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Cyclic crack opening displacement behavior during high-amplitude block loading
Enginming Fmcrun Mechanics Vol. 12. pp. 541-549 PergamonPress Ltd.. 1979. Printed inGreat Britain
CYCLIC CRACK OPENING DISPLACEMENT BEHAVIOR DURING HIGH AMPLITUDE BLOCK LOADING T. YEHt and L. H. BURCK Materials Department, The University of Wisconsin-Milwaukee, Milwaukee, WI 53201,U.S.A. Abstract-Load-crack opening displacement hysteresis behavior was monitored for fifty cycles of highamplitude loading which followed fatigue pre-cracking at low stress intensity factor levels. The material studied was quenched and tempered (400°C)AISI 4140 steel which showed pronounced cyclic softening. Despite this softening behavior, cycle-tecycle decreases in load-COD hysteresis were observed during the initial cycles of high-amplitude loading. Steady state @ad-COD hysteresis behavior was attained by fifty loading cycles in each case and the fifty-cycle hysteresis loop widths agreed well with those for continuously cycled (non-precracked) samples for equivalent loading conditions. The cydes during which the load-COD hysteresis decreased most dramatically represented fatigue crack growth distances equal to approximately 30% of the calculated plane strain monotonic plastic zone size. Greater percentage reductions in load-COD hysteresis were observed for lower stress intensity factor ranges. The observed behavior was in general agreement with that predicted by finite element fatigue crack closure models in the literature. In addition, the level of prior loading was found to have a pronounced effect on subsequently measured fracture toughness values for this material.
INTRODUCTION IT IS APPARENT that fatigue crack propagation by a ductile mechanism requires reversed plastic deformation at the crack tip during each stress cycle for which the crack extends. Furthermore, the existence of such a reversed, or cyclic, plastic zone has been demonstrated by a number of experimental and analytical studies. The reversal of plastic deformation occurs at the crack tip during the unloading portion of the stress cycle as a result of compressive residual stress in the plastic zone in front of the crack. In addition, however, the extent of crack tip plasticity also depends on the effective stress intensity factor range which is determined not only by the applied load and geometry but also by the residual stresses immediately behind the crack tip which are associated with the wake of plastic deformation from previous loading. A well-known example of the loading history effect described above is the transient retardation of fatigue crack growth which is observed to follow isolated stress overloads. Conversely, for the case of high amplitude cyclic loading following fatigue crack growth at lower stress amplitudes; one might expect accelerated crack growth rates during the initial high amplitude cycles and such effects are indicated by crack opening displacement measurements reported by Schijve[l] for spectrum loading conditions. For sustained high amplitude cyclic loading a steady-state condition would eventually be reached indicating that the effects of the preceding low amplitude stress cycling had become negligible. Analytically, recent finite element models[2,3] of fatigue cracks growing under low-to-high amplitude type of block loading predict increasing values of the crack opening and closing stresses during the initial cycles of high amplitude loading. In these models, steady state conditions are reached quite rapidly, e.g. at a distance of crack propagation which is a fraction of the plastic zone size at the higher stress amplitude. In addition to the residual stress effects discussed above, cyclic hardening or softening of the material at the crack tip might also be expected to affect the level of cyclic crack tip plasticity. In particular, for a cyclically softening material, the cyclic plasticity in the reversed plastic zone should produce a progressive increase in cyclic crack tip plasticity until a stabilized flow stress is obtained. The effect of such cyclic softening would then be opposite to that of the residual stress during the initial fatigue cycles. It should be noted that effects of both the residual stress wake and crack tip cyclic hardening/softening behavior are contained inherently in fatigue crack propagation data obtained under constant amplitude cyclic loading. Thus, while of fundamental interest, these effects have little practical significance in terms of application to
tPresently at the China Steel Corporation, P.O. Box 47-29, Hsiao Kang, Kaohsiung, Taiwan, R.O.C. 541
542
T. YEH and L. H. BURCK
constant amplitude or extended block-loading situations. On the other hand, the development of realistic models for the growth of fatigue cracks subjected to random or short-duration block-loading spectra requires information concerning the magnitude and persistence of loading interaction effects. The primary objective of the present study was to determine the extent of influence of low amplitude cyclic loading on subsequent fatigue crack growth under high amplitude conditions by measuring the crack opening and closing hysteresis behavior of cracks during the cycles immediately following low-to-high amplitude loading transitions. For the reasons discussed above, the material chosen for study (AISI 4140 steel) was one which was known to show pronounced cyclic softening[4,5] and thus one which should have produced a divergence from the response predicted by the finite element fatigue crack models if cyclic softening was a significant factor. In addition, the effects of the high amplitude loading cycles on the measured (apparent) fracture toughness were determined.
