Advanced Engineering Properties of Steels

STEEL CONSTRUCTION: APPLIED METALLURGY __________________________________________________________________________

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STEEL CONSTRUCTION:

APPLIED METALLURGY

Lecture 2.3.2: Advanced Engineering

Properties of Steels

OBJECTIVE/SCOPE

To provide a sequel to Lecture 2.3.1, introducing toughness as an important engineering

property.

PREREQUISITES

Lecture 2.3.1: Introduction to the Engineering Properties of Steels

RELATED LECTURES

Lecture 2.1: Characteristics of Iron Carbon Alloys

Lecture 2.2: Manufacturing and Forming Processes

SUMMARY

This lecture introduces the phenomena of ductile and cleavage fracture and the

engineering property of toughness. It summarizes the influences of temperature loading

rate, multi-axial stress conditions and geometry on toughness. It introduces the notched

impact bend test as the most common means of monitoring toughness. It introduces linear-

elastic and elastic-plastic fracture mechanics. It presents the wide plate test and assessment

techniques based on fracture mechanics. It summarizes the means of obtaining an

optimum combination of strength and toughness. It introduces the concept of fatigue, the

principal influences on fatigue behaviour, and the means of ensuring adequate fatigue

endurance.

1. TOUGHNESS

Metals often show quite acceptable properties when small smooth bar specimens are tested

in tension at ambient temperature and at slow loading rates. However they fail in a brittle

manner when large components are loaded or when the loading is performed at low

temperatures or applied rapidly. Susceptibility to brittle fracture is enhanced if notches or

other defects are present. Resistance to brittle fracture is commonly referred to as

toughness.


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Metals with a body-centred cubic lattice, e.g. pure iron and ferritic steels have the

unfortunate characteristic that their fracture mechanism undergoes a dramatic transition

with decreasing temperature from a tough ductile mode in the higher temperature region to

a brittle cleavage mode at lower temperatures. Face-centred cubic metals, e.g. copper,

aluminium and austenitic steels, do not fail by cleavage under all loading conditions and at

all temperatures.

1.1 Types of Fracture

Ductile fracture involves the formation, growth and coalescence of voids. A simple

analogy is the fracture of plasticene or putty containing particles of sand. The voids form

around precipitates or non-metallic inclusions, Figure 1. The ductility or toughness of the

material is basically dependent on the volume fraction of the void nucleating particles, i.e.

the proportion of sand in the previous analogy. The amount of deformation prior to rupture

and thus the toughness of the material increases with its purity.

The macroscopic orientation of a ductile fracture surface may vary from 90 to 45 to the direction of the applied stress. In thick sections most of the fracture surface tends to be

oriented at 90 to the direction of the applied tensile stress. However, ductile fractures commonly have a "shear-tip" near a free boundary as the transverse stresses reduce to zero

causing the plane of maximum shear to be at 45 to the direction of the applied stress.

Cleavage fracture occurs in body-centred cubic metals when the maximum principal

stress exceeds a critical value, the so-called microscopic cleavage fracture stress f.

Certain crystallographic planes of atoms are separated when the stress is sufficiently high

to break atomic bonds. Crystallographic planes with low packing densities are preferred as

cleavage planes. In steels the preferred change planes are the bee cube planes.

The fracture surface lies perpendicular to the maximum principal stress and appears

macroscopically flat and crystalline. When viewed by eye a cleavage fracture usually


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displays characteristic chevron markings which point back to the origin of the fracture.

When brittle fracture occurs in a large structure, such markings can be invaluable in

identifying the site of crack initiation. When viewed in the microscope, cleavage cracks

can be seen to pass through the grains along preferred crystallographic planes

(transgranular cleavage).

If grain boundaries are weakened by precipitates or by the enrichment of foreign atoms,

cleavage cracks can also propagate along grain boundaries (intergranular cleavage).

1.2 Influence of Temperature, Loading Rate, Multi-axiality and Geometry

Temperature influences fracture behaviour mainly due to its effect on yield strength and

the transition from ductile to cleavage fracture. Figure 2 shows schematically the yield

strength and the microscopic cleavage fracture stress as a function of temperature for a

ferritic steel. The yield strength falls with increasing temperature, whereas the cleavage

fracture stress is hardly influenced. The transition temperature is defined by the

intersection between the yield strength and cleavage fracture strength curves. At lower

temperatures specimens fail without previous plastic deformation (brittle fracture).

