Engineering Materialism and Structural Integrity

Journal of Engineering Design, Vol. 9, N o. 4, 1998

Engineering M aterialism and Structural Integrity

M . NEIL JAM ES

S U M M A RY Two prime engineering focuses are concerned with what might be term ed `materialism’ , and w ith structural reliability. This paper discusses the interconnections between these in the context of the historical development of engineering capability, highlighting the associated risk in application and use of this capability, and the accrued bene® ts for mankind. As successful engineering rests on com munication skills, as well as analytical skills, the paper starts by considering word power and status as a precursor to de® ning mechanical engineering and the `design paradox’ associated w ith innovation. It then considers the m utuality between soun d design and effective materials usage, before outlining the advances in m aterials engineering and design philosophies related to crack grow th phenom ena. T hese advances currently allow extremely complex structures to operate w ith known, and statistically de® ned, probabilities of failure.

1. Introduction O ne can reasonably claim that engineering is prim arily concerned with m eeting the following hum an needs:

· Sustainab le infrastructural developm ent (buildings, com m unication, transport, power and water reticulation);

· Higher quality of life through provision of affordable tools, appliances, sp orting and hobby go ods;

· Defence and life support (medical engineering, prostheses). In a capitalist society, quality and reliability in all these areas is driven by public education and expectations (and potential litigation), and by com petition between m anufacturers. That sam e capitalist outlook, however, also requires a m axim ized return on investm ent. Hence, as quality is closely linked with ® rst cost, while reliability is dependent on both ® rst and life-cycle (e.g. inspection and m aintenance) costs, there is always a calculated balance in engineered products, com ponents and structures betw een cost, quality and reliability. Equally, these three param eters are greatly in¯ uenced by m aterials selection and usage (processing, fabrication and environm ent). Thus, tw o prim e engineering focuses are concerned with what m ight be term ed m aterialism and with structural reliability or integrity. In exam ining th is prem ise further, which, in the context of m echanical engineering, is the purpose of this pap er, a useful starting point is the N ew Shorter Oxford D ictionary which de® nes the term s used in th e title as: M. N. Jam es, Professor of Mechanical Engineering, Departm ent of Mechanical and Marine Engineering, University of Plymouth, Drake Circus, Plym outh, Devon P14 8AA , UK . 0954± 4828/98/040329± 14

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· Engineering: The application of science for directly useful purposes; th e action of working artfully to bring som ething about;

· M aterialism: A tendency to lay stress on the m aterial aspect of objects; the · Structural: · Integrity:

doctrine that nothing exists except m atter and its m ovem ents and m odi® cations; O f or pertaining to, building or construction, the m aterials of construction, the arrangem ent and m utual relation of the parts of any com plex whole; U nimpaired or uncorrupted condition; no part or elem ent taken aw ay or lacking.

Hence, one can loosely translate the engineering import of the title as: The application of science and artful working in order to stress m aterials such that the arrangem ent and m utual relation of parts of com plex structures rem ain in an unimpaired and com plete state. O ne can further interpret the title in term s of the basic capitalist driver of ® nance as: The desire to m ake m oney through, and by, engineering has led to greater structural reliability. The àpplication of science and artful wo rking’ is essentially the role of engineering design, which has a key part to play in the creation of wealth by m axim izing the value of engineering products to both purchaser and supplier. As noted, m axim ized value derives from consideration of life-cycle cost as well as ® rst cost, and hence requires understanding of processing± fabrication± property relationships in available m aterials, as well as th eir perform ance throughout the life of a structure. It is clear, therefore, that optim al engineering design m ust take account of these aspects of m aterials usage and, often, is m aterials-lim ited. Innovation is a fundam ental characteristic of `good’ design. This characteristic rests, quite largely, on the expertise of engineers in analytical perception of the critical param eters of a design, and their ability to incorporate these into elegant solutions which provide optim al capability and cost-effectiveness. Clearly, engineers need to be m otivated, highly trained and intelligent people, yet the current low status of engineering as a profession in the U K m akes it dif® cult to attract potential `top ¯ ight’ graduates. This ap pears to be due both to sem antic connotations of engineering term s, and to low salaries relative to dif® culty of the initial training and to the requirem ent for continuous skill updating during a professional career. Thus, the paper will start by brie¯ y considering word power and status as a precursor to de® ning m echanical engineering and the `design paradox’ associated with innovation. It then considers the m utuality betw een sound design and effective m aterials usage, through exam ination of the historical inter-relationships between developm ents in m aterials, progress in engineering capability and the personal bene® t and risk accrued from such activity. Finally, it outlines the advances in m aterials engineering and design philosophies (the application of science and artful working) related to crack growth phenom ena, which currently allow extrem ely com plex structures to operate with know n, and statistically de® ned, probability of failure.