EXPERIMJZNTALPROCEDURE The material tested was quenched and tempered AISI 4140 steel. Specimens were austenitized for one half hour at 87o”C, oil quenched, and tempered for one hour at 400°C. This heat treatment gave an average hardness of Rockwell C 45. Figure 1 shows the geometry of the specimens used to determine the monotonic and the cyclic tensile properties. The cyclic stress-strain curve was generated by the incremental step technique with the maximum strain amplitude being -+1%. Fatigue crack propagation and fracture toughness testing were performed with compact tension specimens such as shown in Fig. 2. Specimens for the cyclic crack opening displacement studies were fatigue pre-cracked at low, diminishing-amplitude cyclic stresses with individual load reductions amounting to less than 15% of the prior load range until the crack had grown to 8 mm beyond the notch tip. After this pre-cracking, the specimens were fitted with a clip-in crack opening displacement gage and were either pulled to failure in order to measure the fracture toughness or were subjected to a block of fifty high-amplitude load cycles during which the crack opening displacement at the specimen edge was continuously monitored as a function of load. In particular, measurements were made of the maximum width of the crack opening and closing hysteresis loop, indicated as 6’ in Fig. 3, for each cycle in the test block. The frequency of the block loading was 0.2Hz. Each specimen was then pulled to failure and an apparent fracture toughness was measured. In addition to the testing described above, two specimens were continuously cycled at constant cyclic load amplitudes in order to establish the rate of fatigue crack growth as a function of stress intensity factor range. These tests were conducted at 1 Hz but were interrupted at appropriate crack lengths so that the clip-in gage could be fitted in order to
/3/8in-16
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iI k Fig. 1.
Fig. 2.
Fig. I. Monotonic and cyclic stress-strain test specimen (dimensions in mm except as noted). Fig. 2. Compact tension fatigue crack propagation and fracture toughness test specimen (dimensions in mm).
Cyclic crack opening displacement behavior during high-amplitude block loading
543
Load
Crack Opening Oisplocement
Fig. 3. Schematic load-COD behavior for one stress cycle.
monitor the crack opening displacement for fifty cycles at a frequency of 0.2 Hz after which the specimens were allowed to cycle until complete failure. In all cases the ratio of minimum to maximum load was 0.05. RESULTS The quenched and tempered AISI 4140 steel showed significant cyclic softening with the monotonic and cyclic yield stresses (0.2% offset) being 1235 and 89OMPa, respectively. The plane strain fracture toughness, measured with a normally precracked (ASTM-valid) compact tension specimen such as shown in Fig. 2, was 55 MPa v(m). Figure 4 shows a representative plot of the measured load-crack opening displacement hysteresis loop widths for a 50 cycle block of high amplitude loading. In the case illustrated the block loading was at a stress intensity factor range (AK) of 48 MPa d(m), i.e. the maximum stress intensity factor of the cycle was 92% of the fracture toughness. As shown, the hysteresis decreased during the first ten cycles but then remained relatively constant for the remaining cycles of the test block. This behavior was typical of all the specimens tested in this manner although, in some cases, loop widths continued to decrease for somewhat larger numbers of cycles. In each case, 90% of the decrease occurred in the first twenty cycles and essentially stable conditions had been reached by fifty cycles. As would be expected, the widths of the loops for the first cycle of loading in each test block increased with increasing stress intensity factor range as shown in Fig. 5. The ratio of the loop opening at the fiftieth cycle to that of the first cycle is shown in Fig. 6. As indicated, smaller percentage decreases in loop width were observed at higher stress intensity factor ranges. The fatigue crack growth rate data which were generated by two specimens cycled at constant cyclic load amplitudes are shown in Fig. 7. As previously noted, the crack opening
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Fig. 4. Load-COD hysteresis behavior for fifty cycles of loading at AK = 48 MPa v(m).
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Fig. 5. Width of the load-COD hysteresis loop for the first cycle of high amplitude loading as a function of stress intensity factor range. Fig. 6. Ratio of the load-COD hysteresis loop width for the fiftyith cycle to that of the first cycle as a function of stress intensity factor range. Fig. 7. Fatigue crack growth rate (da/dN) as a function of stress intensity factor range (AK) for continuous constant cyclic load amplitude testing. Fig, 8. Comparison of stabilized (fifty-cycle) load-COD loop widths with those for specimens continuously cycled at constant load amplitudes.
displacements of these specimens were monitored for fifty cycles when the crack was the same length as that utilized in the block loading tests described above. For these two specimens, no transient decreases in load-COD loop width were observed but rather the loop widths remained constant for the fifty cycles. Furthermore, the amplitudes of the loop widths were in good agreement with the stabilized (fifty-cycle) loop widths of the pre-cracked and cycled specimens as shown in Fig. 8.
Cyclic crack opening displacement behavior during high-amplitude block loading
545
Fracture toughness values measured after application of the fifty cycles of high-amplitude loading were considerably greater than for properly pre-cracked specimens. The specimens which were allowed to cycle continuously to fracture displayed the highest apparent fracture toughness values of all. Apparent fracture toughness values for all of the types of precracking investigated are presented in Fig. 9 as a function of the ratio of the maximum precrack stress intensity factor to the measured apparent fracture toughness. ~a~ng electron fracto~phy revealed that both fatigue and monotonic fracture modes were transgranular and ductile. For example, Fig. 10 is a micrograph of the fracture surface of a test specimen which was precracked, loaded for fifty cycles at a stress intensity factor range of 49IvPav(m), and then fractured monotonically. Since the appearance of each fracture mode was quite distinct, the distance of crack advancement during the fifty cycles of high amplitude loading could be readily determined, e.g. for the case shown the crack grew 6Opm during the high-amplitude loading.
