Fracture mechanics and materials testing: forgotten pioneers of the early 20th century

Fracture mechanics and materials testing:forgotten pioneers of the early 20th century

H . P. R O S S M A N I T HInstitute of Mechanics, Vienna University of Technology, Widener hauptstraße 8-10.325, A-1040 Vienna, Austria

Received in final form 16 April 1999

A B S T R A C T This contribution introduces the work of early researchers in the field of fracturemechanics and materials testing. The development in fracture mechanics around theturn of the century in Germany and Austria-Hungary is presented, and the work ofpioneers, e.g. K. Wieghardt, A. V. Leon, K. Wolf, A. Smekal and P. Ludwig is criticallydiscussed. A comparison with the developments by G. I. Inglis and A. A. Griffith iselaborated.

It will be shown that the work of these pioneers—particularly the 1907 paper byWieghardt on the development of the basic analytical equations of fracture mechanics—predates many of the later developments by several decades. The work by Wieghardtwas in fact directly related to a practical failure case, and the voluminous work of Leonwas mainly driven by practical needs of engineering. The reasons for the neglect ofWieghardt’s fundamental paper of 1907—particularly in the Anglo-American hemi-sphere—are critically discussed.

Keywords fracture mechanics; pioneers; Wieghardt; Leon; Smekal; Wolf; Ludwik;Inglis; Griffith.

apparatus depicted in da Vinci’s notebook in the CodexI N T R O D U C T I O N

Atlanticus is explained, and the results are discussed inthe paper by Irwin and Wells.3 Whereas da Vinci concen-Fracture mechanics has been actively used since neolithic

times when man invented the flint knapping technique trated on wires of different lengths but the same thick-ness, Galileo Galilei4 studied the strength of wires ofto produce more or less sophisticated stone tools for use

in peace and war. The production of blades, adzes and constant length and various thicknesses. In addition, healso studied the fracture of marble columns in bendingother stone tools required at least some knowledge of

how stones would break and chip, but it is doubtful that as well as loaded in axial tension. Galileo’s quasi-analyt-ical approach led to ideas concerning dimensional simili-these early ancestors of modern man understood the

mechanisms of fracture. tude which, particularly in the 19th century, became adominant feature in the development of engineeringSeveral fracture-related incidences which occurred in

12th and 13th century Europe are documented in the design criteria.Around 1650, Louis XIV of France ordered a magnifi-literature. In the 14th century, early quality control and

testing of a bronze cannon was performed by charging cent fountain to be built in the gardens of Versailles, andhis court engineer E. Mariotte5 was entrusted with thisan upside-down placed cannon so as to permit the gun

barrel to be thrown into the air. If, upon the tube falling task which required the containment of substantialamounts of pressurized water. Mariotte conducted severalto earth there was no complete fracture or crack then

the material was considered tough enough and the tests and measured the deformation and burst pressure ofcylindrical pressure vessels, and observed a direct pro-cannon was pronounced safe for service. Should this

dynamic fracture test result in a broken cannon tube portionality between pressure and circumferential stretch.He noted that the vessels would burst when the circumfer-then the device was recast.

In the western countries, the first historically recorded ential elongation increased by a certain fraction. This ledto the practice of using maximum strain (or maximumstudy of fracture strength is due to Leonardo da Vinci,1,2

who studied the strength of iron wires. The testing stress) as a criterion for predicting fracture strength.

© 1999 Blackwell Science Ltd. Fatigue Fract Engng Mater Struct 22, 781–797 781

782 H . P. R O S S M A N I T H

Bach, Bauschinger, Luders, von Karman (one of Prandtl’sT H E I N D U S T R I A L I Z A T I O N O F T H E 1 9 t h

first and finest students), Nadai and others contributedC E N T U R Y A N D T H E E M E R G E N C E O F

a great deal to the understanding of plastic behaviour ofP R O F E S S I O N A L M A T E R I A L T E S T I N G

materials shortly after the turn of the century.Timoshenko in his book, History of Strength ofA great demand for iron and steel developed in the

course of the industrialization of the 19th century. This Materials,10 remarks that the practical importance ofPrandtl’s soap film analogy was recognized by Griffithacceleration, and partly uncontrolled expansion of the

engineering world, was accompanied by a rather large and Taylor.11 While employed at the Royal AircraftEstablishment at Farnborough, with the assistance ofrate of failure of engineering structures. In fact, fracture

of railway axles and rail track was not uncommon and Taylor, Griffith measured the stress elevation at notches,notably longitudinal grooves in aircraft components, e.g.in the 1870s the British magazine Engineering printed

weekly statistics on boiler explosions. This situation led propeller shafts. They used this technique for the deter-mination of torsional rigidities of rods of various cross-to increased public concern and awareness about safety

of railway transport and bridges. As a result, the designers sections, and remarked that the greatest use of thetechnique had been in aeronautics with air-screws andwere forced to become more concerned with the selec-

tion of a suitable steel for a particular application and propellers. However, despite mentioning that ‘.. . a fewisolated experiments had been made in this country andrequired accurate determination of relevant material

properties. The thermal embrittlement of the Krupp- in Germany ...’, they failed to acknowledge the work ofPrandtl which had been well recognized 14 yearsmanufactured alloy steel, introduced around 1870 in

Germany, enhanced the need to develop impact-testing previously.In studying the phenomena of fracture, Prandtl12techniques for the determination of the fracture quality

of steels.6 A large number of material-testing laboratories proposed the existence of two types of fracture failures:were established in Europe, with one of the first and

1 cohesive or brittle fracture; andmost notable being the material-testing laboratory built

2 shear fracture.in 1865 by Kirkaldy7 in London.

Kirkaldy’s results, along with those of his colleagues When tensile testing cylindrical steel specimens, he,as well as Ludwik, observed that in the cup-and-conein other countries, marked the beginning of notched-

bar testing of steel. Notched-bar impact testing of iron formation the crack would start and extend in the flatbrittle centre section and while continuing to stretchand steel was widely used by the end of the 19th century

because these tests indicated the ductile-to-brittle tem- plastically at a conical section of the rim.perature transition in steels and hence assisted in thecontrol of heat treatment. Methods of adjusting design

E A R L Y C O N T R I B U T I O N S T O T H E M E C H A N I C Sloadings for conditions of impact and fracture were based

O F F R A C T U R Ecrudely on fracture failures in service.In 1909, Ludwik8 put forward a theory that helped to Despite enormous technological progress over thousands

of years, one can safely say that, during the early historyexplain the relatively abrupt increase in notched-barfracture work with increase of test temperature. Ludwik’s of fracture, the conditions of failure were only poorly

understood. The viewpoints on strength of materials atwork will be discussed in detail in a later section.the start of the 20th century are presented well byLove13 in his Treatize on the Mathematical Theory of

P R A N D T L A N D E A R L Y I D E A S A B O U T P L A S T I CElasticity, however, those sections dealing with the appli-

D E F O R M A T I O Ncability of linear-elastic concepts show no influence ofthe early fracture studies during the period 1900–1926.Ludwig Prandtl was born 4 February 1875 in Freising

in Bavaria, frequented the Gymnasium in Freising and Love notes that the ‘safety factors’ commonly usedreduce the working stress into a range where linear-Munich and received his higher education at the Munich

Technische Hochschule and later became A. Foppl’s elastic analysis should be quite accurate, and examplesare given of safety factors, e.g. 6 for boilers, 10 forassistant in the materials-testing laboratory. Working at

the Hannover Technische Hochschule in 1903, 1 year pillars, 6–10 for railway bridges, 12 for screw propellershafts and parts of machines subjected to sudden reversal.before he was appointed Associate Professor (in 1907 he

became a Full Professor) at the University of Gottingen, With regard to fracture, Love, as late as in the fourthedition of his book concludes ‘that the properties ofPrandtl9 published his famous membrane analogy of the

torsion problem, where he showed that by using a soap rupture are but vaguely understood’. However, in hisdiscussion of the loss of strength due to repeated loadingfilm all the information on stress distribution in torsion

can be obtained experimentally. Besides Prandtl himself, (fatigue), Love describes this as a ‘gradual deterioration’

© 1999 Blackwell Science Ltd. Fatigue Fract Engng Mater Struct 22, 781–797

F R AC T U R E M E C H A N I C S A N D M AT E R I A L S T E S T I N G 783

of the material, and in this respect he was closer to whatis now called continuum damage mechanics.

After 1900, with the advent of automobiles followedby aeroplanes, the provision of adequate safety factorsbecame increasingly more difficult and the need forbetter understanding of ‘rupture’ more apparent.However, the response was directed mainly toward bettermaterials, improved fabrication and inspection. Withthese aids, the practice of fracture control, consistingmainly of failure experience, safety factors and prooftesting, endured through the 1900–1950 period. As aguard against costs of (large) fracture failures, insurancewas an available option. However, during this periodseveral fracture investigations occurred which assistedthe introduction of fracture mechanics.

W I E G H A R D T — T H E E A R L Y P I O N E E R

The first analytical investigation in fracture mechanics,and application to a practical engineering problem(mixed-mode fracture of a roller bearing case), was dueto Wieghardt14 in 1907.