2. W ord Power and Status An academ ic career could be sum m ed up as à gam e of wo rds’ , but it is less often realized (at least by students) th at the successful practice of engineering also hinges

M aterialism and Structural Integrity

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T A BLE I. W ords associated with engineering activities W ord

Feeling

Perception

Fam iliar: Craftsm anship

W arm Cold Neutral W arm

Skilled; m ade with emotional involvem ent, often using `natural’ m aterials (e.g. wood, leather, stone, glass, brass, etc.) M ore automatic; m ade with little or no emotional involvement a Purposefully m eeting a need Recognizing opportunity; optim izing uncertainty

Neutral W arm Neutral Neutral

To shareholders, accountants, lenders and capitalists, this is the driverb c Adding values to raw m aterials/products through engineering M anagement of the engineering process; marketing d Evolutionary change involving a quantum jum p in capability

Technology Design Innovation Less fam iliar: Finance Bene® ciation Business skills Metam orphosis a

T his is the core of the `heart of darkness’ syndrom e, in which engineers are perceived as being solution-orientated to the extent of becoming inhum ane or environmentally unaware. Classic examples are the developm ent of weapons of m ass destruction, large projects with unfavourable environmental impact (m ines, dam s), global warm ing, etc. The problem is addressed in engineering curricula, but rational public discussion of new projects m ay be hindered by overtones of `political correctness’ . There is also the associated problem of the ìncomprehensibility’ of technology. b Engineering projects have to provide a return on investm ent, even when public m oney is involved. This requires consideration of life-cycle cost as well as ® rst cost, and hence, implicitly has connotations of reliability and risk assessment. c A simple visualization of the process is the increase in cost/kg in going from bauxite ® alumina ® aluminium ® engine components. The complexity of product analysis and design increase at each stage, and the quality and reliability issues, become m ore stringent. Bene® ciation and the associated concept of retaining at least som e of the added value by recycling are becoming m ore important as resources diminish. d This is the design paradox mentioned. The import of this will be discussed.

rather largely on literacy. W hile m athem atical elegance and com plex num erical procedures m ay `blind people with science’ in the short term , long-term acceptance and developm ent of engineering ideas relies upon persuasive m arketing, i.e. winning hearts as well as m inds. The dif® culty with this lies in the feelings and perceptions engendered by words which m ight be associated with engineering in the m ind of the public; in particular, the rather negative prevailing image of technology (see Table I) and traditional engineering disciplines (mechanical, civil, electrical). Thus, th e image of engineers as taciturn, goal-orientated num ber crunchers m ay be a contributory factor to their low esteem in the U K, despite the phenom enal bene® ts that engineering has delivered to society, but wo rd power has not helped; the popular perception of m echanical engineering in this country relates m ainly to its connotations of operating and building m achines (particularly those for delivering rotational energy). Hence, when m achine operators and artisans `dow n tools’ in disputes with m anagem ent, newsp ap er headlines like Èngineers on Strike’ have popular impact, despite being grossly incorrect! This perception is som ewhat at odds with the real root of the term èngineer’ . The N ew Shorter O xford D ictionary has 11 de® nitions of èngine’ ; the ® rst four deal with fundam ental requirem ents of successful engineers and engineering, i.e. natural talent, wit, genius; ingenuity and cunning; instrum ents and tools. O nly the last four deal with m oving parts and energy concepts. In arriving at a m ore apt de® nition of m echanical engineering, let us consider typical words, and th eir associations, that m ight be used in de® ning engineering activity (Table I). D rawing on th ese words and their import, m echanical engineering can be de® ned as:

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M . N . Jam es T AB LE II. Engineering as a business-orientated function Drivers

Enabling areas of innovation

Outcom esÐ

Need M arket Pro® t

Appropriate technology Design M aterial properties Fabrication/m anufacture

Function Form Finance

optim ised

The process, skills and technology used to achieve optim ized `m etam orphosis’ of m aterials into com ponents, m achines and structures. O ptim ization is achieved in term s of cost, concept and cap ab ility, while innovative design and engineering are implicit in the de® nition. This de® nition also em bodies a business orientation to engineering, as shown in Table II. The prim e driver and the desired outcom e of engineering activity is the creation of wealth and it is clear that, of the four enabling areas in the table, design is the linking area and the pivot on wh ich success or failure generally rests.

