lead to a more reasonable solution. This implies a series of …€¦ · · 2014-05-17the role of dislocation redistribution during micro structural crack extension in altering

Manifestation of localized microcrack stability by

the unique pop-in events

A. Bussiba, Y. Katz

Nuclear Research Centre, Negev, Beer-Sheva, Israel

Abstract

There is a tendency to regard the crack stability equation as the balance be-tween the driving force and the fracture resistance terms, normally expressedby the continuum theory. However, in cases of subcritical slow crack growthor in crack initiation-arrest-initiation processes, more of a localized approach isrequired. Here, fluctuations of the crack driving force and resistance occur on afine scale during the semi-equilibrium period, allowing subcritical growth.Moreover, it appears that mutual interactions develop between the resistanceand the driving force suggesting that a generic local crack stability equationactually governs fracture.

The current study provides a viewpoint as related to the discontinuouscrack growth, while considering micro/macro scale circumstances. In order toelucidate the microcrack stability aspects, Fe-3%Si single crystals beside poly-crystalline Al-7075 T651 and AISI-4340 alloys were selected. In contrast to thesingle crystal case in which the subcritical crack growth was enhanced by envi-ronmental interactions, the polycrystalline materials indicated Pop-In (PI)events. Such initiation and arrest potential characterized by the PI enabled todevelop physical insights into the dynamic nature of the subcritical crackgrowth phenomena.

1 Introduction

Several models regarding the crack tip plastic relaxation associated with thedislocation configurations have been discussed elsewhere\ An arrangementsuggested by Lin and Thomson^, with a mini-dislocation near the crack-tip anda super-dislocation, suggested that this local/global plasticity description might

Transactions on Engineering Sciences vol 13, © 1996 WIT Press, www.witpress.com, ISSN 1743-3533

910 Localized Damage

lead to a more reasonable solution. This implies a series of mini-super disloca-tions in order to represent the near tip plastic zone beside a gigantic super-dislo-cation, representing the global plasticity. Such a discretized super-dislocationmodel, which is a revised form of Atkinson and Clements model"* might easethe evaluation of; (i) the stress distribution ahead of a crack (ii) the crack tipshielding effect (iii) the plastic relaxation due to intersecting slip bandsassociated with significant arrest potential during an advancing crack.Following such argumentations, the role of the excess energy for crack exten-sion is introduced caused by the local shielding term. While dealing with mi-cro scale description the present investigation objectives were two-fold; (i) Toextend the study to more general aspects of crack stability by including the PIphenomena in polycrystalline systems (ii) To demonstrate the interwoven orperhaps the inseparable nature of the local driving force in the crack stabilityequation.

In this context, various central aspects become relevant to the meaning offracture mechanic crack stability equation. For example, are there distinguish-able intrinsic differences between nucleation and propagation stages related toa surplus of local stored elastic energy or, an elevated stress at higher strainrates via dislocation dynamics? Moreover, can the local nucleation and arrestevents be consistent with a global propagation controlled crack growth? In fact,these type of issues motivated the present study while recognizing the marginalnature of the crack stability which clearly requires a localized approach. Notethat the following dilemma actually demands continuous exploration, regardingthe role of dislocation redistribution during micro structural crack extension inaltering the local stress field. Or, can the local driving force be diminished andcontribute to the crack arrest?

For the sake of completeness, the current experimental activities includedalso Warm Prestressing tests (WPS). The general idea was, that if consistent,any modification of the local crack-tip stress field might be reflected on the PIbehavior caused by variations of the stored elastic energy. The localized track-ing of crack extension, crack velocities and acoustic emission activities besideoverload studies are demonstrated and further analyzed and discussed.

