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Deformation produced by elevated temperature fatigue crack propagation in type 316 stainless steel
409
METALLOGRAPHY 15:409-422 (1982)
Deformation Produced by Elevated Temperature Fatigue Crack Propagation in Type 316 Stainless Steel
GLENN R. EVERS, HUGH H. SMITH, AND DAVID J. MICHEL
Thermostructural Materials Branch, Material Science and Technology Division, Naval Research Laboratory, Washington, D.C. 20375
The extent and nature of the plastic deformation developed by fatigue crack propagation in type 316 stainless steel at 593°C was investigated using microhardness techniques. Microhardness measurements were made to determine the extent of plastic deformation within the plain strain plastic zone for three specimens tested to different predetermined crack lengths. Extensive plastic deformation was found to be present in a localized envelope that surrounded the crack, and the evolution and shape of this highly strained region was characterized on a three-dimensional scale. The results indicate that the greatest change in microhardness occurred within 0.4 mm of the fracture surface for all specimens and decreased to a constant value dependent upon crack length for each specimen in the plastic zone. Dislocation densities calculated from the microhardness results were consistent with results based on transmission electron microscopy. The results provide additional information concerning the relationship between the crack propagation process and microstructure as a function of crack length.
Introduction The austenitic stainless steels are candidate materials for internal structural components of advanced nuclear energy systems. Although the fatigue crack propagation behavior and failure mode of these materials have been extensively investigated at elevated temperatures, the deformation substructure produced during cyclic and combined cyclic-static loading and its effect on crack propagation mechanisms have received less attention [1, 2]. The existence of a heavily strained region beneath the fatigue fracture surface has been well established for austenitic steels [2-4] and Fe-3 Si steel [5]. A summary of fatigue crack tip plasticity for a variety of other alloys as compared to austenitic steels is provided by Lankford et al. [6]. Despite the small size of the heavily strained region and its inaccessibility, several techniques have been proposed, including the use of elec© Elsevier Science Publishing Co., Inc., 1982 52 Vanderbilt Ave., New York, NY 10017
0026-0800/82/040409 + 14502.75
410
Evers, Smith, and Michel
tron microscopy, the x-ray microbeam, the Moir6 technique, etching, and microhardness measurements [6]. Of the five methods previously described, the measurement of microhardness is a relatively simple and accurate indication of work hardening in austenitic steels [3]. The present study was designed to investigate the relationship between elevated temperature crack propagation behavior and the deformation produced by the crack propagation mechanisms. This report presents the results of microhardness studies to define the shape of the cyclic deformation zone and to determine quantitative hardness numbers as functions of location within this deformation zone. Procedure The chemical composition of the 316 stainless steel used in this study has been given by Michel and Smith [1]. Three single-edge-notch cantilever specimens (6.35 cm x 5.08 cm x 1.27 cm), with side grooves machined to a depth of 5% of the specimen thickness, were given a solution anneal for 1 hr at 1093°C in a vacuum of 1 x 10 -.5 Torr and subsequently furnace cooled. The specimens were tested with a sawtooth loading sequence at I0 cycles/min in air at 593°C using induction heating. During testing the crack length was measured at the side groove using a traveling microscope. Each of the three specimens was run to different predetermined crack lengths of 6.2, 16.3, and 26.4 mm as measured from the notch tip. The crack length was plotted versus the number of cycles to obtain crack growth rates da/dN, which were correlated with the crack tip stress intensity factor range AK. After testing, three sections perpendicular (x-z plane) to the crack surface (y-z plane) and one section ahead of the crack tip were cut from each specimen according to the coordinate system in Fig. 1. Sample preparation for microhardness testing was accomplished by mechanical polishing followed by an etch-polish-etch sequence using Kalling's reagent [2.5 g CuCIz, 100 ml HCI, 100 ml ethanol (95%), and 100 ml H20]. The microhardness of each section was surveyed using a diamond pyramid microhardness (DPH) indentor with a I00 g load. All microhardness measurements were made between 0.025 and 50 mm beneath the fracture surface. Five measurements (approximately 0.025 mm apart) were averaged to determine the reported microhardness values. Grain boundaries were avoided in the measurement process. Because of possible timedependent thermal aging effects, microhardness measurements were taken of unstressed matrix material for each specimen. Although the effects of stress on the thermal aging process are uncertain, the hardness
Fatigue Crack Deformation in T316SS
411
FIG. 1. Schematic representation of single-edge-notch cantilever fatigue specimen and the orthogonal system used to define the location of post-test measurements.
