Engineering Fraca~lure Mechanics, 1969, Vol. 1, pp. 507-S 17. Pergamon Press. Printed in Great Britain

APPLICATION OF FRACTURE MECHANICS IN DESIGN AND ANALYSIS OF PRESSURE VESSELS*

VICTOR SINGER

Structural Engineer, Thiokol Chemical Corporation, Elkton Division, Elkton, Maryland

Abstract-The extent to which-the nominal safety factor describes a pressure vessels strength is regarded as depending upon how well the assumption of Sufficiently flawless composition describes the configuration. For ve!sels where a leak-before-burst or leak-before-yield criterion cannot be satisfied, the nominal safety factor is regarded as applicable to populations of vessels rather than to individuals. Criteria for control of fracture in such vessels are proposed, on the basis that the sensitivity of the structure to the presence of flaws should be a fixed percentage of local thickness at any location. Current capabilities of non-destructive inspection tech- niques are reviewed, with emphasis on how large a flaw may be missed, rather than how small a flaw can be detected. Design implications of fracture considerations in regions experiencing flexure are examined. Bases are established for determination of effective flexural stresses and for assessing the significance of residual stresses. Finally, attention is drawn to often ignored brittle behavior possibilities in attachment regions, and to techniques for their control in the design process.

KZ u

=2/P, Ft, Fttl

t

; .U 6 L P

;

NOTATION

plane stress plastic zone size plane strain fracture toughness stress yield strength ultimate strength section thickness crack depth shape factor strain energy deflection element length applied concentrated load Poissons ratio energy available for crack extension.

INTRODUCTION FROM the classical philosophy of structural safety has evolved the safety factor concept, the ratio of the strength of a material to the level of stress it experiences under service conditions. Design procedures using this concept have developed from much experience with similar materials and similar service conditions, empirical demon- strations of how large a safety factor will assure a successful structure. In all but the simplest structures experiencing the simplest kinds of load distributions, the nominal safety factor is an indication that failure is highly improbable at service load level rather than a definition of a precise level of failure loading. This is because quite often structural behavior is so complex that it is intractable except through approximate representations of its many aspects in the analytical model. For example, materials are

*Presented at the National Symposium on Fracture Mechanics, Lehigh University, Bethlehem, Pa., June 17-19,1968.

507

508 VICTOR SINGER

classically considered to be of sufficiently flawless composition to behave in tension always according to the usual stress-strain curves. Vessels composed of materials capable of resisting through-cracks, anywhere, with length equal to several multiples of local thickness (a leak-before-burst or leak-before-yield criterion), are quite reason- ably described by the classical approximation.

THE SHIFT FROM THE CLASSICAL SITUATION

In recent years, this approximation has become less universally applicable. On the one hand, with the development of extreme high strength metals, the range of the term sufficiently flawless composition must now include flaw sizes so small that their occurrence is disturbingly frequent. In the high strength metals, these small flaws are occasionally sufficient to cause structural failures at stress levels much below the unflawed strength of the material. And on the other hand, with less exotic metals used in cross-sections of ever larger minimum dimension at ever higher stress levels, flaws large enough to control behavior may escape detection. Besides evaluating safety factors on the classical basis, the designer must now treat the assumption of sufficiently flawless composition.

In current pressure vessel practice, this treatment is represented by the proof test. The proof test, however, does not assure the absence of significant flaws, but only that nowhere is there present a flaw large enough to cause failure under the stress conditions imposed on it by the proof load. The demonstrated (initial) factor of safety in such a structure is therefore the minimum value of the ratio of stress imposed anywhere under proof load to the stress imposed in the same location and direction under service conditions. In vessels without leak-before-fracture capability, no larger factor of safety has any basis in fact, except perhaps statistically. Though a larger analytical value may be obtained as the ratio of nominal strength to maximum service stress level, it is a paper number applicable at best only to a large statistical sample of like structures if the material is actually of relatively flawless composition. There is no reason to believe that any individual structure does not represent the outlying data point with all the large flaws in the lot; thus, it could have been at the verge of failure in the proof test.