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DDWJSSION The cyclic softening behavior observed in this study is in agreement with data previously reported by Thielen et a/.[41 for 4140 steel tempered at 400°C. As noted, this softening characteristic partially motivated our choice of material. Also, the measured plane strain fracture toughness (I&) value of 55 MPaV’(m) is consistent with the trend of i(rc values reported for lower tempering temperatures by Thielen and Fine[3]. On the first cycle of the high-amplitude loading block, the precracked specimens gave essentially unaffected crack opening displacement responses. During further cycling two significant changes occurred. First, the continued reversed plastic deformation at the crack tip presumably promoted local softening in line with the cyclic stress-strain behavior of this material. Second, as the fatigue crack propagated into the plastic zone produced by the high-amplitude loading compressive residual stresses began to act behind the crack tip. Because
546
T. YEH and L. H. BURCK
these two factors-would have opposite effects on the plastic component of the crack opening displacement, and because in the present studies the COD hysteresis decreased on each successive cycle as the crack grew into the plastic zone of the high amplitude loading, it is apparent that the effect of the residual stress dominated the cyclic crack opening displacement behavior and overwhelmed any effects of local cyclic softening. In 1970, Elber [6] suggested that crack closure could occur at positive loads as a result of the residual compressive stresses associated with the permanent tensile deformation left behind the tip of a propagating fatigue crack. This closure phenomenon has since been described analytically[2,3,7] and experimentally [8-121 and is thought to be responsible, at least in part, for the fatigue crack growth retardation effects of isolated stress overloads[l2,13], the effects prior of loading on the threshold stress intensity factor for fatigue crack growth [ 141,and for the effects of mean stress on fatigue crack growth rate[l5]. In the present study, the transient decrease in the cyclic plastic component of the crack opening displacement which occurred during the first cycles of high-amplitude loading following pre-cracking also reflects the effects of crack closure. Crack closure reduces the effective stress intensity factor range and thus reduces the amount of reversed plastic flow at the crack tip which is revealed by a narrowing of the load-COD hysteresis loop as the crack propagates into the plastic zone of the highamplitude loading. Since closure effects are more pronounced at lower stress intensity factor ranges, i.e. where the crack is closed for a greater fraction of the stress cycle, it would be expected that greater loop width reductions would occur at the lower test load amplitudes, as was observed in the present study. Crack closure effects during constant amplitude and block loading have recently been studied analytically in considerable detail through finite element models developed by Newman[2] and by Ogura and Ohji[3]. Each of these analyses predicts transient increases in the crack opening and closing stresses during the first cycle of fatigue loading. In general, steady state conditions are predicted after a number of loading cycles which is in agreement with the results of the present study if the crack opening and closing stresses are considered to be inversely related to the amount of cyclic crack tip plasticity. Furthermore, for the crack model of Newman[2], greater closure effects are indicated for lower applied load ranges, as was observed in the present investigation. Although Ogura and Ohji[3] predict the opposite trend, the results of Newman specifically show that this discrepancy is likely the result of too coarse a finite element mesh in the case of the Ogura-Ohji study. As noted previously, relatively steady state cyclic crack opening displacement behavior was observed after approximately twenty cycles of high amplitude loading. The crack growth during these twenty cycles represents a distance equal to about 30% of the plane strain plastic zone size calculated according to the analysis of Irwin[l6]. For example, the fracture surface of Fig. 10 shows 60 km of crack growth during fifty cycles of loading at a stress intensity factor range of 47 MPa d(m) for an average growth rate of 1.2 pm/cycle. This is virtually identical to the growth rate which would be predicted from the data of Fig. 7 for a continuously cycled specimen at the same stress intensity factor range. The calculated monotonic plane strain plastic zone size [ 161for the loading condition of this test is 84 pm, or about 3.5 times the crack growth in twenty cycles. This behavior is in general agreement with that predicted by Newman’s finite element model[2] and also is in accord with observations by Lankford and Davidson[ 171 and by Chanani[ 181 that the maximum retardation effects of single high amplitude stress overloads occur when the fatigue crack tip has propagated less than one-half the overload plastic zone size. It should also be noted that our data indicates that accelerated fatigue crack growth rates, if present in the first cycles of high amplitude loading, are not significant when averaged over fifty load cycles. The effects of prior stress history on the measured fracture toughness have previously been reported with respect to establishing standardized test procedures for fracture toughness measurement[ 19,201. As a result of such studies, ASTM requires that the maximum fatigue crack stress intensity factor not exceed 60% of the measured fracture toughness[21]. In the present case, Fig. 9, fatigue cycling at 70% of the subsequently measured fracture toughness produced an average apparent increase in fracture toughness of 25% as compared to the value measured at a fatigue to fracture toughness stress intensity factor ratio of 0.3. Continuous cycling to fracture produced an average increase in apparent fracture toughness of 40%. Thus,
Cyclic crack opening displacement behavior during high-amplitude block loading
Fig. 10. Scanning electron micrograph of the fracture surface of a specimen which was pre-cracked, subjected to fifty cycles of high amplitude loading (AK = 47 bag, and fractured in monotinic tension.