results indicated that the contribution of thermal aging to the overall hardness level of the unstressed matrix was insignificant. The specimen microhardness profiles were used to calculate a composite average of microhardness as a function of crack length and specimen width at two locations beneath the crack surface (0.025 and 0.15 mm). It should be noted that these locations are within the calculated plastic zone size for the particular crack length. Scanning electron microscopy (SEM) was used to investigate the crack propagation mode of the fatigue specimens. Specimen sections containing the crack surface were prepared from the portion of the fatigue specimens not used for microhardness measurements. The specimen sections were examined at the centerline of the crack surface (midthickness of the specimen) starting at the root of the machined notch. In addition, transmission electron microscopy (TEM) foils for dislocation density measurement were prepared from selected specimen sections following the SEM study. Previously detailed procedures were followed for TEM specimen preparation and examinations [2]. Results Figure 2 illustrates the fatigue crack growth rate da/dN in air at 593°C for type 316 stainless steel tested to final crack lengths of 6.2, 16.3, and 26.4 mm. Figure 2 shows that the results from all specimens fell on the same crack growth rate curve, indicating a high degree of reproducibility. The results were found to be consistent with similar data by Michel and Smith [1]. Figure 2 also shows that the shape of the crack growth rate curves was independent of the final crack length. This was expected in view of the fact that the crack growth process is a continuous occurrence. Figure 3 shows a two-dimensional view of the composite average mi-
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STRESS INTENSITY FACTOR RANGE, AK, MPa,J-~ FIG. 2. The fatigue crack growth curve for solution annealed type 316 stainless steel at 593°C s h o w s a close agreement of growth rates for specimens tested to three crack lengths: O, 6.2 ram; rq, 16.3 mm; and A, 26.4 mm.
crohardness as a function of crack length and as a function of depth beneath the fracture surface. It has been well established that the material that is closest to the propagating crack receives the greatest amount of work hardening [2] and that as the crack propagates a large stress zone is formed that also increases the work hardening [3]. This stress zone is
Fatigue Crack Deformation in T316SS
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CRACK LENGTH, rnm FIG. 3. Microhardness as a function of crack length (©, 6.2 mm; [], 16.3 mm; ~, 26.4 ram) for annealed 316 stainless steel tested at 593°C. Measurement location was along the specimen center line (z = 0) at the indicated distances from the crack surface. The diamond symbols indicate the microhardness values ahead of the crack tip at a distance of 28 mm from the notch.
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DISTANCE FROM SPECIMEN CENTERLINE, mm FIG. 4. Three-dimensional microhardness profile as a function of depth beneath the fracture surface for specimen crack lengths 6.2 mm (©), 16.3 mm (rq), and 26.4 mm (A).
commonly referred to as the plastic zone. Recent studies [3] also indicate that there is a region of high strain hardening that accompanies the crack, referred to as the high hardness region or the reversed plastic zone. Figure 3 shows that there was a drastic increase in hardness (y direction)just beneath the fracture surface (0.025 mm) as the crack length increased. In contrast, the change in hardness as a function of crack length was not as pronounced at a further distance beneath the crack surface (0.15 mm), and, at a distance of 0.4 mm beneath the crack surface, the change in hardness as a function of crack length was negligible. As the crack propagated through the material, the greatest zone of deformation occurred
Fatigue Crack Deformation in T316SS
415
immediately parallel to the crack (y-z plane), and there was a sharp drop in hardness directly ahead of the crack tip (y axis). The sharp drop of hardness indicated that the work hardening was extremely localized at the crack tip. This was consistent with most models that characterize the area of the plastic zone as blunt and small just ahead of the crack tip [3]. Figure 4 illustrates a three-dimensional microhardness profile based on the composite average from the three specimens. The hardness is seen to have decreased from the center of the specimen to the edges (z axis), consistent with the contour of the plastic zone. Although the high hardness region was significantly smaller than the plastic zone, the shape of the high hardness region dictates the shape of the plastic zone. The greatest change of hardness beneath the crack surface was within a 0.4 mm band that was parallel and beneath the surface, regardless of crack length. Beyond this region the change of hardness in the plastic zone was moderate, and beyond the plastic zone the hardness change was negligible (elastic region). The radius r' of the high hardness zone was easily distinguished by determining where the slope of a curve of hardness versus distance changed rapidly. Figure 5 illustrates this type of curve by presenting a plot of microhardness versus distance beneath the crack surface at three crack lengths (z -- 0, x axis). At a crack length of 6.2 mm the change of microhardness was not as pronounced as the change of microhardness at a crack length of 26.4 mm for equivalent distances beneath the crack surface. Beyond a distance of 0.4 mm, the slope of the microhardness curve was relatively constant at all three crack lengths, and this point was taken as the boundary of the high hardness zone (Fig. 4). However, the constant slope of the microhardness curve prevented the location of the plastic zone radius r at a distance greater than 0.4 mm. Figure 6 presents four SEM micrographs taken from the fatigue specimen tested to a crack length of 26.4 mm. The fractographic features shown in Fig. 6 are representative of the corresponding specimens tested regardless of final crack length (i.e., 6.2, 16.3, or 26.4 mm). The micrographs in Fig. 6 illustrate a predominantly transgranular fracture mode, interspersed with intergranular facets. The transgranular failure occurred by cleavage, as evidenced by "river" patterns that run parallel to the direction of crack propagation (seen in Fig. 6). Secondary cracks can be clearly seen in Fig. 6(c) near striations that roughly outline the crack front (light region). These situations became heavily covered with oxide, which created a "mud cracked" appearance. Coarse, but easily defined, striations were formed during fast fracture [Fig. 6(d)], and dimples were initiated at the interface of large particles and the matrix.