Following this line of reasoning, primary attention must be given to the relation- ships among proof load level, service load level and the classical yield and ultimate load levels. It is the designers dilemma to relate these load levels so that three conditions are satisfied in spite of the finite probability of incidence of significant flaws in the as- fabricated structure (flaws inherent to the nature of the material as well as flaws intro- duced in the fabrication process). First, there must be sufficient assurance against an excessive number of proof test failures. Second, the margin between proof load level and service load level must provide suitable assurance against failure in service. And finally, the margin between service load level and the statistically applicable classical yield or ultimate load levels must be small enough that the structure is not too gross to be serviceable or producible. In short, the heart of the problem is to put the margins where they buy the most real safety not only in the average structure described by the classical-flawless - safety factor, but in all the structures, even the statistical extreme values.

THE ARGUMENT FOR A STANDARDIZED MINIMUM DESIGN FLAW SIZE Investigation of many solid propellant rocket motor case designs leads to the

observation that .proof test failures resulting from previously undetected flaws have

Application of fracture mechanics 509

occurred most often in those designs where the depth of a surface flaw sufficient to cause failure at or below proof stress levels-evaluated according to linear elastic fracture mechanics-has been less than about 15 per cent of the wall thickness. This does not suggest that such a flaw was observed in every premature failure; rather it is a characterization of pressure vessel capability in terms of the depth of flaw that could have been present without interfering with behavior more-or-less consistent with the usual stress-strain information. Successful experiences with vessels capable of with- standing larger flaws are probably due to the facts that larger flaws occur less frequently than smaller ones, and that larger flatis ate more readily detected via non-destructive inspection techniques.

Additional verification of a 15 per cent flaw dividing line may be obtained by re- interpretation of Thurstons compilation of pressure vessel burst tests [ 11 summarized from many other sources. For many of the referenced vessels, apparently valid fracture toughness information has been given and roll and weld fabrication practice has not been used. Of this group, those vessels for which the depth of a flaw sufficient to cause premature failure was greater than 15 per cent of thickness, seem to have had no difficulty in achieving burst stress levels substantially in excess of uniaxial strength values. More than Q of the vessels in which the corresponding critical flaw size was smaller than 15 per cent of thickness failed considerably below the yield stress level.

Bitter experiences with current non-destructive inspection techniques in the recent past have shown that there is a large gap between capability to detect occasionally an extremely small flaw advantageously disposed for detection, and capability to detect all flaws of some much larger size which may be present, though disadvantageously disposed for detection. The investigation of the burst of a recent large rocket motor case[2] showed that though flaws with a dimension parallel to the thickness of the inspected part of O-5 per cent of that thickness are sometimes found, flaws of depth equal to 15 per cent of the thickness are sometimes missed, even with very careful inspection. Thus, the size of flaw that will neoer escape detection is certainly not smaller than 15 per cent of the thickness of the inspected part and may even be larger. Another measure of current inspection techniques is obtained from approximately 1000 proof tests of the MINUTEMAN ICBM first stage motor case, in which three failures have occurred from previously undetected flaws in the cylinder welds. The properties of that case material are such that at proof pressure level, a long shallow surface flaw of depth equal to at least 16 per cent of the wall thickness can be tolerated. Inspection techniques therefore afford no better than O-997 probability of detecting flaws of depth equal to 16 per cent of the thickness; since flaws of this dimension were unlikely to have been present in very many of the 1000 cases, the actual probability must certainly be substantially less than 0997.

In a study of present production capabilities of manual and automatic ultrasonic techniques, radiographic techniques, magnetic particle, fluorescent penetrant, infrared, and eddy current methods, [3] indicates conclusions which may be similarly interpreted.

Interesting rationales to explain a 15 per cent flaw dividing line for fracture behavior may be developed in terms of thickness requirements for true plane strain behavior, transitional effects between plane stress and plane strain, increasing significance of through-thickness stresses in the presence of even minor flaws, and the like. However, at this point in time, it is sufficient to recognize that the presence or absence of capability to withstand a 15 per cent flaw may well be of physical significance, and that in any

EF.M. Vd. I No. 3-H

510 VICTOR SINGER

event, the 15 per cent flaw is more-or-less representative of a lower limit of reliable detection capability through sophisticated non-destructive inspection methods.