547
Cyclic crack opening displacement behavior during high-amplitude block loading
549
the ASTM recommended practice for fatigue precracking is not overly conservative for this material and, in fact, the data suggests that pre-cracking effects might also be observed at fatigue to fracture toughness stress intensity factor ratios less than 0.6. In this regard it should be noted that the material studied showed pronounced cyclic softening which would tend to emphasize the effects of stress cycling on fracture toughness by producing a cyclically softened zone at the immediate crack tip. The other contributing factor is of course the residual stress associated with the wake of plastic deformation behind the crack tip. CONCLUSIONS (1) Cycle-to-cycle decreases in the widths of load-COD hysteresis loops were observed during the initial cycles of high amplitude loading following low amplitude fatigue pre-cracking. Such behavior occurred in spite of the fact that the material tested showed cyclic softening which would be expected to produce the opposite effect. The observed behavior is thus attributed to the dominant effect of plastic zone residual stress. (2) Steady-state load-COD hysteresis behavior was reached after approximately twenty high amplitude loading cycles. The steady-state values agreed well with values for samples continuously cycled without pre-cracking and were attained after a crack growth distance equal to approximately 30% of the calculated monotonic plane plastic zone size for the high amplitude loading. (3) Greater percentage reductions in load-COD hysteresis were observed for lower stress intensity factor ranges as would be expected from crack closure arguments. (4) The level of prior fatigue loading was found to have a pronounced effect on subsequently measured fracture toughness values in the material studied. Acknowledgement-This work was supported in part by the Graduate School of the University of Wisconsin-Milwaukee.
REFERENCES [l] J. Schijve, Observations on the prediction of fatigue crack growth propagation under variable-amplitude loading. ASTM STP 595,3-23 (1976). [2] J. C. Newman, Jr., A finite-element analysis of fatigue crack closure. ASTM STP 590, 281-301(1976). [3] K. Ogura and K. Ohji, FEM analysis of crack closure and delay effect in fatigue crack growth under variable amplitude loading. figng Fracture Mech. 9,471-480 (1977). [4] P. N. Thielen and M. E. Fine, Fatigue crack propagation in 4140 steel. Met. Trans. 6A, 2133-2141(1975). [5] P. N. Thielen, M. E. Fine and R. A. Fournelle, Cyclic stress-strain relations and strain-controlled fatigue of 4140steel. Acta Met. 24, l-10 (1976). (61 W. Elber, Fatigue crack closure under cyclic tension. Engng Fracture Mech. 2, 37-45 (1970). [7] 0. Aksogan, Partial closure of a Griffith crack under a general loading. Jnt. J. Fracture 11,65%70 (1975). [8] N. J. I. Adams, Fatigue crack closure at positive stresses. Engng Fracrure Mech. 4,543-554 (1972). [9] P. E. Irving, I. L. Robinson and C. J. Beevers, Fatigue crack closure in titanium alloys. Id. J. Fracture 9, 105-108
\.. ._,. [ 101 T. T. Shih and R. P. Wei, A study of crack closure in fatigue. Engng Fracture Mech. 6, 19-32 (1974). [Ill J. D. Frandsen, R. V. Inman and 0. Buck, A comparison of acoustic and strain gage techniques for crack closure. Jnt. J. Fracfure 11.345-348 (1975). [ 121 W. N. Sharpe, Jr. and A. F. Grand&Jr., A preliminary study of fatigue crack retardation using laser interferometry to measure crack surface displacements. ASTM STP 590.302-320 (1976). [13] P. J. Bernard, T. C. Lindle; and C. E. Richards, Mechanisms of overload retardation during fatigue crack propagation. ASTM STP 595.78-97 (1976). [14] S. W. Hopkins, C. A. Rau, G. R. Leverant and A. Yuen, Effect of various programmed overloads on the threshold for high-frequency fatigue crack growth. ASTM STP 595, 125-141(1976). [15] W. Elber, The significance of crack closure. ASTM STP 486,230-259 (1971). [16] G. R. Irwin, Linear fracture mechanics, fracture transition, and fracture control. Engng Fracture Mech. 1, 241-257 (1968). [17] J. Lankford, Jr. and D. L. Davidson, Fatigue crack tip plasticity associated with overloads and subsequent cycling. ASME J. Engng Mat. Tech. 98, 17-23 (1976). [18] G. R. Chanani, Retardation of fatigue crack growth in 7075aluminium. Metals Engng Quart. 15(l), 4043 (1975). [19] W. F. Brown, Jr. and J. E. Srawley, Commentary on present practice. ASTM STP 463, 216248 (1970). [20] M. J. May, British experience with plane strain fracture toughness (KIc) testing ASTM STP 463.4162 (1970). (211 A!!?M Standard E399, ASTM Annual Book of ASTM Standards. 10 (1974). (Received 15 December 1978; received for publicaGon 21 June 1979)
EN
Vol. 12, No. 4-G
CYCLIC CRACK OPENING DISPLACEMENT BEHAVIOR DURING HIGH AMPLITUDE BLOCK LOADING T. YEHt and L. H. BURCK Materials Department, The University of Wisconsin-Milwaukee, Milwaukee, WI 53201,U.S.A. Abstract-Load-crack opening displacement hysteresis behavior was monitored for fifty cycles of highamplitude loading which followed fatigue pre-cracking at low stress intensity factor levels. The material studied was quenched and tempered (400°C)AISI 4140 steel which showed pronounced cyclic softening. Despite this softening behavior, cycle-tecycle decreases in load-COD hysteresis were observed during the initial cycles of high-amplitude loading. Steady state @ad-COD hysteresis behavior was attained by fifty loading cycles in each case and the fifty-cycle hysteresis loop widths agreed well with those for continuously cycled (non-precracked) samples for equivalent loading conditions. The cydes during which the load-COD hysteresis decreased most dramatically represented fatigue crack growth distances equal to approximately 30% of the calculated plane strain monotonic plastic zone size. Greater percentage reductions in load-COD hysteresis were observed for lower stress intensity factor ranges. The observed behavior was in general agreement with that predicted by finite element fatigue crack closure models in the literature. In addition, the level of prior loading was found to have a pronounced effect on subsequently measured fracture toughness values for this material.
