Corrosion fatigue occurs when the simultaneous action of cyclic stresses and chemical environment is in play. Corrosive environment generally shorten the fatigue life and reduce the endurance limit, as shown in Figure 5.66. There are various ways in which corrosive environment can affect the fatigue behavior. One could be generating pits (pitting corrosion) that can lead to crack nucleation sites. Also, the crack growth rate is increased as a result of the chemical environment. The mode of load application also affects the corrosion fatigue behavior, such as reduction in loading frequency during fatigue testing may result in longer period of time through which the crack stays in opening mode in contact with the corro­sive medium, leading to a reduction in fatigue life.

Corrosion Prevention Methods There are a host of corrosion prevention methods that can be introduced. The first choice of prevention would be to develop an intrin­sically corrosion-resistant alloy if it is economical. One way is to create passive films naturally on the material. There are yet several other ways that can prevent or mini­mize corrosion. For example, even though aluminum appears as very active on the electrochemical series, it forms a thin, impervious layer of alumina, thus protecting it from a variety of corrosive environments. Anodizing is a commercial process by which a much thicker alumina film is developed on aluminum to have usefulness in marine environment. Generally, the thin passive film of aluminum oxide gets destroyed under the exposure of chloride ions in seawater. As already noted, stain­less steel is mainly stainless because of the formation of a thin, impervious film of chromic oxide that occurs due to higher chromium content.

Inhibitors are sometimes used to provide passive surface film over surfaces. Inhibitors are highly oxidized chromate and the like solutions that are adsorbed on the metal surface to be protected. The passive layer formed by inhibitors works like

passive film, but cannot be regenerated. Hence, new inhibitors need to be applied if the layer gets washed out.

Galvanic protection is another way of preventing corrosion. As already men­tioned, one of the ways of achieving galvanic protection is to use a more active metal as anode (sacrificial anode). The sacrificial anode needs to be replaced after it gets exhausted (Figure 5.67). Another way of achieving galvanic protection is to apply a direct current (DC) that feeds electrons into the metal part that needs to be protected. An example would include the use of impressed current minimizing or even stopping corrosion occurring at the underground pipeline (Figure 5.68).

Various types of paints, enamel coating, and so on are also used in various appli­cations for prevention of corrosion. However, they need to be reapplied in regular intervals as they may exfoliate under service condition and restart corrosion.

5.3.3

Corrosion is an electrochemical process that causes the surface ofthe metals/alloys degrade over time in the presence of a chemical environment. Corrosion resistance of materials used in nuclear components is important in many applications to ensure that they serve as desired. The “cost of corrosion” can result in immediate property and life endangerment and increased downtime, leading to substantial losses. Many nuclear components inside the reactor stay in close contact with reactor fluids (e. g., coolant in the form of liquid or gas). These effects get exacer­bated due to the presence ofradiation fields.

1.9.1.3 Design

Although design does not generally fall under the purview of a materials engi­neer, he/she is in a unique position to figure out early whether the faulty design would pose a problem. Designs leaving stress concentration sites (sharp recesses, keyholes, and the like) are typically unwarranted in load-bearing applications since it may interfere with the capability of the component to serve properly. For example, fatigue properties are especially prone to the pres­ence of stress concentration sites.

Here, we will define and discuss grain boundaries. Grain boundaries play an impor­tant role in strengthening in that finer grain sizes lead to higher strength and vice versa, also popularly known as Hall-Petch strengthening. Their presence may lower the thermal/electrical conductivity of the material. They may act as the pre­ferred sites for corrosion (intergranular corrosion), for precipitation of new phases to occur, or may contribute to the plastic deformation or failure at higher tempera­tures (grain boundary sliding) and many other phenomena. A grain boundary can be defined as the interface boundary between two neighboring grains. In a poly­crystalline material, each grain is a single crystal with a particular orientation (Figure 2.35a).