In many design situations, the luxury of a leak-before-yield criterion cannot be provided because of weight or other constraints, yet extremes of brittle behavior must also be avoided. A reasonable design criterion for such vessels requires capacity to withstand proof testing in spite of the presence in any location and with any orientation, of a long shallow surface crack with depth equal to or greater than 20 per cent of the vessel wall thickness at that location. The prediction of fracture behavior should be on the basis of a value of plane strain fracture toughness K,, characteristic of the material, even in the thinner regions where the material thickness may be insufficient for its behavior to be completely characterized by the plane strain condition. The design of the thinnest portion of the vessel would thus reflect a standardized flaw depth ratio shown by previous experience to be fairly adequate. In thicker regions of the vessel, the 20 per cent design flaw would be entirely appropriate for design purposes as a recognition of inspection capabilities, though it would be an overpenalization from the viewpoint of probability of flaw incidence, since the population of flaws in a given sample must be an inverse function of the flaw size. This is because in two samples, the first twice as large as the second, it is unlikely that the probability of incidence of a flaw of size 2a in the first sample would be as great as the probability of incidence of a flaw of size a in the second sample.

The 20 per cent flaw criterion may be represented in rule-of-thumb format for easy use in the design process as foliows: For a linearly elastic material containing a surface crack of semi-elliptical cross-section oriented in a plane normal to a general stress field of magnitude CT, the local situation along a projection of the cracks minor half-axis is described by a stress intensity parameter K, such that[4]

KI= 1.1 crv(rra)[~2-0*212a2/a,,21-2. (1)

The term +, a shape factor, has values between 1.08 and 1,051 for long shallow cracks with length along the surface between 7.5 and 10 times the depth a. The term 0.212 cr2/a,2 is a correction for a small zone of plasticity at the crack tip; for levels of applied stress %r (direct plus flexural) at proof test of 70-100 per cent of the uniaxial yield strength, its value is between O*lOZ and O-212. The entire range of shape factors and stress levels is well represented by a value of unity for the bracketed term. Sub- stituting for a condition of failure where K, forms KIc, the plane strain fracture tough- ness of the material, and where the depth a equals O-2 t, and rearranging, we obtain

maximum allowable stress = amax. = 1 15 KJt/( t ) . (2)

Where this value exceeds the yield strength, the 20 per cent flaw does not govern, i.e., a larger flaw can be tolerated. In contrast to this 20 per cent flaw criterion, the leak- before-burst criterion may be represented as follows:

where the through-thickness crack is about twice the local thickness, and amax. is the local stress at nominal ultimate pressure.

Application of fracture mechanics 511

EPFECTIVE STRESSES DUE TO FLEXUBE

As considered in MIL-HDBKJ [5], flexural failure is regarded as occurring through exceeding a modulus of rupture characteristic of the material and descriptive of its plastic behavior. In the absence of test data, MIL-HDBK-5 allows the assumption that the rupture modulus is 125 per cent of the tensile strength (Para. 2.10.1.1 and others); it allows still higher values based on test data. An equivalent interpretation of the same provision is to deal with effective flexural stresses of 80 per cent (or l/1*25) of the extreme fiber values determined from straight line stress distribution. In effect, the 80 per cent factor amounts to the argument that tensile fracture will not occur due to flexural tension within the 10 per cent of the element thickness closest to the extreme fiber, but rather due to the situation at greater depth, a suggestion that there is some characteristic of the conditions at fracture whereby the behavior of the material is somehow related to proximity to a free surface.

A plausible explanation for such behavior develops from fracture mechanics. Even in extremely brittle materials, sufficiently narrow regions experiencing post-yield conditions can be resisted so long as there is insu~~ient restraint in one or more transverse directions to prevent a process akin to necking. The state of stress of an element near a free surface is very close to plane stress (biaxial stress, triaxial strain) whereas at greater depth, the condition develops toward the plane strain (triaxial stress, biaxial strain) extreme. And further, estimates may be made of the lower limit of the depth of a band of material near the surface within which plane strain (most brittle possible) behavior is impossible.

