Question 8 of 8: Conditions for Creep and Fatigue; Creep Deformation Mechanism; Strain-Rate-Sensitive Yielding and Brittle Fracture

Question 8: Conditions for Creep and Fatigue; Creep Deformation Mechanism; Strain-Rate-Sensitive Yielding and Brittle Fracture (20 marks)

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.

8.1 — (a) Conditions for creep and for fatigue

(i) Creep. Creep requires a sustained (essentially static) stress $\sigma<\sigma_y$ maintained at a sufficiently high homologous temperature, $T/T_m\gtrsim0.3$–$0.4$ (absolute temperature over absolute melting point), for long enough that thermally activated deformation mechanisms — dislocation climb, grain-boundary sliding, diffusional flow — can operate on the timescale of the observation. Below roughly $0.3\,T_m$, these mechanisms are so slow that no measurable time-dependent strain accumulates over any practical service life; the same metal at room temperature under the same stress would show negligible creep, while at $0.5$–$0.7\,T_m$ it creeps readily. Stress and temperature trade off against each other (higher stress lowers the temperature at which creep becomes significant, and vice versa), but both a nonzero sustained stress and an adequately high homologous temperature must be present simultaneously.

(ii) Fatigue. Fatigue requires a cyclic (time-varying) stress or strain, of essentially any waveform, applied for a sufficient number of cycles — unlike creep, elevated temperature is not a prerequisite (fatigue occurs readily at room temperature), though it can combine with, and accelerate, creep damage at high temperature (creep–fatigue interaction) or with an aggressive environment (corrosion fatigue; see the environmentally assisted cracking note in Question 3(b)). What is required is repeated localised plastic slip at a stress concentrator (a crack tip, an inclusion, a surface scratch) on each cycle, even when the far-field nominal stress never exceeds $\sigma_y$; that repeated micro-plasticity nucleates and then incrementally extends a crack (Question 1(b) and Question 3(a) of this paper both quantify this process directly via $da/dN=A(\Delta K)^n$) until the remaining ligament fails by fast fracture or ductile overload.

8.2 — (b) Microstructural mechanism of creep at σ < σ_y: dislocation climb

Below $\sigma_y$, ordinary glide alone cannot produce continuing plastic strain once mobile dislocations pile up against obstacles (forest dislocations, precipitates, sub-grain boundaries) they cannot cut through or bow around at that stress. Dislocation climb is the mechanism that lets deformation continue anyway, given enough thermal energy and time.

1. Vacancy supersaturation and diffusion to the dislocation core. At creep temperatures ($T/T_m\gtrsim0.4$–$0.5$), the equilibrium vacancy concentration is significant and vacancies are mobile enough to diffuse over microstructurally relevant distances within the test/service timescale. An edge dislocation held up at an obstacle can absorb (or emit) vacancies at its core by diffusion.
2. Climb moves the dislocation to a new (parallel) slip plane. Each vacancy absorbed at the extra half-plane effectively removes one atom from the dislocation line, causing it to move one atomic spacing perpendicular to its original glide plane (climb), rather than along it (glide). Enough vacancy absorption over enough time lets the dislocation climb up and over (or around) the obstacle that was blocking pure glide.
3. Glide resumes on the new plane, and the process repeats. Once past the obstacle, the dislocation can glide again on the new plane until it meets the next obstacle, where it must climb again. This alternating glide-climb sequence is the microscopic origin of the secondary (minimum-rate) creep stage: the overall strain rate is controlled by the slower of the two steps, which at typical creep conditions is the diffusion-limited climb step, giving the classic creep-rate dependence on temperature (Arrhenius, activation energy close to that of self-diffusion) and on stress (power-law creep, $\dot\epsilon\propto\sigma^m$, $m$ typically 3–8 for climb-controlled creep).

This mechanism operates entirely below $\sigma_y$ because it does not require overcoming an obstacle by athermal glide resistance at all — it substitutes a slow, thermally activated detour (climb) for the instantaneous, purely mechanical process (glide) that a room-temperature tensile test measures. That is precisely why the smooth-bar $\sigma_y$ from a rapid tensile test says nothing about a component's resistance to creep at the same nominal stress held for years at temperature: they are two different rate processes with two different governing physics.

8.3 — (c) Strain-rate-sensitive yielding and susceptibility to brittle fracture

A material whose yield stress rises sharply with strain rate (a strongly positive strain-rate sensitivity $m$ in $\sigma_y\propto\dot\epsilon^m$ — BCC metals, most notably ferritic steels, are the classic example) becomes progressively less able to yield plastically, relative to fracturing, as the loading rate increases. At a stress concentrator (a notch, a crack tip, an impact site), the local strain rate is always far higher than the nominal applied strain rate — often by several orders of magnitude, because the concentrated deformation at the tip happens in a very small volume over a very short time. In a strain-rate-insensitive material (most FCC metals), the local yield stress at that concentrator stays close to its quasi-static value regardless of how fast the local region is being strained, so the material can still yield and blunt the tip even under rapid or impact loading. In a strongly strain-rate-sensitive material, the local yield stress at the same concentrator rises steeply with the locally very high strain rate, and can be driven above the material's comparatively rate-insensitive cleavage fracture stress before yielding has a chance to blunt the tip — exactly the same competition between yield stress and cleavage stress that governs the temperature-driven ductile-to-brittle transition in Question 5(b), except here the control variable is loading rate rather than temperature. This is why the same steel that behaves ductilely under a slow tensile test can fracture in a brittle, low-energy manner under rapid loading (impact, wave slam, an explosive or ballistic event) at a temperature where it would otherwise be safely above its DBTT, and it is the physical reason Charpy impact testing (a high-strain-rate test) is used to qualify structural steels rather than relying on a quasi-static tensile test alone.