It has been recognized since 1830 that a metal subjected to a repetitive or fluctuating stress will fail at a stress much lower than that required to cause fracture on a single application of load. Failures occurring under conditions of dynamic loading are called fatigue failures, presumably because it is generally observed that these failures occur only after a considerable period of service. Fatigue has become progressively more prevalent as technology has developed a greater amount of equipment, such as automobiles, aircraft, compressors, pumps, turbines, etc., subject to repeated loading and vibration. Today it is often stated that fatigue accounts for al least 90 percent of all service failures due to mechanical causes.

A fatigue failure is particularly insidious because it occurs without any obvious warning. Fatigue results in a brittle-appearing fracture, with no gross deformation at the fracture. On a macroscopic scale the fracture surface is usually normal to the direction of the principal tensile stress. A fatigue failure can usually be recognized from the appearance of the fracture surface, which shows a smooth region, due to the rubbing action as the crack propagated through the section, and a rough region, where the member has failed in a ductile manner when the cross section was no longer able to carry the load. Frequently the progress of the fracture is indicated by a series of rings, or "beach marks", progressing inward from the point of initiation of the failure.

Three basic factors are necessary to cause fatigue failure. These are:

• maximum tensile stress of sufficiently high value,
• large enough variation or fluctuation in the applied stress, and
• sufficiently large number of cycles of the applied stress.

In addition, there are a host of other variables, such as stress concentration, corrosion, temperature, overload, metallurgical structure, residual stresses, and combined stresses, which tend to alter the conditions for fatigue. Since we have not yet gained a complete understanding of what causes fatigue in metals, it will be necessary to discuss each of these factors from an essentially empirical standpoint. Because of the mass of data of this type, it will be possible to describe only the highlights of the relationship between these factors and fatigue.

Stress Cycles

At the outset it will be advantageous to define briefly the general types of fluctuating stresses which can cause fatigue. Figure 1 serves to illustrate typical fatigue stress cycles.

Figure 1a illustrates a completely reversed cycle of stress of sinusoidal form. For this type of stress cycle the maximum and minimum stresses are equal. Tensile stress is considered positive, and compressive stress is negative.

Figure 1b illustrates a repeated stress cycle in which the maximum stress σ_max (R_max) and minimum stress σ_min (R_min) are not equal. In this illustration they are both tension, but a repeated stress cycle could just as well contain maximum and minimum stresses of opposite signs or both in compression.

Figure 1c illustrates a complicated stress cycle which might be encountered in a part such as an aircraft wing which is subjected to periodic unpredictable overloads due to gusts.

Figure 1. Typical fatigue stress cycles. (a) Reversed stress; (b) repeated stress; (c) irregular or random stress cycle.

A fluctuating stress cycle can be considered to be made up of two components, a mean, or steady, stress σ_m (R_m), and an alternating, or variable, stress σ_a. We must also consider the range of stress σ_r. As can be seen from Fig. 1b, the range of stress is the algebratic difference between the maximum and minimum stress in a cycle.

The S-N Curve

The basic method of presenting engineering fatigue data is by means of the S-N curve, a plot of stress S against the number of cycles to failure N. A log scale is almost always used for N. The value of stress that is plotted can be σ_a, σ_max, or σ_min. The stress values are usually nominal stresses, i.e., there is no adjustment for stress concentration. The S-N relationship is determined for a specified value of σ_m, R (R=σ_min/σ_max), or A (A=σ_a/σ_m). Most determinations of the fatigue properties of materials have been made in completed reversed bending, where the mean stress is zero.

It will be noted that this S-N curve is concerned chiefly with fatigue failure at high numbers of cycles (N > 10⁵ cycles). Under these conditions the stress, on a gross scale, is elastic, but as we shall see shortly the metal deforms plastically in a highly localized way. At higher stresses the fatigue life is progressively decreased, but the gross plastic deformation makes interpretation difficult in terms of stress. For the low-cycle fatigue region (N <>4 or 10⁵ cycles) tests are conducted with controlled cycles of elastic plus plastic strain instead of controlled load or stress cycles.

The usual procedure for determining an S-N curve is to test the first specimen at a high stress where failure is expected in a fairly short number of cycles, e.g., at about two-thirds the static tensile strength of the material. The test stress is decreased for each succeeding specimen until one or two specimens do not fail in the specified numbers of cycles, which is usually at least 10⁷ cycles.

The highest stress at which a runout (non-failure) is obtained is taken as the fatigue limit. For materials without a fatigue limit the test is usually terminated for practical considerations at a low stress where the life is about 10⁸ or 5x10⁸ cycles. The S-N curve is usually determined with about 8 to 12 specimens.

Statistical Nature of Fatigue

A considerable amount of interest has been shown in the statistical analysis of fatigue data and in reasons for the variability in fatigue-test results. Since fatigue life and fatigue limit are statistical quantities, it must be realized that considerable deviation from an average curve determined with only a few specimens is to be expected.

It is necessary to think in terms of the probability of a specimen attaining a certain life at a given stress or the probability of failure at a given stress in the vicinity of the fatigue limit. To do this requires the testing of considerably more specimens than in the past so that the statistical parameters for estimating these probabilities can be determined.

The basic method for expressing fatigue data should then be a three-dimensional surface representing the relationship between stress, number of cycles to failure, and probability of failure.

In determining the fatigue limit of a material, it should be recognized that each specimen has its own fatigue limit, a stress above which it will fail but below which it will not fail, and that this critical stress varies from specimen to specimen for very obscure reasons. It is known that inclusions in steel have an important effect on the fatigue limit and its variability, but even vacuum-melted steel shows appreciable scatter in fatigue limit.

The statistical problem of accurately determining the fatigue limit is complicated by the fact that we cannot measure the individual value of the fatigue limit for any given specimen. We can only test a specimen at a particular stress, and if the specimen fails, then the stress was somewhere above the fatigue limit of the specimen. The two statistical methods which are used for making a statistical estimate of the fatigue limit are called probit analysis and the staircase method. The procedures for applying these methods of analysis to the determination of the fatigue limit have been well established.

Effect of Mean Stress on Fatigue

Much of the fatigue data in the literature have been determined for conditions of completely reversed cycles of stress, σ_m = 0. However, conditions are frequently met in engineering practice where the stress situation consists of an alternating stress and a superimposed mean, or steady, stress. There are several possible methods of determining an S-N diagram for a situation where the mean stress is not equal to zero.

Cyclic Stress-Strain Curve

Cyclic strain controlled fatigue, as opposed to our previous discussion of cyclic stress controlled fatigue, occurs when the strain amplitude is held constant during cycling. Strain controlled cyclic loading is found in thermal cycling, where a component expands and contracts in response to fluctuations in the operating temperature. In a more general view, the localized plastic strains at a notch subjected to either cyclic stress or strain conditions result in strain controlled conditions near the root of the notch due to the constraint effect of the larger surrounding mass of essentially elastically deformed material.

Since plastic deformation is not completely reversible, modifications to the structure occur during cyclic straining and these can result in changes in the stress-strain response. Depending on the initial state a metal may undergo cyclic hardening, cyclic softening, or remain cyclically stable. It is not uncommon for all three behaviors to occur in a given material depending on the initial state of the material and the test conditions.

Generally the hysteresis loop stabilizes after about 100 cycles and the material arrives at an equilibrium condition for the imposed strain amplitude. The cyclically stabilized stress-strain curve may be quite different from the stress-strain curve obtained on monotonic static loading. The cyclic stress-strain curve is usually determined by connecting the tips of stable hysteresis loops from constant-strain-amplitude fatigue tests of specimens cycled at different strain amplitudes. Under conditions where saturation of the hysteresis loop is not obtained, the maximum stress amplitude for hardening or the minimum stress amplitude for softening is used. Sometimes the stress is taken at 50 percent of the life to failure. Several shortcut procedures have been developed.

Low-Cycle Fatigue

Although historically fatigue studies have been concerned with conditions of service in which failure occurred at more than 10⁴ cycles of stress, there is growing recognition of engineering failures which occur at relatively high stress and low numbers of cycles to failure. This type of fatigue failure must be considered in the design of nuclear pressure vessels, steam turbines, and most other types of power machinery. Low-cycle fatigue conditions frequently are created where the repeated stresses are of thermal origin. Since thermal stresses arise from the thermal expansion of the material, it is easy to see that in this case fatigue results from cyclic strain rather than from cyclic stress.

The first part of this article has introduced a number of terms dealing with brittle fracture, such as NDT, FTE, FTP, etc. The tests for determining these transition temperatures have been described. Before seeing how they are used in engineering design through the fracture analysis diagram, we redefine these transition points through reference to basic properties of the tension lest.

The subambient temperature dependence of yield strength σ_o (R_p0.2) and ultimate tensile strength σ_u in a bcc metal are shown in Fig.1.

For an unnotched specimen without flaws the material is ductile until a very low temperature, point A, where σ_o = σ_u. Point A represents the NDT temperature for a flaw-free material. The curve BCD represents the fracture strength of a specimen containing a small flaw (a <>f ≈ σ_o. Point C represents the NDT for a specimen with a small crack or flaw.

Fig.1. Temperature dependence of yield strength (σ_o), tensile strength (σ_u), and fracture strength for a steel containing flaws of different sizes

The presence of a small flaw raises the NDT of a steel by about 200°F (110°C). Increasing the flaw size decreases the fracture stress curve, as in curve EF, until with increasing flaw size a limiting curve of fracture stress HJKL is reached. Below the NDT the limiting safe stress is 5,000 to 8,000 psi (∼35 to 55 MPa).

Above the NDT the stress required for the unstable propagation of a long flaw (JKL) rises sharply with increasing temperature. This is the crack-arrest temperature curve (CAT). The CAT defines the highest temperature at which unstable crack propagation can occur at any stress level. Fracture will not occur for any point to the right of the CAT curve.

