Effect of R ratio and ΔK level on the hysteretic energy dissipated during fatigue crack propagation

Scripta METALLURGICA

Vol. 21, pp. 1045-1049, 1987 Printed in the U.S.A.

Pergamon Journals, Ltd. All rights reserved

EFFECT OF R RATIO AND AK LEVEL ON THE NYSTERETIC ENERGY DISSIPATED DURING FATIGUE CRACK PROPAGATION N. RANGANATHAN,K. JENDOUBI, M. BENGUEDIAB and J. PETIT Laboratoire de M~canique et Physique des Mat~riaux ENSMA - Rue Guillaume VII - 86034 POITIERS Cedex

(Received December 24, 1986) (Revised May 26, 1987) Introduction IKEDA et al. / I / f i r s t measured the cyclic work to produce a unit area of fatigue crack U, using micro strain gages stuck in the plastic zone associated with a fatigue crack. LIAW et al. /2/ compiling the experimental measurements of this parameter have shown that U is roughly proportional to the inverse of the cyclic y i e l d stress Oc. for a particular alloy group and have suggested that maximizing the quantity oc.U should mlnlmlse the fatigue crack growth rate. Subsequently, different techniques have been developed to measure this important quantity U, techniques which include subgrain size measurements /3/, micro calorimetry /4/, and infrared thermography /5/. Recent work by the author /6,7/ have shown that the hysteretic work can be directly measured by compliance measurements and at high AK levels the value of U reaches a constant level, U c r . The value of Uc~ measured on the 2024-T351 aluminum alloy was shown to be equal to 2.65 + 0.6.10 5 j/m2, which ~s comparable to what was measured by LIAW et al. /2/ using the s t r a i # gage technique. In this paper the evolution of U with respect to the R r a t i o and the AK level is presented an the 2024-T351 aluminum alloy and the observed results are discussed with respect to available results in the l i t e r a t u r e . Experimental Procedure The tests were conducted using standard compact tension specimens 12 mm thick and 75 mm wide, as shown in figure I . Constant amplitude fatigue crack growth tests were conducted using an INSTRON servohydraulic machine at four R ratios of O.Ol, O.l, 0.33, 0.7 covering a wide AK range f r o m 4 M ~ to 40 MPa J'm at a typical test frequency of 20 Hz in ambiant air. At different &K levels, the test frequencies were reduced to 0.05 Hz and diagrams representing amplified crack mouth opening 6' with respect to the load P were obtained using an X-Y plotter. 6' is defined as : 6' = ( 6 - aP)x M where : 6 is the crack mouth opening displacement measured by an extensometer. a is the specimen compliance for a given crack length M is an electronic amplification factor, M = 25. Examples of 6 vs P and 6' vs P curves are shown in figure 2. The area of the 6'-p diagram is proportional to the hysteretic work Q multiplied by a factor F. The factor F represents the correction factor required to convert crack mouth opening displacement to load line displacement (F < l).The factor F was determined from NEWMAN'S f i n i t e element analysis for the specimens geometry /8/.

1045 0036-9748/87 $3.00 + .00 Copyright (c) 1987 Pergamon Journals Ltd.

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The specific energy U is defined as : U=

Q 2B x da/dN

where B is the specimen thickness potential drop technique.

and da/dN the crack growth rate measured by an electric

Experimental Results and Discussion The evolution of da/dN with respect to AK for the four values of R tested is shown in f i g . 3 . Thesecurves show that for a given AK level da/dN increases with R. Also, these curves show a decrease of slope at moderate AK values as compared to low AK levels . In general an average slope of 4 is observed at high AK levels. The values of AK for which the slope of 4 is f i r s t reached, hereby called AK~., depends upon R as shown in the figure. I t can also be seen in this figure that this chang#Vof slope takes place at a near constant growth rate of about lO-7m/cycle. Theseresults are in accordance with those previously obtained on the same alloy /g/. The relationship between the specific energy U and AK is shown in f i g . 4 . As has been shown previously /6,7/, U reaches a c r i t i c a l minimum level, called Ucr, when AK reaches a c r i t i c a l value called aKcr. The value of Ucr obtained in the present study is equal to 1.66 + 0.27.105 J/m2 which is s l i g h t l y lower than the previously reported one which is 2.65 + 0,6.105-J/m2 /6,7/. I t should be noted that the present study relates to a new series of the-alloy. This difference can also be associated with the correction factor F used in the present study to translate crack mouth opening displacements to load line displacements. This correction factor depends upon the center of rotation and in the present analysis the center of rotation was estimated based on NEWMAN'S f i n i t e element analysis, in plane strain /8/. At higher AK levels plane stress effects might become predominant /lO/, which can lead to a change in the center of rotation. This effect was not taken into account in the present study. The previous results were obtained on modified compliance specimens where the crack opening displacement was d i r e c t l y measured under the loading line. The value Ucr reported in the present study is comparable to the value of U given in Ref.2 where the energy dissipated in the plastic zone was measured using f o i l strain gages on center cracked specimens of the 2024-T4 aluminum alloy. I t can also be noted from figure 4 that for AK < aKcr , U increases gradually. For example at a R ratio of 0.7 and for AK value of 4.5 MPa /-m-m, U is on the order of 5.106 J/m2 which, is about 25 times as high as the Ucr level. Such a dependanceof U with respect to R r a t i o and the AK value has been predicted by the model due to DAVIDSON / l l / . He has proposed that the constant U level at high AK values can be associated with fullydeveloped mode I type crack propagation. The increase of U at low AK values, especially near the threshold according to DAVIDSON / l l / , can be associated with the progressive developmentof a mode I I component at the crack t i p . The present results are however in slight disagreement with the work of JOSEPH and GROSS /4/ concerning the evolution of U with respect to AK in a c6arbo~ steel using microcalorimetry. In that work, U reaches a near constant level of about 7.10 J/m for AK : l O MPa 4--~-which is similar to the present result for AK > AK r" Howeverin t h e i r work, U decreases with AK for lower AK levels. They have associated thi~ decrease with achangein the fracture mode.