INTRODUCTION IT IS APPARENT that fatigue crack propagation by a ductile mechanism requires reversed plastic deformation at the crack tip during each stress cycle for which the crack extends. Furthermore, the existence of such a reversed, or cyclic, plastic zone has been demonstrated by a number of experimental and analytical studies. The reversal of plastic deformation occurs at the crack tip during the unloading portion of the stress cycle as a result of compressive residual stress in the plastic zone in front of the crack. In addition, however, the extent of crack tip plasticity also depends on the effective stress intensity factor range which is determined not only by the applied load and geometry but also by the residual stresses immediately behind the crack tip which are associated with the wake of plastic deformation from previous loading. A well-known example of the loading history effect described above is the transient retardation of fatigue crack growth which is observed to follow isolated stress overloads. Conversely, for the case of high amplitude cyclic loading following fatigue crack growth at lower stress amplitudes; one might expect accelerated crack growth rates during the initial high amplitude cycles and such effects are indicated by crack opening displacement measurements reported by Schijve[l] for spectrum loading conditions. For sustained high amplitude cyclic loading a steady-state condition would eventually be reached indicating that the effects of the preceding low amplitude stress cycling had become negligible. Analytically, recent finite element models[2,3] of fatigue cracks growing under low-to-high amplitude type of block loading predict increasing values of the crack opening and closing stresses during the initial cycles of high amplitude loading. In these models, steady state conditions are reached quite rapidly, e.g. at a distance of crack propagation which is a fraction of the plastic zone size at the higher stress amplitude. In addition to the residual stress effects discussed above, cyclic hardening or softening of the material at the crack tip might also be expected to affect the level of cyclic crack tip plasticity. In particular, for a cyclically softening material, the cyclic plasticity in the reversed plastic zone should produce a progressive increase in cyclic crack tip plasticity until a stabilized flow stress is obtained. The effect of such cyclic softening would then be opposite to that of the residual stress during the initial fatigue cycles. It should be noted that effects of both the residual stress wake and crack tip cyclic hardening/softening behavior are contained inherently in fatigue crack propagation data obtained under constant amplitude cyclic loading. Thus, while of fundamental interest, these effects have little practical significance in terms of application to
tPresently at the China Steel Corporation, P.O. Box 47-29, Hsiao Kang, Kaohsiung, Taiwan, R.O.C. 541
542
T. YEH and L. H. BURCK
constant amplitude or extended block-loading situations. On the other hand, the development of realistic models for the growth of fatigue cracks subjected to random or short-duration block-loading spectra requires information concerning the magnitude and persistence of loading interaction effects. The primary objective of the present study was to determine the extent of influence of low amplitude cyclic loading on subsequent fatigue crack growth under high amplitude conditions by measuring the crack opening and closing hysteresis behavior of cracks during the cycles immediately following low-to-high amplitude loading transitions. For the reasons discussed above, the material chosen for study (AISI 4140 steel) was one which was known to show pronounced cyclic softening[4,5] and thus one which should have produced a divergence from the response predicted by the finite element fatigue crack models if cyclic softening was a significant factor. In addition, the effects of the high amplitude loading cycles on the measured (apparent) fracture toughness were determined.
