TWI Knowledge Summary

The principles of fracture mechanics-based fitness-for-purpose assessments of structures or components containing flaws

It is now well accepted that all welded structures contain flaws, and that these do not necessarily affect structural integrity or service performance. This is implicitly recognised by most welding fabrication codes which specify weld flaw tolerance levels based on experience and workmanship practice. However, these flaw acceptance levels cannot provide quantitative measures of structural integrity, for instance how 'close' a particular structure containing weld flaws is to the failure condition. In addition, flaws can develop during service due to e.g. corrosion and fatigue and the tolerance of the component regarding these needs to be known.

The fracture mechanics based fitness-for-purpose approach enables the significance of flaws to be assessed in terms of structural integrity. It can be used to demonstrate that a given flaw can be left as it is and so avoid unnecessary repairs. Because of its tremendous economic potential, the fitness-for-purpose concept has undergone rapid developments in the past 20 years and so an internationally-recognised and widely used procedure has been developed in the UK, published as the British Standards Institution Guide BS 7910: 2005 ^[1] .

Approach

When applying the fitness-for-purpose approach, all potential failure modes should be identified and an assessment conducted to ensure that the conditions for failure are not reached during the design life of the structure. Typical failure modes to be considered include:

Fracture
Fatigue
Gross yielding or plastic collapse
Leakage
Corrosion and erosion
Stress corrosion and corrosion fatigue
Buckling
Creep and creep/fatigue

Often, a combination of failure modes needs to be considered. For example, a fabrication flaw may initially grow by fatigue to a size where fracture, gross yielding or leakage can occur. In the following, only the failure modes of fracture, gross yielding and fatigue will be considered. An important requirement for any structural assessment is the need to define the size of the flaw present.

Fracture Assessment

Fracture is a failure mechanism that involves the stable or unstable propagation of a crack within a structure. In ferritic steels, the overall fracture behaviour will depend strongly on temperature. At low temperatures, brittle fracture prevails for which, once the crack has started to extend, crack propagation may occur extremely rapidly. At high temperatures and for materials such as austenitic stainless steels, the fracture behaviour is ductile and crack growth takes place by a stable tearing mechanism.

Whatever the mechanism, for fracture or crack growth to occur, a detrimental combination of applied stress, crack dimension and the material's fracture toughness is required, see Fig.1. This condition can be expressed mathematically as:

K _I K _mat

$Factors controlling fracture$

Fig.1. Factors controlling fracture

i.e. if the crack driving force (expressed as the applied stress intensity factor, K _I) is greater or equal than the brittle or ductile fracture toughness, K _mat, fracture will occur. The stress intensity factor characterises the stress field at the crack tip, and it is the conditions at the crack tip which govern the general behaviour of a cracked structure.

The applied stress intensity factor, K _I, is calculated using relations involving the geometry of the component, the magnitude of the applied stresses and the crack dimensions. For elastic-plastic conditions, the strain hardening behaviour of the material in question is also important. The stress analysis should consider stress concentrations, including those which may arise from deviations from the intended design, such as misalignment; and welded residual stresses (of up to yield strength magnitude) must be taken into account.

K _mat is measured using pre-cracked specimens taken from the material which represent the region in which the subject crack is located. For example, if the subject crack is located in weld metal, the fracture toughness specimen will be notched and fatigue pre-cracked into a test weld representing the structural weld. The test procedures are described in national and international standards ^[2,3] . Fracture toughness values are sensitive to material microstructure, heat treatment condition, loading rate and test temperature (particularly in ferritic steels) and, in certain circumstances, specimen thickness.

In most structural materials, plasticity effects precede failure, and, in the limit, gross yielding effects predominate and failure occurs by plastic collapse. To account for the range of possible behaviours, i.e. elastic fracture, plasticity effects through to plastic collapse, a two-parameter approach to failure has been developed. This is expressed in the form of a failure assessment diagram (FAD), see Fig.2.

Fig.2. Failure analysis diagram (FAD) as used in BS7910

In this diagram, the proximity to fracture is given on the vertical axis as the ratio of applied stress intensity, K _I, to fracture toughness, K _mat:

K _r = K _I/K _mat

If K _r = 1, failure is predicted to occur by brittle fracture.

The proximity to plastic collapse is given by the ratio of the applied reference stress, _ref, to the yield strength _Y.

L _r = _ref/ _Y

If L _r = L _{r max} (see various cut-offs in Fig.2.) failure is predicted to occur by plastic collapse.

A failure locus provides the connection between K _r and L _r and any assessment point falling on or below the failure locus means that the flaw is stable and does not present a significant risk of failure. Assessment points above the failure locus represent unacceptable flaws which may cause failure.

For materials which fracture in an elastic-plastic fashion, alternative fracture toughness parameters have been proposed, namely J and the crack tip opening displacement CTOD. CTOD testing and assessment procedures are extensively used in the offshore construction and pipeline industries, whilst J testing procedures are more common in the power generating industries. For cases where these parameters describe fracture, K _I and K _Ic are replaced by J or CTOD using suitable relations. However, the principle of the assessment procedure remains the same.

Fatigue Assessment

Fatigue is a failure mechanism that involves the stable propagation of a crack under repeated or cyclic loading. Each load cycle causes a very small, but finite amount of crack extension. The crack therefore extends steadily until a final failure mode such as fracture or gross yield intervenes.

The basis for all fatigue assessment is the assumption that the increment of crack extension, da, per cycle, dN, is a function of the applied stress intensity factor range, K _I:

da/dN = A K _I ^m

K _I is calculated in the same manner as the applied stress intensity factor, K _I for fracture assessments with the exception that the applied stress ranges rather than the applied stresses are used.

Although the constants in - A and m - are material dependent, extensive experimental work has shown that for steels and aluminium alloys, they have similar values for a wide range of steel yield strengths and microstructures for a given environment. Thus, for steel, fatigue behaviour can be assumed to be independent of microstructure. Experiments have also shown that below a threshold stress intensity factor, no fatigue crack growth occurs in steels (see BS 7910 ^[1]).

The above equation can be invoked to calculate the number of cycles N corresponding to the growth from an initial to a final size, to estimate fatigue life.

The initial flaw size often represents the height of a flaw found by non-destructive testing, and the final flaw size is set by the limiting failure condition, such as through wall cracking, leakage or the maximum tolerable size calculated using the fracture assessment procedure described in the previous section. For an assessment based on the failure analysis diagram ( Fig.2), the final crack size would correspond to a point on the failure locus.

Conclusions

There now exist fully documented and accepted procedures for assessing weld flaws using fitness-for-purpose principles. Application of these procedures offer extensive scope for significant cost saving in design and fabrication; during inspection and operation; and at the end of the design life of welded structures with quantifiably ensured structural integrity.

References

BS 7910:2005: 'Guide to methods for assessing the acceptability of flaws in metallic structures'. London; British Standards Institution, 2005.
BS 7448: 'Fracture mechanics toughness tests: Part 1 : 1991. Method for determination of K _Ic, critical CTOD and critical J values of metallic materials'. London; British Standards Institution, 1991.
ASTM 1820-99, Standard Test Method for Measurement of Fracture Toughness. American Society of Testing and Materials, Philadelphia, PA, 1999.