2 Experimental procedures

2.1 Iron based single crystalHere Fe-3w%Si single crystals were selected. From <001> grown bars, minia-ture prefatigued single edge notched, disc-shaped specimens were produced.The slow crack growth was developed by metal/hydrogen interactions. Thiswas accomplished by external hydrogen tests in latm. gaseous hydrogen inenvironmental chamber. More details about specimen preparation and test pro-cedures may be found elsewhere"*. Crack initiation and growth under sustainedload was activated by initial stress intensity factor of 18 MPa-rn^. To monitorthe crack initiation and the subcritical crack growth, compliance technique via


Localized Damage 911

a crack opening displacement (COD) was utilized, supplemented by a comput-erized acoustic emission (AE) technique. For an appropriate description of thelocal stress field, a discretized type of a super-dislocation model was devel-oped. By this, the elastic/plastic model enabled to account for the microstruc-tural features and their role in affecting the local driving force. This in therange between K^ (the stress intensity factor for dislocation emission) up to K^(the stress intensity for fracture).

2.2 Polycrystalline metallic systemsAs mentioned, the selected polycrystalline materials were the high strength Al-7075 T651 and the high strength AISI-4340 steel in as received (HTO) and inthe quenched and tempered (HT2) conditions. (The chemical compositions aregiven in Table 1). The crack system for the 4340 was perpendicular to the ex-trusion direction, while for the Al alloy, three crack systems were chosen im-posing some changes on the specimen geometries.

Table 1. Chemical composition in wt.%.C Ni Cr Mn Mg Mo Si Cu Zn Al S P Fe

AISI4340Al-7075

0.38 1.9

0.008

0

0

.85

.24

0.80

0.3

025

2.6

0.2

0.5

0

1

.13

.9 6.3

0.05

Bal.

0.004 0.006 bal.

0.7

Three point bending tests were performed on single edge notched speci-mens with dimensions of 10x10x55 mm with initial crack length of 2 mm.Only for the Al-alloy, miniature compact tension specimens with dimensions ofao=5.25 mm, W=13.25 mm, B=7 mm (where a#, W and B are the initial cracklength, width and thickness respectively) were utilized. Preliminary study wasconducted in selecting the appropriate prefatigue conditions in order to mini-mize damage at the crack tip. In order to eliminate WPS effects, the prefatiguetemperature was kept the same as at the final fracture test.

In stroke control mode, crosshead velocities between 0.02 mm/sec up to300 mm/sec at the temperature range between 77K to 296K were applied. Both,COD and AE (with total gain of 85dB with energy and distribution modules)signals were recorded simultaneously with the load signal. The PI velocity wasmeasured using electro-potential technique, which was connected to highresolution scope with memory card option and with appropriate software forfurther analysis. In addition, tests were performed at the lower shelf followingprior WPS. Here, the main attention was given to the PI behavior.

Finally, optical and SEM were utilized for fracture modes classification atthe PI zones and for the non stable crack extension. ED AX was utilized forchemical analysis of metalloid particles on the fracture surface.



3 Experimental results

3.1 Fe-Si single crystals

Some of the mechanical properties for the selected Fe-3%Si crystals were asfollows; a yield strength of 300 MPa with Young's modulus, E^QO] of 1.32-10*MPa and a strain hardening exponent, n = 0.38.

The metal/hydrogen interactions resulted in enhanced slow crack growthconsisted of basically discontinuous cleavage, accompanied by alternating brit-tle/ductile modes. In a crack system {001}<010>, the general characteristic ofthe AE signals consisted of burst type which started at the onset of the crackgrowth as indicated by the COD. The AE, wave emission groups could be re-lated to local events as indicated by the fine scale fracture surface features.These findings associated with the crack extension steps were provided bySEM observations. The arrest time between the emission groups were attrib-uted to the dislocation dynamic affecting the crack-tip stress field while leadingunder the environmental interaction to the next local instability. More about theAE observations has been addressed elsewhere . Thus, the discontinuous slowcrack growth was connected to the crack-tip or to remote source of dislocationemission combined with hydrogen.

As such, the local stress-field was intensified and the resistance was re-duced in sufficient margins to trigger crack instability over a short distance.From AE tracking and SEM observations it was found that distances of aboutljj,m corresponded to initiation-arrest cycle, alluding to the fluctuation natureof the local driving force and the resistance. In such fine scale events, the roleof crystal plasticity (slip bands) were the main origins for the microcrack arrest.