3. Design is the K ey Design, therefore, has a key role to play in the creation of wealth, because it allows m axim ization of th e value of engineered products to a potential purchaser. However, the `design paradox’ m entioned earlier often causes optim al solutions to be m issed or bypass ed in favour of m ore accessible and, probably, m ore m undane solutions. The paradox arises because engineering is easiest when it is a process of evolution based on previous experience. The weight of historical precedent, together with the advantage of hindsight in re® ning details, tend to lim it innovative (quantum jum p) solutions. The advantage of innovation, if it can be achieved, is that it m ay advance technological capability, open up new avenues of design exploration and, hence, allow developm ent of potential new incom e stream s. By de® nition, how ever, innovation involves the presently unknow n and thus, to a degree, requires ability in recognizing opportunities and m anaging uncertainty. It also requires that connections are m ade between seem ingly unrelated concepts/factors to reveal a new relationship in which they provide synergy. Few people appear to be naturally skilled in these activities, and the taught route to innovationÐ the brainstorm ing processÐ is encouraged by apparently unstructured thinking and a (tem porary) suspension of critical analysis. For engineering students, this is in contradiction to the years of structured and critical analytical thought inherent in technical training. The net result is that too m any engineering concepts achieve reality through com plex m undanity rather than elegant sim plicity. Training in innovative thinking is an area of engineering education that rem ains unresolved, although som e linkages are being forged between design activities in engineering departm ents and those given in departm ents of art and design. This m ore broadly based exposure to design philosophies in the early years of degree program m es should yield tangible bene® ts to both parties. It m ay also be possible to gain insight into innovation through considering the lessons learnt from `failures’ of either structure or design, i.e. concepts which `crashed’ in th e m arketplace, either literally or m etaphorically. M any of these failures indicate that innovation, at least partly, is de® ned in term s of current fashions and fads, as well as engineering param eters. Innovation can take place in concept form ation (e.g. shape, com binations of attributes), function (e.g. speed, reliability, lifetim e) or in m aterials use and properties.


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F IG . 1. Inter-relationships between m aterials and design. However, advances in function and concept are often related to the availability and use of improved m aterials. This interweaving of m aterial characteristics with design possibilities/opportunities is fundam ental to successful engineering and is illustrated in Fig. 1. Explicit consideration of the m aterials/design interaction is an integral part of the process in optim ally ensuring:

· Suitability of the design for the required perform ance envelope: H ow m ust it function and in what environm ent?

· Ease and soundness of fabrication: H ow well and how easily can it be m ade? · Ease of m aintenance: H ow sim ple and how cheap is it to own? · Reliability and durability: H ow long and how safely will it perform ?

4. M an and M aterials This pap er has brie¯ y developed the idea that successful and well-optimized design has to be based on consideration of the relevant properties of available m aterials. Such designs m ay still be lim ited in their perform ance, when m aterials engineering cannot deliver th e required level of properties. The classic exam ple of this is the therm al ef® ciency of internal com bustion engines (reciprocating or turbine). This is lim ited by the oxidation, creep, fatigue and fracture resistance of available high-tem perature m aterials. Nonetheless, we have reached a stage of hum an developm ent where, in our interaction with the environm ent, we are able to design or engineer m aterials to possess better properties, as well as design com ponents/structures which better utilize these im proved properties. The importance of m aterials to m ankind, and their pivotal role in developing technological and engineering capability has long been recognized. Thus, the term s stone age, bronze age, iron age, etc., are regularly invoked to identify crucial stages in hum an technological developm ent. It m ay be m ore apposite to de® ne the interaction betw een m aterials engineering and m ankind in term s of the bene® ts, risk and reliability associated with the engineering capability conferred by the level of m aterial properties available at various historical stages. Som e facets of this interaction are presented in Fig. 2. The diagram could be