With increasing applied tension across a crack in a thick section, a small zone of increasing size develops at the cracks leading edge within which stresses are beyond the yield stress level. At the point of imminent failure, the size of the plastic zone is shown in Fig. 1[6,7]. This determination develops from the assumption of completely linear behavior below and beyond the yield point. Depending upon the true stress- strain behavior beyond yield, the actual plastic zone size may be as much as twice as large as in Fig. 1. The essential features of the situation are: First, in a roughly triangular region in the plane of the crack, extending parallel to the surface at least a distance r, from the crack tip and normal to the side surface a distance at least as large, a post-yield condition exists. Second, by virtue of the elastic stress singularity at the crack tip, the elastic stress gradient, or actual strain gradient, ahead of the crack tip is extremely steep. Third, the failure occurs due to the condition in the central region rather than near the surface. if, in a flexural element, the yield condition near the extreme fiber extends no deeper into the cross-section than r,, the situation is obviously less critical than at the crack tip, and failure will not occur. Thus, the customary tests for Kfc (plane strain fracture toughness) may be regarded as determinations of a lower limit of depth of a band of material within which a post-yield condition is insu~cient to produce failure.

On this basis, for conditions other than fully reversible cyclic loading, the e$ective flexural stress may be taken equal to the magnitude which develops at a depth r, = K,Y(27rcr,,2) from the extreme fiber. This implies that in cross-sections which are quite thick compared with rp, the material may well be incapable of developing the full theoretical plastic moment capacity of the section. Only a relatively small amount of plasticity would have to be developed near the tensile extreme fiber before the material could begin to regard the whole plastic region as a flaw. Further, it implies that in cross- sections thinner than 2 r,, the material is incapable of fracture due to flexure; one

512 VICTOR SINGER

CRACK TIP

016rp( PLANE -

$&PLANE STRESS) YP

Fig. 1. Plastic zone at a crack front, with failure imminent, based on completely linear elasticity.

should expect to be able almost to fold such a thin section like paper, without structural difficulties. Vessels with shells thinner than 2 r, may be designed as pure membranes, without regard to flexural stresses; fracture behavior in such shells is controlled solely by the membr~e forces. Those who contemplate design on this basis, however, should perform sharp bend tests or otherwise closely examine material behavior within the range of strains anticipated. It should not be necessary to point out the crucial importance of using valid plane strain fracture toughness information for candidate materials before proceeding with design on the basis above outlined. The complexity of structural integrity analyses of pressure vessels is not really decreased by these considerations; high surface strains due to flexure at severe discontinuities may not be sufficient to cause failure of themselves, but the coincident thickness changes and the resulting increases in direct stresses can be quite important. In addition, discontinuity analyses of vessels where substantial regions may exhibit non-linearly elastic flexural behavior is a formidable task unto itself.

It is pertinent here to inquire as to the possible existence of regions of the structure which may not experience in the proof test a stress field of greater severity than in service, even with test procedures carefully arranged for similitude. Suspect regions for such inquiry are those where load distribution is influenced by fit between mating parts, i.e. threads, Ortman ring or snap ring interconnections, etc. It is easily visualized that the actual distribution of bearing force per circumferential inch in such joints is con- trolled entirely by tolerances for parallelism between the bearing surfaces of internal and external parts, tolerances on pitch of threads. tolerances for width of Ortman or

Application of fracture mechanics 513

snap rings, and tolerances for local curvature of Ortman or snap rings. This is so because the deflections of the bearing points are likely to be smaller by orders of mag- nitude than the differences between extremes of the tolerance ranges. This establishes two possible failure conditions. A brittle failure may occur as a local effect prior to the redistribution of the localized initial load application through yielding in shear and/or flexure to a more-or-less axisymmetric system; or on the other hand, a ductile failure may occur as a general effect after redistribution, under axisymmetric loading, by shear or by direct stresses. The customary analytical procedure for such joints, which pre- supposes the axisymmetric distribution, is meaningless except in terms of margin-on- ultimate, since the very nature of the pre-supposition requires yielding to occur to iron out tolerance effects. Moreover, the dependence on the pre-supposition forces a determination of whether or not, in fact, it is possible for brittle failure to occur prior to local yielding.

It is appropriate to observe in addition that in regions controlled to such an extent by tolerances, two successive assembly operations of the very same parts may bring about local differences sufficient to cause entirely dissimilar local load distribution under pressure. Assurances of safety cannot be obtained by proof test alone in such a situation, since the requirement of similitude cannot with certainty be fulfilled. Comple- mentary analytical demonstrations of high margins against brittle failure, i.e., assurance that yielding must occur long before brittle failure becomes possible, are indispensable in the use of such joints in flaw-sensitive materials.