The temperature above which elastic stresses cannot propagate a crack is the fracture transition elastic (FTE). This is defined by the temperature when the CAT curve crosses the yield-strength curve (point K). The fracture transition plastic (FTP) is the temperature where the CAT curve crosses the tensile-strength curve (point L). Above this temperature the material behaves as if it is flaw-free, for any crack, no matter how large, cannot propagate as an unstable fracture.

Data obtained from the DWT and other large-scale fracture tests have been, assembled by Pellini and coworkers into a useful design procedure called the fracture analysis diagram (FAD). The NDT as determined by the DWT provides a key data point to start construction of the fracture analysis diagram. For mild steel below the NDT the CAT curve is flat.

A stress level in excess of 5,000 to 8,000 psi (35 to 55 MPa) causes brittle fracture regardless of the size of the initial flaw. Extensive correlation between the NDT and Robertson CAT tests for a variety of structural steels have shown that the CAT curve bears a fixed relationship to the NDT temperature. Thus, the NDT+30°F provides a conservative estimate of the CAT curve at stress of σ_o/2. NDT+60°F provides an estimate of the CAT at σ = σ_o, that is, the FTE and NDT+120°F provides an estimate of the FTP. Therefore, for structural steels, once the NDT has been determined, the entire scope of the CAT curve can be established well enough for engineering design.

The curve that has been traced out on Fig. 2 represents the worse possible case for large flaws in excess of 24 in.

Fig.2 Fracture-analysis diagram showing influence of various initial flaw sizes.

One can envision a spectrum of curves translated upward and to the left for smaller, less severe flaws. Correlation with service failures and other tests has allowed the approximate determination of curves for a variety of initial flaw sizes. Thus, the FAD provides a generalized relationship of flaw size, stress, and temperature for low-carbon structural steels of the type used in ship construction.

The fracture analysis diagram can be used several ways in design. One simple approach would be to use the FAD to select a steel which has an FTE that is lower than the lowest expected service temperature. With this criterion the worst expected flaw would not propagate so long as the stress remained elastic.

However, this procedure may prove to be too expensive and overconservative. A slightly less conservative design against brittle fracture, but still a practical approach, would be to design on the basis of an allowable stress level not exceeding σ_o/2. From Fig. 2 we see that any crack will not propagate under this stress so long as the temperature is not below NDT+30°F. If for example, the service temperature is not expected to be below 10°F, we would select a steel whose NDT is 10° - 30°, that is -20°F.

The dynamic tear test (DT) can be used to construct the FAD. Below the NDT the fracture is brittle and has a flat, featureless surface devoid of tiny shear lips. At temperatures above the NDT there is a sharp rise in energy for fracture and the fracture surfaces begin to develop shear lips. The shear lips become progressively more prominent as the temperature is increased to the FTE.

Above the FTE the fracture is ductile, void coalescence-type fracture. The fracture surface is a fibrous slant fracture. The upper shelf of energy represents the FTP. The lower half of the DT energy curve traces the temperature course of the CAT curve from NDT to FTE.

The DT test is a highly versatile test because it is equally useful with low-strength ductile materials which show a high upper energy shelf and with high-strength low-toughness materials which have a low value of upper shelf energy. The large size of the DT specimen provides a high degree of triaxial constraint and results in a minimum of scatter. Extensive correlations are being developed between DT results and fracture toughness and C_v test data.

The Brittle – Fracture Problem

During World War II a great deal of attention was directed to the brittle failure of welded Liberty ships and T-2 tankers. Some of these ships broke completely in two, while, in other instances, the fracture did not completely disable the ship. Most of the failure occurred during the winter months. Failures occurred both when the ships were in heavy seas and when they were anchored at dock. These calamities focused attention on the fact that normally ductile mild steel can become brittle under certain conditions.

A broad research program was undertaken to find the causes of these failures and to prescribe the remedies for their future prevention. In addition to research designed to find answers to a pressing problem, other research was aimed at gaining a better understanding of the mechanism of brittle fracture and fracture in general. While the brittle failure of ships concentrated great attention to brittle failure in mild steel, it is important to understand that this is not the only application where brittle fracture is a problem. Brittle failures in tanks, pressure vessels, pipelines, and bridges have been documented as far back as the year 1886.

Three basic factors contribute to a brittle-cleavage type of fracture. They are

1. a triaxial state of stress,
2. a low temperature, and
3. a high strain rate or rapid rate of loading.

All three of these factors do not have to be present at the same time to produce brittle fracture. A triaxial state of stress, such as exists at a notch, and low temperature are responsible for most service failures of the brittle type. However, since these effects are accentuated at a high rate of loading, many types of impact tests have been used to determine the susceptibility of materials to brittle behavior. Steels which have identical properties when tested in tension or torsion at slow strain rates can show pronounced differences in their tendency for brittle fracture when tested in a notched-impact test.

Since the ship failures occurred primarily in structures of welded construction, it was considered for a time that this method of fabrication was not suitable for service where brittle fracture might be encountered. A great deal of research has since demonstrated that welding, per se, is not inferior in this respect to other types of construction. However, strict quality control is needed to prevent weld defects which can act as stress raisers or notches. New electrodes have been developed that make it possible to make a weld with better properties than the mild-steel plate.

The design of a welded structure is more critical than the design of an equivalent riveted structure, and much effort has gone into the development of safe designs for welded structures. It is important to eliminate all stress raisers and to avoid making the structure too rigid. To this end, riveted sections, known as crack arresters, were incorporated in some of the wartime ships so that, if a brittle failure did occur, it would not propagate completely through the structure.

Notched-bar Impact Tests

Various types of notched-bar impact tests are used to determine the tendency of a material to behave in a brittle manner. This type of test will detect differences between materials which arc not observable in a tension test. The results obtained from notched-bar tests are not readily expressed in terms of design requirements, since it is not possible to measure the components of the triaxial stress condition at the notch. Furthermore, there is no general agreement on the interpretation or significance of results obtained with this type of test.

A large number of notched-bar test specimens of different design have been used by investigators of the brittle fracture of metals. Two classes of specimens have been standardized for notched-impact testing. Charpy bar specimens are used most commonly in the United States, while the Izod specimen is favored in Great Britain.

The Charpy specimen has a square cross section (10x10 mm) and contains a 45° V notch, 2 mm deep with a 0.25 mm root radius. The specimen is supported as a beam in a horizontal position and loaded behind the notch by the impact of a heavy swinging pendulum. The specimen is forced to bend and fracture at a high strain rate on the order of 103 s-1. The Izod specimen, which is used rarely today, has either a circular or square cross section and contains a V notch near the clamped end.

The principal measurement from the impact test is the energy absorbed in fracturing the specimen. After breaking the test bar, the pendulum rebounds to a height which decreases as the energy absorbed in fracture increases. The energy absorbed in fracture, usually expressed in joules, is rending directly from a calibrated dial on the impact tester.

The notched-bar impact test is most meaningful when conducted over a range of temperatures so that the temperature at which the ductile-to-brittle transition takes place can be determined.

The principal advantage of the Charpy V-notch impact test is that it is a relatively simple test that utilizes a relatively cheap, small test specimen. Tests can readily be carried out over a range of subambient temperatures. Moreover, the design of the test specimen is well suited for measuring differences in notch toughness in low-strength materials such as structural steels. The test is used for comparing the influence of alloy studies and heat treatment on notch toughness. It frequently is used for quality control and material acceptance purposes.
Instrumented Charpy Test

The ordinary Charpy test measures the total energy absorbed in fracturing the specimen. Additional information can be obtained if the impact tester is instrumented to provide a load-line history of the specimen during each test. With this kind of record it is possible to determine the energy required for initialing fracture and the energy required for propagating fracture. It also yields information on the load for general yielding, the maximum load, and the fracture, load.

Because the root of the notch in a Charpy specimen is not as sharp as is used in fracture mechanics tests, there has been a trend toward using standard Charpy specimens which arc precracked by the introduction of a fatigue crack at the tip of the V notch. These precracked specimens have been used in the instrumented Charpy test to measure dynamic fracture toughness values (KId).
Significance of Transition-Temperature Curve

The chief engineering use of the Charpy test is in selecting materials which are resistant to brittle fracture by means of transition-temperature curves. The design philosophy is to select a material which has sufficient notch toughness when subjected to severe service conditions so that the load-carrying ability of the structural member can be calculated by standard strength of materials methods without considering the fracture properties of the material or stress concentration effects of cracks or flaws.

The transition-temperature behavior of a wide spectrum of materials falls into the three categories. Medium- and low-strength fcc metals and most hep metals have such high notch toughness that brittle fracture is not a problem unless there is some special reactive chemical environment. High-strength materials (s0 > E/150) have such low notch toughness that brittle fracture can occur at nominal stresses in the elastic range at all temperatures and strain rates when flaws ace present.

High-strength steel, aluminum and titanium alloys fall into this category. At low temperature fracture occurs by brittle cleavage, while at higher temperatures fracture occurs by low-energy rupture. It is under these conditions that fracture mechanics analysis is useful and appropriate.

The notch toughness of low- and medium-strength bcc metals, as well as Be, Zn, and ceramic materials is strongly dependent on temperature. At low temperature the fracture occurs by cleavage while at high temperature the fracture occurs by ductile rupture. Thus, there is a transition from notch brittle to notch tough behavior with increasing temperature. In metals this transition occurs at 0.1 to 0.2 of the absolute melting temperature Tm, while in ceramics the transition occurs at about 0.5 to 0.7 Tm.

