DYNAMIC MIXED MODE FRACTURE. (U)AUG 80 A S KOBAYASHI. M RANIA.U N00014-76-C-0060

UNCLASSIFIED TR-39 ML

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MRRCN l O UhNII', HA

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- LE- VEL'Office of Naval Research

Contract N00014-76-0060 NR 064-478

Technical Report No. 39

DYNAMIC MIXED MODE FRACTURE

by DTICby E LECTE f

~~AUG 18

A. S. Kobayashi and M. Ramulu A

August 1980

The research reported in this techniical report was made possible through

support extended to the Department of Mechanical Engineering, University 7

of Washington, by the Office of Naval Research under Contract N00014-76-C-

0060 NR 064-478. Reproduction in whole or in part is permitted for any

purpose of the United States Government.

Department of Mechanical Engineering

College of Engineering

University of Washington

This docume~nt has hee apro~Ifor public rolc:s atid LOT ij 9 1 C)Wdistribution is UnnilJ/ L -__''°"o" ,.,__ 1 80 8 21 070

DYNAMIC MIXED MODE FRACTURE

A. S. Kobayashi and M. Ramulu

Department of Mechanical Engineering, University of Washington

ABSTRACT

A newly developed data reduction process was us(,d t reeva wo te, (48l i I

photoglAstic results and to extract dynamic stress intensity f acto Vs, K.yand KY , associated with curved and branched cracks in fracturing Hlmdajite -

100 piltes. A branching stress intensity factor approximately 5 times thefracture toughness was identified for thi materA.. Moderate to severecrack curvings were associated with a KI'y and KIt rat.io a- low as (.(05, hotwith positive remote stress component, ,

INTRODUCTION

Two dimensional dynamic photoelasticity has been used by Daily and hisassociates [1,2] and by the author and his associatn[3,4] to determine ex-perimentally the dynamic stress intensity factor KT- , surrounding a propa-gating crack and to establish a dynamic fracture toighness, K , versus crackvelocity A, relation which may control dynamic fracture. Thi;Duse of dynamicphotoelasticity in studying dynamic fracture has been eloquently described byJ. W. Dally in his recent article [1]. As noted by Dally, the dat8 reductionprocedure used by most investigators in the past for calculating KIYn, fromthe transient isochromatics surrounding the propagating crack tip, was re-stricted to Mode I crack tip deformation. A theoretical, near-field, staticisochromatics was first equated to the recorded experimental dynamic isochro-matics and the resultant static stress intensity factor of the former wasconsidered the dynamic stress intensity factor of the latter [2,5]. Errorestimates for using a near-field stress to extract the Mode I dynamic stressintensity factor have been made by several investigators [6-8] and in partic-ular, exhaustively by Rossmanith and Irwin [8].

Studies of the static isochromatic patterns under mixed mode loadingconditions, i.e. in the presence of combined KI and K crack ti3 deforma-

tions were made by C. W. Smith [9,10], Gdousto and Th&caris III and morerecently by Dally and Sanford [12,13] and Rossmanith [14]. These mixed modeisochromatics are all characterized by their uns)miietric patterns with re-spect to the straight crack line. It is also interestinJ to note that. theshapes of these static isochromatics are strongly influenced by the higherorder terms, i.e. terms other than KI and K . In particular, the secondorder term of a , commonly referred to as t4e remote stress component, willdistort the symntry of the isochromatics by significant stretchinq and

shortening of the upper avd luwer loop ;ysiii 114]. or ,i pure modt, I Icrack tip defonation, the isochromatic loo) straddles the crack tip asshows in Figure 1 where a nearly pure shear state of stress is generatedaround branched cracks. The mode II stress intensity factors K 11 , and re-mote stress components oox, associated with these isochroatics re listedin the following Table 1.