Karl Wieghardt (Fig. 1) was born 21 June 1874 inBergeborbeck in the Rhine Province of the newly estab-lished German Empire. He received his primary edu-cation at the Stadtisches Realgymnasium in Essen (RuhrProvince) and studied at the Technische Hochschule inHannover. Wieghardt passed the Staatsprufung (highexamination) in the main subjects of pure mathematics, Fig. 1 K. Wieghardt (born 21 June 1874, Bergeborbeck, Germany,

died 10 June 1924, Dresden, Germany) published the first paper onapplied mathematics and physics in May 1902 at thefracture mechanics in 1907 entitled ‘On splitting and cracking offamous University of Gottingen, and received his doc-elastic bodies’ (see ref. [21]). He was Professor of Mechanics attoral degree from the Faculty of Philosophy from theTechnische Hochschule Wien (1911–1920).same university in December 1902. On 26 July 1904 he

was promoted to the position of a Privatdozent in thefield of mechanics and graphical statics at the Konigliche 1 December 1911 where he was paid 6400 Kronen

(crowns) as a regular salary, 1840 KronenTechnische Hochschule in Aachen.Wieghardt’s next position (6 March 1906–1 August Aktivitatszuschuß (extra expenses for activities) and

800 Kronen for local extras and examination fees for1907) was classified as Privatdozent (with no paymentfrom the running budget) carrying the title teaching mechanics to students of the civil engineering

faculty. Figure 2 shows the ‘Geleitwort’ (preface) of hisAußerordentlicher Professor (associate professor) at theHerzogliche Technische Hochschule in Braunschweig course text on ‘Mechanics for civil engineers’ in his own

handwriting. Wieghardt resigned from this position on(in the northern part of Germany). During this period,Wieghardt wrote his famous but almost forgotten funda- 21 October 1920 and accepted a call to teach at the

Technische Hochschule in Dresden. In fact, he leftmental paper on fracture mechanics. Afterwards, duringthe period 1 August 1907–1 December 1911, he was Vienna during the summer of 1920 before the fall term

started. From the 1920 correspondence of Wieghardt,15employed as and occupied the position of a full professorat the Konigliche Technische Hochschule in Hannover. available in the Archive of the Vienna University of

Technology (formerly k.u.k. Technische HochschuleAt this time, the position of a full professor of mech-anics at the Technische Hochschule in Vienna became Vienna), we learn that he had already left Vienna during

the summer in order to have more time to search for avacant and the long list of possible candidates to beinvited for application was reduced to two experts: primo new home. In this letter he apologizes for not having

had a chance to say ‘Goodbye’ to his colleagues. Whileloco L. Prandtl and secundo loco K. Wieghardt. Finally,Wieghardt was appointed full professor at the Imperial teaching in Dresden, Karl Wieghardt passed away on

10 June 1924.and Royal Technische Hochschule in Vienna as from



the paper was printed ceased publication in 1922. Theappearance of Griffith’s paper in the famous Proceedingsof the Royal Society of London is a tremendous reflectionof Wieghardt’s publication. which was very well known—but predominantly in German-speaking countries. Inaddition, the fact that Wieghardt’s paper is written in19th-century German and is rather difficult to read forany non-German scientist did not contribute to itsappreciation. To my knowledge, the only reference toWieghardt’s historical and fundamental paper during thelast 30 years comes in a footnote in the German bookElastizitatstheorie (Theory of Elasticity) by George Hahn20

from Kaiserslautern in Germany. This footnote arousedthe interest of the present author and he began totranslate Wieghardt’s paper into English to make itknown to the worldwide readership. Discussing this issuewith Keith Miller from Sheffield, the English translationof the Wieghardt paper was then published in the journalFFEMS21 with an introduction by Rossmanith.22

W I E G H A R D ‘ T 1 9 0 7 P A P E R

In 1907, while working at the Herzogliche TechnischeHochschule in Braunschweig, Wieghardt published anFig. 2 K. Wieghardt: preface to his course notes on Mechanics Ielaborate study of the stress field in the vicinity of thefor Civil Engineers which states ‘‘The present abridged version of

my course notes on Mechanics I for Civil Engineers at the k.u.k. tip of a wedge [Fig. 3(a)]. The German original is entitledTechnische Hochschule in Vienna is no less than a textbook of ‘Uber das Spalten und Zerreissen elastischer Korper’mechanics. It cannot replace attending the course. No presentation and was published in the Zeitschrift fur Mathematik undof the material in a textbook whatsoever will suffice to studymechanics from books only. But it shall be a valuable aid inaddition to the course · · · Vienna, 1 November 1913, Prof. DrK. Wieghardt.’’

At the time of Wieghardt’s application for a positionat the k.u.k. Technische Hochschule in Vienna, his listof scientific papers was not very long, but the papersexquisitely reflect the authority of Wieghardt as anexpert in mechanics. The theme of his doctoral thesisproposed to the University of Gottingen was: ‘On thestatics of plane trusses with inactive/slack rods’.16 HisHabilitationsschrift dealt with ‘On a limit in the theoryof elasticity’.17 The third paper ‘On stress surfaces andreciprocal diagrams’18 was co-authored by Wieghardtand the famous mathematician Felix Klein. Furtherpapers dealt with ‘On excessive stresses in highly stati-cally indeterminate trusses’,19 ‘On splitting and crackingof elastic bodies’,14 and a few other subjects. It is thislast paper which entitles Wieghardt to be considered‘The Pioneer’ in fracture mechanics. This paper will bediscussed in detail in the following section.

Fig. 3 The wedge problem. (a) Geometrical configuration of aThis contribution by Wieghardt has not been wedge domain; angle p/a. (b) Geometrical configuration of a crack.adequately recognized by the fracture mechanics com- (c),(d) Coordinate system for the Ansatz by Sommerfeld. (e) Bach’smunity. There seems to be several reasons for this, but problem of fracture of roller bearing cage. (f ) Crack extension

direction due to normal concentrated force.the main reason may have been that the journal in which



Physik 55(1–2), 60–103. The paper consists of an intro- He puts the blame on the classical hypotheses of strength,but concludes that fracture, if it occurs at all, will initiateduction, two sections, and finally an appendix on the

uniqueness of the solution. The special case of a crack at the crack tip. He then proposes to disregard the 1/√r

infinite factor, and suggests that the direction of crackis treated in detail [Fig. 3(b)].The theoretical development rests on a special ansatz initiation will be determined on the basis of customary

hypotheses of strength. According to Mohr,24 there areby Sommerfeld for the solution of the Boussinesq prob-lem for a point load P acting normally on the surface of essentially two hypotheses on the direction of fracture

initiation in an elastic material: the shear stress hypoth-a half space. Sommerfeld’s idea is to transform theboundary value problem of the biharmonic equation esis; and the tensile stress hypothesis. Wieghardt details

that the behaviour of ductile materials, e.g. wrought ironDDF=0 into a simpler boundary value problem for thefunction Dw, where F is the Airy function and D denotes seems to be better described by the shear stress hypoth-

esis, whereas the brittle behaviour of cast iron is in betterthe Laplace operator. Sommerfeld suggests that thespecial ansatz is given by correspondence with the tensile stress hypothesis.

Wieghardt then uses the expressions for the maximumw=DF=−P/ip{1/(f−a)−1/(g−a) (1) shear and maximum tensile stress to derive the possible

directions for crack initiation and, after some lengthywhere f and g are polar coordinates from the apex ofcalculations, arrives at the conclusion that:the wedge [Fig. 3(d)], and ‘a’ is the distance of the load

‘Assuming the validity of the shear stress hypothesisapplication point from the origin of the coordinatefor our cracked material, knowledge of the theoreticalsystem [see Fig. 3(c) and (d)].stress distribution does not allow the direction of crackFor the arbitrary wedge domain, Wieghardt gen-initiation upon exceeding loading to be evaluated witheralizes this ansatz in the form:certainty, and it is not at all possible to determine the

w=DF=−aP/ip{f−1/(fa−aa)−g−1/(ga−aa)} (2) path of further cracking’.And he continues to tell the reader:where p/a defines the opening angle of the wedge‘If we assume the tensile stress criterion to be valid,domain, and shows that this function satisfies the appro-

the results turns out to be more enjoyable’.priate boundary conditions and solves the stress problemIn fact, he recognizes that the tensile stress criterionfor those wedge regions with opening angles having

renders one single possible direction for crack initiation:integer multiples of p.‘. . . upon overstressing the material, the crack willHere, Wieghardt discusses an earlier approach by

initiate in the direction parallel to the crack line and,Venske23 to treat the wedge problem, and finds thatfurthermore, should the crack continue to propagateVenske’s stress function does not appropriately satisfyfurther, cracking occurs along the direction given by thethe stress conditions at infinity.crack because the same conditions prevail after cracking’.After a discussion about the appearance of infinite

At the end of this section, Wieghardt mentions thatstresses at the tip of a crack, Wieghardt derives thethe ansatzcomplete stress field in polar coordinates around a static

crack subjected to a pair of splitting forces P, therebyQ/8p{f1/2/(f1/2−a1/2)+g−1/2/(g1/2−a1/2)} (4)noting the important √r singularity:

corresponds to the stress distribution for a crack problemsr+sy=P/p1/√(ar) sin y/2 (3a)having a tangential force Q in place of P.

sr−sy=P/p1/√(ar)12 sin y cos y/2 (3b) In the second part of his paper, Wieghardt applies his

new theory to a problem of fracture of roller bearingtry=P/p1/√(ar)14 sin y sin y/2 (3c)

cases. It was known from an earlier test series conductedby Bach,25,26 that in roller bearing cases fracture occurredWieghardt now suggests to use these equations to

provide answers to questions on the strength of the crack in the corners ‘a’ and ‘a∞’ [see Fig. 3(e)] upon sufficientoverstressing. Wieghardt argues that Bach’s original (i.e.against the action of the force P. He asks: ‘Given the

strength parameters of our elastic material, what is the ‘customary’) method of calculating the critical load tofracture, as well as the direction of fracture initiationmagnitude of the force P necessary for material fracture?