A well-defined criterion is to base the transition temperature on the temperature at which the fracture becomes 100 percent cleavage. This point is known as nil ductility temperature (NDT). The NDT is the temperature at which fracture initiates with essentially no prior plastic deformation. Below the NDT the probability of ductile fracture is negligible.
Metallurgical Factors Affecting Transition Temperature

Changes in transition temperature of over 55°C (100°F) can be produced by changes in the chemical composition or microstructure of mild steel. The largest changes in transition temperature result from changes in the amount of carbon and manganese. This transition temperature is lowered about 5.5°C (10°F) for each increase of 0.1 percent manganese. Increasing the carbon content also has a pronounced effect on the maximum energy and the shape of the energy transition-tempera lure curves.

The Mn/C ratio should be at least 3/1 for satisfactory notch toughness. A maximum decrease of about 55°C (100°F) in transition temperature appears possible by going to higher Mn/C ratios.

Phosphorus also has a strong effect in raising the transition temperature. The role of nitrogen is difficult to assess because of its interaction with other elements. It is, however, generally considered to be detrimental to notch toughness.

Nickel is generally accepted to be beneficial to notch toughness in amounts up to 2 percent and seems to be particularly effective in lowering the ductility transition temperature. Silicon, in amounts over 0.25 percent, appears to raise the transition temperature. Molybdenum raises the transition almost as rapidly as carbon, while chromium has little effect.

Notch toughness is particularly influenced by oxygen. For high-purity iron it was found that oxygen contents above 0.003 percent produced intergranular fracture and corresponding low energy absorption.

Grain size has a strong effect on transition temperature. An increase of one ASTM number in the ferrite grain size (actually a decrease in grain diameter), results in a decrease in transition temperature of 16°C (30°F) for mild steel. Decreasing the grain diameter from ASTM grain size 5 to ASTM grain size 10 can change the 10 ft/lb Charpy V-notch transition temperature from about 39°C to -33°C (70°F to -60°F).

The energy absorbed in the impact test of an alloy steel at a given test temperature generally increases with increasing tempering temperature. However, there is a minimum in the curve in the general region of 200 to 320°C (400 to 600°F). This has been called 260°C (500°F) embritilement, but because the temperature at which it occurs depends on both the composition of the steel and the tempering time, a more appropriate name is tempered-martensite embrittlement.
Drop-Weight Test and Other Large-Scale Tests

Probably the chief deficiency of the Charpy impact test is that the small specimen is not always a realistic model of the actual situation. Not only does the small specimen lead to considerable scatter, but a specimen with a thickness of 10 mm (0.394 in) cannot provide the same constraint as would be found in a structure with a much greater thickness.

The most logical approach to this problem is the development of tests that are capable of handling specimens at least several inches thick. The development of such tests and their rational method of analysis has been chiefly the work of Pellini and his coworkers at the Naval Research Laboratory. The basic need for large specimens resulted from the inability to produce fracture in small laboratory.

The first development was the explosion-crack-starter test which featured a short, brittle weld bead deposited on the surface of a 14x14x1 in steel plate. The plate was placed over a circular die and dynamically loaded with an explosive charge. The brittle weld bead introduces a small natural crack in the test plate similar to a weld-defect crack. Tests are carried out over a range of temperature and the appearance of the fracture determines the various transition temperatures. Below the NDT the fracture is a flat fracture running completely to the edges of the test plate.

Above the nil ductility temperature a plastic bulge forms in the center of the plate, but the fracture is still a flat elastic fracture out to the plate edge. At still higher temperature the fracture does not propagate outside of the bulged region. The temperature at which elastic fracture no longer propagates to the edge of the plate is called the fracture transition elastic (FTE). The FTE marks the highest temperature of fracture propagation by purely elastic stresses. At yet higher temperature the extensive plasticity results in a helmet-type bulge. The temperature above which this fully ductile tearing occurs is the fracture transition plastic (FTP).

Ductile or fibrous fracture
The higher temperature side of the ductile/brittle transition is associated with a much tougher mode of failure, which absorbs much more energy in the impact test. While the failure mode is often referred to as ductile fracture, it could be described as rupture, a slow separation process which, although transgranular, is not markedly crystallographic in nature.

Scanning electron micrographs of the ductile fracture surface, in striking contrast to those from the smooth faceted cleavage surface, reveal a heavily dimpled surface, each depression being associated with a hard particle, either a carbide or non-metallic inclusion.

It is now well established that ductile failure is initiated by the nucleation of voids at second phase particles. In steels these particles are either carbides, sulphide or silicate inclusions. The voids form either by cracking of the particles, or by decohesion at the particle/matrix interfaces, so it is clear that the volume fractions, distribution and morphology of both carbides and of inclusions are important in determining the ductile behavior, not only in the simple tensile test, but in complex working operations.

Therefore, significant variables, which determine ductility of steels, are to be found in the steel-making process, where the nature and distribution of inclusions is partly determined, and in subsequent solidification and working processes. Likewise, the carbide distribution will depend on composition and on steel-making practice, and particularly on the final heat treatment involving the transformation from austenite, which largely determines the carbide size, shape and distribution.

The formation of voids begins very early in a tensile test, as a result of high stresses imposed by dislocation arrays on individual hard particles. Depending on the strength of the particle/matrix bond, the voids occur at varying strains, but for inclusions in steels the bonding is usually weak so voids are observed at low plastic strains.

Many higher strength steels exhibit lower work hardening capacity as shown by relatively flat stress-strain curves in tension. As a result, at high strains the flow localizes in shear bands, where intense deformation leads to decohesion, a type of shear fracture. While the detailed mechanism of this process is not yet clear, it involves the localized interaction of high dislocation densities with carbide particles.

Role of inclusions in ductility
It is now generally recognized that the deformability of inclusions is a crucial factor which plays a major role, not only in service where risk of fracture exists, but also during hot and cold working operations such as rolling, forging, and machining.

Kiessling has divided the inclusions found in steels into five categories relating to their deformation behavior.

1. Al2O3 and calcium aluminates. These arise during deoxidation of molten steels. They are brittle solids, which are in practical terms undependable at all temperatures.
2. Spinel type oxides are undeformable up to 1200°C, but may be deformed above this temperature.
3. Silicates of calcium, manganese, iron and aluminum in various proportions. These inclusions are brittle at room temperature, but increasingly deformable at higher temperatures. The formability increases with decreasing melting point of the silicate, e.g. from aluminum silicate to iron and manganese silicates.
4. FeO and (FeMn)O. These are plastic at room temperature, but appear gradually to become less plastic above 400°C.
5. Manganese sulphide MnS. This common inclusion type is deformable, becoming increasingly so as the temperature falls. There are three main types of MnS inclusion dependent on their mode of formation, which markedly influences their morphology.

It is now known that ductile failure can be associated with any of the types of inclusion listed above, from the brittle alumina type to the much more ductile sulphide inclusions. However, the inclusions are more effective in initiating ductile cracks above a critical size range. The coarser particles lead to higher local stress concentrations, which cause localized rupture and micro crack formation. Some quantitative work has now been done on model systems, e.g. iron-alumina where the progressive effect on ductility of increasing volume fraction of alumina is readily shown. The reduction in yield stress, also observed, arises from stress concentrations around the inclusions and is already evident at relatively low volume fractions.

The presence of particles in the size range 1-35 μm broadens substantially the temperature range of the ductile/brittle transition in impact tests and also lowers the energy absorbed during ductile failure, the shelf energy. A fine dispersion of non-brittle type inclusions can delay cleavage fracture by localized relaxation of stresses with a concomitant increase in yield stress.

Regarding cyclic stressing, it appears that inclusions must reach a critical size before they can nucleate a fatigue crack but the size effect depends also very much on the particle shape, e.g. whether spherical or angular. It has been found in some steels, e.g. ball bearing steels, that fatigue cracks originate only at brittle oxide inclusions, and not at manganese sulphide particles or oxides coated with manganese sulphide. In such circumstances the stresses, which develop at particle interfaces with the steel matrix, as a result of differences in thermal expansion, appear to play an important part. It has been found that the highest stresses arise in calcium aluminates, alumina and spinel inclusions, which have substantially smaller thermal expansion coefficients than steel. These inclusions have the most deleterious effects on fatigue life.

The behavior of ductile inclusions such as MnS during fabrication processes involving deformation has a marked effect on the ductility of the final product. Types I and III manganese sulphide will be deformed to ellipsoidal shapes, while Type II colonies will rotate during rolling into the rolling plane, giving rise to very much reduced toughness and ductility in the transverse direction. This type of sulphide precipitate is the most harmful so efforts are now made to eliminate it by addition of strong sulphide forming elements such as Ti, Zr and Ca.

The lack of ductility is undoubtedly encouraged by the formation at the inclusion interfaces of voids because the MnS contracts more than the iron matrix on cooling, and the interfacial bond is probably insufficiently strong to suppress void formation. The variation in ductility with direction in rolled steels can be extreme because of the directionality of the strings of sulphide inclusions, and this in turn can adversely affect ductility during many working operations.

Cracking can also occur during welding of steel sheet with low transverse ductility. This takes place particularly in the parent plate under butt welds, the cracks following the line of the sulphide inclusion stringers. The phenomenon is referred to as lamellar tearing.

Role of carbides in ductility
The ductility of steel is also influenced by the carbide distribution, which can vary from spheroidal particles to lamellar pearlitic cementite. Comparing spheroidal cementite with sulphides of similar morphology, the carbide particles are stronger and do not crack or exhibit decohesion at small strains, with the result that a spheroidized steel can withstand substantial deformation before voids are nucleated and so exhibits good ductility. The strain needed for void nucleation decreases with increasing volume fraction of carbide and so can be linked to the carbon content of the steel.