Somewhat above the transition temperature, cleavage fracture can still occur due to the

effect of deformation induced work hardening. At higher temperatures cleavage is not

possible and the fracture becomes fully ductile.

The yield strength rises with increasing loading rate (marked with dashed line in Figure 2)

whereas the microscopic cleavage fracture stress shows almost no strain rate dependence.

This rise causes the ductile-brittle transition temperature to move to higher values at

higher rates of loading. Thus, an increase of loading rate and a reduction of temperature

have the same adverse effect on toughness.

A multi-axial stress state has an important influence on the transition from ductile to

cleavage fracture. A triaxial state of stress, in which the three principal stresses 1, 2 and


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3 are all positive (but not equal), inhibits or constrains the onset of yielding. Under these conditions, yielding occurs at a higher stress than that observed in a uniaxial or biaxial

state of stress. This situation is illustrated in Figure 3 where it can be seen that the

transition temperature arising from the intersection of the cleavage and yield strength

curves is shifted to a higher temperature, i.e. the metal has become more brittle.

The most familiar situation in which multi-axial states of stress are encountered in steel

structures is in association with notches or cracks in thick sections. The stress

concentration at the root of the notch gives rise a local region of triaxial stresses even

through the applied loading may be uni-directional (Figure 4).


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1.3 Notched Impact Bend Test

The notched impact bend test is the most common test for the assessment of susceptibility

to brittle fracture because it is inexpensive and quickly performed. 10mm square bars with

a machined notch, (ISO-V or Charpy specimens), are struck by a calibrated pendulum.

The energy absorbed from the swinging pendulum during deformation and fracture of the

test specimen is used as a measure of the impact energy. The notch impact energy consists

of elastic and plastic deformation work, fracture energy and kinetic energy of the broken

pieces.

Figures 5 and 6 show the notch impact energy as a function of testing temperature. At low

temperatures the failure of ferritic steels occurs by cleavage fracture giving a lustrous

crystalline appearance to the fracture surface. At high temperatures failure occurs by

ductile fracture after plastic deformation. In the transition range small amounts of ductile

fracture are found close to the notch but, due to the elevated stresses near the crack tip, the

fracture mechanism changes to cleavage. Throughout the transition range the amount of

cleavage fracture becomes less and the notch impact energy rises as the testing

temperature increases.


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In order to characterise the transition behaviour, a transition temperature is defined as the

temperature at which:

a defined value of the notch impact energy is reached (eg. T27J, T40J),

half of the maximum impact energy value is reached (T50%), or

50% ductile fracture is observed on the fracture surface (FATT 50: Fracture

Appearance Transition Temperature, 50% ductile fracture).

The impact energy values obtained show a high amount of scatter in the transition area

because here the results depend on the local situation ahead of the crack tip. Beyond this

area, scatter becomes less because there is no change of fracture mechanism.

The notched impact bend test gives only a relative measure of toughness. This measure is

adequate for defining different grades of toughness in structural steels and for specifying

steels for well established conditions of service. For the assessment of known defects and

for service situations where there is little experience of brittle fracture susceptibility, a

quantitative measure of toughness which can be used by design engineers is provided by

fracture mechanics.

1.4 Fracture Toughness

Fracture mechanics provides a quantitative description of the resistance of a material to

fracture. The fracture toughness is a material property which can be used to predict the

behaviour of components containing cracks or sharp notches. The fracture toughness

properties are obtained by tests on specimens containing deliberately introduced cracks or

notches and subjected to prescribed loading conditions.

Depending on the strength of the material and the thickness of the section, either linear-

elastic (LEFM) or elastic-plastic fracture mechanics (EPFM) concepts are applied.


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The Linear-Elastic Fracture Mechanics Approach

The stress intensity factor KI describes the intensity of the elastic crack tip stress field in a

thick, deeply cracked specimen loaded perpendicular to the crack plane.

KI = Y (1) where

- is the nominal stress

a - is the crack depth

Y - is the correction function dependent on the crack and test piece geometry

The critical value of the stress intensity factor for the onset of crack growth is the fracture

toughness KIC.

