A lead pipe at room temperature (25°C) slowly deforms under its own weight over several years, while a steel pipe under identical stress conditions shows no time-dependent deformation. What is the correct explanation?
ALead has a lower yield strength than steel, so it deforms plastically at lower stresses
BRoom temperature is above 0.4 Tm for lead (Tm ≈ 600 K) but well below 0.4 Tm for steel (Tm ≈ 1811 K), placing lead in the creep regime and steel outside it
CLead undergoes elastic deformation rather than plastic deformation, making it more susceptible to creep
DSteel is alloyed with carbon which blocks diffusion-driven deformation mechanisms
The key is homologous temperature T/Tm, not absolute temperature. For lead, Tm ≈ 600 K, so 0.4Tm ≈ 240 K — well below room temperature (298 K). Lead is already deep into its creep regime at room temperature. For steel, Tm ≈ 1811 K, so 0.4Tm ≈ 724 K (≈ 450°C) — far above room temperature. The yield strength argument (option A) is a tempting distraction because lead does have lower yield strength, but that doesn't explain time-dependent flow at stresses below the yield point. Creep is fundamentally a thermal activation phenomenon, not a yield stress phenomenon.
Question 2 Multiple Choice
An engineer designing turbine blades must choose between an alloy with small grains and one with large grains (same composition). Which should she choose to minimize creep deformation, and why?
ASmall grain size — the Hall-Petch effect strengthens grain boundaries and resists all forms of deformation including creep
BLarge grain size — grain boundary sliding is a major creep mechanism, and fewer grain boundaries reduce this contribution
CSmall grain size — finer grains reduce the mean free path for dislocation glide, slowing creep
DGrain size is irrelevant to creep; only the alloy composition determines creep resistance
This is a counterintuitive reversal of the Hall-Petch effect. For room-temperature strength, finer grains are better (Hall-Petch: strength ∝ grain size^−½). But at high temperatures where creep dominates, grain boundaries are sites of weakness, not strength — grain boundary sliding allows adjacent grains to shift relative to each other under sustained stress. Larger grains mean fewer grain boundaries per unit volume, reducing this mechanism. Turbine blade alloys take this to the extreme: directionally solidified columnar grains (aligned with the stress axis to eliminate transverse boundaries) or even single-crystal blades (no grain boundaries at all) are used in the hottest turbine stages.
Question 3 True / False
The steady-state creep rate of a material exhibits an Arrhenius dependence on temperature, with an activation energy that is often similar to the activation energy for self-diffusion.
TTrue
FFalse
Answer: True
The steady-state creep rate is described by ε̇ = A·σⁿ·exp(−Q/RT), where Q is the creep activation energy and R is the gas constant. Experimentally, Q for steady-state creep in metals is typically close to the activation energy for self-diffusion in the same material. This is not a coincidence — the rate-controlling mechanism for creep (dislocation climb) requires dislocations to absorb or emit vacancies, a process that depends on the same atomic diffusion that governs self-diffusion. Measuring the creep activation energy is thus a way to identify the dominant creep mechanism.
Question 4 True / False
Creep mainly occurs at stresses that exceed the material's conventional yield stress measured at room temperature.
TTrue
FFalse
Answer: False
Creep is time-dependent plastic deformation that occurs at stresses well below the conventional yield stress, provided the temperature is high enough. A conventional stress-strain test measures near-instantaneous response — if the stress doesn't cause immediate plastic flow, the material appears to be elastic. But at elevated temperatures, thermally activated mechanisms (dislocation climb, grain boundary sliding, vacancy diffusion) allow slow, continuous plastic strain to accumulate over time even at stresses far below the yield point. This is precisely why creep must be analyzed separately from conventional plasticity in high-temperature design.
Question 5 Short Answer
Why does homologous temperature T/Tm (rather than absolute temperature) determine whether creep is significant, and what does this reveal about the underlying mechanism?
Think about your answer, then reveal below.
Model answer: Creep is driven by thermally activated atomic mechanisms — primarily dislocation climb (dislocations absorbing or emitting vacancies to bypass obstacles) and grain boundary sliding, both of which require atomic diffusion. The rate of these processes depends not on absolute temperature alone, but on how active thermal fluctuations are relative to the binding energy of atoms in the crystal — which scales with the melting point Tm. At T/Tm ≈ 0.4, atoms have enough thermal energy to diffuse at rates that matter on engineering timescales, regardless of whether that's −33°C for lead or 450°C for steel. The homologous temperature is essentially a normalized measure of 'how liquid-like is this solid' — near Tm, atoms are highly mobile; far below, they are locked in place. Because the mechanism requires diffusion, and diffusion rates scale with T/Tm, so does creep significance.
This also explains why the Arrhenius equation applies: the rate of any thermally activated process with activation energy Q scales as exp(−Q/RT). For creep, Q ≈ Q_diffusion, so the creep rate has the same Arrhenius form as the diffusion coefficient. T/Tm is a convenient normalization because Tm is approximately proportional to the cohesive energy of the material — it captures the material's resistance to atomic rearrangement in a single number.