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Mechanical properties and fracture

Which statement about the Vickers hardness test is correct?

  1. AA diamond square pyramid indenter with a 136° angle between opposite faces is pressed in, and hardness is found from the indentation diagonals
  2. BA cemented carbide or steel ball, for example 10 mm in diameter, is pressed in, and hardness is found from the indentation diameter
  3. CHardness is found from the difference in depth of a diamond cone or similar indenter under a minor and a major load, without measuring the indentation size
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Answer: A. A diamond square pyramid indenter with a 136° angle between opposite faces is pressed in, and hardness is found from the indentation diagonals

In the Vickers test, a square-based diamond pyramid indenter with a 136° angle between opposite faces is pressed in, the surface area is found from the mean length d of the two diagonals of the indentation, and HV = 0.1891F/d² (F in N, d in mm). Because the indenter shapes are geometrically similar, the value stays nearly constant as the load changes, which suits measurements on thin layers and small regions (microhardness testing). Pressing in a ball and measuring the indentation diameter is the Brinell test, suited to measuring the average hardness of coarse microstructures. Using the difference in indentation depth is the Rockwell test, convenient for inspecting mass-produced parts. Conversions between test methods are empirical.

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  1. A steel plate with a fracture toughness K_IC = 50 MPa·√m carries a tensile stress of 200 MPa. Using K = Yσ√(πa) with a geometry factor Y = 1.0, which value is closest to the critical crack length a at which fracture occurs?
  2. When the fracture toughness of plates of the same material but different thickness is measured, what happens to the apparent fracture toughness K_c as the thickness increases?
  3. Which statement about fatigue S-N curves is correct?
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