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Fracture mechanics and fatigue

Among the modes of crack deformation, which statement correctly describes Mode I?

  1. AThe crack faces slide over each other in the direction of crack growth, an in-plane shear mode
  2. BThe crack faces slide parallel to the crack front, an out-of-plane shear mode
  3. CThe crack faces are pulled apart by tension perpendicular to them, an opening mode
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Answer: C. The crack faces are pulled apart by tension perpendicular to them, an opening mode

Crack deformation is divided into three modes: Mode I (opening), which pulls the crack faces apart; Mode II (in-plane shear), in which the faces slide in the direction of crack growth; and Mode III (out-of-plane shear), in which they slide parallel to the crack front. The stress intensity factors are likewise written K_I, K_II and K_III. Brittle materials break most easily under Mode I loading, and cracks tend to turn toward the direction that makes them Mode I, so fracture toughness is usually expressed as the critical value for Mode I, K_IC. Sliding in the direction of crack growth is Mode II and sliding parallel to the front is Mode III; these matter for cases such as cracks in shafts under torsion.

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More Fracture mechanics and fatigue questions

  1. 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?
  2. 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?
  3. Which pairing of a feature seen when observing a fracture surface in a scanning electron microscope with the type of fracture is correct?
  4. 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?
  5. 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?