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further subdivided, or arranged in alternate ways, but appears to bring out the salient details of the risk± bene® t relationship. Thus, with only ìntrinsic’ properties available, engineering capability was con® ned to the pre-industrial level. Engineering practice was based alm ost exclusively on prior experience, and expertise was controlled via guilds and the like. There was virtually no understanding of m icrostructure± property relationsh ips, although , for exam ple, it m ight be know n that quenching a steel blade into brine (or blood) gave a better edge than quenching into water. U sage of engineered products was restricted m ainly to utility item s, although the upper echelon of society had access to luxury products of high craftsm anship and beauty. These, however, generally served the sam e purpose as sim pler, m ore widely available item s of the sam e type. The bene® t of engineering cap ab ility to the bulk of the populace was therefore low in life. In death, however, the perceived value of certain products m ight be very high (e.g. th e jade funerary suits from C hina, which were supposed to resist decay of the ow ner and hence assist in conferring imm ortality). In m odern term s, even everyday item s have a high death value because of their archeological context. Pre-industrial engineering capability is associated with a generally low level of risk to users, and the reliability of products is acceptable as there are no alternatives. The situation is really one where the `buyer bewares’ and it is worth noting that even kings have occasionally suffered wh en `leading edge’ technology has failed. For exam ple, early cannon were prone to exploding during ® ring and Jam es II of Scotland was killed in 1460 when a large cannon (® ring a 300 lb projectile) called the `L ion’ burst. R isks to the m aker/tester could be high, and a m acabre exam ple of this was testing of Sam urai sw ords on convicted crim inals in m edieval Japan. Figure 3 shows a typical sw ord-testing diagram from the Y am ada fam ily [1] (courtesy of M rs D .J.S. Jam es), wh ich is labelled in term s of dif® culty of achieving the cut in one stroke (1 indicating the m ost dif® cult and 16 the easiest cut). The stoicism of the convicts is wo rth recording. O ne, on hearing his sentence (to be cut in style 5), is reported as saying that he wished he had known it in advance, because he wo uld have sw allowed several big stones to spoil the sword. In the W est, testing was usually less hazardous and Fig. 4 illustrates a bullet proof-m ark on a suit of arm our, which has been m ade into part of the decoration as the centre of a ¯ ow er [2]. Discovery of the category of m aterial properties term ed ènhanced by engineering’ , allowed prim ary industrial developm ent to occur and includes the period up to th e early part of the tw entieth century. B asic property testing for m aterials was available, but quantitative life prediction for loaded structures was not yet possible. Structures subject to static and dynam ic loading were designed with `factors of safety’ (really factors of uncertainty) incorporated into th e analyses. U se of m achinery becam e widesp read, with the result th at sudden unexpected failures of dynam ically loaded or pressurized structures were com m onplace. R isk levels were high for m achine operators and wo rkers, but rem ained low for capitalists due to the em ergence of an insurance industry and the lack of product liability legislation. The basic necessities of life were rendered m ore com fortable and m ore widely available through increased technological and engineering prowess (in term s of both product choice and purchasing power, i.e. disposable incom e). Q uality of life, as m easured by access to luxury goods and recreational pursuits, extended down to the m iddle class, and there was a fair death bene® t of engineered products (which did not experience planned obsolescence) arising from their cash and inheritance value. The present era is de® ned by high-technology m icroprocessor-controlled industry.

F IG . 2. Illustration of the bene® ts, risk and reliability interaction in m ankind’ s history of m aterials usage.


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M . N . Jam es

F IG . 3. Swo rd Testing (Tam eshigiri) according to the Yam ada fam ily.

Desired m aterial properties can often be conferred through sophisticated engineering of the structure± processing± property relationships, and predicted with go od accuracy. Almost every property can be accurately determ ined by testing, while defect-tolerant design and fracture control plans are widely used to ensure structural reliability to statistically known values. High-quality autom ation of production processes delivers repeatable luxury item s with a high `joy of ow nership’ to the bulk of the populace in the industrialized countries. The death value of m any highly engineered products is, however, low (at least until they becom e antiques) because of fast obsolescence cycles (brought about partly by design and partly by the pace of change in technology). (It m ight also be posited that the change in death value associated with state-of-the-art

F IG . 4. Detail sh ow ing proof m ark on the breast of a suit of arm our m ade for Louis X IV.