Another material property obtained from linear-elastic fracture mechanics is the energy

release rate GI. It indicates how much elastic strain energy becomes free during crack

propagation. It is determined according to Equation (2):

GI = Y2 2 a / E = K12 / E (2) where

E - is the Young's modulus

Analogous to the stress intensity factor, crack growth occurs when GI reaches a critical

value GIc.


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The fracture toughness properties KIc and GIc are determined with fracture mechanics

specimens, generally as shown in Figures 7 and 8.

The great value of the fracture toughness parameters KIc and GIc is that once they have

been measured for a particular material, Equations (1) and (2) can be used to make

quantitative predictions of the size of defect necessary to cause a brittle fracture for a

given stress, or the stress which will precipitate a brittle fracture for a defect of known

size.


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As the designation implies, linear elastic fracture mechanics is applicable to materials

which fracture under elastic conditions of loading. The fracture phenomena in high

strength quenched and tempered steels are of this type. In lower strength structural steels,

extensive plasticity develops at the notch root before failure occurs. This behaviour

invalidates many of the assumptions of linear elastic fracture mechanics and makes testing

difficult or not meaningful. In such cases elastic-plastic fracture mechanics must be

applied.

There are two alternative techniques of elastic-plastic fracture mechanics:

1. Crack Tip Opening Displacement (CTOD) 2. J Integral

Their essential features are summarised below.

The Elastic-Plastic Fracture Mechanics Approach

A consequence of plasticity developing at the tip of a previously sharp crack is that the

crack will blunt and there will be an opening displacement at the position of the original

crack tip. This is the crack tip opening displacement (CTOD). As loading continues, the

CTOD value increases until eventually a critical value c is attained at which crack growth occurs.

The critical crack tip opening displacement is a measure of the resistance of the material to

fracture, i.e. it is an alternative measurement of fracture toughness.

For materials which exhibit little plasticity prior to failure, the critical CTOD, c, can be related to the linear elastic fracture toughness parameters KIc and GIc as follows:

KIc2 = E.Gk / (1 - mE.y.c / (1 -

where

E - is Youngs modulus

y - is the uniaxial yield strength

- is Poissons ratio

m - is a constraint factor having a value between 1 and 3 depending on the state

of stress at the crack tip.

Another way of taking account of crack tip plasticity is the determination of the J-integral.

J is defined as a path-independent line-integral through the material surrounding the crack

tip. It is given by:

J = - (3)


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where

U - is the potential energy

B - is the specimen thickness

a - is the crack length

U = (4)

F - is the load

Vg - is the total displacement

Since the determination of J is difficult, approximate solutions are used in practice.

J = (5)

where

b = w - a

= 2 (for SENB-specimens)

= 2 + 0,522 b/w (for CT-specimens)

The critical value of J is a material characteristic and is denoted JIc. For the linear elastic

case, JIc is equal to GIc.

1.5 Fitness for Purpose

Conventional assessment of components is based on a comparison of design resistance

with applied actions. Toughness criteria are generally satisfied by the appropriate selection

of material quality, as discussed in Lecture 2.5. However there are situations where a more

fundamental assessment has to be carried out because of:

onerous service conditions.

defects during manufacture.

defects, e.g. fatigue cracks, developing during previous service life.

Such assessments can be performed by different methods. If the component is small, it

may be possible to test it. For large or unique structures, such as bridges or offshore

platforms, this method of producing the most realistic data has to be excluded. Tests on

representative details of a component may be performed, if the simulation of the real

structure is done carefully, e.g. accounting for specific service conditions including the


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geometry of the structure and discontinuities, loading rate, service temperature and

environmental conditions. A typical example of such a test method is the wide plate test,

which is discussed below.

Fracture mechanics concepts have been developed to assess the safety of components

containing cracks. Depending on the overall behaviour of the component (linear-elastic or

elastic-plastic) different methods can be used for failure assessment.

1.5.1 Wide plate testing

During the last 20 years, large flat tensile specimens, so-called wide plates, have been

used to simulate a relatively simple detail of a tension loaded large structure. A main

objective of wide plate testing is the evaluation of the deformation and fracture behaviour

of a specimen under service conditions. The second reason for this kind of test is the

application of test results for the development and checking of failure assessment

methods, e.g. fracture mechanics methods.