And furthermore, at which place and in which direction ‘was in bad agreement with reality’.Wieghardt treats the essentially three-dimensionalwill the fracture initiate?’

Regarding the first question, Wieghardt admits that problem as a plane problem and focuses on the re-entrantcorner problem shown in Fig. 3(f ). The stress system inhe—and at that time everybody else too—was at a loss

for an answer because of the unbounded stresses which the roller bearing problem is also simplified first byconsidering the application of single forces.appear at the crack tip for any arbitrarily small load P.



One highlight of the paper is the development of an In the section on the practical use of the alternatingmethod, Wieghardt informs the reader that:alternating method for a wedge domain non-symmetri-

cally loaded by a single normal force P. In this method ‘for the case of the re-entrant corner, the author hasactually performed the calculations involved in the alter-(later applied by various researchers for the derivation

of the stress intensity factors for finite size cracked nating method. A combined analytical and graphicalapproach proved to be most effective’.specimens including the famous edge crack and cracked

strips), the stresses inflicted to a boundary to be The graphical part was concerned with integration.Wieghardt’s calculations showed that in the case of the‘unlocked’ due to stresses acting on another part of the

specimens will be ‘removed’ by successive application of re-entrant corner subjected to a normal load P, the stressin the corner should tend to infinity in the order ofequal but oppositely acting stresses systems on the

adjacent part of the boundary. This alternating tech- r−0.45. He also discloses to the reader that it is exactlythese calculations that have led him to suggest thenique, fortunately, converges very rapidly, this being a

decisive computational advantage considering the tedious validity of Eq. (5)!Wieghardt closes this chapter with the question on‘bone’ work required to arrive at solutions to problems

of this sort at the turn of the last century when no crack initiation in the case of Bach’s roller bearingproblem, i.e. for the re-entrant corner. As before, hecomputers existed, not even slide-rulers.

Several pages of lengthy calculations follow in employs the maximum shear stress hypothesis and themaximum tensile stress hypothesis, and concludes hisWieghardt’s original paper until he arrives at still another

highlight in fracture mechanics. computations with the statement:‘In any case, the results, which are valid for fractureIn the chapter ‘On the behaviour of the stresses in

the vicinity of the apex’, Wieghardt remarks that: initiation and based on the tensile stress hypothesis, arein agreement with the results of the tests by Bach’.‘it is awkward that the alternating method fails pre-

cisely where it is needed the most’. The paper finishes with an appendix on the uniquenessof the solutions found, and clarifies the conditions andHe continues:

‘In all probability and at least for the wedge domains requirements for the forces to decay appropriately atinfinity. The references and notes refer to the book Aa<1, the stresses in the vicinity of the corner may be

factorized into a product of two functions, one of the Treatize on the Mathematical Theory of Elasticity by A. Love(first edition of Ref. [13]), two papers by Airy, one byangular coordinate y and the other of powers of the

radial vector r. J. H. Michell, and four papers by German researcherswritten also in German.

F(r, y)=rn Function of y (5)

F(r, y)=rn[A1 cos ny+A2 cos(n−2)yA F T E R W I E G H A R D T ’ S 1 9 0 7 P A P E R

+B1 sin y+B2 sin(n−2)y] (6) The publication of Wieghardt’s work on the splittingand fracturing of elastic bodies in 1907 was a singularAt present, the author is missing an exact proof of this

decomposition ...’. issue. The publication of this paper in a German journal,soon to cease to exist (in 1922) and in German language,Wieghardt then uses Eqs (5) and (6) for P as well as

the analogue for the shear force Q, and arrives at the was not favourable for the dissemination of this work.In addition, the fact that Wieghardt, a student offollowing result:

‘In general, in the vicinity of a corner, the stresses A. Sommerfeld and at times a co-worker of Felix Klein,did not consider himself a practical engineer challengedgenerated by the action of a concentrated normal force

differ in their order of unboundedness from those by industrial consulting projects did not earn him areputation as a practitioner.stresses produced by the action of tangentially acting

concentrated forces; the normal force is associated with The author, however, believes that around 1907 thedecisive missing item was the lack of large-scale fracturethe smaller value of the two roots. Thus, when compared

with tangential forces, the normal forces are associated failures in industry and the ensuing driving force ofindustry to solve fracture problems. This only happenedwith a higher order singularity of the stresses at the

apex. The situation becomes more pronounced for wedge some 40 or 50 years afterward when G. R. Irwin enteredan arena of engineering characterized by practicaldomains between the half-plane and the formation

characterized by the condition tan(p/a)=p/a, where environment; one which eventually promoted the devel-opment of fracture mechanics as an engineeringonly those stresses generated by normal concentrated

forces but not those due to tangential forces become discipline.It is, however, interesting to note that Griffith’s paperinfinitely large. In the case of a crack, both stress systems

become unbounded at the crack tip’. of 1920 very quickly became well known, and several



researchers in Vienna and elsewhere rapidly respondedto its publication. On the other hand, German was notan entirely exotic language at that time, although manyof the papers by Prandtl and Einstein and others werealso published in the German language. In fact, Prandtl’spaper9 on the soap film membrane analogy was knownand referred to by Griffith and Taylor.11

Wieghardt’s pioneering paper of 1907 does not seemto have played any important role in the developmentof fracture mechanics as an engineering discipline norwas it followed by any other paper in this field by itsauthor. One can only speculate what might have hap-pened if the First International Congress on Mechanicshad taken place shortly after Wieghardt finished hispaper and he had presented his paper then to an inter-national audience.

Not having ignited the torch which led to the foun-dation of fracture mechanics, nevertheless, Wieghardt’spaper, and even more so his professorship in Vienna atthe Technische Hochschule, was of some importance toseveral Austrian professors who worked in the field ofmaterials testing and mechanics.

A L F O N S L E O N

Alfons Vincenz Leon (Fig. 4), born 9 September 1881in Ragusa in the Dalmatinian coastland of the HabsburgEmpire where his father was stationed, received his

Fig. 4 A. V. Leon (born 9 September 1881 in Ragusa, Austria-primary education at the Volksschule in Innsbruck andHungary, died 30 May 1951, Vienna, Austria) worked on problemsMeran in Tirol, and his secondary schooling at the k.k.of the theory of elasticity and developed a criterion for combinedStaatsoberrealschule in Innsbruck earning a bachelor’s tension-shear fracture.

degree in 1898. He performed his higher education atthe Civil Engineering School of the TechnischeHochschule in Vienna where he received his doctor’sdegree with first class honours on 18 February 1905. Engineers and Architects offered him the Ghega Award

and in the same year the Austrian Ministry of EducationDuring the period 1903–1916, he occupied various pos-itions at the TH Vienna, the Technologisches financially supported Leon’s research trip to the USA.

Thus, he was given the chance to visit and study theGewerbemuseum, and the University of Agriculture inVienna. He became Assistant Professor at the Institute work performed at numerous materials-testing labora-

tories in Germany, Switzerland, France, England, USA,of General and Technical Physics during the period1 October 1903–30 September 1905.27 The k.k. niedero- Belgium, The Netherlands, Denmark and Italy. Leon

was married and had two daughters who became andsterreichische Statthalterei granted Leon an annualremuneration of 2400 Kronen and an extra allowance of married medical doctors. Leon was fluent in German,

English, French and Italian, he translated numerous600 Kronen for the period 1 May 1909–30 April 1911.28

He served as an expert consultant to industry and foreign papers into German for a wide audience andreadership of many journals and technically orientatedcommerce in Vienna, notably working for the Austrian

Federal Railways. During the period 1916–1918, he newspapers.Leon’s passion for expressing his opinion in a franktaught at the Deutsche Technische Hochschule Brunn

in Brno in the present day Czech Republic. From 1918 way several times led him into confrontations withofficials and resulted in his relocation to other insti-to 1934, Leon occupied the position of a full professor

heading the Mechanical-Technical Laboratory at the tutions of teaching and learning. While working in Grazat the Technische Hochschule, Leon founded theTechnische Hochschule in Graz. Previously, in 1906,

Leon was awarded the Lielegg Travel Scholarship (400 Materials Testing Laboratory at the TechnischeHochschule Graz, and conducted and investigated moreguilders in gold), and in 1908 the Austrian Society of



than 2000 research projects for industry. However, his supplied by the external forces to rupture the material.He, Tetmajer, further explains: ‘The absolute value ofopposition to the national-chauvinistic and anti-Semitic

movement in the late 1920s catapulted Leon overnight the work capacity is directly related to the toughness ofthe material; it is smallest for brittle materials and largestinto politics and the press, and so retirement became

inevitable. His apolitical and strictly objective way of for tough materials’ (see Ref. [32]).Leon was a busy traveller. While working on problemsconducting examinations (knowledge and innovation

more important than political opinion and military hon- associated with railways during the period 1906–1908,Leon became confronted with the difficulties faced byours and decorations) was carefully noted by the rulers

to come. When, in 1934, the Montanistische Universitat the Swiss tunnelling engineers in connection with, pri-marily, the Simplon-tunnel. Leon’s early publications onin Leoben and the Technische Hochschule in Graz were

merged, Leon’s position fell victim to a rigorous savings the stresses induced by circular holes and sphericalcavities,33–37 and the damage formation in the region ofprogram and he was forced to retire.