Pearlitic cementite also does not crack at small strains, but the critical strain for void nucleation is lower than for spheroidized carbides. Another factor, which reduces the overall ductility of pearlitic steels, is the fact that once a single lamella cracks, the crack is transmitted over much of a pearlite colony leading to well-defined cracks in the pearlite regions. The result is that the normal ductile dimpled fractures are obtained with fractured pearlite at the base of the dimples.

Intergranular embrittlement

While cleavage fracture in steels is a common form of embrittlement, in many cases the embrittlement is intergranular (IG), i.e. it takes place along the grain boundaries, usually the former austenitic boundaries. This behavior is encountered in as-quenched steels, on tempering (temper embrittlement), after heating at very high austenitizing temperatures (overheating and burning), and in rock-candy fracture in cast steels.

These forms of embrittlement are exhibited at or around room temperature. There are, however, other phenomena involving failure along grain boundaries, which are essentially high temperature events, e.g., hot-shortness during the hot working of steels and high temperature creep failure.

It is clear that no mechanism will explain the various types of embrittlement, but the processes leading to intergranular fracture all lead to reduced cohesion along the grain boundaries. This can arise in different ways but the most relevant appear to be

* Segregation of solute atoms preferentially to grain boundaries
* Distribution of second phase particles at grain boundaries.

Temper embrittlement

Many alloy steels when tempered in the range 500°C-650°C following quenching to form martensite become progressively embrittled in an intergranular way. A similar phenomenon can also occur when the steels are continuously cooled through the critical range. It is revealed by the effect on the notched bar impact test, where the transition temperature is raised and the shelf energy lowered, the transgranular fracture mode being replaced by an Intergranular embrittlement (IG mode) below the transition temperature.

This phenomenon is now known to be associated with the segregation of certain elements to the grain boundaries, which reduce the intergranular cohesion of iron. Elements, which segregate, fall into three groups of the Periodic Classification. It has been shown that many of these elements reduce the surface energy of iron substantially and would, therefore, be expected, to lower the grain boundary energy and to reduce cohesion. Moreover, the actual segregation of atoms to the boundaries has been conclusively demonstrated by Auger electron spectroscopy on specimens fractured intergranularly within the vacuum system of the apparatus.

This technique has allowed the precise determination of the concentrations of segregating species at the boundaries, usually expressed in terms of fractions of a monolayer of atoms. These fractions vary between about 0.3 and 2.0 for steels containing the above elements, usually in bulk concentrations well below 0.1 wt%.

With the individual elements, the tendency to embrittle appears to increase both with Group and Period number, i.e. S, Se and Te in increasing order are the most surface-active elements in iron. However, it is doubtful whether they contribute greatly to temper embrittlement because they combine strongly with elements such as Mn and Cr, which effectively reduce their solubility in iron to very low levels.

While the elements in Groups IVB and VB are less surface active, they play a greater role in embrittlement because they interact with certain metallic elements, e.g. Ni and Mn, which are common alloying elements in steels. These interactions lead to co segregation of alloy element and impurity elements at the grain boundaries, and to resultant lowering of cohesion by the impurity element. Analysis of the composition of grain boundaries by Auger spectroscopy has confirmed strong interactions between Ni-Sb, Ni-P, Ni-Sn and Mn-Sb.

Therefore, the driving force for segregation to boundaries is a stronger interaction between the alloying element and the impurity element than between either of these and iron. If the interaction is too strong, segregation does not take place. Instead a scavenging effect is obtained, as exemplified by Ti-P and Mo-P interactions in Ni-Cr steels. In this connection it is well known that molybdenum additions to Ni-Cr steels can eliminate temper embrittlement. A third inter-alloy effect is also possible which is that one alloying element, e.g. Cr, promotes the segregation of Ni and P, also Ni and Sb.

In addition to solute atom segregation to boundaries, there are also microstructural factors, which influence the intensity of temper embrittlement. In most alloy steels in which this phenomenon is encountered the grain boundaries are also the sites for carbide precipitation, either cementite or alloy carbides. It is likely that these provide the sites for IG crack nuclei.

As in the nucleation of cleavage fracture, dislocations impinge on a grain boundary carbide particle and as it is not deformable the carbide will either crack or the ferrite/carbide interface will part. The latter separation is more likely if the interracial energy has been reduced by segregation of impurity atoms to it. This can occur by rejection of these impurity atoms during the growth of the carbide or by equilibrium segregation. Interfacial separation has been observed in iron containing coarse grain boundary iron carbide, the interfaces of which contained Sb, As, Sn or P. The effectiveness of this nucleating stage of IG crack formation will be influenced by the extent of grain boundary carbide and the concentration of surface active impurities in the steel, in particular at carbide /matrix interfaces.

The propagation of the grain boundary crack will depend not only on the cohesion of the boundary but also on the relative toughness of the grain interior. For example, if the grain interior has a microstructure, which gives high toughness, the IG crack nucleus is more likely to propagate along the boundary. Further, as the yield stress of a steel rises sharply with decreasing temperature IG failure will, like cleavage fracture, be encouraged by reducing the testing temperature. Increasing the austenite grain size, by use of high austenitizing temperatures, under the same conditions, should increase the embrittlement because the size of the dislocation arrays impinging on the grain boundary carbides will be larger and thus more effective in forming crack nuclei.

The optimum temperature range for temper embrittlement is between 500 and 575°C. However, in some steels embrittlement occurs in the range 250-400°C. This phenomenon is called 350° embrittlement, and occurs at too low a temperature to attribute it to the diffusion of metalloids such as Sb to the austenite grain boundaries. It seems more likely that it could arise from smaller and more mobile atoms, e.g. P, which would be rejected during grain boundary growth of iron carbide, which takes place in this temperature range. However, the morphology of the grain boundary Fe3C, if predominantly sheet-like, could be a prime cause of low ductility in this temperature range.

Stress corrosion cracking (SCC) involves failure by cracking in the presence of both a stress and of a corrosive medium. It can occur in either a transgranular or an intergranular mode. The latter mode appears to be encouraged in some alloy steels by heat treatments, which produce temper embrittlement. For example, a temper embrittled Cr-Mo steel cracks along the grain boundaries when stressed in a boiling NaOH solution. Use of a heat treatment to remove the temper embrittlement also removes the sensitivity to stress corrosion.

Overheating and burning
Many alloy steels when held in the range 1200-1400°C and subsequently heat treated by quenching and tempering, fail intergranularly along the original austenitic boundaries. There is strong evidence to suggest that this phenomenon is associated with the segregation of sulphur to the austenite grain boundaries at the high temperature, and indeed the phenomenon is not obtained when the sulphur content of a steel is less than 0.002%.

Sulphur has been shown to be one of the most surface-active elements in iron. Work by Goux and colleagues on pure iron-sulphur alloys has shown that an increase in sulphur content from 5 to 25 ppm raises the ductile/brittle transition temperature by over 200°C. Further, Auger spectroscopy on the intergranular fracture surfaces has given direct evidence of sulphur segregation.

However, this embrittling effect of sulphur as a result of equilibrium segregation is only seen in pure iron and not in steels where there are other impurity elements, and also where interaction of sulphur occurs with alloying elements, notably manganese and chromium. The presence of manganese substantially lowers the solubility of sulphur in both γ- and α-iron, with the result that when sulphur segregates to high temperature austenite boundaries, manganese sulphide is either formed there or during subsequent cooling.

In either case, the manganese sulphide particles lying on the austenite boundaries are revealed by electron microscopy of the intergranular fracture surfaces where they are associated with small dimples. Thus, the grain boundary fracture process is nucleated by the sulphide particles, and the mode of fracture will clearly be determined by the size distribution, which will in turn be controlled by the rate of cooling from the austenite temperature, assuming that MnS forms during cooling. With very slow cooling rates, the intergranular fracture is replaced by cleavage or transgranular fibrous fracture as the grain boundary sulphide distribution is too coarse.

Oil quenching from the austenitizing temperature does not eliminate the phenomenon which is accentuated on tempering in the range 600-650°C. This arises from the redistribution of carbides, which will strengthen the grain interiors, and by precipitation at the grain boundaries, which may further reduce grain boundary ductility.

When very high austenitizing temperatures are used (1400-1450°C) extensive MnS precipitate is formed, often in impressive dendritic forms. In extreme cases, partial formation of liquid phase occurs (liquation) which, on subsequent heat treatment, greatly accentuates the intergranular embrittlement. In the absence of manganese, e.g. in wrought iron, liquid films of the iron-iron sulphide eutectic cause embrittlement during hot working processes down to 1000°C (hot shortness).

The fact that in normal steels burning occurs only at very high temperatures should not be allowed for detract from its significance. The phenomenon may well intrude in high temperature working processes such as forging if temperature control is not exact, but in any case it can certainly be significant in steels which are cast, and by definition pass through the burning and overheating temperature range. In many cases intergranular fracture is encountered in cast alloy steels where the as-cast grain structure is clearly involved. Examination of the fractures reveals extensive grain boundary sheets of manganese sulphide, often only 0.2-0.5 μm thick but covering large areas.

Marked embrittlement can occur in the as-cast state or after subsequent heat treatment in the range 500-650°C, and is often referred to as cast brittleness or rock candy fracture. Precipitation of aluminum nitride may also play an important role in this type of fracture.

Most groups of alloys can exhibit failure by cracking in circumstances where the apparent applied stress is well below that at which failure would normally be expected. Steels are no exception to this, and probably exhibit a wider variety of failure mechanisms than any other category of material. While ultimate failure under excessive stress must occur and can be reasonably predicted by appropriate mechanical tests, premature failure is always dangerous, involving a considerable element of unpredictability.

However, a detailed knowledge of structure and of the distribution of impurities in steels is gradually leading to a much better understanding of the origins and mechanisms of the various types of cracks encountered. Furthermore, the now well-established science of fracture mechanics allows the quantitative assessment of growth of cracks in various stress situations, to an extent that it is now frequently possible to predict the stress level to which steel structures can be confidently subjected without the risk of sudden failure.