3.2 Polycrystalline materials

The standards mechanical properties for the selected materials are summarizesin Table 2. For the Al-7075 T651, properties were widely temperature de-pendent, while for the AISI 4340 increase of the yields stress and dramatic de-crease in toughness was obtained at low temperatures..

Table 2. Some mechanical properties for the selected materialsMaterial Mech./Thermal <jy KJC

Treatment (MPa) (MPaW*)296K 228K 77K 296K 228K 77K

AISI 4340 HTO. 350 450 680 65 30.5HT2. 1520 1620 1810 52 37 25.5

Al-7075 T651 530 560 24 23.5 22.1



3.2.1 The AISI 4340 steel caseThe AE events activity during the monotonic loading on sharp prefatiguedspecimens is illustrated in Fig. 1. Note, some AE activity at the linear portionof the loading curve accumulated up to the first PI occurrence. This behaviorexist also for the others consecutive PL More refined view on the wave emis-sion group (obtained from Fig. l(b) test) in terms of the number of counts en-ergy distribution (cell number) and time is given in Fig. 2. As shown, most ofthe events can be related to the low energy regime while some actually followthe high energy emission with a finite time delay.

The average PI velocity trends and their thermal dependency for variouscrosshead velocities are demonstrated in Fig. 3. Although the PI jump is verysharp (see arrows in Fig. 4), crack extension within the PI is clearly discontinu-ous as shown by using the more refined expand mode.

T=296K, V=0.02 mm/sec

5-j

4-1

Jl JLi-0 10 20 30 40 50 60 70

Time (sec)

4.5 ^

4.0 |

3.5-j

3.0-j

1.5 i

1.0 •

0.5- V

0.0 -0

T=228K, V=0.02mm/sec (b)

Time (sec)Figure 1: Load and AE events counts versus time for: (a) 4340-HO; (b) 4340-H2

(a) T=228K,V=0.02mm/sec

10020 40 60 80Energy (Arbitrary Units)

Figure 2: AE activity of the 4340-HT2 curve (Fig. Ib test): (a) two dimen-sional energy/counts; (b) Three dimensional display, including time.



1E+4

1E+3 -

1E+2

1E+1

1E+0160

A 0.02 mm/sec* 8 mm/sec• 300 mm/sec

200 240 280Temperature (K)

Time (msec)0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

320

6.05.5 -5.04.5 -4.03.5 -3.0-2.5 -2.01.5 -

(

Expanded PI

~' i T ^50

Tin

\

y ...

f

100le (msec)

- ,;«/"'

/PI

150 2(

- 5.25

5.00

4.75

4.50

4.25

- 4.000

Figure 3: Average PI velocities as a Figure 4: Indication of discontinuousfunction of temperature and crosshead crack growth, by the expansion of thevelocities. PI localized event..

3.5 -

3.0 -

2.5 -

20-

1.5 -

1.0 -

0.5 -

(a)

T=:296K, V=0.02 mm/sec

b __^-^a

aa

3.5 -

2.5 -a

? 20-

f .-5-

1.0 -

pop-in- crack arrest A Ai i i i i , i i > i i i i i

(b) ,—r

T=228K, V=0.02 mm/sec a

JaI — — — -^a

a

a - pop-inb - crack arrest

i 1 < 1 i 1 <1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 0.0 0.5 1.0 1.5 2.0

Time (sec) Time (sec)Figure 5: Discontinuity in crack extension during fracture toughness testing.Notice the PI and crack arrest regimes: (a) 296K; (b) 228K.

A typical crack extension up to fracture at temperature of 296K and 228Kis given in Fig. 5. Note the consecutive Pi/arrest events with some indication ofslow crack growth or blunting. Generally, higher excess energy situation (Fig.5 a) resulted in more intensified PI crack extension, as compared to a similartest at 228K (Fig. 5b).