The grain boundaries are the regions of misfit where the atoms are confused. When the misorientation angle (0) between the grains is small (~10°), the bound­ary is called a low-angle boundary. Low-angle boundaries can be described as an array of dislocations and are of two types: tilt and twist. Tilt boundaries can be gen­erated by bending a single crystal with the rotation axis being parallel to the bound­ary plane (Figure 2.36a), while the twist boundary is created when the rotation axis is normal to the boundary plane (Figure 2.36b). Tilt boundaries can be described as an array of parallel edge dislocations, as illustrated in Figure 2.37. The tilt angle (0) is given by

tan(0) — 0 — b/h, (2.16)

where b is the Burgers vector of the dislocation and h is the vertical distance of separation between two neighboring edge dislocations at the boundary. The tilt boundaries are generated during a metallurgical process known as recovery when excess dislocations of the same type arrange themselves one below the other. The

twist boundaries refer to similar low-angle boundaries formed by arrays of screw dislocations.

High-angle boundaries (0 > 10-15°) can be extrapolated from the simple the­ory of low-angle grain boundaries. But the dislocation model becomes invalid when there are too many dislocations at the boundary such that the adjacent dislocation cores start overlapping. To overcome this difficulty, grain boundaries are often described by the coincident site lattice model; however, a complete dis­cussion is outside the scope of the chapter. The high-angle boundaries generally have a “free space” or “free volume,” whereby solutes can collect and a solute — drag effect can be generated. The energy of high-angle grain boundary varies from 0.5 to 1.0 J m~2 for most metals. Migration of high-angle boundaries occurs due to atom jumps across the boundary during the grain growth, which can be influenced by the grain boundary crystallography, presence of impurities, and temperature.

From the definition of a dislocation being the line of demarcation between slipped and unslipped regions, dislocations cannot end inside a crystal except at a node. The node is a point where two or more dislocations meet. The existence of dislocation nodes affirms that different types of dislocation reactions occur inside a crystal. How­ever, a dislocation reaction is totally different from a chemical reaction. So, we should not confuse ourselves looking for similarities between the two. The

dislocation reactions pertain to the addition or dissociation of initial dislocation(s) into new product dislocation(s). However, they cannot just happen arbitrarily. The dislocation reaction should follow certain geometrical and energetic rules. The energy criterion used to decide whether a dislocation addition or dissociation reaction is feasible or not is known as Frank’s rule. The underlying basis of this rule is that the total energy needs to be minimized for the reaction to be energetically feasible. To elucidate the rule, let us take an example of a dislocation reaction where two dislocations with Burgers vectors b1 and b2 meet to form a third dislocation with a Burgers vector b3. That is, the reaction is b1 + b2 ! b3. According to Frank’s rule, the reaction will be feasible when bj + b2 > b3. In case of a reaction b1! b2 + b3, the energetic feasibility condition of the reaction would be b1 > bj + b3, accord­ing to the Frank’s rule. This implies that the reaction should be vectorially correct and energetically favorable. With little introspection, we can find out that the Frank’s rule actually stems from Eq. (4.13).

& Example 4.4

Show that the following dislocation reaction is feasible:

ao [їм] ^ a0 [2ii]+a0 [112]. 2 6 6

Solution

To test the feasibility of the reaction, a two-step procedure needs to be fol­lowed. The first step is to ascertain whether the reaction is geometrically sound or not. This can be accomplished by verifying that the x, y, and z com­ponents are equal on both sides of the reaction:

ao 2ao ao

x components: — = —— + — 2 6 6

ao ao ao

y components: — (0) = 0 = — — + — 2 6 6

ao ao ao

z components: — (—1) = =

2 2 6

Therefore, the given dislocation is geometrically (or vectorially) possible. If any reaction that does not happen, there is no need to go to the second step for validation.

For the dislocation reaction to be energetically favorable, we need to show that b1 > b2 + b2.

Original dislocation: b1 = [101].

The magnitude ofthe Burgers vector is

Hence,

b1 — ^.

1 2

Product dislocation : b2 = — [211].

6 L

The magnitude of Burgers vector is b2 = | (22 + (-1)2-

Hence,

b2- a» b2 — 6 •

Product dislocation: b3 — — [112].

