Materials for engineering, 3rd Edition - (Malestrom)

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Materials for engineering
3. Equation [2.9] gives the Weibull distribution for the probability of survival
in the fracture testing of brittle solids, where σ o is mean stress at failure
for a given material. We may define P s = n/(N + 1), where N is the total
number of samples.
A set of ten square ceramic bars was tested in tension with the following
results for the fracture strengths measured in MPa:
Bar number (n) 1 2 3 4 5 6 7 8 9 10
Fracture strength 170 160 159 154 143 135 128 118 105 100
(a) What is the value of σ o ?
When the volume of the specimens V = V 0 , what is the probability of
survival (P s ) when:
(b) σ = σ o
(c) σ = 2σ o
(d) σ = 1 / 2 σ o
(e) What is the Weibull modulus (m) for the given ceramic?
[Answers: (a) 137.2 MPa; (b) 0.368; (c) 1.3 × 10 –14 (d) 0.969; (e) 5.419]
4. A plate of brittle material contains a crack of length 1 mm. It fractures
under a tensile stress, applied normal to the crack, of 600 MPa. Estimate
the apparent surface energy of the material and comment on the magnitude
of your result. (Young’s modulus of the material = 200 GPa).
[Answer: 1414 J m –2 ]
5. Calculate the minimum size of defect in a thin plate of maraging steel
that would give rise to brittle fracture when a stress equal to 2 / 3 of
the proof stress is applied. (For the maraging steel, proof stress =
1200 MPa, Young’s modulus = 200 GPa and G c = 24 kJ m –2 ) (Y = unity
in equation [2.17].
[Answer: 6.2 mm]
6. The creep strain ε measured as a function of time t for a nickel specimen
at 1000 K may be fitted to a curve of the form illustrated in Fig. 2.12
(curve A). Neglecting the initial instantaneous elastic strain, the data
may be fitted to the following expression:
ε = at 1/3 + bt + ct 2
Explain, giving experimental details, how the coefficients a, b and c can
be measured.
[Answer: If the strain, the strain rate and the time are measured at the
point at which the creep strain rate is a minimum, then:
t t
t
a = 9( ε – ˙ ε ) ; b = 2 ˙ ε – ε ε
; c = – ˙ ε ⎤
1/3
5t
t
2
5t
⎥
⎦
7. A specimen in a tensile creep test at 800°C ruptures after 1000 h. If the
activation energy for the dominant creep mechanism under these test