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T ABLE III. Causes of all failures of boilers and pressure vessels in the UK (1962± 1967) [3] Number Cause of failure: Cracks Maloperation Manufacturing defect Corrosion creep

Cause of cracking Fatigue Corrosion (including stress corrosion and corrosion fatigue) Manufacturing defect Unknown

Percentage

118 8 3 2 1

89 6 2 2 1

47

40

24 10 37

20 8 32

engineered products re¯ ects the m ove in society from a spiritual outlook to a m ore m aterialistic one! W hether th e change is a cause or an effect is not clear.) C om prehensive occupational safety and product reliability legislation has reduced the risk to wo rkers and operators and m ade it incum bent on capitalists to ensure that they com ply with safety codes. Hum an fallibility and/or unforeseen circum stances still lead to occasional catastrophic failures.

5. Designing For Structura l R eliability The preceding part of this paper has brie¯ y considered the topic of engineering m aterialism and its impact on developm ent of technological capability; it now discusses som e of the background to structural reliability issues. Engineering m aterialism and structural reliability have a strong linkage, which is m ade clear from several powerful drivers wh ich have spurred the developm ent of structural reliability codes. These drivers include:

· Desire of insurers to m ake m oney: G uidelines on design and m aintenance were · · ·

implem ented as a prerequisite of cover; equally, skills in failure analysis were developed to `close the design loop’ ; Litigation for com pensation in th e event of failure: This includes product liability, dam ages and loss of production/pro® ts; Com petition for business between m anufacturers and fabricators; Increased expectation of quality and reliability from the public, arising from higher levels of education.

The particular focus of consideration is two phenom ena which were largely unknow n, and certainly not de® ned, prior to the industrial revolution (prim ary industrial stage)Ð fatigue and fast fracture. C racking accounts for, by far, the large m ajority of catastrophic engineering failures, with fatigue being the single m ost important cause (Table III). Hence, developm ent of expertise in defect-tolerant design and fracture control plans has been crucial in allowing industry, and hence m ankind, safe exploitation of the bene® ts of technological and engineering capability. H ow ever, structural reliability design which takes explicit account of m aterial behaviour is a recent developm ent. Early design practice took a continuum m echanics

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F IG . 5. C yclic bending loading of a wrought iron beam by Fairbairn in 1864. approach based on uncracked com ponents. The intention in the rem ainder of th is paper is to outline som e of the advances in understanding the behaviour of cracked m aterials and show how these advances m odi® ed design philosophies, leading to predictive m ethods for the response of cracked bodies under load (the discipline of fracture m echanics). Fatigue describes the failure of engineering m aterials under dynam ic loading, by a process of crack initiation and growth. The initiation phase m ay be bypassed in the presence of a pre-existing crack-like defect. The term was coined in the m iddle part of the last century to describe failures of rotating parts (particularly railway axles) wh ich had, apparently, `tired’ of carrying the load after perform ing satisfactorily for a period of tim e. Fast fracture describes sudden catastrophic collapse which can occur under static loading, steadily increasing loading or as the ® nal stage of a fatigue fracture. De® ning characteristics of failures from these m echanism s are that crack growth occurs under loads, generally, well below the tensile yield strength of the m etal and with, usually, little prior indication of imm inent collapse. The ® rst stress± life (S± N) fatigue tests of structural com ponents were perform ed before 1871 (e.g. Fig. 5 shows the apparatus used by Fairbairn to apply cyclic bend loading to a wrought iron beam [4]). Around the sam e tim e, fatigue was recognized as a process of crack initiation and growth, although m etallographic evidence to support this was not forthcom ing until the early twentieth century. C lassic work by W oÈ hler in G erm any established th e importance of local stress concentrations to fatigue strength (Fig. 6) [5]. Such work led to the safe-life philosophy of fatigue design, which is based on obtaining statistically m eaningful S± N data under appropriate conditions of, for exam ple, surface state, load type and environm ent. Failures tend to occur when using this approach where there is:

· Incorrect assessm ent of: Loads, resonant frequencies, environm ent; · Unforeseen changes in: U sage, environm ent, surface condition (inadvertent dam ·

age); Hum an error: poor fabrication/m achining, poor inspection/m aintenance, incorrect operating procedures, change in technology.

Thus, for safety-critical applications, particularly in the aircraft industry, the philosophy was extended into fail-safe design. This approach takes account of:

· Incorporation of redundant load paths; · Explicit inspection intervals;


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F IG . 6. W oÈ hler’ s S± N data on the in¯ uence of notches on fatigue strength.