Fracture surface mixed mode at 296K and PI enhanced cleavage at 173Kare shown in Fig. 6 respectively.

3.2.2 The Al 7075 caseThe fracture toughness in terms of locality and anisotropy is illustrated in Fig.7 including thermal effects. The T-S (crack arrester) orientation, indicated thehighest toughness values as compared to the L-T (crack divider) orientation



Figure 6: (a) SEM fractography of mixed mode fracture obtained at 296K; (b)and enhanced cleavage at 173K with test velocity of 300mm/sec.

with intermediate or, the S-T (crack delamination) with the lowest toughness

values.Cumulative damage is clearly indicated by the AE activities starting at the

linear/elastic regime which was later intensified by the multy PI events (see

Fig. 8).Finally, beside the anisotropic nature of the Al-7075, the role of second

phase metalloid particles on fracture resistance is well recognized. For exam-ple, the second phase particles morphology for the S-T orientation is shown inFig. 9(a) in comparison to fatigue fractography for the L-T orientation withlower particles distribution (Fig. 9b).

10100 12 16 20 24

Time (sec)150 200 250Temperature (K)

Figure 7: Toughness dependency on Figure 8: Load and AE events countstest temperature for the three orienta- versus time for the L-T orientation.

tions



Figure 9: Fracture modes (a) brittle particles in fracture of S-T at 173K (b) fa-tigue fracture in T-S orientation at 296K.

4 Discussion

Theoretically and experimentally based, it appears that at least three dominantelements control the local instability which might result in substantial slowcrack growth region. First, the shielding effects on the applied stress intensityfactor caused by the combination of several factors. Second, regardless the ex-act origins for crack-tip shielding, stored elastic energy provides sufficientdriving force for initiation and growth. Third, an available arrest potentialmanifested on different scales in the cases of the environmental enhanced sub-critical crack growth or in the multiple PI. Regarding the shielding factors, at-tributed to the crack tip dislocation arrays, tip blunting, residual stresses,different steps deviating from the crack line or side ligaments due to the crackfront tunneling all provide excess elastic energy. Crack front effects and liga-ments as also the interaction of the crack front/elastic-plastic waves might af-fect the dynamic crack propagation allowing sufficient origins for arrest. Theoccurrence of PI and the discontinuous nature of a running crack is not uniqueto crystalline materials. The pop-in mode in polycarbonate has been addressedby Key & Katz\ Moreover, some selected tests in PMMA polymers indicatedirregular crack growth with arresting marks even at crack velocities as high as250 m/sec . Thus, in crystalline systems by recognizing the role of the crack tipdislocation structures on the local stress field beside the influence of the localplasticity on the effective surface energy (crack resistance) introduce by itselfthe local interactive driving force/arrest behavior. Along this it seems benefi-cial to consider the meaning of the crack stability equation in a marginal local-ized terms;

G = 2y (1)



while G the elastic strain energy release rate and y the effective surface energy.Accordingly, the marginal term G-R (where the resistance R = 2y) has to

be regarded as the dominant value governing the crack extension in a fluctuat-ing manner. Velocity variations or kinetic factor affect the margins as beingdemonstrated here, experimentally.

On the computational and the simulation procedures, only the single crys-tal case is currently discussed. The elastic-plastic dislocation model simulationhas been addressed previously^. While assuming a single arrangement of theemitted crack-tip dislocation four major stress sources and their governingequations were considered which included; (i) the stress due to dislocation in-teraction with each other in the array - cf m (") the stress due to the interactionof the crack and all dislocations - a^n™> (iii) the interaction of the externalstress and crack - cf ^, (iv) the external applied stress -T . Thus the totalstress tensor a^n was expressed by;