EXPERIMJZNTALPROCEDURE The material tested was quenched and tempered AISI 4140 steel. Specimens were austenitized for one half hour at 87o”C, oil quenched, and tempered for one hour at 400°C. This heat treatment gave an average hardness of Rockwell C 45. Figure 1 shows the geometry of the specimens used to determine the monotonic and the cyclic tensile properties. The cyclic stress-strain curve was generated by the incremental step technique with the maximum strain amplitude being -+1%. Fatigue crack propagation and fracture toughness testing were performed with compact tension specimens such as shown in Fig. 2. Specimens for the cyclic crack opening displacement studies were fatigue pre-cracked at low, diminishing-amplitude cyclic stresses with individual load reductions amounting to less than 15% of the prior load range until the crack had grown to 8 mm beyond the notch tip. After this pre-cracking, the specimens were fitted with a clip-in crack opening displacement gage and were either pulled to failure in order to measure the fracture toughness or were subjected to a block of fifty high-amplitude load cycles during which the crack opening displacement at the specimen edge was continuously monitored as a function of load. In particular, measurements were made of the maximum width of the crack opening and closing hysteresis loop, indicated as 6’ in Fig. 3, for each cycle in the test block. The frequency of the block loading was 0.2Hz. Each specimen was then pulled to failure and an apparent fracture toughness was measured. In addition to the testing described above, two specimens were continuously cycled at constant cyclic load amplitudes in order to establish the rate of fatigue crack growth as a function of stress intensity factor range. These tests were conducted at 1 Hz but were interrupted at appropriate crack lengths so that the clip-in gage could be fitted in order to
/3/8in-16
-_ -k-_ _ -__
N.C. THD
iI k Fig. 1.
Fig. 2.
Fig. I. Monotonic and cyclic stress-strain test specimen (dimensions in mm except as noted). Fig. 2. Compact tension fatigue crack propagation and fracture toughness test specimen (dimensions in mm).
Cyclic crack opening displacement behavior during high-amplitude block loading
543
Load
Crack Opening Oisplocement
Fig. 3. Schematic load-COD behavior for one stress cycle.
monitor the crack opening displacement for fifty cycles at a frequency of 0.2 Hz after which the specimens were allowed to cycle until complete failure. In all cases the ratio of minimum to maximum load was 0.05. RESULTS The quenched and tempered AISI 4140 steel showed significant cyclic softening with the monotonic and cyclic yield stresses (0.2% offset) being 1235 and 89OMPa, respectively. The plane strain fracture toughness, measured with a normally precracked (ASTM-valid) compact tension specimen such as shown in Fig. 2, was 55 MPa v(m). Figure 4 shows a representative plot of the measured load-crack opening displacement hysteresis loop widths for a 50 cycle block of high amplitude loading. In the case illustrated the block loading was at a stress intensity factor range (AK) of 48 MPa d(m), i.e. the maximum stress intensity factor of the cycle was 92% of the fracture toughness. As shown, the hysteresis decreased during the first ten cycles but then remained relatively constant for the remaining cycles of the test block. This behavior was typical of all the specimens tested in this manner although, in some cases, loop widths continued to decrease for somewhat larger numbers of cycles. In each case, 90% of the decrease occurred in the first twenty cycles and essentially stable conditions had been reached by fifty cycles. As would be expected, the widths of the loops for the first cycle of loading in each test block increased with increasing stress intensity factor range as shown in Fig. 5. The ratio of the loop opening at the fiftieth cycle to that of the first cycle is shown in Fig. 6. As indicated, smaller percentage decreases in loop width were observed at higher stress intensity factor ranges. The fatigue crack growth rate data which were generated by two specimens cycled at constant cyclic load amplitudes are shown in Fig. 7. As previously noted, the crack opening
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t 20
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30
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Number of Cycles
Fig. 4. Load-COD hysteresis behavior for fifty cycles of loading at AK = 48 MPa v(m).
544
T. YEH and L. H. BURCK
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fiK (MPdii) Fig.7.
Fig. 5. Width of the load-COD hysteresis loop for the first cycle of high amplitude loading as a function of stress intensity factor range. Fig. 6. Ratio of the load-COD hysteresis loop width for the fiftyith cycle to that of the first cycle as a function of stress intensity factor range. Fig. 7. Fatigue crack growth rate (da/dN) as a function of stress intensity factor range (AK) for continuous constant cyclic load amplitude testing. Fig, 8. Comparison of stabilized (fifty-cycle) load-COD loop widths with those for specimens continuously cycled at constant load amplitudes.
displacements of these specimens were monitored for fifty cycles when the crack was the same length as that utilized in the block loading tests described above. For these two specimens, no transient decreases in load-COD loop width were observed but rather the loop widths remained constant for the fifty cycles. Furthermore, the amplitudes of the loop widths were in good agreement with the stabilized (fifty-cycle) loop widths of the pre-cracked and cycled specimens as shown in Fig. 8.
Cyclic crack opening displacement behavior during high-amplitude block loading
545
Fracture toughness values measured after application of the fifty cycles of high-amplitude loading were considerably greater than for properly pre-cracked specimens. The specimens which were allowed to cycle continuously to fracture displayed the highest apparent fracture toughness values of all. Apparent fracture toughness values for all of the types of precracking investigated are presented in Fig. 9 as a function of the ratio of the maximum precrack stress intensity factor to the measured apparent fracture toughness. ~a~ng electron fracto~phy revealed that both fatigue and monotonic fracture modes were transgranular and ductile. For example, Fig. 10 is a micrograph of the fracture surface of a test specimen which was precracked, loaded for fifty cycles at a stress intensity factor range of 49IvPav(m), and then fractured monotonically. Since the appearance of each fracture mode was quite distinct, the distance of crack advancement during the fifty cycles of high amplitude loading could be readily determined, e.g. for the case shown the crack grew 6Opm during the high-amplitude loading.
a0 ka ( MPaJiiif
70
60
50
0
0.2
0.4
0.6
0.8
1.0
Kmax Kc!
