.

plastic cyclic shear strain, γ pl., curve for a single crystal of copper oriented for single slip. (After H. Mughrabi, Mater. Sci. Eng., 33 (1978) 207.) The terms γ pl,M. and γ pl,PSB refer to cyclic plastic shear strain in the matrix and persistent slip bands, respectively.

(c) Intrusions/extrusions in a tin-based solder due to thermal fatigue. (Courtesy of N. Chawla and R. Sidhur.)

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Fatigue: mechanisms

(a) Crack nucleation at the PBS

(b) Evidenzce at SEM of

intrusion/extrusion mechanism in a copper thin foil

• (Courtesy of M. Judelwicz and B. Ilschner.)

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Fatigue: mechanisms

Other mechanisms for crack nucleation in fatigue

(After J. C. Grosskreutz, Tech. Rep. AFML-TR-70–55 (Wright– Patterson AFB, OH: Air Force Materials Laboratory), 1970.)

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• STAGE I: when initiated a fatigue crack

subjected to constant stress amplitude cycling propagates at 45° along planes with larger maximum resulved shear stress. This is called stage I or o short crack propagation. Crack can grow until it encounters a microstructural barrier (grain boundary, inclusions, or

pearlitic region).

• This explain why grain refinement can

increase significantly fatigue resistance since it introduce a large number of barrier in the material.

• Same effect with surface treatments that

contribute to increase barriers (i.e. shot

peening).

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Fatigue: mechanisms

• STAGE II: when stress intensification increases as a consequenceof the crack growth, slips develops in different planes near the tip of the crack

• Propagation in stage II is controlled by normal stress

• This stage is characterized by the presence of striations which can only be seen at SEM.

• Not all material show striations: this is characteristics of ductile materials

• In fig 2 examples of striation in steel and aluminum alloy

• Striations are claimed to be the consequence of blunting and re-sharpening at the crack tip: NOT TRUE!

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different planes near the tip of the crack

• Propagation in stage II is controlled by normal stress

• This stage is characterized by the presence of striations which can only be seen at SEM.

• Not all material show striations: this is characteristics of ductile materials

• In fig 2 examples of striation in steel and aluminum alloy

• Striations are claimed to be the consequence of blunting and re-sharpening at the crack tip: NOT TRUE!

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Fatigue: mechanisms

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Microscopic fracture modes in fatigue.

(a) Ductile striations triggering cleavage.

(b) Cyclic cleavage.

(c) α − β interface fracture.

(d) Cleavage in an α − β phase field. (e) Forked intergranular cracks in a hard matrix.

(f) Forked intergranular cracks in a soft matrix.

(g) Ductile intergranular striations.

(h) Particle-nucleated ductile intergranular voids.

(i) Discontinuous intergranular facets.

(Adapted from W. W. Gerberich and N. R. Moody, in Fatigue Mechanisms, ASTM STP 675 (Philadelphia: ASTM, 1979) p. 292.)

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Fatigue: mechanisms

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Fatigue: morphology

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The Chevron pattern forms as the crack propagates from the origin at

different levels. The pattern points back to the origin

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Fatigue

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• Intensity of the stress state

• Stress amplitude

• High number of cycles

• Stress risers

• Corrosion

• Temperature

• Overloads

• Microstructure (metallurgy)

• Residual stresses

• Multiaxial loading

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Fatigue: governing factors

Effect of temperature on fatigue 1)Low temperature fatigue

1) -Fatigue strength increases with decreasing temperature below room temperature.

2) -Fatigue failure is associated with vacancy formation and condensation.

2)High temperature fatigue

1) Fatigue strength decreases with increasing temperature above room temperature

2) Mild steel shows maximum fatigue strength at 200~300 ˚C due to strain aging at this temperature.

3) Above room temperature, fatigue failure transits to creep failure with increasing temperature.

4) Ferrous materials have no fatigue limit at above 340 ˚C.

5) Fine grain has better fatigue life at lower temperature.

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Failure theories