Evers, Smith, and Michel
416
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DISTANCE FROM CRACK SURFACE, mm FIG. 5. Microhardness as a function of depth beneath the fracture surface for annealed 316 stainless steel. Measurement location was along the specimen center line at the indicated crack lengths (O, 6.2 ram; 7q, 16.3 mm; A, 26.4 mm).
Fatigue Crack Deformation in T316SS
417
Discussion The results of this study confirm that the deformation associated with fatigue crack propagation is highly localized to the material immediately adjacent to the fracture surface. Further, since the microhardness level reflecting the deformation defines the spatial extent of the plastic zone, the results show the relationship between the plastic zone size and the crack length through the stress intensity. The plastic zone size r and the stress intensity factor AK are related according to [6] r = ~
,
(1)
where r is the plastic zone radius (m), AK the stress intensity (MPa ml/2), and (rys the yield stress (at 593°C gys = 120.7 MPa). Therefore, the plastic zone size increases with the increase in stress intensity factor as a function of crack length. Within the plastic zone, however, the size of the region of highest deformation or "high hardness zone," r', has not been quantitatively defined for 316 stainless steel. Bathias and Pelloux have [3] reported that the size of this zone, perpendicular to the direction of crack propagation (x-z plane; see Fig. l), is simply a fraction of the plastic zone size. However, the present results suggest that for 316 stainless steel the greatest amount of deformation occurred within a relatively constant distance beneath the fracture surface, 0.4 mm, regardless of crack length. This value was approximately the same as the observed value, 0.5 mm, for a comparable austenitic 16-13 steel [3] and the calculated value, 0.7 mm, for 316 stainless steel using dislocation densities [2]. The relationship between plastic zone size and the high hardness zone size is
f = r'/r,
(2)
where f is the size fraction, r' is the radius of the high hardness zone (mm), and r is the radius of the plastic zone (mm). Table 1 presents a summary of the high hardness zone size fraction at the three crack lengths and the corresponding stress intensities AK. The results in Table l show that the high hardness zone radius was a large fraction of the plastic zone radius at small stress intensities, whereas the converse was true at high stress intensities.
418
Evers, Smith, and Michel
FIG. 6. Scanning electron micrographs of the fracture surface of type 316 stainless steel tested at 593°C. The crack lengths are (a) 0 mm, (b) 6.2 mm, (c) 16.3 mm, and (d) 26.4 ram. The direction of crack propagation was from left to right.