FOURTEENTH FRAME FIFTEENTH FRAME448 j Seconds 482 /4 Seconds

(a) INNER BRANCH CRACK

FIFTEENTH FRAME SIXTEENTH FRAME482 ks Seconds 531 us Seconds

(b) OUTER BRANCH CRACK

Fig. 1 Typical Mode II Dynamic Isochromatic Pa'tterns of Arresting BranchedCracks. Homalite-IO0 Single Edge Notched Specimen Under Fixed-GripLoading. Specimien No. B5

Table 1. KII and o for Arrested Branch

Cracks in Fig. 1

(a) Inner Branch Crack

14th Frame 15th frameK 0. 4 MlPa./ 0.44 Mllav/1)o 0.32 MPa -0.04 Mlla

Ac i. i on r or ~ ox

RI6 G:J.AI (b) Outer Branch Crack(DDC TABI}nnxoun-ced 15th frame 16th fraiJ."stif ic ition Y if 0.44 M~la',II 0.1 MlaiA1

- O. 11, MPd 0.(18 M1

Dlrt sI s ' l

A

In actual dynamic photoelastic analysis of dynamic fracture, dynamic iso-chromatics surrounding a running crack often exhibits moderate unsymmetrybut such photoelastic patterns were heretofore considered experimental ab-normalities and were ignored by averaging the unsymmetric patterns during thedata reduction process. Careful postnortem inspection of the fracture speci-mens, however, show that the slightly unsynunetric isochromatics are oftenassociated with slightvn curved crack paths which undoubtedly are causedby the small dynamic Kit , coexisting with the dominating dynamic KYn value.This effect is akin to the small but noticeable influence of a smali K, onfatigue crack propagation reported fifteen years ago [15]. The exact flationbetween the amount of crack curving and the dynamic K and possibly otherhigher order terms of the near field stresses associated with the propagatingcrack tip would thus provide a dynamic crack propagation law under mixed-modecrack tip deformation similar to the KID versus A relation under considerationfor Mode I dynamic crack propaqation.

With the ,xelopment of a data reduction procedure for evaluating K11 to-gether with K values, it became possible to investigate experimentaldythe role of mixed mode dynamic near field stresses in dynamic fracture. Theauthors used such procedure to evaluate the stress intensity factors associ-ated with crack branching and crack curving [16]. The purpoe nof this Raperis to use this data reduction procedure to further extract K and K Ifrom the previouly recorded dynamic isochromatics surrounding runnin cracktips of curved and branched cracks.

DATA REDUCTION PROCEDURE

A three parameter, mixed mode, near-field state of stresses surroundinga crack propagating at constant velocity [17,18] was used to derived a rela-

t~on between the Modes I and II dynamic stress intensity factors, K yn andKT and the remote stress component o , and the dynamic isochroiatics.THs relation together with an overdeterhfnistic, least-square method formedthe basiayqf a daOnreduction procedure for extracting the three dynamic para-meters K and K and ax from the recorded dynamic photoelastic patternsurrounding a run!lng craclx Further details of this data reduction proced-ure can be found in Reference [16].

Figure 2 shows two frames out of a 16-frame dynamic photoelastic recordof a curving crack in a notch bend specimen 9.58mm (3/8 inch) thick, 88.9 x400ram (3 1/2 x 15 3/4 inch) Homalite-lO0 beam with a blunt initial crack of6.4mm (7/32 inch) in length and which was impact loaded by a drop weight of1.48 kg (3.25 lbs) [19]. The crack emanated from the blunt saw-cut pre-crack and propagated through much of the height of the beam prior to curvingas it approached the region of impact loading. Further details of the experi-mental setup, crack velocity measurements and dynamic calibration of theHBTlite-lRO material used are found in Reference [19]. Figure 3 shows theK and K yn and (3 x variations obtained from the dynamic photoelasticp~tterns p4Cedinnd immediately after crack curving shown in Fi(ure 2.The negligible KIn with respect to the K W leads to Sleh1oation that theimportant factor' overning the crack curving is not the K component ofthe mixed mode local dynamic state of stress, but rather Ue ') componentwhich heretofore was ignored in past static analyses. The dirtional ta-