This, however, did not break his enormous will-power twin-tunnels38,39 had a decisive influence on tunnelling.Fig. 5 is taken from the original paper,40 and showsto work. Serving as a continuous co-worker to many

technical journals, Leon wrote thousands of notes and regimes of severe fracturing around a twin-tunnel. In1909, Leon inspected several ammunition factories inreports during the years 1938–1943 when he was forced

to retire again from official teaching and research, but Germany, and material-testing labs in Germany,Switzerland and France.continued to work as a freelance writer to several techni-

cal journals. During the period 1943–1945, Leon, who In 1909, he attended the 5th International Congresson Materials Testing and Technology in Copenhagen,refused to become a member of the NSDAP, was com-

manded to work for the Reichsluftfahrtministerium and the 6th ICMT in New York and Washington. Onthis occasion, Leon visited the east coast of the USA(Ministry of Aeronautics of the Deutsches Reich)

encircled by co-workers who were all members of the and stayed there for 7 weeks. He paid a visit to thefamous material-testing machinery production company,NSDAP, SA or SS. As Leon explains in his CV, this

work ordered by the Ordnance Department had nothing Olsen & Co., in Philadelphia. He was expected to reporton his experience to the Chamber of Commerce of theto do with the war. After WWII, Leon was rehabilitated

and offered the position of a full professor for materials Province of Lower Austria what he did. One of thesereports was written jointly with P. Ludwik, who was onescience at the Technische Hochschule in Vienna. He was

now in charge of the Institute which his late friendProfessor P. Ludwik had established. Pneumonia con-tracted on the return flight from Madrid, where heattended the 5th Congress of the InternationalAssociation of Laboratories for Testing and Research forConstruction Materials and Constructions (30April–5 May), proved to be fatal for Professor Leon andled to his passing away on 30 May 1951.29–31

A L F O N S L E O N — H I S W O R K

Leon’s first paper addressing the issue of fracture wasdevoted to thickness shapes of rotating disks leading toequal zones of fracture probability. Leon calculates thestress field for the rotating solid disk and sphere as wellas for the centrally punched disk and sphere with acentral cavity.32

The paper discussed several fracture hypotheses,including those based on a critical stress, strain andwork. A work-based fracture hypothesis is due to L. vonTetmajer, founder, in 1901, of the Laboratory forMaterials Testing and Research associated with theTechnische Hochschule, Vienna. Tetmajer suggested touse the work capacity of the various materials as a Fig. 5 A damage pattern around a twin-tunnel subjected tomeasure of quality against fracture, i.e. the larger the uniaxial compressive stress loading (overburden). Numbers refer to

relative stress levels; ‘‘sprode’’ ≈ brittle.40work capacity of a material the more work has to be



of his best friends. Leon returned to the USA in 1912 problems. The construction of the twin-tunnel at theSimplon posed unexpectedly serious difficulties withwhen he travelled for 3 weeks to see numerous works

and institutions in New York, Pittsburgh (Carnegie Steel regard to stable stress equilibrium in the region betweenthe two tunnels. In 1913, Leon carefully studied thisCompany, Homestead Steel Works, National Tube

Company, US Mines Bureau, Bureau of Standards, problem theoretically and performed numerousaccompanying experiments. It turned out that the decis-Westinghouse Electric & Manufacturing Company, and

many others), Buffalo, NY (Niagara Falls Power ive parameter is the distance between the two axes ofthe tunnels, and this parameter entirely controls theCompany, etc.) and Washington D.C. (Bureau of

Standards). appearance of excessive compressive stresses in the wallbetween the tunnels and the sequence of damageDuring the period 1913–1926, Leon was a frequent

visitor to almost all materials-testing laboratories in inflicted.51

The development and increased use of reinforcedGermany and neighbouring countries. In an addition tohis biography entitled Studienreisen (Educational trips),41 concrete in industry naturally attracted the attention of

many researchers to problems of stress concentrationsLeon informs the reader about his travels which notonly were of a technical nature, but also included visits around embedded elastic inclusions, i.e. around the steel

armament embedded in the concrete matrix. This workto places of art.Leon devoted a considerable amount of time to the was a direct extension of Leon’s work on notch stresses

to composites.45–47 It was Leon who called the attentionsolution of problems associated with notch stresses,42

and the stress distribution in punched and notched of engineers to the difference between the definition ofstrain as customary in the theory of elasticity and thestrips,43,44 composites45–47 and tension bars.43 In 1913,

Leon and his colleagues published two particularly inter- definition based on the logarithmic strain.52

In his later work, Leon contributed to the clarificationesting papers on the testing of glass and ceramics: onewith P. Fillunger on the testing of glass cylinders48 and of the hypothesis of strength for concrete53 by proposing

a parabolic form of the enveloping limit state. Thisthe other with H. Linder on the testing of internallypressurized ceramic tubes.49 It is sad to reflect that enabled Leon to combine the fact that brittle materials,

e.g. concrete fracture in tension when pulled and inP. Fillunger in later years competed with Terzaghi onthe correct version of the soil mechanics basic equations, shear when compressed. Leon’s enveloping parabola

agreed very well with practical data of his own experi-and eventually—when realizing a grave mistake in histheory—together with his wife and research promoter ments as well as from other researchers. This work was

presented by Leon at the 4th International Congress forcommitted suicide.Leon’s contribution to the theory of notch stresses (at Technical Mechanics in Cambridge in 1934.54

Leon was a true workaholic; he not only publishedthe time one of the most important questions in thetheory of elasticity and strength of materials) was of a technical papers, but was interested in engineering poli-

tics, in the way that nature would teach and inform tolasting nature. It was known that abrupt changes incross-sections, and geometrical as well as material engineers and, last but not least, in the history of science

and engineering. In 1912, he wrote a lengthy paper ‘Theinhomogeneities in components will induce very largelocal stress elevations. These stress concentrations were development and the tendencies of materials testing’,37

which gives the most detailed account of the history ofmade responsible for fracture failures particularly inconnection with cyclic loading in ductile materials as materials testing particularly with regard to fracture

failures.well as in brittle materials subjected to static load levelsfar below the fracture stress. Design formulae frequently Leon was a great and enthusiastic teacher who fav-

oured the modern style of teamwork. In his presen-used in practice did not take into account these stressconcentrations. It is to Leon’s merit, not only to have tations, he always pointed the students to open questions

and unsolved problems, and introduced a seminary-styleemphasized the importance of these stresses, but to haveworked out solutions to a number of important notch of teaching. This method of teaching was unheard of at

that time but was very well accepted by all. His teachingsproblems, either in closed form or in an approximatefashion. Leon solved the problem of the stress concen- were condensed in the form of so-called ‘Merkblatter’

(pamphlets or memos) of which he produced more thantration in the vicinity of a spherical cavity.33,50

Based on his work on notch stresses in punched 2000. These memos—a novelty at that time—werehighly appreciated by engineers in industry. Another ofbodies, Leon studied the deformation and damage

around a circular tunnel subjected to overburden press- his favourite ‘hobbies’ was the organization of excursionsto various companies and testing laboratories all overure and lateral confinement stresses. This work became

internationally known and was very well accepted, and Europe where he always managed to receive amplefunding for his students. All of these excursions excelledLeon became heavily engaged with tunnelling and its



through perfect organization and efficiency. Leon seemsto have had the energy and will-power of a giant. Leon’swork was highly appreciated and was included in thebook by Nadai.55

Leon’s character can best be described by a noteaddressed to the Rector of the Technische HochschuleVienna dated 2 March 1949, where he complains:

‘Tuesday, 1 March 1949 without any advanced warningthe telephone service has been interrupted at 4 pm. Iwas supposed to conduct very important business bytelephone with a few other heads of institutes whichturned out to be impossible. Today I learned that thedisbanding of the telephone service occurred with regardto Carnival. I do request that any such arbitrary actionand disconnections without advanced notice which occurfrequently be prevented’,56 and, on another occasion,57

he requests his office telephone number be included inthe public phone directory as he felt that foreignresearchers who want to visit him in Vienna would notbe able to contact him on Saturday afternoons andSundays—Leon used his office as his private residencein Vienna!