Fatigue Crack Deformation in T316SS
Fie. 6. (Continued)
4|9
420
Evers, Smith, and Michel TABLE 1
Ratio of the High Hardness Zone Radius to the Plastic Zone Radius for 316 Steel Crack length (mm)
AK (MPa m t/2)
r' (ram)
r(calculated) (ram)
(r'/r)
f
6.2 16.3 26.4
21.8 33.0 54.9
0.4 0.4 0.4
1.7 4.0 11.0
0.23 0.10 0.04
It is well known that the increase in microhardness produced by the deformation of materials can be directly related to an increase in dislocation density. The microhardness increment AH in the high hardness zone can be evaluated from [7] A H = Hcl - nmatrix ,
(3)
where Hcl is the hardness value at a given crack length and Hmatrix is the hardness value of the matrix material (GPa). Since the individual values of Hd are related to the square root of the dislocation density, the expression for the microhardness increment can be rewritten [7] An
= 6alxb(V~pd
-
X/Pmatrix) ,
(4)
where a is the loop cluster barrier parameter (a = 0.5), ~ is the shear modulus (at 25°C Ix = 77 GPa), b is the Burgers vector (b = 2.54 x 10 -8 cm), p~ is the dislocation density at a given crack length, and Pmatrix is the matrix dislocation density outside the plastic zone (2 x 109 cm/cm2). TABLE 2
Hardness Values and Calculated Dislocation Densities at Various Crack Lengths Beneath the Center of the Fracture Surface of 316 Steel Crack length
Hd
Hmatrix
(mm)
(kg/mm :)
(kg/mm 2)
6.2 16.3 26.4
199 283 307
6.2 16.3 26.4
186 207 240
AH (GPa)
Dislocation density (cm/cm 3) calculated
measured
measured 12]
0.025 mm beneath the fracture surface 175 175 175
0.235 1.058 1.274
7.2 x 109 5.0 x 101° 6.8 x 10 l°
----
m
0.150 mm beneath the fracture surface 175 175 175
0.108 0.314 0.637
4.0 x 109 9.6 x 109 2.4 x 10 I°
1.1 × 10 I° 3.7 x 10 I° --
-4 × 10 t° --
Fatigue Crack Deformation in T316SS
421
Using Eq. (4) and the parameter values for type 316 stainless steel, the value of the dislocation density pcl at any crack length may be calculated. The calculated dislocation densities and hardness values at two locations beneath the fracture surface are summarized in Table 2. The results show that the dislocation densities were highest near the fracture surface and increased for successively longer specimen crack lengths. Comparison of the calculated results in Table 2 with the previously reported TEM results from specimens tested similarly to those used in this work [2] and with the TEM results from the present specimens examined in an identical manner shows that the calculated dislocation densities are in reasonable agreement with the experimentally measured values at equivalent x-y locations. It is important to note that the overall relationship between microhardness level and crack length observed within the high hardness zone was evident in the material within the calculated plastic zone. This may be seen from Fig. 5 for those measurements taken at distances from the crack surface greater than approximately 0.4 mm for all three specimen crack lengths. In this region the relatively constant microhardness level of each respective specimen increases for successively longer crack lengths. This suggests that the dislocation densities within the plastic zone reflect the same relationship with the crack length as the dislocation densities in the immediate vicinity of the crack surface.
Summary and Conclusions Microhardness measurements were made to determine the extent of plastic deformation as a function of crack length and specimen width and depth. The microhardness level directly reflects the dislocation substructure at any stress level, and the results provide further evidence of a direct relationship between the crack propagation mechanism and the substructure developed during elevated temperature fatigue crack propagation. The specific conclusions to be drawn from this study are as follows: 1. Deformation produced by the fatigue crack propagation in type 316 stainless steel at 593°C is highly localized in the immediate vicinity of the crack surface. 2. The region of localized deformation or maximum hardness change occurred within 0.4 mm of the fracture surface and remained relatively independent of crack length. 3. The localized deformation is a decreasing fraction of the calculated plastic zone size as a function of crack length.
Evers, Smith, and Michel
422
. T h e d i s l o c a t i o n d e n s i t i e s c a l c u l a t e d f r o m the m i c r o h a r d n e s s r e s u l t s a r e in r e a s o n a b l e a g r e e m e n t w i t h t h e m e a s u r e d v a l u e s f r o m p r e v i o u s T E M work on related specimens.
The authors express their appreciation to C. D. Beachem for assistance with the interpretation of the scanning electron micrographs. The authors also wish to acknowledge the helpful assistance of E. Woodall, Jr., in the crack propagation testing. This research was supported by the Office of Naval Research and was performed while one of the authors (G.R.E.) was a Junior Fellow at the Naval Research Laboratory.
References 1. D. J. Michel and H. H. Smith, Effect of hold time on elevated temperature fatigue crack propagation in Types 304 and 316 stainless steel, in Creep Fatigue Interaction, MPC-3 (R. M. Curran, ed.), American Society for Mechanical Engineers, New York (1976), pp. 391-415. 2. D. J. Michel and H. H. Smith, Observations of the dislocation substructure produced by elevated temperature fatigue crack propagation in Type 316 stainless steel, Eng. Fracture Mech. 9:925-930 (1977). 3. C. Bathias and R. M. Pelloux, Fatigue crack propagation in martensitic and austenitic steels, Met. Trans. 4:1265-1273 (1973). 4. A. G. Pineau and R. M. Pelloux, Influence of strain-induced martensitic transformation of fatigue crack growth rates in stainless steels, Met. Trans. 5:1103-1112 (1974). 5. G. T. Hahn, R. G. Hoagland, and A. R. Rosenfield, Local yielding attending fatigue crack growth, Met. Trans. 3:1189-1202 (1972). 6. J. Lankford, D. L. Davidson, and T. S. Cook, Fatigue crack tip plasticity, cyclic stressstrain and plastic deformation of fatigue crack growth, ASTM STP 637, American Society for Testing and Materials, Philadelphia (1977), pp. 36-55. 7. H. H. Smith and D. J. Michel, The effect of irradiation on the fatigue and flow behavior of TZM alloy, J. Nuclear Mater. 66:125-142 (1977).
