21-Mat-A4 Deformation Behaviour and Properties of Materials · May 2017
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format. National Exams, May 2017 — 12-Mtl-A4, Mechanical Behaviour and Fracture of Materials. Three hours, closed book, one approved non-communicating calculator. Eight questions of 20 marks each; the rubric marks only the first five questions as they appear in the answer book. All eight are solved here. This sitting's own printed content is fracture mechanics, fatigue crack growth, creep, toughness, strengthening, composites and plastic instability.
Reference texts. The answers below are keyed to the works normally recommended for this syllabus code:
Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.
Creep testing. A cylindrical specimen — here a Ni-based superalloy turbine-blade material is a natural choice, given Question 4(b) — is loaded in a furnace-mounted uniaxial tensile creep frame with a constant applied load (constant engineering stress) at a fixed elevated temperature, typically above about $0.4\,T_m$ on the absolute scale. An extensometer continuously records specimen elongation against time until rupture. The single test therefore reports strain as a function of time at one stress/temperature combination; the full property set is built from a family of such tests at several stress levels and temperatures.
Fatigue testing. A polished, notch-free specimen is subjected to a fully reversed (or otherwise cyclic) stress of controlled amplitude, most commonly in a rotating-bending or axial servo-hydraulic machine, and the number of cycles to failure $N_f$ is recorded. The test is repeated at a series of stress amplitudes on nominally identical specimens; each (amplitude, $N_f$) pair becomes one point on the resulting property curve.
(i) Elastic deformation — modulus of resilience. When only elastic deformation is considered, "toughness" is properly called resilience: the strain energy per unit volume the material can absorb up to the elastic limit and fully recover on unloading, $U_r=\sigma_y^2/2E$ (the triangular area under the stress-strain curve up to yield). It measures energy-storage capacity, not damage tolerance.
(ii) Plastic deformation — static (tensile) toughness. When the material is allowed to deform plastically, toughness is the total area under the engineering stress-strain curve from zero strain to fracture, $U_T=\int_0^{\varepsilon_f}\sigma\,d\varepsilon$ — the total energy per unit volume absorbed before rupture, combining both the elastic and plastic contributions. A material can be strong but not tough (high $\sigma_y$, little ductility, small area) or tough without being especially strong (moderate strength, large ductility, large area).
(iii) Fast fracture — fracture toughness. In the presence of a sharp crack, unstable ("fast") fracture is governed not by the bulk stress-strain curve at all but by the critical stress-intensity factor $K_{Ic}$, the material's resistance to unstable crack propagation under plane-strain conditions. $K_{Ic}$ is an intrinsic material property (units MPa$\sqrt{\text{m}}$) that, together with the applied stress and flaw size, sets the condition $K=Y\sigma\sqrt{\pi a}=K_{Ic}$ for catastrophic failure — and, as Question 1 shows, a component can fracture this way at a nominal stress well below the yield stress the tensile-toughness definition in (ii) would suggest is "safe."