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Wide plate tests require testing facilities with high loading capacities due to the fact that

such tests are usually carried out at full thickness. The maximum dimensions of wide

plates tested on large test rigs with a load capacity of up to 100MN are as follows:

specimen width W 3000mm

specimen thickness to 300mm

specimen length l 5000mm

Figure 9 shows different types of specimen containing discontinuities for tests on the base

metal or welded joints. The discontinuities may be through-thickness or surface notches or

cracks. The configuration of the plate is usually chosen according to the specific structural

situation to be assessed.


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Stress or strain criteria can be used as safety criteria which must be fulfilled to assure the

safety of a specific structural element. The production of a given amount of overall strain

is in some cases used as the failure criterion. The gross-section-yielding concept requires

that gross-section-yielding (GSY) occurs prior to fracture. Based on this concept, wide

plates with different crack lengths are tested under similar loading conditions to determine

a critical crack length just fulfilling the GSY-criterion. Figure 10 shows the ratio of the

maximum gross-section stress in the structure to ultimate tensile strength as a function of

the crack length ratio 2a/W of centre-notched wide plates. The upper limit line describes

the theoretical maximum stress, if the ultimate tensile strength is reached in the cross-

section containing the discontinuity. All test results show lower values than are implied by

the theoretical line, resulting from the important influence of toughness in the presence of

discontinuities. Only in the case of infinite toughness can the theoretical line be reached.

The intersection of the experimentally determined curve and the yield strength line marks

the critical crack length ratio 2ac/W. As long as the 2a/W ratio is smaller than the critical

ratio, the GSY-criterion is fulfilled. Unfortunately, the critical 2ac/W ratio depends

strongly on the dimensions of the crack and the plate, so that different types of cracked

components always require a series of specific wide plate tests. This concept is therefore

only used if other concepts cannot be applied.

1.5.2 Fracture mechanics concepts

The basis of a fracture mechanics safety analysis is the comparison between the crack

driving force in a structure and the fracture toughness of the material evaluated in small

scale tests. The application of one of the concepts depends on the overall behaviour of the

structure which may be linear-elastic (K-concept) or elastic-plastic (CTOD- or J-Integral-

concepts). For a safe structure the crack driving force must be less than the fracture

toughness. In general the toughness values of the material are evaluated according to

existing standards. The crack driving force can be calculated on the basis of analytical

solutions (K-concept), empirical or semi-empirical approaches (CTOD-Design-Curve

approach, CEGB-R6-procedures) or using numerical solutions (indirectly: EPRI-

handbook, directly: finite-element calculations). The different methods are explained

briefly below:

K-concept

The K-concept can be applied in the case of linear-elastic component behaviour. The crack

driving force, the so-called stress intensity factor KI, defined in Section 1.4, has been

evaluated for a large range of situations and calculation formulae are for example given in

the stress-analysis-of-cracks handbook.

Usually the critical fracture toughness KIc of the material is evaluated according to the

ASTM standard E399 or the British Standard BS5447. Brittle failure can be excluded as

long as:

KI < KIc

For a given fracture toughness the critical crack length or stress level can be calculated

from:


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ac =

c =

CTOD-Design-Curve approach

A critical crack length or stress level can be determined using the limit curve of the

CTOD-Design-Curve approach for the driving force assessment together with measured

values of CTODcrit for the material. The limit curve has been adopted by standards, e.g.

the British Standard BS-PD 6493. The latest version of the limit curve is shown in Figure

11 and can be used for:

2a/W 0,5 and net YS.


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Analysis can only be performed under global elastic conditions (net YS) although local plastic deformation may occur in front of a crack tip which is accounted for in the CTOD-

value of the material.

CEGB-R6-routines

The CEGB-R6-routines can be used to assess the safety of structures for brittle and ductile

component behaviour. The transition from linear-elastic to elastic-plastic behaviour is

described by a limit curve in a failure analysis diagram (Figure 12). The ordinate value Kr

can be regarded as any of three equivalent ratios of applied crack driving force to material

fracture toughness as follows:

Kr = =

=

Other methods

Other methods are emerging. The Electrical Power Research Institute (EPRI) in New York

has used a detailed analysis by finite elements to determine limiting J contour values for


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standard geometries. Alternatively the J contour values may be obtained by direct finite

element analysis of the particular situation.