6

The magnitude of the Burgers vector is
b3 — a0 (12 +12 + (-2)2)1/2.

Hence,

4.2.4

In circumstances where safety is extremely critical, the full-scale engineering com­ponents may be tested in their worst possible service condition. An example of a full-scale engineering test could be crash of a train carrying the spent fuel casks to see the effect of crash on the integrity of the casks. However, such full-scale tests are extremely expensive and very rarely conducted. Before the advent of fracture mechanics as a discipline, impact-testing techniques were used to determine the

fracture characteristics of materials. Impact tests are designed to measure the resistance to failure of a material under a sudden applied force in such a way so as to represent most severe conditions relative to the potential of fracture — (i) defor­mation at low temperatures, (ii) high deformation rate, and (iii) a triaxial state of stress (by introducing a notch in the specimen). The impact tests measure the impact energy or the energy absorbed prior to failure. The most common methods of measuring impact energy are Charpy and Izod (Figure 5.19a). The techniques differ in the manner of specimen support and specimen design. Charpy V-notch test is most commonly used in the United States (Figure 5.19b). In this test, the load is applied as an impact blow from a weighted pendulum hammer that is

— 80

Volume of second phase, %

Figure 5.18 Effect of second-phase particles on tensile ductility. From Ref. [2].

released from a fixed position at a fixed height (h1). Upon release, a knife-edge mounted on the pendulum strikes and fractures the specimen at the notch that acts as a stress raiser site for the high-velocity impact blow. After fracturing the specimen, the pendulum continues in its trajectory to reach a height h2, depending on the absorbed energy during impact. The energy absorption is calculated from the difference between the pendulum’s static energies at h1 and h2, that is, the impact energy is Mg(h1 — h2), where M is the pendulum’s mass and g is the acceler­ation due to gravity. In reality, the machine is equipped with a scale and a pointer that shows the impact energy after the test is done. Nowadays, more sophisticated, instrumented impact testers are used that can follow the load versus time or dis­placement during the impact event.

Variables including specimen size and shape as well as notch configuration and depth influence the test results. One of the main purposes of the Charpy test is to determine whether or not a material experiences a ductile-brittle transition with decreasing temperature. Figure 5.20 shows a description of ductile-brittle

transition behavior. Plane strain fracture toughness is quantitative in nature in that a specific property of the material is determined (i. e., KIC). The results of impact tests are more qualitative in nature and are of little use for design purposes. Impact energies are of interest mainly in a relative sense and for making comparisons — absolute values are of little significance. Attempts have been made to correlate frac­ture toughness and Charpy impact energy, but with limited success.

Cold work changes dislocation network density and has been found to have a significant effect on the swelling characteristics of metallic materials. The higher dislocation density restricts the nucleation and growth of voids. The effects of cold work and fluence reveal that the same amount of cold work pro­vides less effect at higher fluences since cold work enhances the incubation dose for swelling but does not diminish the swelling rate in the linear swelling region at higher doses. This is thought to be a result of the fact that the disloca­tion density decreases in cold worked material during irradiation, while that in an annealed material increases. This accounts for the decreasing effect at higher doses.

Effect of Grain Size

Guthrie et al. [14] have demonstrated the effectiveness of fine grain size in inhibit­ing void formation by studying a film of sputtered nickel with ~0.5 pm thickness.

Under neutron exposure, the film with the ultrafine grain size did not show evi­dence of voids, while a nickel foil with a grain size of 30 pm produced voids. Also, similar experiments carried out in finer grain size material have shown similar results. The reason for this behavior is that the grain boundaries present in greater numbers in a fine grain size material act as efficient sinks for point defects. Recently, people have tried to investigate various forms of nanocrystalline material to see whether they are more resistant to radiation effects. However, the issue has not been resolved decisively to date.