Cleavage fracture in iron and steel
Cleavage fracture is familiar in many minerals and inorganic crystalline solids as a crack propagation frequently associated with very little plastic deformation and occurring in a crystallographic fashion along planes of low indices, i.e. high atomic density.

This behavior would appear to be an intrinsic characteristic of iron but it has been shown that iron, highly purified by zone refining and containing minimal concentrations of carbon, oxygen and nitrogen, is very ductile even at extremely low temperatures. For example, at 4.2 K reductions in area in tensile tests of up to 90 % have been observed with iron specimens of the highest available purity.

As the carbon and nitrogen content of the iron is increased, the transition from ductile to brittle cleavage behavior takes place at increasing temperatures, until in some steels this can occur at ambient and above-ambient temperatures. Clearly, the significant variables in such a transition are of great basic and practical importance.

Factors influencing the onset of cleavage fracture
The propagation of a cleavage crack in iron and steel requires much less energy than that associated with the growth of a ductile crack. There are several factors, some interrelated, which play an important part in the initiation of cleavage fracture:

* The temperature dependence of the yield stress
* The development of a sharp yield point
* Nucleation of cracks at twins
* Nucleation of cracks at carbide particles
* Grain size.

All body-centered cubic metals, including iron, show a marked temperature dependence of the yield stress, even when the interstitial impurity content is very low, i.e. the stress necessary to move dislocations, the Peierls-Nabarro stress, is strongly temperature dependent. This means that as the temperature is lowered the first dislocations to move will do so more rapidly as the velocity is proportional to the stress, and so the chances of forming a crack nucleus, e.g. by dislocation coalescence, will increase. The interstitial atoms, carbon and nitrogen, will cause the steel to exhibit a sharp yield point either by the catastrophic breakaway of dislocations from their interstitial atom atmospheres (Cottrell-Bilby theory), or by the rapid movement of freshly generated dislocations (Oilman-Johnson theory).

In either case, the conditions are suitable for the localized rapid movement of dislocations as a result of high stresses, which provides a favorable situation for the nucleation of cracks by dislocation coalescence.

The nucleation and the propagation of a cleavage crack must be distinguished clearly. Nucleation occurs when a critical value of the effective shear stress is reached, corresponding to a critical grouping, ideally a pile-up, of dislocations which can create a crack nucleus, e.g. by fracturing a carbide particle.

In contrast, propagation of a crack depends on the magnitude of the local tensile stress, which must reach a critical level. Simple models of slip-nucleated fracture assume either interaction of dislocations or cracks formed in grain boundary carbides. However, recently it has been realized that both these structural features must be taken into account in deriving an expression for the critical fracture stress. This critical stress does not appear to be temperature dependent. At low temperatures the yield stress is higher, so the crack propagates when the plastic zone ahead of the crack is small, whereas at higher temperatures, the yield stress being smaller, a larger plastic zone is required to achieve the critical local tensile stress.

This tensile stress has been determined for a wide variety of mild steels. The scatter probably arises from differences in test temperature and carbide dimensions. This is conclusive evidence for the role of finer grain sizes in increasing the resistance to crack propagation. Regarding grain boundary carbide size, effective crack nuclei will occur in particles above a certain critical size so that, if the size distribution of carbide particles in particular steel is known, it should be possible to predict its critical fracture stress.

Therefore, in mild steels in which the structure is essentially ferrite grains containing carbide particles, the particle size distribution of carbides is the most important factor. In contrast, in bainitic and martensitic steels the austenite grains transform to lath structures where the lath width is usually between 0.2 and 2 ìm. The laths occur in bundles or packets with low angle boundaries between the laths. Larger misorientations occur across packet boundaries. In such structures, the packet width is the main micro structural feature controlling cleavage crack propagation.

Practical aspects of brittle fracture
At the onset of fracture, elastic energy stored in the stressed steel is only partly used for creation of the new surfaces and the associated plastic deformation and the remainder provides kinetic energy to the crack.

The phenomenon of brittle fracture became particularly prevalent with the introduction of welding as the major steel fabrication technique. Previously, brittle cracks often stopped at the joints of riveted plates but the steel structures resulting from welding provided continuous paths for crack propagation. Added to this, incorrect welding procedures can give rise to high stress concentrations and also to the formation of weld-zone cracks which may initiate brittle fracture.

While brittle failures of steels have been experienced since the latter half of the nineteenth century when steel began to be used widely for structural work, the most serious failures have occurred later, as the demand for integral large steel structures has greatly increased, e.g. in ships, pipelines, bridges and pressure vessels. Spectacular failures took place in many of the all-welded Liberty ships produced during the Second World War, when nearly 1500 incidents involving serious brittle failure were recognized and nineteen ships broke completely in two without warning.

Despite our increasing understanding of the phenomenon and the great improvements in steel making and in welding since then, serious brittle failures still occur. Brittle fractures of thick-walled steel pressure vessels are reminder that human error and lack of scientific control can be disastrous. Bearing in mind the temperature dependence of the failure behavior, and the widening use of steels at low temperatures, e.g. in Arctic pipelines, for storage of liquid gases etc., it is increasingly necessary to have steels with very low transition temperatures and high fracture toughness.

While there are many variables to consider in achieving this end, including the detailed steel-making practice, the composition including trace elements and the fabrication processes involved, the most important is probably grain size refinement.

The development of high strength low alloy steels (HSLA) or micro-alloyed steels, in the manufacture of which controlled rolling plays a vital part, has led to the production of structural steels with grain sizes combined with good strength levels and low transition temperatures. In these steels, to which small concentrations (<0.1%) of niobium, vanadium or titanium are added, the carbon level is usually less than 0.15 % and often below 0.10 %, so that the carbide phase occupies a small volume fraction. In any case, cementite, which forms relatively coarse particles or lamellas in pearlite, is partly replaced by much finer dispersions of alloy carbides, NbC etc.

Addition of certain other alloying elements to steel, notably manganese and nickel, results in a lowering of the transition temperature. For example, alloy steels with 9 % nickel and less than 0.1 % carbon have a sufficiently low transition temperature to be able to be used for large containers of liquid gases, where the temperature can be as low as 77 K. Below this temperature, austenitic steels have to be used.

Of the elements unavoidably present in steels, phosphorus, which is substantially soluble in an iron, raises the transition temperature and thus must be kept to as low a concentration as possible. On the other hand, sulphur has a very low solubility, and is usually present as manganese sulphide with little effect on the transition temperature but with an important role in ductile fracture. Oxygen is an embrittling element even when present in very small concentrations. However, it is easily removed by deoxidation practice involving elements such as manganese, silicon and aluminum.

Finally, the fabrication process is often of crucial importance. In welding it is essential to have a steel with a low carbon equivalent, i.e. a factor incorporating the effects on harden ability of the common alloying elements. The main hazard in welding is the formation of martensite in the heat-affected zone (HAZ), near the weld, which can readily lead to micro cracks. This can be avoided, not only by control of hardenability but also by preheating the weld area to lead to slower cooling after welding or by post heat treatment of the weld region. However, in some high strength steels, slower cooling may result in the formation of upper bainite in the HAZ, which encourages cleavage fracture.

Attention must also be paid to the possibility of hydrogen absorption leading to embrittlement. The presence of hydrogen in steels often leads to disastrous brittle fracture, e.g. there have been many failures of high strength steels into which hydrogen was introduced during electroplating of protective surface layers. Concentrations of a few parts per million are often sufficient to cause failure. While much hydrogen escapes from steel in the molecular form during treatment, some can remain and precipitate at internal surfaces such as inclusion/matrix and carbide/matrix interfaces, where it forms voids or cracks. Cleavage crack growth then occurs slowly under internal hydrogen pressure, until the critical length for instability is reached, and failure occurs rapidly. Hydrogen embrittlement is not sensitive to composition, but to the strength level of the steel, the problem being most pronounced in high strength alloy steels.

Temper embrittlement is inherent in many steels and can be characterized by reduced impact toughness. The state of temper embrittlement has practically no effect on other mechanical properties at room temperature.

Figure 1 shows schematically the effect of temperature on impact toughness of alloy steel which is strongly liable to temper embrittlement. Many alloy steels have two temperature intervals of temper embrittlement. For instance, irreversible temper brittleness may appear within the interval of 250-400°C and reversible temper brittleness, within 450-650°C.

The impact toughness of quenched steel after tempering at 250-400°C is lower than that obtained on tempering at temperatures below 250°C. If brittle steel tempered at 250-400°C is heated above 400°C and transferred into a tough state, a second tempering at 250-400°C cannot return it to the brittle state. The rate of cooling from the tempering temperature within 250-400°C has no effect on impact toughness.

Steel in the state of irreversible temper embrittlement has a bright intercrystalline fracture at boundaries of former austenitic grains. This type of brittleness is inherent to some extent to all steels, including carbon grades. For that reason medium-temperature tempering is, as a rule not employed in practice, though it can ensure a high yield limit.

Irreversible temper embrittlement is thought to be due to the formation of carbides on decomposition of martensite, in particular, precipitation of carbides in the form of films at grain boundaries. At higher temperatures of tempering, this film disappears and cannot be restored on repeated heating at 250-400°C. Silicon in low-alloy steels can prevent irreversible temper embrittlement by retarding the decomposition of martensite.

The embrittlement on high-temperature tempering may manifest itself in two different ways:

• as a result of heating at 450-600°C (irrespective of the rate of subsequent cooling) and effect of temperature, and
• as a result of tempering at temperatures above 600°C with subsequent slow cooling within the range of 600-450°C.