P A U L L U D W I K

Paul Ludwik (Fig. 6), born 15 January 1878 in Schlan inBohemia in the present Czech Republic was the son ofthe director of a large machine manufacturing company.He studied and earned a degree in mechanical engineer- Fig. 6 P. Ludwik (born 15 January 1878 in Schlan in Bohemia,ing in Prague and worked in his father’s company for Austria-Hungary, died 31 July 1934 in Vienna, Austria) developed2 years. He went to Vienna, worked as a design engineer the famous Ludwik hypothesis which combines the yield stress and

cohesive strength for ductile steel.and, in 1904, he received a doctor’s degree from theTechnische Hochschule Vienna. From 1905 to 1934, heoccupied various professorial positions at the TH Viennaincluding the position of head of the testing laboratories Mechanics)8 addresses the flow of metallic materials sub-

jected to various loading conditions, e.g. tension, com-founded by Tetmajer in 1901 during the period1923–1934. Ludwik published 68 scientific papers of pression and shear, and—for the first time—discusses

the influence of the strain rate on material behaviour.which a large number contained ideas which couldimmediately be put to work. In his later years, he wasalso concerned with philosophical questions about life

T H E L U D W I K H Y P O T H E S I Sand the meaning of human life.

Suffering from serious kidney problems, Ludwik In 1909, Ludwik8 put forward a theory that helped toexplain the relatively abrupt increase of notched-bardecided to terminate his life in his study by deliberate

inhalation of coal gas on 31 July 1934. Professor Ludwik, fracture work with increase of test temperature, i.e. thetransition behaviour. He proposed that the behaviour ofwhile breathing the deadly coal gas, meticulously noted

his impressions and feelings from the onset of light steel would be characterized by two parameters. First,Ludwik assumed that steel had a plastic flow (yieldbreathing problems to illegible scribbling before final

collapse. strength) which decreased with temperature. Secondly,there also was an independent cohesive (fracture)strength which was nearly independent of temperature.

P A U L L U D W I K — H I S W O R K When elevating the test temperature to the point wherethe yield strength is less than the fracture strength,Ludwik was a pioneer in the field of materials testing

and materials science. His fundamental book Elemente extensive plastic deformation occurs prior to fracture,whereas at sufficiently low temperatures, the yieldder technologischen Mechanik (Elements of the Technological



which would be proportional to the volume of the testpiece; and the work expended in progressive extensionof the crack after its start whereas the second part mightbe nearly proportional to the severed area, and wouldbe responsible for the observed fracture size effect.

Ludwik’s work had its eastern counterpart in the workin Davidenkov60 and his school. The existence of a largefracture size effect became again evident in staticnotched-bar bend tests conducted by Docherty61,62 inthe 1930s to eliminate dynamic uncertainties inherentin the tests by Stanton and Batson; see Rossmanith.63

O L D I D E A S R E I N V E N T E D

As the concept of toughness is associated with thebreaking of materials—the tougher a material, the harderFig. 7 Ludwik’s hypothesis in a sketch by G. R. Irwin (taken fromit is to break—the original measure of toughness wasG. R. Irwin’s Lecture Notes on Fracture Mechanics from the

University of Maryland, 1978). the amount of work done in breaking a bar (the Tetmajerhypothesis) and, in 1975, toughness was still defined byASTM as the ability of a metal to absorb energy anddeform plastically before breaking. It is usually taken tostrength exceeds the fracture strength and brittle fracture

is observed. Ludwik’s theory is sketched in Fig. 7 which be the measured energy loss in a notched-bar impacttest and corresponds to the area under the stress–strainwas provided to the author by Professor G. R. Irwin,

who, for his numerous pioneering and fundamental curve in tensile testing. Consequently, a brittle-behavingmaterial is one that absorbs little energy, while tough-contributions to fracture mechanics (a term invented by

him) is nowadays considered to be the ‘father of fracture behaving materials would require a large expenditure ofenergy in the fracture process.mechanics’. Ludwik’s simplistic theory,58 although rela-

tively simple and capable of qualitatively explaining many After WWI, engineers on both sides of the AtlanticOcean developed renewed interest in notch effects,64,65of the features observed, lost favour because at least

some plastic strain was observed during cleavage crack as they very soon realized that fracture and fatigue aregreatly influenced by notches. One can tacitly say thatinitiation and propagation in structural steels, regardless

of the degree of brittleness. the story of failure is a tale of notches, nicks, key-ways,oil holes, screw threads, scratches, rough surfaces,The Ludwik theory was formulated in terms of stress

and strain, so that one could infer that the laws of quenching cracks, grinding cracks, sharp changes insection, thin outstanding fins, poor fillets, tool marks,dimensional similitude should apply. Experiments con-

ducted on notched-bars of structural steel, however, soon inclusions in the metal, corrosion pits, etc., i.e. somelocalized nucleus from which failure started. The factdemonstrated that the similitude argument was invalid.

The first tests showing size effects in fracture were that only a tiny spot need be stressed above a criticallimit in order for the entire piece to fail by a crackreported by Stanton and Batson from the National

Physical Laboratory in Teddington,59 when they conduc- developing from that spot deserves emphasis.At that time, it was well known that the safety factorsted impact tests on notched-bar bend specimens of

structural steel, and found that a substantial decrease in customarily used in design depended considerably uponjudgement estimates of the possibilities of fracture, how-the fracture work per unit volume occurred as the

specimen dimensions were increased. In fact, the tem- ever, no attempts were made to replace the notch by anatural crack and measure the sensitivity of the steels toperature of brittle–ductile transition could be increased

by increasing the test bar size and the fracture work the presence of crack-like defects. In fact, at that time,in the 1940s, there was still inadequate recognition thatdecreased with scaled increase of bar dimensions. The

serious implications of this finding as regards the general cracks or crack-like defects were significant factors inreducing the load-carrying capacity of structures madeapplicability of notched-bar testing and upon structural

strength estimates based on the usual scaling laws as from high-strength steels. The early work on notchsensitivity was rarely criticized because the notches werewell, were not overlooked in published discussions of

the Stanton–Batson paper. Contributed discussions not sharp enough (Leon’s work was on semicircularnotches!). If they resembled cracks, they were ratherbrought out that, apparently, the fracturing energy con-

sisted of two parts: the bending of the bar as a whole thought to be too sharp to represent any practical



situation of high-stress concentration that might be square holes, star-shaped holes and surface notches, andprovided a simple expression for maximum stress at theencountered in service.

There was an awakening of interest toward improve- tip of a notch which is still useful. He shows that themaximum stress equation has the form smax=ment of design details stimulated by Neuber’s work,

particularly his book on notch stress analysis.66 R[1+2√(a/r)], where ‘a’ is the half-length of the equiv-alent notch and r is the notch root radius.In addition, prior to 1950, it was not customary for a

fracture failure report to cite a fabrication-induced crack The description of fatigue growth given by Inglis isquite modern, but his paper has been usually referencedas being responsible for the failure. All specifications

stated that fabrication cracks (of any size) were not with regard to stress elevation at notches, for which hiswork received practical use widely, e.g. in Peterson’sacceptable, and there appeared to be a reluctance to

recognize that fabricated structures, so perfect as to book68 on notch stress concentrations, and his studyformed the basis of Neuber’s book66 on notch stresscontain no crack-like flaws, are highly improbable. When

the size of the initial crack was ignored, it was rarely analysis.possible to decide how the cause of failure should bedistributed between stress level, toughness and prior

G R I F F I T H ’ S A P P R O A C H T O F R A C T U R Ecrack size, the three quantities in Griffith’s formula and

M E C H A N I C Sin the Irwin analysis.Following 1913, England was at war and aeroplaneswere receiving the first usage in armed combat. The

I N G L I S ’ W O R K O N S T R E S S C O N C E N T R A T I O N Sequations provided by Inglis’ paper were used to verifycertain aspects of the experimental results. The under-Professor Inglis67 is usually credited with having pub-

lished in 1913 the first significant and fundamental paper standing of surface tension and familiarity with the Inglispaper proved to be very useful relative to Griffith whenon elliptical openings subjected to stresses from which

the special case of a crack could be derived. Inglis writing his famous 1920 paper.Alan Arnold Griffith was born in London on 13 Junedeveloped and provided a function theory solution for

the stress field near an elliptical opening of arbitrary 1893 and received his BEng from the University ofLiverpool in 1914, and his MEng and DEng in 1917eccentricity in a plate loaded by remote tension. In his

opening comments, Inglis makes it clear that the purpose and 1921, respectively, from the same university. Griffithjoined the Royal Aircraft Factory (later Royal Aircraftof his analysis was to assist the understanding of crack

extension, particularly by load fluctuations as in fatigue Establishment) in Farnborough in July 1915, and was anactive and ingenious inventor and contributed greatly totests of structural metals as encountered in ship-building.