Received March 1982; accepted May 1982
METALLOGRAPHY 15:409-422 (1982)
Deformation Produced by Elevated Temperature Fatigue Crack Propagation in Type 316 Stainless Steel
GLENN R. EVERS, HUGH H. SMITH, AND DAVID J. MICHEL
Thermostructural Materials Branch, Material Science and Technology Division, Naval Research Laboratory, Washington, D.C. 20375
The extent and nature of the plastic deformation developed by fatigue crack propagation in type 316 stainless steel at 593°C was investigated using microhardness techniques. Microhardness measurements were made to determine the extent of plastic deformation within the plain strain plastic zone for three specimens tested to different predetermined crack lengths. Extensive plastic deformation was found to be present in a localized envelope that surrounded the crack, and the evolution and shape of this highly strained region was characterized on a three-dimensional scale. The results indicate that the greatest change in microhardness occurred within 0.4 mm of the fracture surface for all specimens and decreased to a constant value dependent upon crack length for each specimen in the plastic zone. Dislocation densities calculated from the microhardness results were consistent with results based on transmission electron microscopy. The results provide additional information concerning the relationship between the crack propagation process and microstructure as a function of crack length.
Introduction The austenitic stainless steels are candidate materials for internal structural components of advanced nuclear energy systems. Although the fatigue crack propagation behavior and failure mode of these materials have been extensively investigated at elevated temperatures, the deformation substructure produced during cyclic and combined cyclic-static loading and its effect on crack propagation mechanisms have received less attention [1, 2]. The existence of a heavily strained region beneath the fatigue fracture surface has been well established for austenitic steels [2-4] and Fe-3 Si steel [5]. A summary of fatigue crack tip plasticity for a variety of other alloys as compared to austenitic steels is provided by Lankford et al. [6]. Despite the small size of the heavily strained region and its inaccessibility, several techniques have been proposed, including the use of elec© Elsevier Science Publishing Co., Inc., 1982 52 Vanderbilt Ave., New York, NY 10017
0026-0800/82/040409 + 14502.75
410
Evers, Smith, and Michel
tron microscopy, the x-ray microbeam, the Moir6 technique, etching, and microhardness measurements [6]. Of the five methods previously described, the measurement of microhardness is a relatively simple and accurate indication of work hardening in austenitic steels [3]. The present study was designed to investigate the relationship between elevated temperature crack propagation behavior and the deformation produced by the crack propagation mechanisms. This report presents the results of microhardness studies to define the shape of the cyclic deformation zone and to determine quantitative hardness numbers as functions of location within this deformation zone. Procedure The chemical composition of the 316 stainless steel used in this study has been given by Michel and Smith [1]. Three single-edge-notch cantilever specimens (6.35 cm x 5.08 cm x 1.27 cm), with side grooves machined to a depth of 5% of the specimen thickness, were given a solution anneal for 1 hr at 1093°C in a vacuum of 1 x 10 -.5 Torr and subsequently furnace cooled. The specimens were tested with a sawtooth loading sequence at I0 cycles/min in air at 593°C using induction heating. During testing the crack length was measured at the side groove using a traveling microscope. Each of the three specimens was run to different predetermined crack lengths of 6.2, 16.3, and 26.4 mm as measured from the notch tip. The crack length was plotted versus the number of cycles to obtain crack growth rates da/dN, which were correlated with the crack tip stress intensity factor range AK. After testing, three sections perpendicular (x-z plane) to the crack surface (y-z plane) and one section ahead of the crack tip were cut from each specimen according to the coordinate system in Fig. 1. Sample preparation for microhardness testing was accomplished by mechanical polishing followed by an etch-polish-etch sequence using Kalling's reagent [2.5 g CuCIz, 100 ml HCI, 100 ml ethanol (95%), and 100 ml H20]. The microhardness of each section was surveyed using a diamond pyramid microhardness (DPH) indentor with a I00 g load. All microhardness measurements were made between 0.025 and 50 mm beneath the fracture surface. Five measurements (approximately 0.025 mm apart) were averaged to determine the reported microhardness values. Grain boundaries were avoided in the measurement process. Because of possible timedependent thermal aging effects, microhardness measurements were taken of unstressed matrix material for each specimen. Although the effects of stress on the thermal aging process are uncertain, the hardness
Fatigue Crack Deformation in T316SS
411
FIG. 1. Schematic representation of single-edge-notch cantilever fatigue specimen and the orthogonal system used to define the location of post-test measurements.