3

bi-lity of the static Mode I crd(.k extension with o xas d dominant factor,however, has been presented recently [20] and thus it is conceivable thatthe second order term, i.e. (o in the dynamic near-field stresses, may alsogovern the crack path of a ra idly propdqatinq crack. Crack CUrvinq aissocia-ted with the large positive va ltivs iii Fiq. 3 tends0 to nfirn th it spvcu-lation. ox

SEVENTH FRAME EIGHTH FRAME175 jL Seconds 185 ± Seconds

Fig. 2 Typical Dynamic Isochroniatics or a Curved Crack. Hoialite-iQO notchbend specimen. Specimen No. I-C042574

IL0.8 3

0.6-

t 0_

UCRACK PATH a

z K

35 40 45 50 55 60PROJECTED CRACK LENGTH (MM)

Fig. 3 Modes I and 11 Dynamic Stress Intensity Factors of the Curved CrackShown in Fig. 2.

01

i£

Figure 4 shows a slightly slanted crack and the associated Kdyn Kdyn anda in a fracturing, wedge-loaded, double cantilever beam specimin of-4'6mm(98 inch) thick, 76.2 x 152.4m (3 x 6 inch) Homalite-lO( plate. Details ofthis experiqRtdl seh, (tc., can be futrrd in Retiene i I I . %l'nie f luc.u-ations in K and K throu)ut the crack propagation history is noted.Again, the lonsistentiy low K1

' values and the large positive o associatedwith significant crack curving tend to verify the previous findi g regardingthe importance of a in dynamic crack curving. It appears then that a frac-ture dynamic theory omparwe to that of Ref. [20] and in the presence ofsmall but non-negligible K I" may provide insight to dynamic crack curving.

_ . 0.8I

dyn0_K 0.6 K-3

in0.4 1 CRACK PATH -2

0.2 \ -- -

40 60 so0 10O0 120 140PROJECTED CRACK LENGTH (mm)

Fig. 4 Modes I and 11 Dynamic Stress Intensity Factors of a Slanted Crack ina Wedge-Loaded Rectangular Double Cantilever Specimen. Homalite-0Specimen No. L31S-030274.

Figure 5 shows two dynamic photoelastic patterns of a branched crackin a single edge-notched 9.5mm (3/8 inch) thick, 254 x 254mm (10 x 10 inch)Homalite-lO0 plate subjected to fixed grip loading condition. Other branchedcracks from this same specimen were shown in Fi(I. I and the expv rimental ov,-tails of this test can be tound in Reference [?] A, %ho)wn ii li(l. 1), withiiithe 49 micro-second interval, the propagating crack turned about 741) and ar-rested. The %Rd Mode srcss intensit factors prior to this severe crackkinking were K. " =O K. " = 0.41 MPa nd 0.18 MPa. After crackkinking at whilh time the rack arrested, K T 8 .34 MPavi,, K H 0.08 MPavmand ao = 1.4 MPa. This severe crack curvihg, 1'e. crack kihling can alsooccur u nder the more traditional high KII1 state of stress.

5L

,I-

. . . . . .. . . . . .. . .. . .. , , . . . . ". .. . i m l l . . . . . . . " " - ; . . - l l l ] m li li i m r i . . . . . . . . . . ". ,-i.. . .

- 41k

FIFTEENTH FRAME482 . Seconds

SIXTEENTH FRAME

531 k" Seconds

Fig. 5 Dynamic Isochromatics Prior To and After Crack Kinking. Homalite-lO0Single Edge Notched Specimen Under Fixed Grip Loading. Specimen No.B5

The above three sets of data are obviously not sufficient tq establish adynamic crack curving criterion. Quantitative correlation of Ksyn KO vn and

Y with the degree of crack curving as well as the possible dependen oncAck velocity are lacking at this time.

CRACK BRANCHING

FOURTH FRAME FFTH FRAME SEVENTH FRAME

102 ,u Seconds 134 u Seconds 212 K Seconds

Fig. 6 Typical Crack Branching Dynamic Photoelastic Pdtterns Holiialite-1(0OSingle Edge Notched Specimen (Fixed Grip Loading) Specimen No. B8.

