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Fracture mechanics and fatigue

Which statement about low-cycle fatigue (roughly 10⁴ cycles or fewer to failure) is correct?

  1. AThe basic approach is to rate it with stresses in the elastic range at a constant stress amplitude
  2. BWith so few cycles, no fatigue cracks form, and failure is the same ductile fracture as from a single overload
  3. CPlastic strain occurs in every cycle, and the relation between plastic strain amplitude and life is expressed by the Coffin–Manson law
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Answer: C. Plastic strain occurs in every cycle, and the relation between plastic strain amplitude and life is expressed by the Coffin–Manson law

In low-cycle fatigue, large plastic deformation is repeated in every cycle, and the plastic strain amplitude, rather than the stress, governs the life. It is therefore rated in tests at a constant strain amplitude, and the relation between the plastic strain amplitude Δεp/2 and the number of reversals to failure 2Nf is expressed as Δεp/2 = εf′(2Nf)ᶜ (c is about −0.5 to −0.7), a straight line on log-log axes. This is the Coffin–Manson law. Rating by stress amplitudes in the elastic range is the method of high-cycle fatigue, which uses S-N curves and Basquin's law. Low-cycle fatigue also ends in failure through crack initiation and growth, and it is a problem in power plants that start and stop repeatedly and in parts subject to thermal strain.

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More Fracture mechanics and fatigue questions

  1. Which statement correctly describes the curve of fatigue crack growth rate da/dN plotted against the stress intensity factor range ΔK on log-log axes?
  2. Fatigue crack growth in a steel plate is described by the Paris law da/dN = C(ΔK)ᵐ (C = 1.0×10⁻¹², with da/dN in m/cycle, ΔK in MPa·√m, and m = 4), and ΔK = Δσ√(πa) (geometry factor 1). Under cycling with a stress range Δσ = 200 MPa, which value is closest to the number of cycles for the crack to grow from 1.0 mm to 5.0 mm? Assume that ΔK over this range (about 11–25 MPa·√m) is well above the threshold and within the range where the Paris law holds.
  3. The theoretical strength of a perfect crystal is estimated at roughly one tenth of the Young's modulus, yet the actual fracture strength of brittle materials such as glass is often only a few tens to a few hundreds of times smaller than that. What is the main reason?
  4. An elliptical hole in a wide plate (radius along the major axis a = 1.0 mm, radius of curvature at the end of the major axis ρ = 0.040 mm) carries a tensile stress of 100 MPa perpendicular to the major axis. Estimating the maximum stress at the end of the hole with σmax = σ₀(1 + 2√(a/ρ)), which value is closest?
  5. A glass (Young's modulus E = 70 GPa, surface energy γs = 1.0 J/m²) has a surface crack of length a = 1.0 µm. Which value is closest to the fracture stress estimated with the Griffith equation σf = √(2Eγs/(πa))?