results indicated that the contribution of thermal aging to the overall hardness level of the unstressed matrix was insignificant. The specimen microhardness profiles were used to calculate a composite average of microhardness as a function of crack length and specimen width at two locations beneath the crack surface (0.025 and 0.15 mm). It should be noted that these locations are within the calculated plastic zone size for the particular crack length. Scanning electron microscopy (SEM) was used to investigate the crack propagation mode of the fatigue specimens. Specimen sections containing the crack surface were prepared from the portion of the fatigue specimens not used for microhardness measurements. The specimen sections were examined at the centerline of the crack surface (midthickness of the specimen) starting at the root of the machined notch. In addition, transmission electron microscopy (TEM) foils for dislocation density measurement were prepared from selected specimen sections following the SEM study. Previously detailed procedures were followed for TEM specimen preparation and examinations [2]. Results Figure 2 illustrates the fatigue crack growth rate da/dN in air at 593°C for type 316 stainless steel tested to final crack lengths of 6.2, 16.3, and 26.4 mm. Figure 2 shows that the results from all specimens fell on the same crack growth rate curve, indicating a high degree of reproducibility. The results were found to be consistent with similar data by Michel and Smith [1]. Figure 2 also shows that the shape of the crack growth rate curves was independent of the final crack length. This was expected in view of the fact that the crack growth process is a continuous occurrence. Figure 3 shows a two-dimensional view of the composite average mi-
Evers, Smith, and Michel
412 KSI 10
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STRESS INTENSITY FACTOR RANGE, AK, MPa,J-~ FIG. 2. The fatigue crack growth curve for solution annealed type 316 stainless steel at 593°C s h o w s a close agreement of growth rates for specimens tested to three crack lengths: O, 6.2 ram; rq, 16.3 mm; and A, 26.4 mm.
crohardness as a function of crack length and as a function of depth beneath the fracture surface. It has been well established that the material that is closest to the propagating crack receives the greatest amount of work hardening [2] and that as the crack propagates a large stress zone is formed that also increases the work hardening [3]. This stress zone is
Fatigue Crack Deformation in T316SS
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CRACK LENGTH, rnm FIG. 3. Microhardness as a function of crack length (©, 6.2 mm; [], 16.3 mm; ~, 26.4 ram) for annealed 316 stainless steel tested at 593°C. Measurement location was along the specimen center line (z = 0) at the indicated distances from the crack surface. The diamond symbols indicate the microhardness values ahead of the crack tip at a distance of 28 mm from the notch.
414
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DISTANCE FROM SPECIMEN CENTERLINE, mm FIG. 4. Three-dimensional microhardness profile as a function of depth beneath the fracture surface for specimen crack lengths 6.2 mm (©), 16.3 mm (rq), and 26.4 mm (A).