The results could be used, in the limiting case, to model the science of aircraft propulsion.In 1920, Griffith69 published a technical paper ona crack as a slender elliptical cavity, for which the exact

2D stress field could be derived. In fact, Inglis points fracture strength of glass, which was of continuinginterest and value. The paper was essentially Griffith’sout that, when the shape of the ellipse becomes crack-

like, the regions close to the tip of the major axis will PhD thesis in the Engineering Department atCambridge University under the guidance of his princi-experience large reversals of plastic strain even for load

fluctuations of relatively small size. With regard to a pal advisor G. I. Taylor. Griffith assumed that the surfaceof the soda-lime glass tube and bulb specimens containedplate of less ductile material which contains a crack-like

opening, Inglis writes as follows: numerous small, crack-like flaws, and that a crack in abrittle material, e.g. glass, would have a crack-tip radius‘.. . a small pull applied to the plate across the crack

would set up a tension at the ends sufficient to start a which was essentially zero. He assumed that under tensileloading, crack extension and fracture would occur whentear in the material. The increase in length due to the

tear exaggerates the stress yet further and the crack the loss of the stress field energy per increment of crackextension became greater than the gain of surface energy.continues to spread in the manner characteristic of

cracks’. Equations for the rate of loss of the stress field energywith crack extension were obtained using the equationsSubsequent parts of Inglis’ paper dealt with the use of

his results to assist estimates of stress elevations in a of Inglis adjusted for zero root radius. The calculationof the energy loss rate was not an easy task and wasplate near notches. Inglis points out that any narrow

groove with a well-defined root radius will have the completed nearly without error. The paper describesGriffith’s supportive experiments and presents measure-same stresses at the tip region as if the shape was

elliptical. From considerations of the stress near the tip ments of solid glass surface energy in detail. In theanalysis of the experimental results for the comparisonof the ellipse, he developed equations for calculating the

stress concentrations due to cavities of other shapes, e.g. with stress field energy loss, Griffith needed only the



remote tension required to initiate fracture of the glass observed in a solid exposed to an aggressive environment,the behaviour was sometimes explained in terms of acontaining a small crack of known size. For that purpose,

Griffith used thin-walled spheres and cylinders which lowering of the surface energy of the solid due to attackfrom the environment. However, the most useful resultwere precracked and subjected to an increase in internal

pressure. The fracture stress values obtained in this way of Griffith’s 1920 paper is the proportionality of fracturestress to the inverse square root of crack size, a relationsupplied estimates of the stress field energy loss rate for

comparison to twice the value of the surface energy. The which is still important in fracture failure analysis andassists judgements related to fracture control. Griffithresult was an energy loss rate of only 20%, too low for

exact agreement, but an exciting confirmation of a noted that the theory was only applicable to glass andother brittle materials, thereby excluding most struc-novel idea.

Griffith noted that crack-like flaws in glass should be of tural metals.The agreement claimed between theoretical predictionunimportant size in freshly drawn glass fibres and provided

confirming measurements. The use of hot-work orien- and experimental results appears now to have beencoincidental.tation of flaws parallel to the direction of the tension

expected in service and the concept of the stress field The level of knowledge in fracture testing prior to1960 did not provide a clear understanding of Griffith’senergy loss rate as an important factor relative to crack

extension were the features of lasting value in Griffith’s 1920 paper. As a result, it was generally assumed thatGriffith had shown a close relationship between solid1920 paper. The attention given to surface energy as the

resistance to crack extension was a distraction. state surface energy and fracture strength of glass.Subsequent investigations of the effect of environmentGriffith’s 1920 paper was reviewed by G. I. Taylor and

accepted for publication prior to the discovery of an (moisture, etc.) on fracture strength of ceramic materialsfrequently referenced Griffith’s paper. The pro-oversight error in Griffith’s equation for the relationship

between tension normal to the crack and the loss rate of portionality between fracture stress and inverse squareroot of the radius of the mirror area, for plate glassthe stress field energy. The corrected calculation indi-

cated an energy loss rate larger than twice the surface fractures, was noted and often used to assist fracturefailure analysis for plate glass.energy by a factor of three. A brief footnote was added

to the paper stating that no correction of the text was In this manner, interest in Griffith’s 1920 paper con-tinued into the post-WWII period, when Irwin70 andneeded as only ‘order of magnitude’ agreement was of

importance. Actually, an accurate measurement of energy Orowan71 introduced their ‘modified Griffith’ ideas.However, the substantial interest in Griffith’s 1920 paperloss rate was not possible using thin-walled test vessels

with internal pressure due to outward bulging of the during the following years was not shared by Griffith,and he published only one additional paper related tocrack walls. This effect of outward bending of the shell

flanges adjacent to the precrack and also the effect of fracture in 1924 for the First IUTAM Conference inDelft.72 However, this paper does not use the stress fieldmoisture-assisted slow-stable crack extension in glass

were not taken into account. Following the introduction energy loss idea and reflects no significant interest inthe energy balance idea.of fracture mechanics methods, tests using flat plates of

similar glass and low humidity indicated a rate of loss ofthe stress field energy larger than twice the surface

S M E K A L A N D T H E G R I F F I T H A P P R O A C Henergy by a factor of about 13!

The contribution most often derived from the Griffith Griffith’s pioneering paper is critically discussed in a paperby A. Smekal, a professor of physics at the University ofpaper has been the equation relating the fracture stress to

crack size, sf√(pa)=√(2cE ), where sf is the fracture Vienna.73 Smekal states that the idea of using the specificsurface energy as the characteristic quantity in deriving astress and E is Young’s modulus. The surface energy term,

2c (later termed GC) is the strain-field energy loss per theory of fracture had been suggested before Griffith, e.g.by E. Lohr of the Technische Hochschule Brunn (Brno,increment ‘d’ of crack extension, and ‘a’ is the half-length

of a central crack, normal to the tension applied, in a large Czech Republic) even before WWI, and with respect toliquids it can be found in Boltzmann’s work. However,plate. To derive this equation, Griffith used Inglis’ stress

equation for an elliptical opening in a large plate subjected Smekal expressively gives credit to Griffith for havingrecognized the importance of this idea and having con-to tension. It was necessary to revise these equations, so as

to represent a straight crack in a plate, and then to calculate structed what is now called the Griffith theory of fracture.In the ensuing discussion, Smekal is concerned about thethe rate of loss of the strain-field energy with an increase

in crack size assuming fixed boundaries. This was a formi- difference between the molecular strength of a material andthe strength derived from a tensile test. He arrives at adable task with the analysis tools then available.

After 1920, when low-stress slow-stable cracking was factor of 100.



ics and theoretical physics decidedly was of great advantageK A R L W O L F — A P H Y S I C I S T I N M E C H A N I C S

in attacking complicated problems. Wolf’s paper74 on theintegration of the biharmonic equation by means of polyn-Karl Wolf (Fig. 8) was born on 13 November 1886 in

Bielitz in the Habsburg Empire province of Austria–Silesia, oms for the case of an arch dam earned him the positionof an Associate Professor of Theoretical Mechanics at thenow part of the Czech Republic. He was the son of a

classical philologist and was very proud of his dependency Technische Hochschule Vienna in 1915.After WWI, K. Wolf was appointed successor ofof hillside farmer lineage. He entered the Vienna

University in 1905, and studied mathematics and physics. K. Wieghardt who accepted a call to Dresden. A seriesof papers published under the heading ‘ContributionsWolf’s teacher and mentor was Fritz Hasenohrl, the suc-

cessor of L. Boltzmann. Boltzmann died in 1906. On 18 to the plane theory of elasticity’ in the Zeitschrift furtechnische Physik address important problems of the stressNovember 1910, Wolf received his ‘Doktor of

Philosophie’ from the Vienna University for his funda- distribution in the vicinity of an elliptical hole or cracksubjected to an arbitrarily inclined uniaxial state ofmental work in theoretical physics on the propagation of

electromagnetic waves in a conducting hollow cylinder. stress.75,76 These papers were very well accepted and theresults were rapidly integrated into the German textbooksThe turning point in Wolf’s academic life came when he

accepted an assistant professor position at the Institute of on elasticity theory. Wolf increasingly became interestedin problems of fracture and, after having read the funda-Theoretical Mechanics and Graphical Statics under the

leadership of J. Finger, and shortly afterwards as a mental contribution by Griffith,69 he wrote the paper ‘OnGriffith’s theory of fracture’77 which he presented at theco-worker of K. Wieghardt, an alumni of the University

of Gottingen and an expert in the theory of elasticity. 19 September 1922 Treffen der Naturforscher (Meetingof the Natural Scientists) in Leipzig. In this paper, heThe theory of elasticity became Wolf’s favourite field of

research, and his earlier university education in mathemat- reveals a deficiency in Griffith’s derivation of the basicequation and offers a much simpler way to derive thisformula. Wolf explicitly mentions that it was Griffith’smerit to have presented an energy-based treatment of afracture and established contact with Griffith himself. Wolfalso generalizes Griffith’s theory to the case of in-planebending, and provides an extension of Griffith’s formulaby combining tension and shear loading, thus, proposingthe first mixed-mode fracture criterion.

