4.3 Creep and Stress Rupture
4.3.1 High-Temperature Failure
The mechanical strength of a metal at elevated temperatures is usually lim- ited by creep rather than by yield strength or other mechanical properties.
Creep is one of the primary concerns that could cause the failure of engine turbine blades, which might operate at temperatures above 1,000°C. The primary metallurgical factor affecting metal rupture behavior at elevated temperatures is the transition from transgranular to intergranular fracture.
Figure 4.13 is a schematic diagram of grain and grain boundary cohesive strengths as a function of temperature. The grain cohesive strength is lower
Equi-cohesive temperature Grain cohesive
strength Polycrystalline
bonding strength
Grain boundary cohesive strength
Temperature
Cohesive Bonding Strength
FIgurE 4.13
Cohesive bonding strength of polycrystalline metals.
than the grain boundary cohesive strength at lower temperatures. When the temperature increases, the grain boundary cohesive strength decreases more quickly than the grain cohesive strength does. At the equi-cohesive temperature, the controlling strength of a polycrystalline metal shifts from grain cohesive strength to grain boundary cohesive strength. This explains why most fracture modes at elevated temperature are intergranular.
Creep is a time-dependent progressive deformation that occurs under stress at elevated temperatures. In general, creep occurs at a temperature slightly above the recrystallization temperature of the metal involved. The atoms become sufficiently mobile to allow gradual rearrangement of posi- tions at this temperature. A creep test explores the creep mechanism and studies the relationship between stress, strain, and time. Figure 4.14 is a schematic of a typical engineering creep curve tested under constant load.
It is a record of strain or elongation against time. The microstructure has a profound effect on creep behavior. For example, the Ti–6% Al–2% Sn–4%
Zr–2% Mo alloy shows distinctive creep curves with different microstruc- tures, and the presence of β or pseudo-β microstructure will give the highest creep strength.
A typical creep curve has three stages: primary, secondary, and tertiary.
The test specimen has an instant extension as soon as the load is applied.
It is marked as the initial strain, εo, in Figure 4.14. The deformation rate will gradually slow down in the primary creep stage, and reaches a con- stant creep rate in the secondary creep stage. This constant creep rate is also the minimum creep rate and is usually referred to as the steady-state creep rate, or simply the creep rate. The slope of the curve can be calculated using Equation 4.19, where ε⋅ is the creep rate and ε and t are creep deformation and time, respectively.
I II III
Time, t εo
= minimum creep rate dεdt
Primary creep
Secondary creep
Tertiary creep
Strain, ε
FIgurE 4.14
Schematic of creep curve under constant load.
ε= dε
dt (4.19)
The creep rate increases very rapidly in the tertiary creep stage until the specimen finally fractures. The acceleration of creep rate in the final stage can be attributed to many factors, such as the reduction of the load-carrying cross-sectional area due to specimen necking, void formation, or metallurgi- cal changes such as recrystallization, grain or precipitate coarsening, etc.
The stress rupture test is very similar to the creep test except that it is tested at a higher load to cause fracture in a shorter period of time. In contrast to the creep test, the primary focus of the stress rupture test is to study the relation- ship between stress and rupture time, but not creep mechanism. The stress rupture test fills in the gap between the tensile and creep tests. It provides a set of short-time test data to predict long-time performance by extrapolation.
The stress rupture test data are usually presented with a plot of stress against rupture time at a specific temperature on a logarithmic scale, as illustrated in Figure 4.15. Curve 1 is based on a naturally aged aluminum alloy with a com- position of Al–3.78% Cu–1.40% Mg–1.63% Li tested at 200°C. Curves 2 and 3 are based on an aluminum alloy with a composition of Al–4.16% Cu–1.80%
Mg–0.96% Li–0.50% Mn tested at 200°C as well. Specimens for curve 2 are solution treated at 510°C and naturally aged, while specimens for curve 3 are solution heat treated at 510°C and artificially aged. The stress rupture data might be composed of sections of linear straight lines on the logarithmi- cal scale, as illustrated by curve 3 with different slopes due to metallurgical evolutions, such as the transition from transgranular to intergranular frac- ture, recrystallization or grain growth, etc. The stress rupture data do not report deformation rate, and can only be used to determine the amount of deformation after fracture or average deformation rate indirectly. The creep deformation rate reflects the combined effects of elastic and plastic defor- mation. However, the deformation measured after failure in a stress rup- ture test only shows plastic deformation. Creep failure is often initiated by
Hours
103 102 1 2
3
Stress (MPa)
600
200
100 400
10–1 100 101
FIgurE 4.15
Stress rupture curves.
a distinctive primary crack, and it subsequently grows to a point when the specimen ultimately fails. In contrast, multiple cracks are usually observed in a stress rupture specimen. The adjacent cracks sometimes grow and link together. Figure 4.16a shows multiple cracks observed at the surface of a tita- nium specimen subject to 379 MPa (55 ksi) at 648.9°C (1,200°F). Figure 4.16b shows the linkage between two cracks. The linkage between separate cracks can form a continuous crack that eventually fails the specimen. Figure 4.16c is an SEM fractography of this alloy showing a mixed intergranular ductile dimple and brittle stress-ruptured surface. Nonetheless, the stress rupture data are still of great engineering value in machine design, and therefore in reverse engineering. With a given operating temperature and required ser- vice life (rupture time), the design engineer can easily determine the allowed stress from the stress rupture curve. It can also demonstrate that the reverse engineered part has an equivalent or better stress rupture (or creep) resis- tance than the original OEM counterpart.
4.3.2 larson–Miller Parameter (Prediction of