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Fracture mechanics and fatigue

In a ductile metal such as steel, the energy needed for a crack to advance (the critical energy release rate G_c) is orders of magnitude larger than 2γs (a few J/m²) estimated from the surface energy. What is the main reason?

  1. APlastic deformation occurs at the crack tip, and a large amount of energy is consumed as plastic work
  2. BThe surface energy of metals is thousands of times larger than that of ceramics
  3. CMetals contain almost no cracks, so Griffith's idea does not apply to them
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Answer: A. Plastic deformation occurs at the crack tip, and a large amount of energy is consumed as plastic work

Orowan and Irwin extended Griffith's idea to metals and wrote the energy needed for a crack to advance as G_c = 2γs + γp. Here γp is the plastic work consumed in the plastic zone at the crack tip; in ductile steels it exceeds 10⁴ J/m², far larger than 2γs. The surface energy of metals is roughly 1–3 J/m², not different from that of ceramics by orders of magnitude. Metals also contain inclusions and cracks, and Griffith's energy balance is still used as the foundation, with the plastic work added. In materials that hardly deform plastically, such as glass, G_c is a small value of the same order as 2γs.

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More Fracture mechanics and fatigue questions

  1. In a steel with a yield stress of 500 MPa, the stress intensity factor at a crack tip is K = 30 MPa·√m. Estimating the size of the plane-stress plastic zone (its distance from the crack tip) with r_p = (1/2π)(K/σy)², which value is closest?
  2. Which pairing of a feature seen when observing a fracture surface in a scanning electron microscope with the type of fracture is correct?
  3. Which statement correctly describes the initiation of fatigue cracks when a stress amplitude below the yield stress is repeatedly applied to a metal with a smooth surface?
  4. The fracture surface of a part that failed by fatigue shows shell-like patterns visible to the naked eye (beach marks) and fine lines visible in an electron microscope (striations). Which statement about them is correct?
  5. A cyclic stress with a mean stress σm = 200 MPa is applied to a steel with a fully reversed fatigue limit σw = 300 MPa and a tensile strength σB = 800 MPa. Using the modified Goodman relation σa = σw(1 − σm/σB), which value is closest to the stress amplitude corresponding to the fatigue limit?