Fig. 9. Apparent fracture toughness (Ko) as a function of maximum pre-crack-to-measured fracture toughness stress intensity factor ratio. (I&,&).
DDWJSSION The cyclic softening behavior observed in this study is in agreement with data previously reported by Thielen et a/.[41 for 4140 steel tempered at 400°C. As noted, this softening characteristic partially motivated our choice of material. Also, the measured plane strain fracture toughness (I&) value of 55 MPaV’(m) is consistent with the trend of i(rc values reported for lower tempering temperatures by Thielen and Fine[3]. On the first cycle of the high-amplitude loading block, the precracked specimens gave essentially unaffected crack opening displacement responses. During further cycling two significant changes occurred. First, the continued reversed plastic deformation at the crack tip presumably promoted local softening in line with the cyclic stress-strain behavior of this material. Second, as the fatigue crack propagated into the plastic zone produced by the high-amplitude loading compressive residual stresses began to act behind the crack tip. Because
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T. YEH and L. H. BURCK
these two factors-would have opposite effects on the plastic component of the crack opening displacement, and because in the present studies the COD hysteresis decreased on each successive cycle as the crack grew into the plastic zone of the high amplitude loading, it is apparent that the effect of the residual stress dominated the cyclic crack opening displacement behavior and overwhelmed any effects of local cyclic softening. In 1970, Elber [6] suggested that crack closure could occur at positive loads as a result of the residual compressive stresses associated with the permanent tensile deformation left behind the tip of a propagating fatigue crack. This closure phenomenon has since been described analytically[2,3,7] and experimentally [8-121 and is thought to be responsible, at least in part, for the fatigue crack growth retardation effects of isolated stress overloads[l2,13], the effects prior of loading on the threshold stress intensity factor for fatigue crack growth [ 141,and for the effects of mean stress on fatigue crack growth rate[l5]. In the present study, the transient decrease in the cyclic plastic component of the crack opening displacement which occurred during the first cycles of high-amplitude loading following pre-cracking also reflects the effects of crack closure. Crack closure reduces the effective stress intensity factor range and thus reduces the amount of reversed plastic flow at the crack tip which is revealed by a narrowing of the load-COD hysteresis loop as the crack propagates into the plastic zone of the highamplitude loading. Since closure effects are more pronounced at lower stress intensity factor ranges, i.e. where the crack is closed for a greater fraction of the stress cycle, it would be expected that greater loop width reductions would occur at the lower test load amplitudes, as was observed in the present study. Crack closure effects during constant amplitude and block loading have recently been studied analytically in considerable detail through finite element models developed by Newman[2] and by Ogura and Ohji[3]. Each of these analyses predicts transient increases in the crack opening and closing stresses during the first cycle of fatigue loading. In general, steady state conditions are predicted after a number of loading cycles which is in agreement with the results of the present study if the crack opening and closing stresses are considered to be inversely related to the amount of cyclic crack tip plasticity. Furthermore, for the crack model of Newman[2], greater closure effects are indicated for lower applied load ranges, as was observed in the present investigation. Although Ogura and Ohji[3] predict the opposite trend, the results of Newman specifically show that this discrepancy is likely the result of too coarse a finite element mesh in the case of the Ogura-Ohji study. As noted previously, relatively steady state cyclic crack opening displacement behavior was observed after approximately twenty cycles of high amplitude loading. The crack growth during these twenty cycles represents a distance equal to about 30% of the plane strain plastic zone size calculated according to the analysis of Irwin[l6]. For example, the fracture surface of Fig. 10 shows 60 km of crack growth during fifty cycles of loading at a stress intensity factor range of 47 MPa d(m) for an average growth rate of 1.2 pm/cycle. This is virtually identical to the growth rate which would be predicted from the data of Fig. 7 for a continuously cycled specimen at the same stress intensity factor range. The calculated monotonic plane strain plastic zone size [ 161for the loading condition of this test is 84 pm, or about 3.5 times the crack growth in twenty cycles. This behavior is in general agreement with that predicted by Newman’s finite element model[2] and also is in accord with observations by Lankford and Davidson[ 171 and by Chanani[ 181 that the maximum retardation effects of single high amplitude stress overloads occur when the fatigue crack tip has propagated less than one-half the overload plastic zone size. It should also be noted that our data indicates that accelerated fatigue crack growth rates, if present in the first cycles of high amplitude loading, are not significant when averaged over fifty load cycles. The effects of prior stress history on the measured fracture toughness have previously been reported with respect to establishing standardized test procedures for fracture toughness measurement[ 19,201. As a result of such studies, ASTM requires that the maximum fatigue crack stress intensity factor not exceed 60% of the measured fracture toughness[21]. In the present case, Fig. 9, fatigue cycling at 70% of the subsequently measured fracture toughness produced an average apparent increase in fracture toughness of 25% as compared to the value measured at a fatigue to fracture toughness stress intensity factor ratio of 0.3. Continuous cycling to fracture produced an average increase in apparent fracture toughness of 40%. Thus,
Cyclic crack opening displacement behavior during high-amplitude block loading
Fig. 10. Scanning electron micrograph of the fracture surface of a specimen which was pre-cracked, subjected to fifty cycles of high amplitude loading (AK = 47 bag, and fractured in monotinic tension.