· Identi® cation of critical areas from full-scale testing; · Codi® ed design procedures. 6. Application of Fracture M echanics A num ber of high-pro® le structural failures, such as the Liberty ship-cracking problem s, the C om et aircraft disasters and bridge failures (e.g. Point Pleasant over the O hio River), spurred investigation of the behaviour of cracked bodies under load, leading to developm ent of the discipline of fracture m echanics in the period since 1945, and its application to fatigue crack growth. In m odern codes for fracture-safe design, such as the C EG B R6 docum ent [6], a tw o-param eter ap proach is adopted, which considers the conjoint possibility of plastic yield and fast fracture. Early work centred on linear elastic fracture m echanics, where m acroscopic behaviour of the com ponent or structure rem ained elastic. The foundations for this had been laid earlier in the century by workers like Inglis [7] and Grif® th [8]. This work was extended by Irwin wh o analyzed the stresses and strains near a crack tip [9] and introduced th e concept of th e crack tip `stress intensity factor’ K. This param eter characterizes the ìntensity’ , or m agnitude, of

F IG . 7. Effect of a notch on ¯ ow stress.

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the near-crack tip stress and strain ® eld under linear elastic conditions, and K is, therefore, the num erator in th e crack tip stress equations, i.e.

s

ij

5 f

S D Î a

W

s

Î

a f ij ( v )

(1)

r

where s is the nom inal stress rem ote from the crack tip, f(a/W ) is a ® nite geom etry correction, a is crack length, and r and v are distance of the point of interest and its angle, relative to th e crack tip. This allows ap plied load cycles to be de® ned in term s of K m ax , K min and D K . The propensity for `critical’ crack growth (fracture) can be related to K max , and that for `sub-critical’ crack growth (fatigue) to D K. W hether or not brittle fracture occurs depends on the relative ease with wh ich perm anent deform ation can occur (by slip or twinning in m etals). Ease of slip is a function of crystal structure (through Peierls± Nabarro stress, num ber of slip system s, sh ort- and long-range order), m icrostructure, stress state and strain rate. The stressstate in¯ uence is often critical in the occurrence of fast fracture and arises from the presence of a notch or crack-like defect. This induces a state of triaxial stress near the crack tip wh ich elevates the plastic ¯ ow stress by a factor of up to 3. Particularly for the case of ferritic alloys, which show a strong tem perature dependence of ¯ ow stress, and under high strain rate loading, this m ay m ake brittle fracture m ore likely than plastic ¯ ow at norm al am bient tem peratures (see Fig. 7). M icrostructure also plays an important role in the ease with which crack nuclei can develop. Standard tests for fracture toughness have been developed and codi® ed, together with standard procedures to assess the criticality of defects. Cleaner, tough er steel com positions have been developed together with th erm o-m echanical processing routes that optim ize m icrostructure to give good com binations of toughness and strength. W elded joints require particular attention, due to the potential for defects, graded m icrostructures (epitaxial growth and constitutional supercooling in the weld m etal, differential therm al cycles and associated phase changes in the heat affected zone) and dilution effects in the weld m etal. Q uanti® cation of fatigue crack growth has bene® ted greatly from improvem ents in the sensitivity and discrim ination available from non-destructive testing (ND T), and from the realization by Paris and Erdogan [10] in the early 1960s that the range of stress intensity factor characterized fatigue crack growth rates over m uch of the industrially useful life of cracked com ponents (growth rates in the range 10 2 2 m m /cycle to 10 2 6 m m /cycle). The equation relating D K and growth rate da/dN is da dN

5

C D Km

(2)

This can be readily integrated to provide a quantitative estim ate of the life to grow a crack between tw o sizes, and N DT em ployed to check the accuracy of th e prediction. This is defect-tolerant design, or a philosophy of `living with cracks’ , which accepts that m anufacturing and fabrication processes m ay introduce defects into com ponents and structures. Successful implem entation requires setting explicit inspection intervals together with the correct level of inspection (to ensure th at cracks in critical regions are detectable at a safe length). Provided that a suitable K calibration exists for the cracked geom etry of interest, and a crack growth rate curve for the particular alloy and environm ent is available, life prediction is fairly straightforward.