Wolf pointed out the mistake in Griffith’s 1920 paper,and must have been in correspondence either withGriffith himself or with the publisher. In 1924, Griffithpresented a new paper ‘The theory of rupture’72 at theFirst International Congress of Mechanics in Delft wherehe corrected the erroneous calculations of the strainenergy. However, it was the editors (!) of the proceedingsthat added to Griffith’s contribution a note indicatingthat a German (!) review of Dr Griffith’s theory ofrupture had been given by K. Wolf, Professor ofMechanics at the Technische Hochschule in Vienna.

B. Cotterell,78 working on a paper for the G. R.Irwin Anniversary Volume63 shows that Wolf made thesame mistake as Griffith—only he used a different wayof calculating the strain energy. However, Wolf statesthat his and Griffith’s result for the decrease of thestrain energy release rate differ by a factor of two, andhe argues that this will be favourable with respect toagreement between theory and practice in Griffith’scase.

In later years, Wolf became interested in problemsassociated with air flow in caves, as he was an enthusiasticFig. 8 Wolf (born 13 November 1886 in Bielitz in Austria-mountaineer and skier. Wolf suffered a heart stroke andHungary, died 10 January 1949 in Vienna, Austria) corresponded

with Griffith and corrected his 1920 paper. passed away on January 10 1949.79



4 G. Galilei (1638) Discorsi e Dimostrazioni Matematiche Sopra dueS U M M A R Y Nuove Scienze, Elsevier Science, Leiden.

5 E. Mariotte (1686) Traite de Mouvement des Eaux, Paris.This contribution highlights the development in mech-6 I. Todhunter and K. Pearson (1886) History of the Theory of

anics and materials testing at the turn of the last century Elasticity and of the Strength of Materials, Cambridge Universityperformed in Europe, especially in the German-speaking Press, UK.countries. Particular emphasis is given to the ‘first paper 7 D. Kirkaldy (1866) Experiments on Wrought-Iron and Steel, 2nd

edition, D. Kirkaldy Publishing, London.on fracture mechanics’ by K. Wieghardt. The appoint-8 P. Ludwik (1909) Elemente der Technologischen Mechanik,ment of Wieghardt to a professorship of mechanics at

Springer, Berlin.the Technische Hochschule in Vienna started intensive9 L. Prandtl (1903) Zur Torsion von prismatischen Staben.research work in the field of notch effects and stress

Physikalische Zeitschrift 4, 758–759.distributions around circular, elliptical and crack-like 10 S. P. Timoshenko (1953) History of Strength of Materials,openings and discontinuities. McGraw-Hill, NY.

The pioneering work by Wieghardt and the impressive 11 A. A. Griffith and G. I. Taylor (1917) The use of soap films insolving torsion problems. In: Proceedings Inst. Mech. Eng.,work by Leon anticipate many of the results in fracturepp. 755–809.mechanics which were derived decades later, e.g. the

12 L. Prandtl (1907) Verhandlungen deutscher Naturforscher undstress distribution at the apex of a wedge-type opening,Arzte, Public lecture, Dresden.a mixed-mode fracture criterion and the direction

13 A. E. H. Love (1926) A Treatise on the Mathematical Theory ofof crack initiation under combined loading by Elasticity, Dover Publications, NY.Westergaard,80 Williams81,82 and Muskhelishvili.83

14 K. Wieghardt (1907) Uber das Spalten und Zerreissen elas-The importance of Ludwik’s work in the development tischer Korper. Z. Mathematik Physik. 55, 60–103. (for English

translation, see Ref. [21]).of the understanding of the relationship between yield15 K. Wieghardt (1920) Letter to the Rector of the TH Vienna,strength and brittleness of a material is highlighted, as

Dresden, October 12, 1920.well as the interaction of Wolf and Smekal with the16 K. Wieghardt (1903) Uber die Statik ebener Fachwerke mitwork by Griffith. schlaffen Staben. Doctor Thesis, University of Gottingen.

The fact that most of these contributions have been 17 K. Wieghardt (1904) Uber einen Grenzubergang derpublished in German in journals comparatively little known Elastizitatslehre. Habilitationsschrift, Technische Hochschuleoutside Germany, Austria-Hungary, etc. may partly be Aachen, Germany.

18 K. Wieghardt and F. Klein (1905) Uber Spannungsflachen undmade responsible for their having fallen into oblivion.reziproke Diagramme. Archiv der Mathematik und Physik III,Renewed interest in the historical development of a disci-Reihe, VIII.pline and a more subjective viewpoint will unveil the names

19 K. Wieghardt (1906) Uber die Uberspannungen bestimmterof the forgotten pioneers in fracture research and bring to hochgradig statisch unbestimmter Fachwerke.light, and appreciation, their early work. 20 G. Hahn (1985) Elastizitatstheorie (Theory of Elasticity),

Teubner, Stuttgart.21 H. P. Rossmanith (1995) English translation of Ref. [14]. Fatigue

Acknowledgements Fract. Engng Mater. Struct. 12, 1371–1405.22 H. P. Rossmanith (1995) An introduction to K. Wieghardt’s

The author would like to thank the Austrian Science historical paper ‘On splitting and cracking of elastic bodies’.Foundation for financially supporting this work under Fatigue Fract. Engng Mater. Struct. 12, 1367–1369.contract #P 10326 GEO. He would also like to express 23 O. Venske (1901) Zur Integration der Gleichung VVu=0 fur

ebene Bereiche (On the integration of the equation VVu=0his deep appreciation to the late Professor Dr G. R.for plane domains). Nachrichten der kongl Gesellschaft d.Irwin and Dr Paul C. Paris for the numerous stimulatingWissenschaften zu Gottingen.technical discussions, and their kind hospitality and

24 O. Mohr (1906) Welche Umstande bedingen diecooperation in the course of this work. The authorElastizitatsgrenze und den Bruch eines Materials? (What con-

would also like to acknowledge the help of E. Jiresch, ditions imply the limits of elasticity and fracture of a material?).Head of the Archive of the Vienna University of Abhandlungen Aus Dem Gebiete der Technischen Mechanik,Technology. Figs 1, 4, 6 and 8 have been provided by Wilhelm Ernst & Sohn, Berlin.

25 C. Bach (1902) Eine Stelle an manchen Maschinenteilen, derenthe Archive of Photography of the TU Vienna.Beanspruchung auf Grund der ublichen Berechnung starkunterschatzt wird (On a particular location in machine partswhere on the basis of conventional theories the stresses will beR E F E R E N C E Shighly underestimated). Mitteilungen uber Forschungen, VDI,

1 Leonardo da Vinci (date unknown) Codice Atlantico, folio 82 Issue 4.recto-B. 26 C. Bach (1905) Elastizitat und Festigkeit (Elasticity and Strength),

2 A. Uccelli (1956) Leonardo da Vinci, Reynal & Co, NY. Julius Springer, Berlin.3 G. R. Irwin and A. A. Wells (1965) A continuous mechanics 27 AVTU Archive of the Vienna University of Technology (1903)

Document dated September 18.view of crack propagation. Metallurg. Rev. 10, 223–270.



28 AVTU Archive of the Vienna University of Technology (1909) von kreisformigen Lochern in einem elastisch festen Korperauftretenden Spannungs-und Verzerrungsstorungen (On theDocument dated February 1 .

29 A. Slattenscheck (1922) Obituary to A. V. Leon. Verlag der stress and strain disturbances in an elastic solid caused by a rowof circular holes). Zeitschrift des Osterr. Ing.-u. Architekten-VereinTechnischen Hochschule, Vienna.

30 A. Slattenscheck (1965) Ehrung Paul Ludwik (Honoring Paul 66, 424–428.45 A. V. Leon (1909) Uber die Spannungsstorungen beim VerbundLudwik). Festschrift der TU Wien.

31 K. Girkmann (1951) Alfons Leon zum Gedenken (In memoriam verschiedener Materialien (On the stress disturbances in dis-similar composites). In: Mitteilungen Des InternationalenAlfons Leon). Festschrift der TU Wien.

32 A. V. Leon (1907) Uber Formen gleicher Bruchgefahr mit Verbandes fur die Materialprufung der Technik, Vth Congress,Kopenhagen, Paper No VIII-10, pp. 377–382.besonderer Berucksichtigung rotierender Scheiben (On the

shapes of equal fracture danger with special regard of rotating 46 A. V. Leon (1909) Uber die Spannungsverteilung in Verbund-korpern (On the stress distribution in composite media). Osterr.disks). Osterr. Ing.- u. Architekten-Verein 28, 511–512.

