Typical Vickers indentation on a 4 vol% carbon nanotube (CNT) reinforced ZrB2 ce

Question

Typical Vickers indentation on a 4 vol% carbon nanotube (CNT) reinforced ZrB2 ceramic composite shows cracks emanating from the indentation corners (see figure). The indentation was obtained using load of 1000 g and holding time of 15 s (Vickers Hardness tester). Fracture toughness and Hardness of material are given by expressions: 1/2 o i) KIC0.016 1.854P where E is Young's Modulus of the composite (GPa); H is Vickers Hardness (GPa); P is applied load (N) c is diagonal crack length emanating from corner (m); and L is average length of indentation diagonal. Moduli of elasticity for ZrBz ceramic and carbon nanotubes are 500 GPa and 1 TPa, respectively. Assuming rule of mixture for composite modulus (iso-strain conditions), calculate fracture toughness mag WDdet spot H 2 120 9.9 mm ETD 25 10.00 kV 12:1051 PM 6/20/2011

Explanation / Answer

From figure,

'L'(average lenght of indentation diagonal) =40×10-6m

H=(1.854×P)÷L2

H=(1.854×1×9.81)÷(40×10-6)2

H=11.3121 GPa

Now, Fracture Toughness we require equivalent modulus of elasticity which is given by

Eeq=(2E1E2)÷(E1+E2)

Eeq=(2×500×1000)÷(500+1000)

Eeq=666.66 GPa

Kic=0.016×(666.66÷11.3121)(1÷2)×(1×9.81)÷(40×10-6)(3÷2)

Kic=4.763 Gpa answer

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