The largest possible dense packing in a cubic system is achieved in the FCC crystal system. That is why it is sometimes referred to as close-packed cubic (CPC) crystal structure. Each cube face (i. e., six of them in a cube) has one atom at the center of the cube face in addition to eight corner atoms (Figure 2.6a). The effective number of atoms in an FCC unit cell is then given by (6 x 1/2) + (8 x 1/8) = 4, because each face-centered atom is shared by two unit cells and each corner atom is shared by eight unit cells. This structure has a coordination number of 12. The packing factor can be calculated in much the same way as the BCC crystal structure, and is found to be about 0.74. Following a similar method, the relationship between the atom radius (r) and the lattice constant (a) can be found for an FCC unit cell. Figure 2.6b shows the cube face of an FCC unit cell. The face diagonal is (r + 2r + r) = 4r, and now applying the Pythagorean rule, we also know that the face diagonal is ^/2a when the cube edge is a so that 4r = 2a.

Metals such as aluminum, y-Fe, gold, silver, platinum, lead, nickel, and many others have FCC crystal structures. The theoretical density of FCC metals can also be derived from the first principles if the lattice constant and the atomic weight of the metal are known as shown earlier for BCC in Example 2.1.

Let us assume the following relation is applicable for determining the lattice self — diffusivity value in copper (FCC, lattice parameter a0 = 0.3615 nm):

where b is the number of positions an atom can jump to, d is the dimension (if for one-dimensional flow, d = 1; for two-dimensional flow, d = 2; and for three­dimensional flow, d = 3), and other terms are already defined in Eq. (2.43).

Determine b, l, and DL, given that diffusion takes place along (110) direction at 500 °C (773 K) and Q = 209 kJ mol-1.

Solution

For an FCC along (110) direction, b = 12, and l is given by half of the face diagonal length (P2 a0/2), that is, 0.2566 nm or 2.566 x 10-8 cm.

Therefore, using the given equation, we obtain

12 2 DL = 2—3 (2.556 x 10-8 cm (1013 s-1) exp

= 9.83 x 10-14 cm2 s-1.

The activation energy for vacancy diffusion is composed of two terms, activation enthalpy (or energy) for migration and activation enthalpy for vacancy formation. Calculated and experimental activation energies for diffusion in gold and silver through vacancy mechanism are shown in Table 2.6. The activation energy for dif­fusion of self-interstitials appears in the form similar to the vacancy diffusion (i. e., both formation energy and migration energy are included). Although for interstitial impurity diffusion the formulation is almost the same, for vacancy diffusion, it does not involve any probability factor similar to the vacancy formation energy; instead, it contains only the migration energy term. That is why the substitutional diffusion (including self-diffusion) occurring through vacancy mechanism is much slower than the interstitial impurity diffusion. see the example in Figure 2.48

showing carbon (interstitial) diffusion in у-iron, Cr substitutional diffusion, and self-diffusion in у-iron. Substitutional impurity diffusion is also influenced by the atom size and charge effects of the impurities. Generally, oversized (compared to the host atom) substitutional impurities have a higher migration energy than that of the undersized substitutional impurities. Increase in the valence of the substitu­tional impurity atom has been found to reduce the activation energy. When solute- vacancy complexes are created, they would also affect the diffusion.

For a given crystal structure and bond type, <Q;elf /RTm is more or less constant, where Tm is the melting temperature (K). It has been found that most close-packed metals tend to possess a Qself/RTm of ~18. The activation energy for self-diffusion is proportional to the melting temperature. For example, Figure 2.49 gives the acti­vation energy for self-diffusion of various FCC metals plotted against their melting temperatures. Correlations by Sherby and Simnad [8] revealed the following rela­tion between the activation energy for self-diffusion, melting point, and valence:

Q self = R(K 0 + V )Tm, (2.47)

300

2000

Figure 2.49 Activation energy for lattice self-diffusion versus melting temperature for various FCC metals [8].

14 for BCC 16 for HCP 18 for FCC 20 for diamond structure

(2.48)

K о

While this formulation worked well for many metals, some metals such as Zr, Ti, Hf, U, and Pu were noted to deviate from the predictions.