commonly referred to as the plastic zone. Recent studies [3] also indicate that there is a region of high strain hardening that accompanies the crack, referred to as the high hardness region or the reversed plastic zone. Figure 3 shows that there was a drastic increase in hardness (y direction)just beneath the fracture surface (0.025 mm) as the crack length increased. In contrast, the change in hardness as a function of crack length was not as pronounced at a further distance beneath the crack surface (0.15 mm), and, at a distance of 0.4 mm beneath the crack surface, the change in hardness as a function of crack length was negligible. As the crack propagated through the material, the greatest zone of deformation occurred
Fatigue Crack Deformation in T316SS
415
immediately parallel to the crack (y-z plane), and there was a sharp drop in hardness directly ahead of the crack tip (y axis). The sharp drop of hardness indicated that the work hardening was extremely localized at the crack tip. This was consistent with most models that characterize the area of the plastic zone as blunt and small just ahead of the crack tip [3]. Figure 4 illustrates a three-dimensional microhardness profile based on the composite average from the three specimens. The hardness is seen to have decreased from the center of the specimen to the edges (z axis), consistent with the contour of the plastic zone. Although the high hardness region was significantly smaller than the plastic zone, the shape of the high hardness region dictates the shape of the plastic zone. The greatest change of hardness beneath the crack surface was within a 0.4 mm band that was parallel and beneath the surface, regardless of crack length. Beyond this region the change of hardness in the plastic zone was moderate, and beyond the plastic zone the hardness change was negligible (elastic region). The radius r' of the high hardness zone was easily distinguished by determining where the slope of a curve of hardness versus distance changed rapidly. Figure 5 illustrates this type of curve by presenting a plot of microhardness versus distance beneath the crack surface at three crack lengths (z -- 0, x axis). At a crack length of 6.2 mm the change of microhardness was not as pronounced as the change of microhardness at a crack length of 26.4 mm for equivalent distances beneath the crack surface. Beyond a distance of 0.4 mm, the slope of the microhardness curve was relatively constant at all three crack lengths, and this point was taken as the boundary of the high hardness zone (Fig. 4). However, the constant slope of the microhardness curve prevented the location of the plastic zone radius r at a distance greater than 0.4 mm. Figure 6 presents four SEM micrographs taken from the fatigue specimen tested to a crack length of 26.4 mm. The fractographic features shown in Fig. 6 are representative of the corresponding specimens tested regardless of final crack length (i.e., 6.2, 16.3, or 26.4 mm). The micrographs in Fig. 6 illustrate a predominantly transgranular fracture mode, interspersed with intergranular facets. The transgranular failure occurred by cleavage, as evidenced by "river" patterns that run parallel to the direction of crack propagation (seen in Fig. 6). Secondary cracks can be clearly seen in Fig. 6(c) near striations that roughly outline the crack front (light region). These situations became heavily covered with oxide, which created a "mud cracked" appearance. Coarse, but easily defined, striations were formed during fast fracture [Fig. 6(d)], and dimples were initiated at the interface of large particles and the matrix.
Evers, Smith, and Michel
416
330 [
,,,
30O
250 A
.1a. a
. . . .
20O
°
q~ iii Z
a
Ix:
<
l,g----..-
150
DX
"I0 nr
100
50--
0
I .1
I .2
I .3
I .4
I .5
I .6
I .7
I .8
I .9
1 1.0
1.1
DISTANCE FROM CRACK SURFACE, mm FIG. 5. Microhardness as a function of depth beneath the fracture surface for annealed 316 stainless steel. Measurement location was along the specimen center line at the indicated crack lengths (O, 6.2 ram; 7q, 16.3 mm; A, 26.4 mm).
Fatigue Crack Deformation in T316SS
417
Discussion The results of this study confirm that the deformation associated with fatigue crack propagation is highly localized to the material immediately adjacent to the fracture surface. Further, since the microhardness level reflecting the deformation defines the spatial extent of the plastic zone, the results show the relationship between the plastic zone size and the crack length through the stress intensity. The plastic zone size r and the stress intensity factor AK are related according to [6] r = ~
,
(1)
where r is the plastic zone radius (m), AK the stress intensity (MPa ml/2), and (rys the yield stress (at 593°C gys = 120.7 MPa). Therefore, the plastic zone size increases with the increase in stress intensity factor as a function of crack length. Within the plastic zone, however, the size of the region of highest deformation or "high hardness zone," r', has not been quantitatively defined for 316 stainless steel. Bathias and Pelloux have [3] reported that the size of this zone, perpendicular to the direction of crack propagation (x-z plane; see Fig. l), is simply a fraction of the plastic zone size. However, the present results suggest that for 316 stainless steel the greatest amount of deformation occurred within a relatively constant distance beneath the fracture surface, 0.4 mm, regardless of crack length. This value was approximately the same as the observed value, 0.5 mm, for a comparable austenitic 16-13 steel [3] and the calculated value, 0.7 mm, for 316 stainless steel using dislocation densities [2]. The relationship between plastic zone size and the high hardness zone size is
f = r'/r,
(2)
where f is the size fraction, r' is the radius of the high hardness zone (mm), and r is the radius of the plastic zone (mm). Table 1 presents a summary of the high hardness zone size fraction at the three crack lengths and the corresponding stress intensities AK. The results in Table l show that the high hardness zone radius was a large fraction of the plastic zone radius at small stress intensities, whereas the converse was true at high stress intensities.
418
Evers, Smith, and Michel
FIG. 6. Scanning electron micrographs of the fracture surface of type 316 stainless steel tested at 593°C. The crack lengths are (a) 0 mm, (b) 6.2 mm, (c) 16.3 mm, and (d) 26.4 ram. The direction of crack propagation was from left to right.