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FATIGUE

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One possible reason for the differences observed in the relationships between U and AK can be the fact that the hysteretic energy measured in the present work takes into account the total mechanical energy dissipated during a cycle, while JOSEPH and GROSSmeasured the heat generated at the crack t i p during fatigue cycling. I t is possible that some of the mechanical work, which is stored in the material and which can be associated with the blocking of dislocations is not converted into heat /12/. A second reason is that the present measurements do not take into account the possible effect of crack closure which can result in some hystereticlosscaused bycrack surface contact. However, the evolution of U with respect to AK for tests at R = 0.7, where no crack closure could be detected show a similar trend as for tests conducted at lower R values, but for the evolution of AKcr. I t has been previously reported that the relationship between U and AK depends upon that relating da/dN and AK and U showntobe independent of AK when the Paris law exponent is equal to 4 /4, l l / . In the present study for AK > AKcr , the value of U is constant and equal to Ucr, value of AKcr can thus be compared to aKcv as defined in t h i s study (Table I ) .

aKcv MPa~ O.Ol

the

AKcr (MPaV-m)

ll,2

20

O.l

9,5

14

0.33

7,8

12

0.7

6,8

lO

TABLE l : Relationships between AKcv,AKcr and R. I t can be seen here that the aKcv and AKcr values are comparable except for R = O,Ol. At this R value the effect of crack closure can lead to some mechanical energy loss because of crack surface cohtact. This phenomenon is under investigation based on f o i l strain gage measurements in the plastic zone for the same alloy. Conclusions

l) The hysteretic mechanical work to create a unit crack surface during fatigue crack propagation has been measured for 4 R ratios for the 2024 T351 aluminum alloy. 2) The value of U reaches a constant minimum level for AK values greater than a c r i t i c a l level called aKcr. 3) AKcr decreases as R increases. 4) The value of U increases for AK < AKcr. 5) The effect of crack surface contact may lead to some mechanical energy loss at low R values.

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References / l / S. IKEDA, Y. IZUMI and M.E. FINE, Engng. Frac. Mech., 9, 123 (1977) /2/ P.K. LIAW, S.I. KWUNand M.E. FINE, Metall. Trans., 12A, 49 (1981). /3/ P.K. LIAW, M.E. FINE and D.L. DAVIDSON, Fat. Engng. Mat. Str., 3, 59 (1980) /4/ A.D. JOSEPH and J.S. GROSS, Engng. Frac. Mech., l , 63, (1985). /5/ C.SAIX and P. JOUANNA, J. Mec. Appl. 5, l , (1981). /6/ N. RANGANATHAN, J. PETIT and J. de FOUQUET, Strength of Metals and alloys, H.J. Mc Queen et al eds., Pergamon Press, U.K., 2, 1267 (1985) /7/ N. RANGANATHAN, B. BOUCHET and J. PETIT, Fractography of Modern Engineering Materials, American Society for Testing and Materials, Philadelphia USA ASTM STP (in press). /8/ J.C. NEWMANJr, Fracture analysis, American Society for Testing and Materials, Philadelphia, USA, ASTMSTP, 566, I05 (1974). /9/ N. RANGANATHAN, Doc. es Sc. Thesis, University of Poitiers, 1985. /lO/ J.K. KNOTT, Fondamentals of Fracture Mechanics, Rutterwith, London (1973). / l l / D.L. DAVIDSON, Fat. Engng. Mat. Str., 3, 229 (1981). /12/ A. CHRYSOCHOOS,Journal de M~canique th~orique et appliqu6e, 4, 5, 589 (1985).

FIG.I - Specimen geometry used in the present study.

Thickness 12

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F I G . 2 - Examples of 6 curves.

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