Such a complementary analysis may be prepared on the basis of mathematical exag- geration of the pertinent features of the keyway or thread root region to the extent that the model becomes amenable to effective treatment via fracture mechanics techniques rather than on the basis of theoretical stress concentration factors. Fracture mechanics has consistently demonstrated excellent correlation with experimental behavior, while examples are common of behavior broadly divergent from expectations based on theoretical notch factors [8].

Assurance that shear yield must occur prior to brittle failure at the root of a keyway or buttress thread may be obtained through relatively simple treatment of the structure as a cantilever beam and through treatment of the root as an infinite stress concentration or singularity. In the unit width cantilever configuration in Fig. 2, neglecting the normal component of applied load, the strain energy v in the element, in terms of the deflection S under the load P, is

2P3L3 =F+

PZL( 1+ V) Et

(4)

For the idealization of the root configuration, in which a stress singularity occurs at the root, the energy 9 available to produce an increment of crack extension[9] is

9 = p-$2.$ (5)

The first term on the right of the equality is the work done by the force P in the incre- mental translation due to lengthening of the beam, while the second term is the in-

VICTOR SlNGER

BUTTRESS THREAD CONFIGURATION

t, AT PITCH DIAMETER

THREAD OR LIP CONFIGUR~ION

L t= MEAN DEPTH OF THREAD OVER LENGTH t OR SHEAR LiP DEPTH

IDEALIZED CONFIGURATION AT ROOT

Fig. 2. Shear lip or buttress thread configurations.

crement of strain energy in the beam. After d~~ere~tiat~on and conversion to the equivalent stress field approach, the severity of the singularity, measured by the stress intensity parameter Kr (assuming plane strain) is obtained:

(6)

The maximum possible value is obtained when P is sufficiently large to cause shear yield of the thread (at P = t,, X O-577 ore) or of the shear lip (at P = t x O-577 otlp). The brittle failure condition has not been attained if KI is less than the critical value for the material; no problem is anticipated if

I& > KI = 0.577 a,?, 6L2+t2(1+v) 12 1 t3(1-9) - (7)

Other thread forms are amenable to similar treatment, though the approximation occasionally becomes gross.

ASSOCXATED PROBES WITH BOLTS In the use of bolted pressure vessel connections, particularly in rocket vessels

where flange dimensions are intentionally minimized for inert weight control, bolts are often subjected not only to direct tension due to the separation loads on connected parts and the prying action between flanges, but also to flexure resulting from head or nut rotations consistent with the deflections of the connected parts. Though bolt capacities are customarily catalogued in terms of force rather than stress, the effect of the added flexure is always difficult to assess using classical methods. It is dealt with quite easily using the ideas above described.

Considering, for example, a design proportioned for bolts with a minor diameter = d = O-15 in., where the direct tensile load amounts to 1.50 ksi, and the head rotation is sufficient to produce extreme fiber flexural stresses (linear determination) of + 150 ksi, the problem is to select a bolt. The parameters of the problem are given in Table I.

For this application, the best bolt is clearly bolt # 3 with the lowest strength; no difficulty could be anticipated through its use. On the other hand, the strongest bolt would probably fail, and the intermediate strength bolt appears unsuitable, though it

Application of fracture mechanics 515

Table 1. Effective stress in a bolt with O-15 in. minor diameter d subjected to 150 ksi tension and f 150 ksi extreme fiber flexural stress

muIJ &C (ksi) (ksi (in.)*)

rp

(in.)

O*Sd-r,

0.5d

(%)

Effective flexural stress (ksi)

Total effective

stress (ksi)

Bolt # 1 240 25 040172 97.7 146 2% Bolt # 2 195 75 0.0235 68.65 103 253 Bolt # 3 165 120 04841 0 0 150

could be shown to be suitable through more refined techniques. Bolt # 3 would yield at the extreme fiber, i.e. it would be permanently bent in use, but it would hold the load.

RESIDUAL SIIWSSES AND INITIAL SET All discussion thus far has been limited to consideration of the application of

stresses resulting from a loading environment to a zero initial stress regime. Since the ever present flaw sees only total stress, and does not distinguish between stresses due to load and stresses initially present, it is pertinent to examine the assumption.