6i

rA

Figure 6 shows three frames out of a 16-frame dynamic photoelastic recordof a crack propagating and branching in a 3.2mm (1/8 inch) thick, 254 x 254mm(10 x 10 inch) Homalite-QO0 plate loaded under fixed grip tension. Detailsof the experiment can be found in Reference [22].

Figure 7 shows the Kdyn and Kdyn Sq; two branches of the cracks shown inFigure 6. By extrapal.ting the'1 KI associated with tw8 y ranch cracks,an after-branchng KY = 1.2 Pa vii (10.90 psivTn.) and Kl,' 0.45 MPa vi(410 psi /Tji) are obtained. The branching stress 9lensity factor, i.e. im-mediately prior to branching, is estimated to be Kt 2.03 MPa vrim (1850psi /Tn).

U, Ut

3.0- 7 '-RIGHT BRANCH CRACK -

254,.. - LEFT BRANCH CRACK- --

2 2.5-S .254mm

ul - 0.216 fm

2.0 -ug -0.20om

U dyfl

1.0-I-

z K0

,i 1.0 I , I ,

0 20 40 60 so 100 120CRACK LErNOTM.o (mam)

Fig. 7 Modes I and 11 Dynamic Stress Intensity Factors ot the BranchedCracks Shown in Fig. 6.

dy 05 dyn

Kr = 1.02 MPa A (920 psi /-n) and K Y = -0.2 MPa A/ (180 psi vin) are ob-t~ine .._ The extrapolated dynamic strell in~i~sty factors prior to branching(1 50 psi -) and K 0

The average brnhinq and Dy amtr- r,n(hin ,tr,, itr,,y fa(cred

the above 8o ant se of for tch %imil(,xio rs.d r.porlin Reference [15p yield the followin: [h

aydK'~ 0 ~ vi 92 s Vi)an ~ -. ~af 18 s vT)ar b

Branchiny Ky 2. 03 Mi AII 850 Ps i i n)

Kdyn*1II @

After Branching K 1.0 MPa (950 psi /n)

Kdyn = 0.2 MPa vi (180 psi i-)

2- ==-0-o0 j-2254 Mm--.

u u.0. 152m m

t K1

z 1.0U)

z A0 - dyn

120 140 160 0 200 220 240CRACK LENGTH,a (mm)

Fig. 8 Model I and II Dynamic Stress Intensity Factors ot a branched Crackin a Homalite-lO0 Single Edge Notched Specimen Under Fixed GripLoading. Specimen No. B9.

dynThe above branching Kd data is ig1tical to that quoted in Reference

[1]. The ratio of before over after K . of 2.03/1.0 " 2.0 is consistentwith the postulate that crack branching occurs to dissipate fracture energyalong two propagating cracks buS ,s higher than the expected 2 value. It isalso interesting to note tha, K which is prior to crack branching regainsa small magnitude immediately ater crack branching and is consistent withthe static results of Reference [23].

DISCUSSIONS

The above dynamic photoelastic data on crack curving and crack branchingshould be considered as preliminary since the data is not sufficient in quan-tity for establishing a dynamic crack curving or a crack branching criteria.Evaluation of the accumulated dynamic photoelastic experiments usinq Lhe newlydeveloped data reduction procedure is continuing and the new crack (urvinqJand crack branching dynamic photoelastic experiments are planned.

P,

ACK'I0WLE DGEMEIT

The results of this investigation were obtained in a research contractfunded by the Office of Naval Research under Contract N00014-76-C-0060 NR064-478. The authors wish to acknowledge the support and encouragement ofDr. N. R. Perrone of ONR durinq the course of this investigation.

REFERENCES

[I] Dally, J. W., "Dynamic Photoelastic Studies of Fracture", ExperimentalMechanics, Vol. 19, No. 10, October 1979, pp. 349-367.