2. OPTIMAL COMBINATION OF STRENGTH AND

TOUGHNESS

Preceding sections have described the influence of the micro structure on strength and

toughness using metallurgical mechanisms. Chemical and physical metallurgy can change

microstructural characteristics so that optimum strength and toughness requirements may

be obtained. By combining the various treatments it is possible to achieve a wide range of

steel properties (Figure 13):

Chemical metallurgy treatments

Variation of the chemical composition of a steel by adding alloying elements aims to

increase strength and/or increase resistance to brittle fracture. Solid solution hardening

generally lowers toughness and is not widely employed. Precipitation hardening also

increases strength and decreases toughness. The addition of manganese and nickel

produces a small increase in strength due to solution hardening but a more significant


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reduction is impact transition temperature due to grain refinement (Figure 14). Alloying

with the micro-alloying elements Niobium, (Nb) Vanadium (V) and Titanium (Ti)

producing carbides and nitrides simultaneously raises strength by precipitation hardening

and toughness by grain refinement. Decreasing the content of elements such as S and P

improves the degree of purity, which has positive effects on toughness and weldability.

Physical metallurgy treatments

The microstructure of a steel can be greatly affected by heat treatment or forming.

Correctly chosen temperature, degree of deformation, time between deformation steps and

cooling rate can reduce the grain size and control the state of precipitation, thus raising

toughness and strength (Figure 15).

This combination of heat treatment and forming known as thermo-mechanical treatment

leads to even better results if micro-alloying elements such as V or Nb are added, causing

additional grain refinement with improved toughness and strength properties.


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3. FATIGUE PROPERTIES

When considering the response of metallic materials to cyclic loading, it is essential to

distinguish between components such as machined parts, which are initially free of

defects, and those such as castings and welded structures, which inevitably contain pre-

existing defects. The fatigue behaviour of these two types of component is quite different.

In the former case, the major part of the fatigue life is spent in initiating a crack; such

fatigue is 'initiation-controlled'. In the second type of component, cracks are already

present and all of the fatigue life is spent in crack propagation; such fatigue is

'propagation-controlled'.

For a given material, the fatigue strength is quite different depending on whether the

application is initiation- or propagation-controlled. Also the most appropriate material

solution may be quite different depending on the application. For example with initiation-

controlled fatigue, the fatigue strength increases with tensile strength and hence it is

usually beneficial to utilise high strength materials. On the other hand, with propagation-

controlled fatigue, the fatigue resistance may actually decrease if a higher strength

material is employed.


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3.1 Initiation-Controlled Fatigue

3.1.1 Testing

The fundamental diagram in fatigue testing is the Whler or S-N-diagram (Figure 16).

Specimens are exposed to cyclic loading with a constant amplitude and the number of

cycles to fracture is recorded. This parameter is plotted against the corresponding stress

amplitude with a double- or semi-logarithmic scale. The diagram is divided into two parts.

In the first part, life time increases with decreasing alternating stress amplitude. In the

second part for most-ferritic steels the curve becomes horizontal and defines a 'fatigue

limit' stress below which failure can never occur. The transition or 'knee' between the two

parts of the curve lies between 3 and 10 x 106 cycles, depending on the material. For other

alloys, e.g. fcc-metals, which do not show a fatigue limit, an 'endurance limit' is defined as

the stress amplitude corresponding to a life of 107 cycles.

One characteristic feature of fatigue properties is the wide scatter of results under constant

testing conditions. Therefore 6-10 experiments must be performed for each stress

amplitude. The analysis is done by means of statistical evaluation leading to different S-N

curves for various life time probabilities (10%, 50%, 90% curves).


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3.1.2 Fatigue damage

Crack-free stage

During the first 104 stress cycles, although the loading is nominally elastic, dislocation

activity occurs in localised areas and leads to the formation of bands of localised plastic

deformation known as "persistent slip bands" (PSB).

Crack initiation

Crack initiation generally takes place within the persistent slip bands. In the case of pure

metals, crack initiation usually occurs at the surface. In commercial quality materials,

crack initiation usually occurs at non-metallic inclusions or other impurities which act as

microscopic sites of strain concentration.

Crack propagation

Once initiated the crack propagates through the first few grains in the direction of

maximum shear stress, i.e. at 45 to the normal stress. When the crack has attained a length of a few grain diameters, continued propagation is controlled by the cyclic stress

intensity field at the crack tip and the crack path becomes oriented at 90 to the maximum principal stress direction. Although the major part of the fatigue life is spent in crack

initiation, this is not apparent from examination of the fracture surface where only the

final propagation stage can be seen.