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Cyclic crack opening displacement behavior during high-amplitude block loading
549
the ASTM recommended practice for fatigue precracking is not overly conservative for this material and, in fact, the data suggests that pre-cracking effects might also be observed at fatigue to fracture toughness stress intensity factor ratios less than 0.6. In this regard it should be noted that the material studied showed pronounced cyclic softening which would tend to emphasize the effects of stress cycling on fracture toughness by producing a cyclically softened zone at the immediate crack tip. The other contributing factor is of course the residual stress associated with the wake of plastic deformation behind the crack tip. CONCLUSIONS (1) Cycle-to-cycle decreases in the widths of load-COD hysteresis loops were observed during the initial cycles of high amplitude loading following low amplitude fatigue pre-cracking. Such behavior occurred in spite of the fact that the material tested showed cyclic softening which would be expected to produce the opposite effect. The observed behavior is thus attributed to the dominant effect of plastic zone residual stress. (2) Steady-state load-COD hysteresis behavior was reached after approximately twenty high amplitude loading cycles. The steady-state values agreed well with values for samples continuously cycled without pre-cracking and were attained after a crack growth distance equal to approximately 30% of the calculated monotonic plane plastic zone size for the high amplitude loading. (3) Greater percentage reductions in load-COD hysteresis were observed for lower stress intensity factor ranges as would be expected from crack closure arguments. (4) The level of prior fatigue loading was found to have a pronounced effect on subsequently measured fracture toughness values in the material studied. Acknowledgement-This work was supported in part by the Graduate School of the University of Wisconsin-Milwaukee.
REFERENCES [l] J. Schijve, Observations on the prediction of fatigue crack growth propagation under variable-amplitude loading. ASTM STP 595,3-23 (1976). [2] J. C. Newman, Jr., A finite-element analysis of fatigue crack closure. ASTM STP 590, 281-301(1976). [3] K. Ogura and K. Ohji, FEM analysis of crack closure and delay effect in fatigue crack growth under variable amplitude loading. figng Fracture Mech. 9,471-480 (1977). [4] P. N. Thielen and M. E. Fine, Fatigue crack propagation in 4140 steel. Met. Trans. 6A, 2133-2141(1975). [5] P. N. Thielen, M. E. Fine and R. A. Fournelle, Cyclic stress-strain relations and strain-controlled fatigue of 4140steel. Acta Met. 24, l-10 (1976). (61 W. Elber, Fatigue crack closure under cyclic tension. Engng Fracture Mech. 2, 37-45 (1970). [7] 0. Aksogan, Partial closure of a Griffith crack under a general loading. Jnt. J. Fracture 11,65%70 (1975). [8] N. J. I. Adams, Fatigue crack closure at positive stresses. Engng Fracrure Mech. 4,543-554 (1972). [9] P. E. Irving, I. L. Robinson and C. J. Beevers, Fatigue crack closure in titanium alloys. Id. J. Fracture 9, 105-108
\.. ._,. [ 101 T. T. Shih and R. P. Wei, A study of crack closure in fatigue. Engng Fracture Mech. 6, 19-32 (1974). [Ill J. D. Frandsen, R. V. Inman and 0. Buck, A comparison of acoustic and strain gage techniques for crack closure. Jnt. J. Fracfure 11.345-348 (1975). [ 121 W. N. Sharpe, Jr. and A. F. Grand&Jr., A preliminary study of fatigue crack retardation using laser interferometry to measure crack surface displacements. ASTM STP 590.302-320 (1976). [13] P. J. Bernard, T. C. Lindle; and C. E. Richards, Mechanisms of overload retardation during fatigue crack propagation. ASTM STP 595.78-97 (1976). [14] S. W. Hopkins, C. A. Rau, G. R. Leverant and A. Yuen, Effect of various programmed overloads on the threshold for high-frequency fatigue crack growth. ASTM STP 595, 125-141(1976). [15] W. Elber, The significance of crack closure. ASTM STP 486,230-259 (1971). [16] G. R. Irwin, Linear fracture mechanics, fracture transition, and fracture control. Engng Fracture Mech. 1, 241-257 (1968). [17] J. Lankford, Jr. and D. L. Davidson, Fatigue crack tip plasticity associated with overloads and subsequent cycling. ASME J. Engng Mat. Tech. 98, 17-23 (1976). [18] G. R. Chanani, Retardation of fatigue crack growth in 7075aluminium. Metals Engng Quart. 15(l), 4043 (1975). [19] W. F. Brown, Jr. and J. E. Srawley, Commentary on present practice. ASTM STP 463, 216248 (1970). [20] M. J. May, British experience with plane strain fracture toughness (KIc) testing ASTM STP 463.4162 (1970). (211 A!!?M Standard E399, ASTM Annual Book of ASTM Standards. 10 (1974). (Received 15 December 1978; received for publicaGon 21 June 1979)
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Vol. 12, No. 4-G