Omn =<*' mn +& " mn +<*' " mn +Tmn (2)

where, m = 1,2,3 and n = =1,2.While performing the simulation , a constraint must be satisfied in which

the internal flow stress should be uniform in the sense of intrinsic materialproperty. The main point in this section of the simulation was, to estimate thestress field following the crack initiation onset. First, the crack-tip is shieldedby dislocations emitted from the tip. Second, the dislocations from secondarysources are added in front of the crack tip while the tip is still at original posi-tion. Third, the crack tip allowed to jump one step (about Ifim) forward with acorresponding adjustment of dislocations positions to satisfy constraints. Byextending the stationary situation to this quasi-static dynamic process

Gyy* (the local stress peak) drop down by as much as 6000 MPa. Even ignor-

ing the role of interactive agents (the single crystal/hydrogen case) such a sig-nificant decrease of the stress ahead of the crack-tip might be enough to slowdown or even arrest the crack. Actually this suggests a possible role of a dimin-ished driving force aiding arrest in conjunction with plasticity or complex as-pects of y f. The latter is clearly associated with the resistance component inthe crack stability equation.

Similar features were actually revealed by observing the relatively macro-scopic PI events. The state of stress aspects influencing the surface plasticity,ligaments effects and the intrinsic driving force/resistance dependency on thevelocity provide enough origins for localized subcritical crack initiation andarrest. By following this rationale, the WPS tests become very interesting. Justbriefly, the cases of AISI 4340 steel and the U-Ti alloy are mentioned in which,under WPS conditions, the PI phenomena was not observed, very consistentfinding while recognizing the role of the surplus elastic stored energy .



5 Summary and conclusions

Crack instability activated by solely mechanical driving force, or by mechani-cal and environmental interactions might result in semi-equilibrium subcriticalcrack growth. Experimentally based, there are sufficient origins for diminisheddriving force assisting arrest in order to enable altering nature of crack growth.Based on experimental findings, this behavior was illustrated even in relativelyfast running cracks. Here, the key point remains in recognizing the origins forthe elastic energy surplus via the arrest potential. The local interactive behaviorbetween the driving force and the fracture resistance was focused while explor-ing the possibility for initiation-arrest-initiation behavior caused by the local-ized fluctuating and marginal sense of the crack stability equation.

Accordingly the following are concluded;(1) Fracture events are localized and require local/global computational and

experimental approaches.(2) The discontinuous nature of the crack growth was confirmed in a slow

crack growth and in fast running crack situations even in the brittle regime.(3) In all cases cumulative damage mechanism was dominated in contrast the

early proposed weakest link theory.(4) Pop-in mode in fracture is highly mechanistically and microstructually

controlled and require ad-hoc assessments.(5) However, the study of local instability becomes beneficial in developing

physical insights into fracture processes.

Acknowledgments

The authors wish to express their gratitude to Mr. H. Alush, Mr. M. Kupiec andMr. E. Woodbeker from the NRCN for experimental assistance and concern.

References

1. Chen, X.F., Foecke, T., Lii, M.I, Katz, Y. & Gerberich, W.W. Engng.Fmcrwrg A&cA., 1990, 35, 997.

2. Lin. I.H. & Thomson, R. Acta Metall, 1986, 34, 187.3. Atkinson, C. & Clements, D.L.I973, Acta Metall, 21, 55.4. Lii, M.J., Chen, X.F., Katz, Y. & Gerberich, W.W. Acta Metall., 1990, 38,

2435.5. Key, P.L. & Katz, Y. Inter. J of Fmcfwrg Mec&., 1969, 5, 63.6. Bussiba, A., Alush, H. & Katz, Y. - unpublished results.7. Katz, Y., Chen, X., Lii, M.J., Lanxner, M. & Gerberich, W.W. Engng.

Fracture Mech., 1992, 41, 541.8. Katz, Y., Kupiec, M. & Bussiba, A., in Fracture of Eng. Materials and

Structures (Ed. Teoh, S.H. & Lee, K.H.) p. 558, Elsvier Applied Science,London/NY, 1991.


lead to a more reasonable solution. This implies a series of …€¦ · · 2014-05-17the role of dislocation redistribution during micro structural crack extension in altering

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