Lezione 5 di Costruzione di macchine

fino ad ora si è considerato un profilo senza intagli (ma ci sono sforzi concentrati nell'intaglio)

è sempre da indicare il punto in cui si sta lavorando!

ORA SI ANALIZZA L'INTAGLIO!

• comportamenti ≠ anche se σ̅ rimane costante (niente raccordo!)
• fattore di tensione in fatica
• limite fatica NO taglio
• limite fatica SI taglio

K_f = K_fσ (Sf,3D) / S_f,3D(notch)

• tensione effettiva
• σ_max è la max tensione

k_f ≠ k_t

si considerà quindi la σ effettiva NON PIU σ_max

N = constant

P(σ_{m, nom}, σ_{a, nom})

Specimen

Component

e' sempre da indicare il punto su cui si sta lavorando!

ORA SI ANALIZZA L'INCAGLIO!

• Notch effect in fatigue

comportamenti ≠ anche se = d(noto raccordo!)

• In static, the notch effect alters the local stress state in magnitude and distribution. Moreover, the stress magnitude strongly increase and often it switches from mono-axial to bi-axial or tri-axial in the neighbour of discontinuity.
• The fatigue strength decrease

Fattore di tensione in fatica

Limite fatica NO taglioLimite fatica SI taglio

KF =

• In static loading, the notch effect amplify all the stress distribution. Consequently all applied load affects the notched component. In dynamic loading, the stress in the process zone is important, thus, the static stress peak is less representative of the fatigue failure.
• Consequently, the stress concentration factor have to be reviewed in order to take into account of the stress distribution in the process zone. The maximum stress that lead to the failure in static is different from the fatigue:

tensione effettivauna e' la max tensionee c

kρ ≠ kt

si considererà quindi la σ effettiva, NON PIU σmax

➢ The reduction is taken into account with a Fatigue Stress-Concentration Factor K_f:finite life: vs infinite life:

➢ The effect on fatigue is less than the theoretical value: 1 ≤ K_f ≤ K_t

➢ A Notch Sensitivity Factor q is defined as follows: q = (K_t - 1) / (K_f - 1)

➢ The Stress Concentration Factor can be calculated then as: K_f = 1 + q(K_t - 1)

➢ For reversed (R=-1) bending or reversed (R=-1) axial loads

➢ Notch sensitivity q depends on the material➢ Thus K_f depends on the material (q), the notch geometry and loading mode (K_t)

➢ q = 1 / (1 + √(ρ / r))

➢ Due to the described influencing factors, the fatigue strength σ_D-1 (that comes from rotating bending tests, 10 mm specimen diameter, polished) must be corrected➢ The fatigue limit of the component σ_D-1 will be:➢ Component without notches: σ_{c_D-1} = C_LC_SC_FC_RΦ_D-1

➢ Component with notches: σ_a = K_f · σ_a,nomσ_m = K_f · σ_m,nom

➢ The working point of a notched component P(σ_m, σ_a) can be seen on the Haigh Diagram

TRATTAMENTI SUPERFICIALI

• A local load is applied on the surface.
• This local load induces yield in compression.
• The material tends to expand laterally.
• The central internal part (“heart”) of the component, always remaining in the elastic regime, prevents the expansion of the surface which remains in a compression state of residual stress.

Mechanical treatments shot peening (pallinatura)

• It generates compression residual stresses due to the hammering action of small steel spheres launched over the surface at high speed (by using a centrifugal action or compressed air):
  • The depth of the affected zone by the compression residual stresses if around 1 mm
  • It is more effective on medium hardness steels and cast iron (20-35% σ_D-1 increase) than on hard and light alloys steels
  • Typical applications: leaf springs
• Patented by Föppl, in Germany in 1929 and introduced by Almen (GM) during the 1930’s to increase fatigue strength of leaf springs in automotive suspensions

Mechanical treatments cold rolling (rullatura a freddo)

• Similar effect as shot peening
• Maximum depth of the zone affected by compression residual stresses is around 10 mm
• It leaves a more regular, smooth surface
• Typical applications: crankpins-web/counterweights fillet in crankshafts

Mechanical treatments cold forming (in metal sheets)

• It generates a compression residual state of stress on one side, tension on the other side
• The effect must be carefully checked

It has a negative effect because it is always accompanied by surface decarburization

• It decreases the surface layer strength
• It decreases the surface layer volume which contraction is prevented by the underlying material
• It causes dangerous tension residual stresses!

Chemical/physical treatments surface coatings

• Coatings are used to solve corrosion, wear problems, or for aesthetic purposes:
• Chromium and Nickel plating:
  • Are the most widespread surface coatings for steels
  • They induce a tension state of stress, therefore they significantly decrease the fatigue strength
  • The effect is more pronounced as much as:
    • the strength of material is higher
    • a higher endurance is expected
    • the thickness of coating layer is higher
  • Shot peening or nitridation are used to mitigate these problem, especially with nickel plating
• Cadmium plating:
  • It does not have a significant effect on fatigue strength
    • Used against corrosion
    • Gives higher wear resistance
• Electrically deposed coatings, in the case of metallic materials, if not properly controlled, can induce hydrogen embrittlement
• Anodizing
  • Typical of light alloys (aluminum alloys…)
  • It forms a brittle film that fractures under cyclic loads starting the fatigue process
  • This effect is (negatively) synergic with the action of corrosion
  • The decrease in fatigue strength is around 20-30%

Thermal and diffusive treatments

• Residual stresses can be caused by:
  • Local phase changes
  • Diffusive process
  • Thermal gradients and differential thermal expansion/contraction (differential cooling)
• Empirical rule: the parts last cooling remain in tension
• Residual stresses occur in welding, flame cutting (oxi-fuel cutting), etc. but also in metal working (for example in wheel grinding)

Thermal and Diffusive Treatments Carburizing/Carburization and Nitriding

• Diffusive processes with beneficial effects on fatigue strength
  • They induce surface hardening.
  • A compression residual stress state comes in the layer interested by diffusive process by an increasing in volume.
  • The interested layer is around 1 mm

Thermal Treatments quenching

In ferrous materials quenching (heating at the austenitization temperature followed by rapid cooling) causes the martensitic transformation with a linear expansion around 0.5%

In surface quenching, the non-quenched inner material prevents surface material expansion inducing a residual compression state of stress

Induction hardening allows the selective hardening of a part to achieve the required hardness over a specific area and depth. Very effective since it leaves a tougher core