Special Note Direct measurement of self-diffusivities is not easy because of the difficulty in tracking identical, individual atoms. That is why tracers (such as radioisotopes) that are chemically the same as the host atoms but detectable by analytical methods are often used. However, tracer diffusivity is quite close to the self-dif — fusivity, yet it is little less. It occurs because the tracer jumps could be correlated in that they can jump back to the sites wherefrom they originally started the jump. Because of these basically "wasted” jumps, the tracer diffusivity (Dtracer) values are less than the self-diffusivity (Dse|f), that is, Dtracer =f Dse|f, where f is the correlation factor. Based on exhaustive geometric principles, the correlation factors can be found out. For vacancy diffusion, the following are the correlation factors for different crystal structures (0.781 for FCC, 0.721 for HCP, and 0.655 for BCC). In general, we can see that the variation due to the correlation factors is mostly quite small since the accuracy with which diffusivity can be determined is limited. Furthermore, consideration of correlated jumps is required in the case of associated defects (such as the solute-vacancy complex).

Plastic deformation in single crystals is guided by relatively simple laws. However, in polycrystalline materials, it becomes complicated. Strength is inversely related to the dislocation mobility. That is, the dislocation movement can be obstructed by various factors that can, in turn, strengthen (or harden) the material. Grain bound­aries can act as such an obstacle to the dislocation motion (refer to Section 2.2 for more information on the grain boundaries). The grain boundary ledges are a com­mon feature — these steps can be produced by external dislocation joining the grain boundary or packs of dislocations in the grain boundary. Thus, the density of ledges increases with increasing misorientation angle. Grain boundary ledges act as an effective source of dislocations. Hence, before we introduce the topic of grain size strengthening, we need to know some fundamentals of the grain size effect on the plastic deformation in polycrystals. Grain size strengthening is not possible in a single crystal (i. e., single grain) for the obvious reasons.

In a polycrystal unlike a single crystal, during plastic deformation the continuity must be maintained between the deforming crystals. If not maintained, it will read­ily form flaws leading to fast failure. Although it is true that each of the grains attempts to deform as homogeneously as possible in concert with the overall defor­mation of the material, the geometrical constraints imposed by the continuity requirement cause significant differences between neighboring grains and even in

parts of each grain. As the grain size decreases, the deformation becomes more homogeneous. That is why decreasing grain size in conventional materials gener­ally improves ductility. Due to the constraints imposed by the grain boundaries, slip occurs on several systems even at low strains. As the grain size is reduced, more of the effects of grain boundaries will be felt at the grain center. Thus, the strain hard­ening of a fine grain size material will be greater than that of a coarse-grained poly­crystalline material. Theoretically, it has been shown that the strain hardening rate (da/de) for an FCC polycrystalline material is ~9.6 times that of (dt/dy) for a sin­gle crystal as noted in Eq. (4.34):

da —2 dt

de — MdC ’

where M is called Taylor’s factor (for FCC lattice, it is taken as 3.1). This has also been verified by experiments.

Von Mises [27] showed that for a crystal to undergo a general change of shape by slip requires the operation of five independent slip systems. Crystals having less than five slip systems are never ductile in polycrystalline form even though small elonga­tions can be obtained through twinning or a favorable preferred orientation. Gener­ally, cubic metals easily satisfy this requirement (higher ductility), whereas HCP and other low symmetry metals do not (lower ductility). At elevated temperatures, other slip systems can get activated and thus increase the number of slip systems to at least five.

At temperatures above ~0.5Tm (Tm is the melting point), deformation can occur by sliding along grain boundaries. Grain boundary sliding becomes more promi­nent with increased temperature and decreasing strain rate. A general way to find­ing out when grain boundary sliding may start operating is the use of equicohesive temperature concept. Above this temperature, the grain boundary is weaker than grain interior and strength increases with increasing grain size. Below this tem­perature, the grain boundary region is stronger than the grain interior and strength increases with decreasing grain size. The grain size strengthening mech­anism to be discussed below is thus applicable only to lower homologous temper­ature regimes.