[2] Kobayashi, T. and Dally, J. W., "The Relation Between Crack Velocityand Stress Intensity Factor in Birefrinqent Polymers", Fast Fractureand Crack Arrest, (edited by G. T. 11ahn and 'I. F. Kanninen), ASTI STP627m 1977, pp. 257-273.

[3] Bradley, W. B. and Kobayashi, A. S., "An Investigation of PropagatingCrack by Dynamic Photoelasticity", Experimental Mechanics, Vol. 10,No. 3, 1970, pp. 103-113.

[4] Bradley, W.- B. and Kobayashi, A. S., "Fracture Mechanics - A Photo-elastic Investigation", Engineering Fracture Mechanics, Vol. 3, 1971,pp. 317-332.

[5] Irwin, G. R., "Discussion of the Dynamic Stress Distribution SurroundingA Running Crack - A Photoelastic Analysis", Proc. of SESA, Vol. 16, No.1, 1958, pp. 93-96.

[6] Kobayashi, A. S., Wade, B. G. and Bradley, W. B., "Fracture Dynamics ofHomalite-QO0", Deformation and Fracture of High Polymers, (edited byH. H. Kausch, J. A. Hassell and R. I. Jafee), Plenum Press, New York,1973, pp. 487-500.

[7] Irwin, G. R., Dally, J. W., Kobayashi, T., Fourney, W. L., Ktheridge,Mi. J., and Rossmanith, H. P., "On the Determination of the (-K relation-ships for Birefringent Polymers", Experimental Mechanics, Vol. 19, No.4, 1979, pp. 121-128.

[8] Rossmanith, H. P. and Irwin, G. P., "Analysis of Dynamic IsochromaticCrack-Tip Stress Patterns", University of Maryland Report, 1979.

[9] Smith, D. G. and Smith, C. 14., "Photoelastic Detenmination of !IixedMode Stress Intensity Factors", Engineering Fracture Mechanics, Vol. 4,No. 2, 1972, pp. 357-366.

[10] Smith, C. W., Jolles, M. and Peters, '4. H., "Stress Intensities forCrack Emnanatino from Pin-loded 1lol ,s", Flaw ,rnwth and Frac(:ture, ASTMSTP 631, 1977, pp. 190-201.

[11]. Gdoutos, E. E., and Theocaris, P. S., A Photoelastic Determination ofMixed-Mode Stress Intensity Factors", Experimental Mechanics, Vol. 18,March 1978, pp. 87-96.

[12] Dally, J. W. and Sanford, R. J., "Classification of Stress-IntensityFactors from Isochromatic Fringe Patterns", Experimental Mechanics,Vol. 18, No. 12, Dec. 1978, pp. 441-448.

[13] Sanford, R. J. and Dally, J. W., "A General Method for Determining Mixed-Mode Stress Intensity Factors from Isochromatic Fringe Patterns", En-gineering Fracture Mechanics, Vol. 11, 1979, pp. 621-633.

[14] Rossmanith, H. P., "Analysis of Mixed-Mode Isochromatic Crack-TipFringe Patterns", Acta Mechanics, Vol. 34, 1979, pp. 1-38.

[15] lida, S. and Kobayashi, A. S., "Crack Propagation Rate in 7075-T6 PlatesUnder Cyclic Tensile and Transverse Shear Loading", J. of Basic Engin-eering, Trans. of ASME, Vol. 91, Series D (4), Dec. 1964, pp. 764-769.

[16] Kobayashi, A. S. and Ramulu, M., "Dynamic Stress Intensity Factors forUnsynnetric Dyninic Isochroma ti cs", to be published in lxperinlntltilMechanics.

[17] Freund, L. B., "Dynamic Crack Propagation", The Mechanics of Fracture,Vol. 19, edited by F. Erdogan, ASME, 1976, pp. 105-134.

[18] Freund, L. B., "The Mechanics of Dynamic Shear Crack Propagation",Journal of Geophysical Research, Vol. 84, No. 35, 1978, pp. 2199-2209.

[19] Kobayashi, A. S. and Chan, C. F., !'A Dynamic Photoelastic Analysis ofDynamic-tear-test Specimen", Experimental Mechanics, Vol. 16, No. 5,May 1976, pp. 176-181.