3.1.3 Influences of various parameters

The relationships between initiation-controlled fatigue strength and other parameters are

complex and sometimes only known qualitatively. Nevertheless they are of great

importance for material selection and dimensioning of structural parts. Therefore a number

of different parameters are discussed below with respect to their influence on fatigue

properties.

Loading: Different loading conditions include cyclic tension and compression,

cyclic torsion, cyclic bending and any possible combination of these. As discussed

in the context of yielding in Section 2.3 of Lecture 2.3.1, such complex stresses

can be combined by means of the Hencky-von Mises expression to generate an

equivalent stress which can be compared with the fatigue strength obtained from

uniaxial loading.

Mean stress: Fatigue strength is reduced by tensile mean stress and increased by

compressive mean stress.

Frequency: For most materials no influence is observed over a wide range. Some

alloys show a smaller life time for lower frequencies because corrosion effects

interfere.

Microstructure: The influence of microstructural modification on fatigue strength

is similar to that on tensile strength. In general fatigue strength increases in

proportion to tensile strength. For example, for a wide range of wrought steels, the

fatigue strength is between 40% and 50% of the tensile strength. Improved purity

raises fatigue strength.


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Residual stresses: As with mean stress effects, compressive residual stress

improves fatigue strength, whereas internal tensile stress has the opposite effect.

To optimise fatigue strength, surface compressive residual stress is generated by

techniques such as shot peening, and surface rolling.

Surface: Surface finish has a large influence on fatigue; the smoother the surface

the better the fatigue strength. The treatment of surfaces during manufacturing

often causes strain hardening and compressive residual stresses which both

increase fatigue strength. The influence of notches is described under "Geometry".

Geometry: Notches and changes of section act as sites of stress concentration and

hence have a considerable influence on fatigue properties. For large smooth

notches, the stress concentration must be evaluated and incorporated in the fatigue

analysis. Sharp notches behave as crack-like defects and cause the fatigue

behaviour to be propagation-controlled.

Welding: Welding inevitably generates small crack-like defects which greatly

lower the fatigue strength and cause the fatigue to be propagation- controlled.

Corrosion: Exposure to a corrosive environment facilitates both crack initiation

and propagation. Consequently the fatigue strength is reduced. The fatigue limit in

steels may be eliminated in a corrosive element.

3.1.4 Fatigue limit under actual service conditions

The S-N diagram characterises material behaviour under single-amplitude loading. For

weight-saving constructions exposed to complex stresses, the parameters determined by

such tests are not sufficient.

For testing under realistic conditions, an analysis of the actual stresses has to be obtained.

For that purpose the sequence and duration of different stress levels, as well as their rise or

fall, are recorded. This stress-time function is either reproduced under laboratory

conditions, or special testing programmes are calculated from these data and used in

experiments. Results obtained by this method cannot be transferred to different materials

and loading conditions.

3.1.5 Prediction of cumulative damage

The fundamental method of life time cumulative damage prediction was formulated by

Miner. The damage from each cycle at a certain stress level is defined as the reciprocal

value of the number of cycles to fracture (1/Ni). Fracture occurs when the sum of cycles at

each level (ni) related to the number of cycles to failure (Ni) is equal to unity. The

mathematical expression is:

Since this is a very simple equation, results are widely scattered. In reality the values form

a Gaussion distribution with a maximum around 1. To guarantee safe construction,

calculations are made with factors smaller than 1 and stresses below their maximum

values. Furthermore it is possible to take the effects of different loading levels into

account with respect to their number, maximum stress and sequence.


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3.2 Propagation-Controlled Fatigue

Steel castings, rough forgings and welded structures invariably contain surface

imperfections which behave as minute crack-like defects which effectively eliminate the

crack-initiation stage in fatigue. Consequently the whole of the fatigue life is concerned

with crack propagation. The rate of crack advance is determined by the cyclic stress

intensity Kr which is the cyclic equivalent of the stress intensity factor KI defined in Section 1.5.

KI = Y

where

- is the cyclic stress range

a - is the crack depth

Y - is the correction function dependent on the crack and test piece geometry.