Surveys of residual stress after heat treatment[ 101 or machining operations [l 11 usually show that where significantly large residuals exist, they are surface conditions only. If at depth r, from the surface, the residuals have all but disappeared, or if the section thickness is less than 2 r,, the presence or absence even of large residuals should not materially affect fracture behavior, except marginally from the point of view of stress corrosion. In the intermediate region, there is no substitute for experi- mental verification of design assumptions, either with the specific design in question, or through much experience with the particular material in comparable configurations and with comparable processing parameters.

From the idea that in any individual vessel of material capable of brittle behavior, the only real safety in service is what has been demonstrated by the proof test, it follows that the interests of economy and structural efficiency are best served by minimizing reliance upon paper-only safety beyond the proof test pressure. For a given design, the highest practicable proof pressure level will be just below that which would produce unacceptable geometry changes. Permanent extensional deformations of O-2 per cent offset will not usually exceed acceptable diametral tolerance ranges, while permanent inextensional - flexural - deformations considerably larger may not be excessive in discontinuity regions. In instances where during proof testing, the maxi- mum effective stress (at rp from the extreme fiber) is equal to the yield, the only causes for concern are the post-test effect of the resulting residual stress or possible stress corrosion during the test. The residual stresses are easily evaluated by routine methods, and will be compressive on the surface which has experienced tensile yielding. Low level tension will exist on the opposite surface. The effects of the residuals, as well as the situation during the test, may be characterized via stress corrosion techniques [ 121. Upon repressurization at a service pressure level lower than proof, no further yielding occurs; the behavior is linearly elastic all the way up to the proof pressure, even at the tensile extreme fiber, because of the presence of the residual compression.

CONCLUSION Criteria are proposed for the control of fracture in highly stressed pressure vessels

through design to accommodate in every region of the vessel, flaws with depths of 20

516 VICTOR SINGER

per cent (or more) of local thickness during the proof test. In discontinuity regions of vessels thus proportioned, stresses of any magnitude within a distance r, = KIc2/ (277@, ) from the extreme fiber may be disregarded, since they cannot cause fracture. During proof test, an allowable level of total effective stress (membrane+effective flexural + residual where applicable) at r, from the extreme fiber is established as the lesser of the following:

urnax. =

1

a,; or

1.15 K&(t).

These considerations are made with some sacrifice of mathematical rigor, in the con- servative direction, in order to obtain relationships easily applied in the design process. Finally, attention is drawn to the characteristics of certain types of attachment systems for which the proof test is inconclusive, and to design techniques for such regions, through which dangerous situations may be avoided.

REFERENCES [ 1] R. C. A. Thurston, The notch toughness of ultra-high strength steels in relation to design consideration.

Proc., Tripartite Technical Cooperative Program (TTCP) Symp., Washington, D.C. 26-28 October 1964; DMIC Rep. No. 2 10 (1964).

[2] J. E. Srawley and J. B. Esgar, Investigation of hydrotest failure of 260-in. motor case. National Aero- nautics and Space Administration, Rep. No. TM-X- 1194 (1966).

[3] C. F. Tiffany, J. N. Masters and R. E. Regan, Large motor case technology evaluation. Air Force Materials Laboratory, Wright-Patterson Air Force Base, Ohio, Tech. Rep. No. AFML-TR-67-190 (1967).

[4] The slow growth and rapid propagation of cracks. 2nd Report of ASTM Committee on Fracture Testing of High Strength Metallic Materials; Mater. Res. Stand. 389 (1961).

[5] MIL-HDBK-5 Metallic materials and elements for flight vehicle structures. Department of Defense, Washington, D.C. (1962).

[6] G. R. I&n, Plastic zone near a crack and fracture toughness. Proc. 7th Sagamore Ordnance Mater. Res. Conf. (1960). Svracuse Universitv Press MET. E. 661-61 l/F. (1960).

[7] W. F. Brown, Jr. and J. E. Srawley; Plane strain crack toughness testing of high strength metallic materials. Am. Sot. Test. Mater. Spec. Tech. Publ. No. 410 (1966).