A high-rate cooling from a tempering temperature above 600°C, for instance, water-cooling, can prevent the appearance of temper embrittlement. On the other hand, a quick cooling on tempering at 450-600°C cannot prevent temper embrittlement. Thus, entering the dangerous temperature interval from either "below" (on heating and holding at that temperature) or from "above" (on slow cooling) can produce the same result.

The most important feature of embrittlement on high-temperature tempering is that the process is reversible. If a steel embrittled through tempering at a temperature above 600°C with subsequent slow cooling or through tempering at 450-600°C (with any rate of cooling) is again heated above 600°C and cooled quickly, its impact toughness will restore to the initial value. If the steel then again enters the dangerous interval of tempering temperatures, it is again embrittled. A new heating at a temperature above 600°C, followed with quick cooling, can eliminate the embrittling effect, and so on. This is why the phenomenon discussed is called reversible embrittlement.

Carbon steels with less than 0.5% Mn are not prone to reversible temper embrittlement. The phenomenon can only appear in alloy steels. Alloying elements may have different effects on steel after tempering at the steel proneness to temper embrittlement. Unfortunately, the most widely used alloying elements, such as chromium, nickel, and manganese, promote temper embrittlement. When taken separately, they produce a weaker effect than in the case of combined alloying. The highest embrittling effect is observed in Cr-Ni and Cr-Mn steels. Small additions of molybdenum (0.2-0.3%) can diminish temper embrittlement, while greater additions enhance the effect.

A fundamental fact is that alloy steels of very high purity are utterly unsusceptible to temper embrittlement which is caused by the presence of various impurities, in the first place of phosphorus, tin, antimony and arsenic, in commercial steels.

The rate and degree of development of temper embrittlement depend on the temperature and time of holding steel within the dangerous temperature interval (450-600°C). With a certain temperature of tempering within this interval, the initial stages of embrittlement appear appreciably sooner than at a higher or a lower temperature.

Many scientists adhered for a long time to the "solution precipitation" hypothesis, according to which the loss in impact toughness was caused by precipitation of some phases, such as phosphides, at grain boundaries. These phases were thought to pass into the á-solution on heating up to approximately 650°C and to precipitate from the solution and embrittle the steel on slow cooling; quick cooling should prevent the precipitation of embrittling phases. As has been found by electron-microscopic analysis, however, there are no special precipitates at grain boundaries in embrittled steel, so that the "solution precipitation" hypothesis turned to be inconsistent.

Another hypothesis explained temper embrittlement by an increased concentration of impurities in boundary layers of the solid solution. This was proved by an increased etchability of grain boundaries in embrittled steel by picric acid. The hypothesis on the leading role of impurity segregates has been fully confirmed in the recent years by a brilliant series of research work using Auger spectroscopy, a method enabling determination of concentrations of elements in monatomic surface layers. Using this method makes it possible to detect segregations of phosphorus and other impurity elements at the fracture surface in embrittled steel and measure their concentrations (as also the concentrations of alloying elements) at the fracture surface. It has also been shown that the development of temper embrittlement is directly linked with the rise of impurity concentration near the prior austenite boundaries.

Owing to equilibrium segregation, the concentration of harmful impurities at the surface of a fracture may exceed tens or hundreds times their average concentration in the steel. The concentration of impurities in commercial purity steels is usually a few thousandths or hundredths of a percent, but amounts to a few percent at the surface of fracture.

As the temperature increases, the diffusion process of grain boundary segregation is accelerated, with the absolute value of equilibrium segregation being simultaneously decreased owing to thermal motion. At temperatures above 600-650°C, the segregation of impurities either disappears fully (Sb) or drops to a very low level (P). On subsequent cooling of the steel in water, the segregates have no time to restore.

The role of alloying elements in the development of temper embrittlement is not less than that of impurities. The segregation of harmful impurities in iron-carbon alloys is so small that causes no temper embrittlement. In the presence of alloying elements (Ni, Cr or Mn), the segregation of impurities increases appreciably. In this process, the alloying elements themselves, which cause no equilibrium segregation in high-purity steels, segregate at grain boundaries in the presence of harmful impurities.

Therefore, we can assume that an alloying element and impurity interact with each other in the á-solution and thus mutually promote their segregation. It can be also assumed that if atoms of an impurity and alloying element attract one another stronger than atoms of that impurity and iron, the segregation of the impurity and alloying element will be mutually enhanced. Namely in this way behave P and Ni, P and Cr, Sb and Ni, Sb and Mn and other "impurity - alloying element" pairs. A second alloying element can additionally enhance segregation of an impurity. For instance, nickel and chromium, when present together in steel, can cause a greater segregation of antimony than might be expected from simple summation of their separate effects.

An increased concentration of harmful impurities in boundary layers of the solid solution, which may be caused by the effect of alloying additions, weakens the intergranular bondage and is one of the main causes why alloy steels containing Ni, Cr or Mn are highly susceptible to temper embrittlement. The main measures to prevent temper embrittlement are as follows:

• of the content of harmful impurities in steel;
• accelerated cooling from the temperature of high-temperature tempering (above 600°C);
• alloying of steel with small additions of molybdenum (0.2-0.3%); and
• subjecting the metal to high-temperature thermo-mechanical treatment.

Current and developing applications for materials at low temperatures include structures, vehicles, and pipeline equipment for arctic environments, storage and transport equipment for liquefied fuel gasses, oxygen and nitrogen, and superconducting machinery, devices and electrical transmission systems. Most of these applications relate to the production and distribution of energy and have attained greater prominence because of the current energy shortage.

According to available information on the fracture toughness of high-strength alloys at low temperatures, the effect of low temperatures on toughness is generally dependent on the alloy base. For many aluminum alloys, the fracture toughness tends to increase or remain generally constant as the testing temperature is decreased. Titanium alloys tend to have lower toughness as the testing temperature is decreased, but the effect is influenced by the alloy content and heat treatment. Certain titanium alloys retain good toughness at very low temperatures. Alloy steels normally exhibit decreasing fracture toughness as the testing temperature is decreased through transition temperature range, when the structure contains ferrite or tempered martensite. The transition temperature is influenced by the alloy content, grain size and heat treatment.

Carbon and low alloy steels represent body-center-cubic (bcc) atomic lattices and exhibit toughness transition temperature ranges either above, at, or below room temperature depending on a number of factors. At temperatures above the transition temperature, the alloy has substantially better toughness than at lower temperatures. Furthermore, the lower strength steels generally are strain-rate sensitive, while the higher strength steels are not strain-rate sensitive

The curves for parent metal and welds in ASTM A517F steel plate indicate that the weld metal and heat-affected zones have lower transition temperatures than the parent metal. However, the weld metal in the specimens of A542 steel had higher transition temperatures than the parent metal. The fracture toughness of A533 Grade B Class 1 steel has been studied extensively for nuclear reactor pressure vessels. This study has shown that for testing temperatures above -100^oF (approx. -70^oC), the toughness increases substantially as the testing temperature is increased.

Thus the required thickness of the specimens must be increased in order to increase the constraint that is necessary at the crack tip to simulate plane-strain conditions at the initiation of fracture.

Results of fracture toughness tests on three ASTM forging steels may have similar general trends in the toughness data, but the compositions, grain sizes, and other factors have marked effects on the transition temperatures. Test results for HY-130 steel indicate that this steel in the temperature range down to -320^oF (approx. -195^oC) is not strain-rate sensitive.

These steels are not intended for use at temperatures in or below the transition temperature range, and there is no accepted method for indicating the specific transition temperature from a transition temperature curve. Furthermore, there is no accepted method relating the transition temperature to a safe minimum service temperature for structural components. However, if Kic data are obtained for given alloy at low temperatures, the critical crack sizes may be estimated in the low-temperature range at the maximum service stress of the structure.

The effects of variations in composition on a series of Ni-Cr-Mo-V steels has been studied in order to show the effects of the alloying elements on the low-temperature fracture toughness. Bars of these steels were quenched and tempered to about 170 ksi yield strength (approx. 1170 MPa) and tested as precracked bend specimens. The effects of carbon and nickel content were the most significant. An increase of carbon content and nickel content from 0.28 to 0.41 raised the transition temperature based on KQ data. Increasing the nickel content from 1.26 to 6.23 percent decreased the KQ transition temperature. This represents one of the major attributes of nickel additions to the alloy steels.

The specimens of D6ac steel were austenitized at about 1650^oF, furnace cooled to 975^oF, and quenched in oil or molten salt according to several different procedures, to simulate quenching of the welded forging that comprise the F111 wing cary-through structure. The high-toughness specimens were quenched in oil, while the medium-toughness specimens were quenched in salt. Regardless of the quench, the yield strength of the specimens was approximately 217 ksi (1495 MPa) after tempering twice at 1000 to 1025^oF. The fracture roughness tests were very sensitive indicators of the effect of the variation in quenching rate on the toughness. The specimens that had the highest toughness at room temperature also had the highest toughness at -65^oF (-54^oC).

Available fracture toughness data at low temperature for other alloy steels: AISI 4340, 300M, HP9-4-20, HP9-4-25, and 18 Ni (200) maraging steel usually have the trend of decreasing toughness as the testing temperature is decreased. The one exception is HP9-4-25 in the temperature range +75 to -75^oF (+24 to -59^oC). At lower temperature, the expected trend would be for the toughness to drop as indicated for HP9-4-20 in the range from -100 to -320^oF (-73 to -195^oC). The data obtained by Steigerwald for AISI 4340 steel and by Wessel for the HP9-4-20 alloy steel were obtained before ASTM Method E 399 was available and are designated as KQ values.