The rate of crack propagation is then given by the following relationship which is known

as Paris' Law:

= C KIm

N = Number of cycles

C - is a material constant which is inversely proportional to Young's modulus E.

The power m has a value of about 3 for most metallic materials.

The advantage of the fracture mechanics description of crack propagation is that the rate

equation can be integrated to determine the number of cycles required for a crack to

propagate from some initial length ai to same final length af. Thus for m = 3;

Nf = 2 (1/ai - 1/af

) / (CY333/2)

ai may be a known crack size or an NDT limit, af may be a critical defect size for

unstable fracture or a component dimension such as the wall thickness of a vessel.

In the above equation for the fatigue life, the constant C is dependent on the type of

material but is not sensitive to variations in microstructure or strength level. Consequently,

for a given cyclic stress range, , the fatigue life is independant of the strength of the material. If, however, the stress range increases in proportion to the material yield

strength, then the fatigue life will be less for the higher strength material. For example, a

two-fold increase in stress range produces almost a ten-fold reduction in fatigue life. This

is a major constraint on the utilisation of higher strength structural steels for fatigue

dominated applications.


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The fatigue behaviour of welded joints is propagation-controlled. However it is

impracticable to apply a fracture mechanics analysis because the initial defect size cannot

be evaluated and the cyclic stress range is amplified by local stress concentration effects

associated with the weld profile. Instead the fatigue strength is determined experimentally

for the range of weld types and welding processes which are commonly employed in

welded structures. This data is presented as a series of S-N curves for different weld

classifications as shown in Figure 16.

The fatigue strength of welded joints is not sensitive to the strength of the parent plate.

Consequently, as explained previously, it is difficult to take full advantage of higher

strength steels in welded structures where there is significant exposure to cyclic loading.

4. CONCLUDING SUMMARY

Steels may fail by unacceptable brittle fracture.

Satisfactory ductility has generally to be achieved by ensuring ductile rather than

cleavage fracture.

The tendency for brittle fracture increases in:

Reducing temperature

Increasing strain rate

Multi-axial tension

Geometric discontinuities causing stress concentrations.

Fracture mechanics is a valuable means of quantifying the resistance of a material

to fracture.

The notched impact bend test (Charpy test) is a cost effective means of

qualitatively monitoring toughness.

More accurate methods of monitoring toughness, e.g. CTOD testing, have

developed from the understanding of fracture mechanics.

The optimal balance of strength and toughness can be achieved by a combination

of chemical and physical metallurgical treatments.

Structures under repeated loading may fail by fatigue.

Resistance to fatigue is influenced by stress range, number cycles, mean stress,

geometry, residual stresses and defects, especially those associated in welding.

5. ADDITIONAL READING

1. Griffith, A.A., Phil. Trans. Royal Society A221 (1921). 2. Wells, A.A., Unstable Crack Propagation in Metals: Cleavage and Fast Fracture,

Proc. Symp. Crack Propagation, Cranfield 1961, Vol. 1.

3. E 813-81 Standard Test Method for JIC, A Measure of Fracture Toughness, ASTM 1981.

4. Method for crack opening displacement testing, BS5762, British Standard Institution, London 1979.

5. Methods of tests for plain strain fracture toughness (KIc) of metallic materials, BS5447, British Standard Institution, London 1977.


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6. Milne, I. et al, Assessment of the integrity of structures containing defects, CEGB-R/H/R6-Rev. 3, Central Electricity Generating Board, London, 1986.

7. Guidance on Methods for assessing the acceptability of flaws in fusion welded structures, PD 6493: British Standards Institution, London 1991.

8. Kumar, V. et al, An Engineering Approach for Elastic-Plastic Fracture Analysis, Electric Power Research Institute (EPRI), NP 1931, Project 1237-1, Final Report,

General Electric Company, New York.

9. Dahl, W. et al, Application of Fracture Mechanics Concepts to the Failure of Wide Plates, Nuclear Engineering Design 1985.

APPENDIX 1

Fracture toughness values of different materials

Material Kc (MNm-3/2) Material Kc (MNm

-3/2)

Ductile metals, e.g. Cu 200 cast iron 15

Grade Fe430B structural

steel (room temperature)

140 glass

reinforced

plastic

40

12

Grade Fe 430B structural

steel (-100 C)

40

Pressure vessel steels 170

Advanced Engineering Properties of Steels

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