33 A. V. Leon (1908) Uber die Storungen der Spannungsverteilung Wochenzeitschrift fur den offentlichen Baudienst 15, 18–24, 32–38.47 A. V. Leon (1909) Zur Theorie der Verbundkorper (On thedie in elastischenKorpern durch Bohrungen und Blaschen ent-

stehen (On the disturbances in the stress distribution in elastic theory of composites). Z Armierter Beton 9, 343–351; 10,408–416.bodies due to boreholes and cavities). Osterr. Wochenschrift fur

den offentlichen Baudienst 14, 163–168. 48 A. V. Leon and P. Fillunger (1913) Physikalisch-technischePrufung von Glaszylindern (Physical-technical testing of glass34 A. V. Leon (1908) Uber die Spannungsstorungen durch

Kerben und Tellen und uber die Spannungsverteilung cylinders). Mitteilungen des Technischen Versuchsamtes Wien 2 (3),38–46; 2, 29–49.in Verbundkorpern (On the stress disturbances due to notches

and dents and on the stress distribution in composite bodies). 49 A. V. Leon and H. Linder (1909) Die Festigkeit vonSteinzeugrohren auf Innendruck (On the strength of internallyOsterr. Wochenschrift fur den offentlichen Baudienst 14, 770–776,

783–787. pressurised ceramic tubes). Zeitschrift des Osterr. Ing.-u.Architekten-Vereins 65, 504.35 A. V. Leon and F. Willheim (1910) Uber die Zerstorungen in

tunnelartig gelochten Gesteinen—Teil I (On damage in rock 50 A. V. Leon and F. Willheim (1915) Uber die Spannungs-storungen die in elastischen Korpern durch Hohlungen,mass weakened by a tunnel—Part I). Osterr. Wochenzeitschrift

fur den offentlichen Baudienst 16, 641–648. Inhomogenitaten und eingeschlossenen Flussigkeiten bewirktwerden (On stress disturbances in elastic bodies caused by36 A. V. Leon and F. Willheim (1912) Uber die Zerstorungen in

tunnelartig gelochten Gesteinen—Teil II (On damage in rock cavities, inhomogeneities and fluid inclusions). Zeitschrift furArchitektur und Ingenieurwesen 45–62.mass weakened by a tunnel—Part II). Osterr. Wochenzeitschrift

fur den offentlichen Baudienst 18, 281–285. 51 J. Stini (1950) Tunnelbaugeologie (Tunnel Construction Geology),Springer, Vienna.37 A. V. Leon (1912) Die Entwicklung und die Bestrebungen der

Materialprufung (On the development and the tendencies 52 A. V. Leon (1908) Wie ist das Hooke’sche Gesetz zu verstehen?(How to understand Hooke’s law?). Zeitschrift des Osterr. Ing.-of materials testing). Verlag des Osterr. Verbandes fur die

Materialprufungen der Technik. 1–78. u. Architekten-Vereins 60, 473–475.53 A. V. Leon (1933) Uber das Maß der Anstrengung bei Beton38 A. V. Leon and F. Willheim (1913) Uber den Einfluß der

Achsen-entfernung auf die Zerstorungserscheinungen in einem (On the extent of strength of concrete). Ingenieur-Arch. 4,421–431.Doppeltunnel (On the effect of the distance of the tunnel axes

on damage formation in a twin tunnel). Osterr. Wochenzeitschrift 54 A. V. Leon (1934) Uber die Verbindung von Trenn- und Schub-bruch (On the combination of tensile and shear fractures). In:fur den offentlichen Baudienst 19, 18–21.

39 A. V. Leon and F. Willheim (1913) Zur Frage uber die durch Proc. 4th International Congress on Applied Mechanics, Cambridge.55 A. Nadai (1950) Theory of Fracture and Flow of Solids, McGraw-einen Doppeltunnel bewirkten Spannungsstorungen im Gebirge

und deren Beeinflussung durch die Achsenentfernung (On the Hill, New York.56 AVTU Archive of the Vienna University of Technology (1949)stress disturbances caused by a twin tunnel in a rock mass and

the effect of the distance of the tunnel axes). Rundschau Technik Document dated March 2.57 AVTU Archive of the Vienna University of Technology (1949)Wirtschaft 6, 1–3.

40 A. V. Leon and F. Willheim (1914) Die Verteilung des Document dated May 7.58 P. Ludwik (1928) Bruchgefahr und Materialprufung (FractureGebirgsdruckes und dessen Storungen durch den Bau tieflieg-

ender Tunnel (The distribution of the overburden pressure and danger and materials testing). Schweiz. Verband fur dieMaterialprufungen der Technik. Report No. 13, Zurich,its disturbances due to the construction of deep level tunnels).

Zeitschrift fur Architektur und Ingenieurwesen. 191–199. November.59 T. E. Stanton and R. G. C. Batson (1921) On the characteristics41 A. V. Leon (1927) Autobiography by A.V. Leon. Produced and

distributed by the author. of notched-bar impact tests. Minutes of Proceedings Inst. CivilEng. 211, 67–100.42 A. V. Leon and P. Ludwik (1909) Vergleichende statische und

dynamische Kerbbiegeproben (Comparison between static and 60 N. N. Davidenkov, E. Shevandin. and F. Wittmann (1947)Influence of size on the brittle strength of steels. Amer. Soc.dynamic notch bent specimens). Osterr Wochenschrift fur den

offentlichen Baudienst 15, 1–12. Mech. Eng. 69, 63–69.61 J. G. Docherty (1932) Bending tests on geometrically similar43 A. V. Leon and F. Willheim (1914) Uber die Spannungsvertei-

lung im gelochten und gekerbten Zugstab (On the stress notched bar specimens. Engineering 133, 645–647.62 J. G. Docherty (1935) Slow bending tests on large notcheddistribution in a punched and notched tension bar). Mitteilungen

des Technischen Versuchsamtes Wien 3(1), 33–50, 37–52. bars. Engineering 139, 211–213.63 H. P. Rossmanith (1997) Fracture Research in Retrospect (Edited44 A. V. Leon and F. Willheim (1914) Uber die durch eine Reihe



by H. P. Rossmanith), G. R. Irwin 90th Birthday Anniversary 75 K. Wolf (1921) Beitrage zur ebenen Elastizitatstheorie, Teil I:Volume, Balkema, Rotterdam. Einfluss eines elliptischen Loches bzw. Spaltes auf einen einach-

64 E. Orowan (1945) Notch brittleness and the strength of metals. sigen Spannungszustand (Contributions to the plane theory ofTrans, Inst. Engineers Shipbuilders Scotland 89, 165–215. elasticity, Part I: Influence of an elliptical opening or crack on

65 E. Orowan (1955) Energy criteria of fracture. Welding Journal. the uniaxial state of stress). Z. Technische Physik 2, 209–216.Res. Sup. 34, 157s–160s. 76 K. Wolf (1922) Beitrage zur ebenen Elastizitatstheorie, Teil II:

66 H. Neuber (1937) Kerbspannungslehre (Theory of Notch Stresses), Einfluss eines elliptischen Loches bzw. Spaltes auf denSpringer, Berlin. Spannungszustand im Falle der reinen und der zusammen-

67 C. E. Inglis (1913) Stresses in a plate due to the presence of gesetzten Biegung (Contributions to the plane theory of elas-cracks and sharp corners. Proceedings Inst. Naval Arch. 55, ticity, Part II: Influence of an elliptical opening or crack on the219–241. state of stress in the case of pure and general bending). Z.

68 R. E. Peterson (1940, 1974) Stress Concentration Factors, John Technische Physik 3, 160–166.Wiley, NY. 77 K. Wolf (1922) Zur Bruchtheorie von A. Griffith (On Griffith’s

69 A. A. Griffith (1920) The phenomena of rupture and flow in theory of fracture). Z Angewandte Mathematik Mechanik 3,solids. Phil. Trans. Roy. Soc. London. A 221, 163–198.

107–112.70 G. R. Irwin (1948) Fracture dynamics. In: Fracturing of Metals,

78 B. Cotterell (1996) Private communication by letter datedASM, Cleveland, OH, pp. 147–166.Nov. 7.71 E. Orowan (1949) Fracture and strength of solids. Reports Prog.

79 A. Basch (1951) Obituary to K. Wolf. Verlag der TechnischenPhysics 12, 185–232.Hochschule Wien, Leiden.72 A. A. Griffith (1924) The theory of rupture. In: Proceedings of

80 H. M. Westergaard (1939) Bearing pressures and cracks. J. Appl.the First International Congress for Applied Mechanics, Delft,Mech. Trans. ASME 6, A49–A53.pp. 55–63.

81 M. L. Williams (1952) Stress singularities resulting from various73 A. Smekal (1922) Technische Festigkeit und molekulareboundary conditions in angular corners of plates in extension.Festigkeit (Technical strength and molecular strength). DieJ. Appl. Mech. 74, 526–528.Naturwissenschaften 10, 799–804.

82 M. L. Williams (1957) On the stress distribution at the base of74 K. Wolf (1914) Zur Integration der Gleichung DDF=0 durcha stationary crack. J. Appl. Mech. Trans. ASME 24, 109–114.Polynome im Falle einer Staumauer (On the integration of the

83 N. I. Muskhelishvili (1953) Some Basic Problems in the Theory ofequation DDF=0 by means of polynoms in the case of an archdam). Mitteilungen der k.u.k. Akademie der Wissenschaften Wien. Elasticity, Noordhoff, The Netherlands.


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Fracture mechanics and materials testing: forgotten pioneers of the early 20th century