The 18Ni (200) grade maraging steel also exhibits considerable reduction in toughness as the testing temperature is reduced from -100 to -320^oF (-73 to -195^oC), but at -320^oF, this heat of the 200 grade retained a toughness of about 80 ksi in.1/2. From limited information on the toughness of the 200 grade, it appears that there is considerable range in results of KIc tests at room temperature. This level of toughness at -320^oF probably can be achieved only if the alloy has a toughness of about 160 ksi in.1/2 or over at 75^oF (+24^oC).

The effect of low temperatures on the static and dynamic fracture toughness of bend specimens of 18Ni (200) maraging steel is a straight line relationship between the Kic values and the testing temperature in the range from 75 to -320^oF. At -320^oF, the KIc value was about 40 ksi in.1/2, and the alloy is not strain-rate sensitive in the low-temperature range. Tests results on part-through surface-crack specimens of 200 grade maraging steel has shown that these heats had high toughness at 75^oF and also retained relatively good toughness at -320^oF. With optimum welding conditions, the weld metal also retains good strength and toughness at -320^oF.

The effect of carbon additions between 0.3 and 0.8%
In hypoeuteetoid steels containing between 0.3 and 0.8% carbon, proeutectoid ferrite is the continuous phase and forms primarily at austenite grain boundaries. The pearlite forms inside the austenite grains and makes up between 35-100% of the microstructure. More than one colony (set of parallel ferrite and cementite plates) forms within each austenite grain so that the pearlite is polycrystalline.

Since the strength of the pearlite is greater than that of the proeutectoid ferrite, the pearlite constrains the flow of the ferrite. The yield strength and strain-hardening rate of these steels increase with increasing pearlite (carbon) content because the constraint effect increases with increasing amounts of the hard aggregate and because pearlite refines the size of the proeutectoid grains.

In steels containing large-volume fractions of pearlite, deformation in the pearlite can initiate microcleavage crack formation at low temperatures and/or high strain rates. Since the fracture path is primarily along the cleavage plane in the ferrite plates (although there is some intercolony fracture), this indicates that there is some preferred orientation between ferrite plates in adjacent colonies within a prior austenite grain.

The Fracture of Bainitic Steels. The addition of 0.05% molybdenum and boron to low carbon (0.1%) steels is able to suppress the austenite-ferrite transformation, which normally occurs between 700° and 850°C, without affecting the kinetics of the austenite-bainite transformation which then takes place between 675° and 450°C.

Bainite formed between 675° and about 525°C is called "upper bainite" and bainite formed between 525° and 450°C is called "lower bainite". Both structures consist of acicular ferrite and dispersed carbides. The tensile strength of these un-tempered bainites increases from 85,000 to 170,000 psi (585 - 1170 MPa) as the transformation temperature drops from 675° to 450°C.

Since the transformation temperature is determined by the amount of alloying elements (e.g., Mn and Cr) that are present, these elements exert an indirect effect on the yield find tensile strengths. The high strengths obtained in these steels is the result of two effects:

* the progressive refinement of the bainitic ferrite plate size as the transformation temperature is lowered, and
* the fine carbide dispersion, which occurs within the grains of the lower bainite. Fracture characteristics of these steels is strongly dependent on the tensile strength and hence on the transformation temperature.

Two effects should be noted. First, at a given tensile strength level the impact properties of tempered lower bainite are far superior to that of untempered upper bainite. The reason for this behavior is that in upper bainite, as in pearlite, the cleavage facets traverse several bainite grains and the "effective grain size" for fracture is the prior austenite grain size rather than the ferrite grain size.

In lower bainite the cleavage planes in the acicular ferrite are not aligned so that the effective grain size for quasicleavage fracture is the ferrite needle size. Since this is one to two orders of magnitude smaller than the prior austenite grain size, the transition temperature of the lower bainite is much below that of upper bainite, at the same strength level.

A second feature that is important is the distribution of the carbides. In upper bainite these lie along grain boundaries and may promote brittleness by lowering γm as described previously in connection with furnace-cooled ferritic steels. In tempered lower bainite the carbides are more uniformly distributed in the ferrite and raise γm by interfering with cleavage cracks and promoting tearing as in the case of spherodized pearlites.

A second effect that should be noted is the variation of transition temperature with tensile strength in the untempered alloys. In the upper bainite a decrease in transformation temperature produces a refinement of ferrite needle size and this raises Rp0.2.

Tensile strength levels of 120,000 psi (830 MPa) or greater are obtained in lower bainite and the transition temperature decreases with increasing tensile strength. Because the fracture stress of the upper bainite is dependent on austenite grain size, and since the carbide particles are already large, tempering has little effect on tensile and impact properties.

The Fracture of Martensitic Steels
The addition of carbon and other alloying elements to steel retards the transformation of austenite to either ferrite and pearlite, or bainite, and if the cooling rate after austenitizing is sufficiently rapid, the austenite will transform to martensite by a shear process that requires no measurable diffusion of atoms.

The features that are pertinent to the fracture of martensite are as follows:

* Because the transformation occurs at very low temperatures (200°C or lower) the size of the tetragonal ferrite or martensite needle is very small, at least in two of its three dimensions.
* Because the transformation occurs by shear, the carbon atoms do not have time to diffuse out of their lattice position in the austenite and hence the ferrite is supersaturated with carbon; this causes the martensite to have an elongated (bodycentered tetragonal) crystal structure and leads to lattice expansion.
* The martensitic transformation occurs over a range of temperatures because the formation of the first martensite plates increases the difficulty of transforming the remaining austenite. Thus transformation structures can be mixtures of martensite and retained austenite.

To produce stable steel that can be satisfactorily used in engineering applications, it is necessary to temper it. Three stages of tempering occur in high (greater than 0.3%) carbon martensites, tempered for about one hour in various ranges as follows:

1. At temperatures up to about 100°C some of the supersaturated carbon precipitates out of the martensite to form very fine particles of epsilon (hexagonal) carbide, which are dispersed in a martensite that consequently has a decreased carbon content.
2. Between 100° and 300°C any retained austenite is able to transform to bainite and epsilon carbide.
3. In the third stage of tempering, which begins about 200°C, depending on carbon content and alloy composition, the epsilon carbides dissolve and the low carbon martensite loses both its tetragonality and its carbon. As the temperature of tempering increases up to the eutectoid temperatures (723°C), the carbide precipitates coarsen and Rp0.2 decreases. Tempering just below the eutectoid temperature causes the cementite particles to assume a relatively large (1-10 μp) spheroidal shape, similar to that obtained by annealing a pearlitic structure for long periods of time.

Fracture of medium strength steels (620 MPa < Rp0.2 < 1240 MPa)
In addition to the removal of residual stress there are two effects associated with tempering that increase notch toughness. The first is the transformation of retained austenite. The austenite should be transformed at low temperatures (around 300°C) to the tough, acicular lower bainite. If it is transformed by tempering at a higher temperature, say 600°C, the brittle pearlite structure will form. Consequently steels that are to be tempered at 550°-600°C are first tempered at around 300°C to avoid this problem. This procedure is called "double tempering".

Secondly, there is the decrease in yield strength and the increase in dispersed carbide content (γm increases), both of which cause the impact-transition tempering range to be lowered as the tempering temperature is increased. Tensile ductility and Cv (max) increase, at the same strength level, as the microstructure is refined.

Temper embrittlement is reversible. If the tempering temperature is raised above the critical range, the transition temperature is lowered, but it can be raised back again if the material is reheat treated in the critical range. The presence of trace elements appears to be responsible for the embrittlement. The most important of these are antimony, phosphorus, tin, and arsenic, with manganese and silicon having a small effect. Molybdenum reduces temper brittleness when other alloying elements are present. Nickel and chromium appear to have little effect.

Fracture of high strength steels (Rp0.2 > 1240 MPa)
High strength steels are produced by basically one of three processes; quenching and tempering, deforming the austenite before quenching and tempering (ausforming), or annealing and aging to produce precipitation hardening (e.g., maraging). In addition, further increases in strength can be achieved by straining and retempering or by straining during tempering.

The high strength level of these steels makes them extremely brittle, especially when particular environments such as water vapor or hydrogen are present.

The Fracture of Stainless Steels
Stainless steels are basically iron-chromium and iron-chromium-nickel alloys to which small amounts of other elements have been added to improve mechanical properties and corrosion resistance. Their resistance to corrosion arises from the formation of an impervious layer of chromium oxide on the metal surface, which, in turn, prevents any further oxidation of the metal.

Consequently these steels are corrosion-resistant in oxidizing atmospheres, which strengthen this layer, but are susceptible to corrosion in a reducing environment, which breaks down the layer. The corrosion resistance (in oxidizing environment) increases with increasing chromium content and also with increasing nickel content. The latter element increases the overall passivity of the iron.

Carbon is also added to improve mechanical properties (yield and tensile strength) and to stabilize the austenitic stainless steel. Generally speaking, the stainless steels can be classified by their microstructures:

* Martensitic. These are iron-chromium alloys that can be austenitized and subsequently heat-treated to form martensite. They normally contain about 12% chromium and 0.15% carbon (type 410).
* Ferritic. These alloys contain about 14-18% chromium and 0.12% carbon (type 430) and are completely ferritic since chromium is a ferrite stabilizer; the austenite phase is completely suppressed in alloys containing more than 13% Cr.
* Austenitic. Nickel is a strong austenite stabilizer and alloys containing 8% nickel and 18% chromium (type 300) are austenitic at room temperature and below, as well as at high temperatures. These steels, like the ferritic grade, cannot be hardened by martensitic transformation.

The fracture characteristics of ferritic and martensitic stainless steels are similar to those of other ferritic or martensitic steels at the same strength level, grain size, and so on.

Austenitic stainless steels have a FCC structure and consequently do not fracture by cleavage, even at cryogenic temperatures. After heavy cold rolling (80%), 310 type steels have an extremely high yield strength combined with a notch sensitivity ratio of 1.0 at temperatures as low as -253°C and consequently are used in missile systems for storage tanks for liquid hydrogen. Similarly 301 type stainless can be used down to -183°C (e.g., for liquid oxygen storage tanks), but below this temperature the austenite is unstable and deforms to brittle, untempered martensite if any plastic deformation occurs at the low temperatures.