A mathematical description of the grain size strengthening can be expressed in terms of a general relationship between yield stress and grain size, first proposed by Hall (1951) and later extended by Petch (1953):

ay — ai ^ (4.35)

where ay is the yield stress, ai is the friction stress (also can be defined as yield strength at an infinite grain size), ky is the unlocking parameter (that measures relative hardening contribution ofthe grain boundaries), and d is the grain diame­ter. The Hall-Petch relation has also been found to be applicable for a wide variety of situations, such as the variation of brittle fracture stress on grain size, grain size- dependent fatigue strength, and even to the boundaries that are not such grain boundaries as found in pearlite, mechanical twins, and martensite plates.

Figure 4.33 A schematic of a dislocation pileup is shown to form by the dislocations originating from a Frank-Read source in the center of Grain-1. The leading edge of the dislocation pileup produces enough stress concentration to create dislocations in Grain-2.

The Hall-Petch relation was developed based on the concept that grain bounda­ries act as barriers to the dislocation movement (as noted earlier during discussion of dislocation pileups). As the grain orientation changes at the grain boundary, the slip planes in a grain get disrupted at the grain boundary. This implies that slip planes are not continuous in a polycrystalline material from one grain to another. Thus, the dislocations gliding on a slip plane cannot burst through the grain boundary. Instead, they get piled up against it. In a larger grain, the number of dislocations in a pileup is higher. The magnitude of the stress concentration at the leading edge of the pileup (as shown in Figure 4.33) varies as the square root of the number of dislocations in the pileup. Hence, a greater stress concentration would be created at a larger grain. However, this event can trigger dislocation sources in the next grain quite readily. The situation is schematically shown in Figure 4.33. Now if the grain size is smaller, the stress concentration in Grain-1 will not be enough to produce slip in the next grain readily, and thus fine grain sized material will exhibit higher yield strength.

4.4.3

Failure by fatigue is a possibility at elevated temperatures (less than melting point). This type of failure can occur with less plastic deformation and will have the char­acteristics of a fatigue failure. However, it is generally observed that both fatigue and static strength properties get reduced with increasing temperature. Figure 5.51 illustrates the stress versus fatigue life curve at various temperatures, including room temperature for N-155 alloy (a high temperature alloy of Fe-21Cr-20Ni-20Co — 3Mo-2.5W-1.5Mn-1Nb, wt.%). As already discussed, application of a load particu­larly at higher homologous temperatures would produce time-dependent plastic deformation or creep. The creep-rupture strength decreases with increasing tem­perature. Usually, the alloys that are creep resistant are also found to be fatigue resistant. However, it does not mean that a material with best creep strength will also provide the best fatigue strength. Therefore, it becomes necessary to design against both creep and fatigue, and testing needs to be carried out in a state where both fatigue and creep loading are applied. The main method of investigating creep-fatigue properties is to conduct strain-controlled fatigue tests with variable frequencies with and without intermittent holding period (hold time) during the test. A lower frequency (<104 cycles s-1) and hold times allow creep effects to take place. At higher frequencies and short hold times, the fatigue mode predom­inates and failures just as pure fatigue failure (cracks start at surface and

propagates transgranularly inside the bulk material). At longer hold times or decreased frequencies, the creep effect starts playing a growing role and creep — fatigue interaction becomes important. In this regime, the mixed mode fracture is observed, that is, both fatigue cracking and creep cavitation. At another extreme, when the holding time is extended considerably with cyclic loads occurring only sparsely, the situation resembles pure creep deformation. However, where oxida­tion effects are present, the creep-fatigue interaction becomes much more com­plex. The ASTM E2714-09 standard (Standard Test Method for Creep-Fatigue Testing) describes the specifics of a creep-fatigue test.

Note that creep-fatigue and thermomechanical fatigue are not the same phe­nomena. Creep-fatigue is carried out at constant nominal temperatures, whereas thermomechanical fatigue involves thermal cycling (i. e., fluctuating temperatures).

5.2