[8] J. G. Kaufman, Role of theoretical stress-concentration factor in evaluating notch toughness. ASTM Mater. Res. Stand. (1967).

[9] P. C. Paris and G. C. Sih, Stress analysis of cracks. Fracture toughness testing and its applications. Am. Sot. Test. Mater. Spec. Tech. Publ. No. 381, pp. 30-81 (1965).

[lo] The Boeing Company, Large motor case technology evaluation. First Year Summary Progr. Rep., Vol. l,AFMLContractAF33(615)-1623 (1965).

[ll] M. Field and J. F. Kahles, Surface integrity of machined and ground high strength steels. Proc. Tripor- tite Technical Cooperative Program (TTCP) Symp., Washington, D.C. 26-28 October 1964; DMIC Rep.No.210(1964).

[12] C. F. Tiffany and J. N. Masters, Applied fracture mechanics. Fracture toughness testing and its applica- tions. Am. Sot. Test. Mater. Spec. Tech. Publ. No. 38 1, pp. 249-277 (1965).

(Received 25 January 1968)

R&sum&On considere que la portee du facteur nominal de sbcurite d6crivant la resistance dun recipient B pression depend de la manibre dont est d&rite la configuration en supposartt une compositon suffisamment sans dbfaut. Pour des &ipients ou il est impossible de satisfaire au critbre de fuite avant rupture ou fuite avant deformation plastique le facteur nominal de sCcuritC est considtre comme applicable aux groupes de recipients plutBt quaux ticipients pris individuellement. On propose des criteres pour le contr6le de la rup- ture darts de tels recipients en se basant sur le fait que la senbilite de la structure a la presence de dkfauts, devrait etre un nourcentaae fixe de Itpaisseur locale en nimporte quel point. On revoit les possibilites courantes de techniques d%spection non destructives, en sappuyant sur le plus grand defaut quil est pos- sible de manquer pluti3t que le plus petit d6faut quil est possible de dttecter. On examine les implications de modeles de considerations de rupture darts les zones de flexion. On examine les sujetions de forme, dans les

Application of fracture mechanics 517

zones en flexion, entrainees par des conside ration de resistance a la fracture. On Ctablit des bases pour la determination des efforts de flexion effectifs et pour Cvaluer Iimportance des efforts residueIs. Finalement. on attire Iattention sur la possibilite, souvent ignorees, dun comportement fragile darts les zones dattache et sur les techniques pour en tenir compte au tours du projet.

Zusammenfassung- Es wird angenommen, dass das Ausmass, in welchem der Nennsicherheitsbeiwert die Festigkeit eines Druckbehalters zum Ausdruck bringt, davon abhiingt, wie weit die Voraussetzung gentigend fehlerfreier Zusammensetzung zutrifft. Bei Druckbehaltern wo das Kriterium Leckverlustvor-Bersten oder Leckverlust-vor-Fliessen nicht erfiillt werden kann, wird der Nennsicherheitsbeiwert als lediglich auf eine grossere Zahl von Behiiltem und nicht etwa auf Einzelbehiilter, anwendbar erachtet. Es werden Kriterien fur die Bruchverhtitung solcher Behalter vorgeschlagen, und zwar auf der Grundlage, dass die Empfind- lichkeit derartiger Behalter gegentiber dem Vorhandensein van Rissen ein fester Prozentsatz der drtlichen Wanddicke an einer beliebigen Stelle sein soll. Es wird ein Uberblick iiber die Brauchbarkeit der gegen- wlrtigen zerstiirungsfreien Prtifmethoden gegeben und zwar mit der Betonung auf der Rissgrosse, die mijglicherweise unbemerkt bleiben kann, und weniger darauf, wie klein ein Riss sein kann, urn noch ent- deckt zu werden. Femerhin wird das Problem untersucht, wie die Bruchgefiihrdung biegebeanspruchter Zonen beim Entwurf beriicksichtigt werden kann. Es wird eine Grundlage fur die Ermittlung wirksamer Biegespannungen und fur die Abschltzung der Bedeutung von Eigenspannungen geschatfen. Schliesslich wird auf die oft unbeachtet bleibend Moglichkeit des Auftretens von Sprddigkeit an Anschlusstellen hingewiesen, sowie auf Methoden zur Berticksichtigung derselben in der Konstruktionsphase.