Most austenitic stainless steels are used in corrosive environments. When they are heated in the temperature range 500-900°C (e.g., during welding), chromium carbide precipitates at austenite grain boundaries, resulting in a depletion of chromium from the region near to the boundaries. This depleted layer is very susceptible to corrosive attack (particularly in hot chloride environments), and localized corrosion, in the presence of applied stress, leads to inter-granular brittle fracture.

To alleviate this problem, small quantities of elements which are stronger carbide formers than chromium, such as titanium or niobium are commonly added. These elements combine with the carbon to form alloy carbides, which prevents chromium depletion and subsequent susceptibility to stress corrosion cracking. This process is called "stabilizing".

Austenitic stainless steels are used extensively in high-temperature applications (e.g., pressure vessels) where both corrosion resistance and creep resistance are required. Some of these steels are susceptible to cracking in the heat-affected zone near welds during postwelding heat treatments and/or elevated temperature service. The cracking is the result of precipitation of niobium or titanium carbides in the grains and grain boundaries when the weld is reheated.

There are literally thousands of steels available today, each one characterized by a particular trade name or alloy composition. Although a quantitative value of fracture toughness parameters (e.g., NDT temperature and KIC) for each grade would greatly facilitate the selection of a material for a particular application, these parameters are available for only a very few of the steels.

There are primarily two reasons for this. First, because a wide range of microstructures can be obtained in a steel of given alloy composition, simply by variations in thermomechanical treatment. Secondly, because the concentration of fabrication defects (i.e., blow holes, inclusions, and so on) is extremely sensitive to mill practice and can vary between heats of steel of the same composition or even in different parts of the same billet.

Since it is microstructure and defect concentration that primarily determine toughness, rather than composition per se, a large variation in toughness can be produced in a given steel simply by varying the thermomechanical treatment and fabrication practice.

A detailed understanding of the fracture of steel therefore requires an understanding of both the physical metallurgical aspects of the material (e.g., what microstructure will result from a given heat treatment) as well as an understanding of how this particular microstructure affects the toughness of a structure of given geometry.

The Fracture of Ferritic-Pearlitic Steels
Ferritic-pearlitic steels account for most of the steel tonnage produced today. They are iron-carbon alloys that generally contain 0.05-0.20% carbon and a few per cent of other alloying elements that are added to increase yield strength and toughness.

In these steels the microstructure consists of BCC iron (ferrite), containing about 0.01% carbon and soluble alloying elements, and Fe3C (cementite). In very low carbon steels the cementite particles (carbides) lie in the ferrite grain boundaries and grains, but when the carbon content is greater than about 0.02%, most of the Fe3C forms a lamellar structure with some of the ferrite. This lamellar structure is called pearlite and it tends to exist as "grains" or nodules, dispersed in the ferrite matrix. In low carbon (0.10-0.20%) steel (i.e., mild steel) the pearlite accounts for between 10-25% of the microstructure.

Although the pearlite grains are very hard, they are so widely dispersed that the ferrite matrix can deform around them with little difficulty. It should be noted, however, that the ferrite grain size generally decreases with increasing pearlite content because the formation of pearlite nodules during the transformation interferes with ferrite grain growth. Consequently the pearlite can indirectly raise σy by raising d-1/2.

From the point of view of fracture analysis, two ranges of carbon content are of most interest in the low carbon steels: (1) steels containing less than 0.03% carbon where the presence of pearlite nodules has little effect on toughness, and (2) steels containing higher carbon contents where the pearlite does have a direct effect on toughness and the shape of the Charpy curve.

The effect of processing variables. It has been pointed out that the impact properties of water-quenched steels are superior to those of annealed or normalized steels because the fast cooling rate prevents the formation of grain boundary cementite and causes a refinement of ferrite grain size.

Many commercial grades of steel are sold in the "hot-rolled" condition and the rolling treatments have a considerable effect on impact properties. Rolling to a lower finishing temperature (controlled rolling) lowers the impact-transition temperature. This results from the increased cooling rate and corresponding reduced ferrite grain size. Since thick plates cool more slowly than thin ones, thick plates will have a larger ferrite grain size and hence are more brittle than thin ones after the same thermomechanical treatment. Therefore, post rolling normalizing treatments are frequently given in order to improve the properties of rolled plate.

Hot rolling also produces an anisotropic or directional toughness owing to combinations of texturing, pearlite banding, and the alignment of inclusions and grain boundaries in the rolling direction. Texturing is not considered to be important in most low carbon steels. Pearlite bands (due to phosphorous segregation during casting) and elongated inclusions are dispersed on too coarse a scale to have an appreciable effect on notch toughness at the low temperature end of the Charpy transition temperature range.

The effect of ferrite-soluble alloying elements. Most alloying elements that are added to low carbon steel produce some solid solution hardening at ambient temperature and thereby raise the lattice friction stress σi.

It is important to appreciate that equation cannot be used to predict the lower yield stress unless the resultant grain size is known. This, of course, depends on factors such as normalizing temperature and cooling rate. The importance of this type of approach is that it allows prediction of the extent that individual alloying elements will decrease toughness by increasing σi, since NDT increases by about 2°C per ksi increase in σi.

Regression analyses for NDT temperatures or other Charpy transition temperatures have not been reported at this time and it is only possible to discuss the effects of the individual alloying additions on a qualitative basis.

Manganese. Most commercial steels contain about 0.5% manganese to serve as a deoxidizer and to tie up sulfur as manganese sulfide, thereby preventing the occurrence of hot-cracking. In low carbon steels this effect is outweighed by the ability of manganese:

* to decrease the tendency for the formation of films of grain boundary cementite in air-cooled or furnace-cooled specimens containing 0.05% carbon, thereby lowering the value of γm;
* to cause a slight reduction in ferrite grain size;
* to produce a much finer pearlite structure.

The first two of these effects account for the lowering of the NDT temperature with increasing Mn additions. The third effect as well as the first cause the Charpy curves to become sharper.

In steels containing higher carbon contents the effect of manganese on the 50% transition temperature is less pronounced, probably because the amount of pearlite rather than the distribution of grain boundary cementite is the most important factor in determining this transition temperature when the pearlite content is high. It should also be noted that if the carbon content is relatively high (greater than 0.15%) a high manganese content may have a detrimental effect on the impact properties of normalized steels because the high hardenability of the steel causes the austenite to transform to the brittle upper bainite structure rather than ferrite or pearlite.

Nickel. Nickel, like manganese, is able to improve the toughness of iron carbon alloys. The magnitude of the effort is dependent on carbon content and heat treatment. In very low (about 0.02%) carbon steels, nickel additions up to 2% are able to prevent the formation of grain boundary cementite in hot-rolled and normalized alloys and cause a substantial decrease in the initiation-transition temperature TS(N), and a sharpening of the Charpy curves.

Further additions of nickel produce substantially smaller improvements in impact properties. In alloys containing carbon contents lower than this, such that carbides are not present after normalizing, nickel has a smaller effect on the transition temperature. The principal beneficial effect of nickel additions to commercial steels containing about 0.1% carbon results from the substantial grain-size refinement and reduction of free nitrogen content after normalizing. The reasons for this behavior are not clear at present; it may be related to the fact that nickel is an austenite stabilizer and consequently lowers the temperature at which the austenite decomposition will take place.

Phosphorous. In pure iron-phosphorus alloys, intergranular embrittlement can occur from the segregation of phosphorous at ferrite grain boundaries, which lowers the value of γm. Also, phosphorus additions produce a significant increase in σi and a coarsening of ferrite grain size since phosphorus is a ferrite stabilizer. These effects combine to make phosphorus an extremely effective embrittling agent, even when fracture occurs transgranularly.

Silicon. Silicon is added to some commercial steels to deoxidize or "kill" them, and in this respect the silicon produces beneficial effects on impact properties. When manganese and aluminum are present, a large fraction of the silicon is dissolved in the ferrite and this raises σi by solid solution hardening. This effect, coupled with the fact that silicon additions raise ky, causes the 50% transition temperature to increase by about 44°C per wt per cent silicon in iron-carbon alloys of constant grain size. In addition, silicon, like phosphorus, is a ferrite stabilizer and hence promotes ferrite grain growth. The net effect of silicon additions in normalized alloys is to raise the average energy-transition temperature by about 60°C per wt per cent silicon added.

Aluminum. The effect of alloying or killing a steel with aluminum is twofold. First, the aluminum combines with some of the nitrogen in solution to form AlN. The removal of this free nitrogen leads to a decrease in transition temperature because σi is decreased and γm/ky is increased, as described above. Second, the AlN particles that form interfere with ferrite grain growth and consequently refine the ferrite grain size. These combined effects cause the transition temperature to decrease about 40°C per 0.1% aluminum added. However, additions of aluminum greater than that required to tie up the nitrogen have little effect.

Oxygen. Oxygen additions promote intergranular fracture in iron alloys. These fractures are thought to result from the segregation of oxygen to ferrite grain boundaries. In alloys that contain a high oxygen content (greater than 0.01 %), fracture occurs along the continuous path provided by the embrittled grain boundary.

In alloys of lower oxygen content, cracks are nucleated at the grain boundary and then propagate transgranularly. The problem of oxygen embrittlement can be solved by the addition of deoxidizing elements such as carbon, manganese, silicon, aluminum, and zirconium, which react with the oxygen to form oxide particles, thereby removing the oxygen from the boundary region. These oxide particles are beneficial in their own right because they retard the growth of the ferrite grains, thereby increasing d-1/2.