[20] Streit, R. amd Finnie, I, "An Experimental Investigation of Crack-pathDirectional Stability", Experimental Mechanics, Vol. 20, No. 1, January1980, pp. 17-23.

[21] Kobayashi, A. S., Mall, S. amd Lee, M. H., "Fracture Dynamics of Wedge-Loaded Double Cantilever Beam Specimen", Cracks and Fracture, ASTM STP,601, June 1976, pp. 274-290.

[22] Kobayashi, A. S., Wade, B. G., Bradley, W. B. and Chiu, S. T., "CrackBranching in Homalite-100 Sheets", Engineering Fracture Mechanics, Vol.6, 1974, pp. 81-92.

[23] Kalthoff, J. F., "On the Propagation Direction of Bifurcated Cracks",Dynamic Crack Propagation (edited by G. C. Sih), Noordhoff Internation-al Leyden, 1973, pp. 449-458.

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UNCLASSIFIED- EcuRi?' .LA%%PrIATIIN OF 10.I A. PAI;F (When flI*t P,io-,0

Nl All INS;i'"14l I li)N!,

REPORT DOCUMENTATION PAGE _I____ __,__-I_ I __ING. _____

I. REPORT NUMULP "2. GOVT ACCESSION NO. 3. RE T . rALO6 NUMBER

TR No. 39 4F 7 TR-39

4. TITLE (and Subitle) S. TYPE OF REPORT & PERIOD COVERED

. InterimDY NAM IC M IX ED M OD E FR ACTU R E $

/ . .. AS J ,M '-g -E -_ NUM BR

/ _ __ _ __ _ _ __ _ __ _ _ __ _ __ _ _ 39ATNOR(a) . CONTRACT OR GRANT NUMBER(e)

N00l14-76-C-006G 01.. S. obayashi - M. ulu _' NR 064-478.- PERFOhMINO ORGANIZATION NAME AND ADDRESS W0. PROGRAM ELEMENT. PROJECT. TASK

AREA & WORK UNIT NUMBERS

University of WashingtonDepartment of Mechanical Engineering

II. ONTRLLIN OF1C N.AMEAND ADDRESS/f Ag 87

Office of Naval Research 13. NUMBER Of PAGES

Arlington, Virginia 10

14. MONITORING AGENCY NAME & ADDRESS(II dlfftorwl Irom Contlrollng OIlIeo) 15. SECURITY CLASS. (ot thie repotf)

/, % ,Unclassified

150. DECL ASSIICATION/DOWNGRADINGSCHEDULE

I6 DISTRIBUTION STATEMENT (of ts R,. ptbo,,e) ved

Unlimited for pubic nelr-n"I and scl: iidistiribution is unlim,.ted.

17. DISTRIBUTION STATEMENT (of the abstract entered In Block 20. It dilloremn from Report)

IS. SUPPLEMENTARY NOTES

It. KEY WORDS (Continue on revere aide If necessary and Identify by block number)

Fracture Mechanics Fracture DynamicsCrack Propagation Dynamic PhotoelasticityCrack Arrest Dynamic Finite Element AnalysisCrack Branching

20. ABSTRACT (Contlnue on reverse *de If necessary and Idenrlfy by block number)

A newly developed data reduction process was used to reevaluate dynamic;photoelastic results and to extract dynamic stress intensity factors ,.and associated with curved and branched cracks in fracturing Homa' te-100 -p'tes. A branching stress intensity factor approximately 5 times the-fracture toughness was identified for t mater al. Moderate to severeyhf Ayn

crack curvings were associated with a Kj),.- and D ratio as low as 0.05, but

with positive remoste stress component, X)/

DD , , 1473 EDITION OF I NOV GS IS OSOI I I-1/114 0102-011 06o-. I UNCLASqIFIRD

"SO._j l "ll I I.LA131It1' 11f"i lr THiII lArr IShon f l* a 0l0 Ad