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7. M aterial Issues The accuracy of fatigue life prediction is affected by a num ber of m aterials-related issues, som e of which are quite subtle and are still not com pletely resolved. Considering, ® rst, the crack growth rate curve, values of growth rate are in¯ uenced by m echanical factors (mean stress in the fatigue cycle), environm ent and m icrostructure. However, the effects of m ean stress and environm ent are, them selves, often in¯ uenced by alloy com position and m icrostructure (through a phenom enon known as crack closure, which is a crack tip shielding m echanism , i.e. it prevents the crack tip process zone from experiencing the full range of applied D K ). The slope of the growth rate curve (the power m in equation (2)) is a function of growth rate m echanism , which is also dependent on alloy and m icrostructure. Several other problem s derive from the continuum m echanics assum ptions of a hom ogeneous, isotropic m aterial that are attendant on the use of K. These assum ptions im ply that tw o cracks of different sizes, which experience the sam e D K values, have the sam e size of crack tip plastic zone and identical stress and strain ® elds outside the plastic zone. This sim ilitude can break down wh ere non-continuum effects predom inate, i.e. for sm all cracks which are on the sam e scale of size as local plasticity or m icrostructural dimensions. It also fails where local crack tip K values re¯ ect m icrostructural and growth m echanism effects and do not scale to th e global applied K values in the sam e way, i.e. where crack tip shielding m echanism s are operative [11]. Thus, th e response to stress in fatigue and fracture is:

· At the local (crack tip process zone) level, largely controlled by non-continuum , anisotropic m aterial characteristics;

· At the global level, am enab le to continuum m echanics description. Problem s in life prediction arise when these tw o responses vary in a non-system atic, and signi® cant, way between test specimens and the real structure of interest. Areas where this m ay occur include:

· Anisotropic m aterials (e.g. ® bre com posites); · The presence of large-scale m icrostructural phases; · Brittle or environm entally sensitive phases; · Sm all cracks;

· Variable am plitude and random loading; · M ulti-axial loading. Be that as it m ay, the increased m echanistic understanding of fatigue and fracture, which has been driven by engineering m aterialism , has enabled developm ent of tougher, m ore weldable alloys in thick sections (which tend to be m ore prone to brittle fast fracture than th inner onesÐ sim plistically, this can be visualized as a consequence of energy released during crack growth being a volum e term , while energy ab sorbed is largely an area term ). Life prediction for very com plex structures can be perform ed at a sm all percentage of their cap ital cost (perhaps 2± 5%). Such structures as aircraft and offshore platform s operate reliably for long periods of tim e with a de® ned probability of failure. Thus, it could be prem ised that capitalism , underpinned by sound m echanical and m aterials engineering, has, in this instance at least, led to a capability in structural reliability and risk assessm ent th at illustrates the best aspects of a com petitive m arket place.

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REFER EN C ES [1] J O LI , H.L. & H O JIT ARO , I. (1962) T he Sword and Sam eÂ (Holland Press) (reprinted: W hitstable, K ent, Latim er, Trend). [2] F F O ULK ES , C. (1988) The Armourer and His Craft (reprinted: New York, Dover Publications). [3] L A NC AST ER , J. (1996) Engineering CatastrophesÐ Causes and Effects of M ajor Accidents (Cam bridge, Abington Publishing). [4] F A IRBA IRN , W . (1864) Exp erim ents to determ ine the effect of impact, vibratory action and long continued changes of load on wrought iron girders, Philosophical Transactions of the R oyal Society, 154, pp. 311± 325. [5] W OÈ H LER , A. (1871) U ber die festigkeitversuche m it eisen und stahl, Engineering, XI, pp. 199± 200, 221, 244± 245, 261, 299± 300, 326± 327, 349± 350 (English account). [6] Assessment of the Integrity of Structures Containing Defects, R6Ð R evision 3, C entral Electricity G enerating Board, February 1997. [7] IN G LIS , C .E. (1913) Stresses in a plate due to th e presence of cracks and sharp corners, Transactions of the Institute of N aval Architects, 55, pp. 219± 230. [8] G R IFFITH , A.A. (1920) The phenom ena of rupture and ¯ ow in solids, Philosophical Transactions, Series A, 221, pp. 163± 198. [9] IR W IN , G .R. (1957) Analysis of stresses and strains near the end of a crack traversing a plate, Journal of Applied M echanics, 24, pp. 361± 364. [10] P ARIS , P. & E RD O GA N , F. (1963) A critical analysis of crack propagation laws, Journal of Basic Engineering, December, Vol. 850, N o. 4, pp. 528± 534. [11] R ITC H IE , R .O. & Y U , W . (1986) Sh ort crack effects in fatigue: a consequence of crack tip shielding, in: R IT C H IE , R.O. & L A N KF O RD , J. (Eds), Sm all Fatigue Cracks (Pennyslvania, The M etallurgical Society).