Fatigue Crack Deformation in T316SS
Fie. 6. (Continued)
4|9
420
Evers, Smith, and Michel TABLE 1
Ratio of the High Hardness Zone Radius to the Plastic Zone Radius for 316 Steel Crack length (mm)
AK (MPa m t/2)
r' (ram)
r(calculated) (ram)
(r'/r)
f
6.2 16.3 26.4
21.8 33.0 54.9
0.4 0.4 0.4
1.7 4.0 11.0
0.23 0.10 0.04
It is well known that the increase in microhardness produced by the deformation of materials can be directly related to an increase in dislocation density. The microhardness increment AH in the high hardness zone can be evaluated from [7] A H = Hcl - nmatrix ,
(3)
where Hcl is the hardness value at a given crack length and Hmatrix is the hardness value of the matrix material (GPa). Since the individual values of Hd are related to the square root of the dislocation density, the expression for the microhardness increment can be rewritten [7] An
= 6alxb(V~pd
-
X/Pmatrix) ,
(4)
where a is the loop cluster barrier parameter (a = 0.5), ~ is the shear modulus (at 25°C Ix = 77 GPa), b is the Burgers vector (b = 2.54 x 10 -8 cm), p~ is the dislocation density at a given crack length, and Pmatrix is the matrix dislocation density outside the plastic zone (2 x 109 cm/cm2). TABLE 2
Hardness Values and Calculated Dislocation Densities at Various Crack Lengths Beneath the Center of the Fracture Surface of 316 Steel Crack length
Hd
Hmatrix
(mm)
(kg/mm :)
(kg/mm 2)
6.2 16.3 26.4
199 283 307
6.2 16.3 26.4
186 207 240
AH (GPa)
Dislocation density (cm/cm 3) calculated
measured
measured 12]
0.025 mm beneath the fracture surface 175 175 175
0.235 1.058 1.274
7.2 x 109 5.0 x 101° 6.8 x 10 l°
----
m
0.150 mm beneath the fracture surface 175 175 175
0.108 0.314 0.637
4.0 x 109 9.6 x 109 2.4 x 10 I°
1.1 × 10 I° 3.7 x 10 I° --
-4 × 10 t° --
Fatigue Crack Deformation in T316SS
421
Using Eq. (4) and the parameter values for type 316 stainless steel, the value of the dislocation density pcl at any crack length may be calculated. The calculated dislocation densities and hardness values at two locations beneath the fracture surface are summarized in Table 2. The results show that the dislocation densities were highest near the fracture surface and increased for successively longer specimen crack lengths. Comparison of the calculated results in Table 2 with the previously reported TEM results from specimens tested similarly to those used in this work [2] and with the TEM results from the present specimens examined in an identical manner shows that the calculated dislocation densities are in reasonable agreement with the experimentally measured values at equivalent x-y locations. It is important to note that the overall relationship between microhardness level and crack length observed within the high hardness zone was evident in the material within the calculated plastic zone. This may be seen from Fig. 5 for those measurements taken at distances from the crack surface greater than approximately 0.4 mm for all three specimen crack lengths. In this region the relatively constant microhardness level of each respective specimen increases for successively longer crack lengths. This suggests that the dislocation densities within the plastic zone reflect the same relationship with the crack length as the dislocation densities in the immediate vicinity of the crack surface.
Summary and Conclusions Microhardness measurements were made to determine the extent of plastic deformation as a function of crack length and specimen width and depth. The microhardness level directly reflects the dislocation substructure at any stress level, and the results provide further evidence of a direct relationship between the crack propagation mechanism and the substructure developed during elevated temperature fatigue crack propagation. The specific conclusions to be drawn from this study are as follows: 1. Deformation produced by the fatigue crack propagation in type 316 stainless steel at 593°C is highly localized in the immediate vicinity of the crack surface. 2. The region of localized deformation or maximum hardness change occurred within 0.4 mm of the fracture surface and remained relatively independent of crack length. 3. The localized deformation is a decreasing fraction of the calculated plastic zone size as a function of crack length.
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. T h e d i s l o c a t i o n d e n s i t i e s c a l c u l a t e d f r o m the m i c r o h a r d n e s s r e s u l t s a r e in r e a s o n a b l e a g r e e m e n t w i t h t h e m e a s u r e d v a l u e s f r o m p r e v i o u s T E M work on related specimens.
The authors express their appreciation to C. D. Beachem for assistance with the interpretation of the scanning electron micrographs. The authors also wish to acknowledge the helpful assistance of E. Woodall, Jr., in the crack propagation testing. This research was supported by the Office of Naval Research and was performed while one of the authors (G.R.E.) was a Junior Fellow at the Naval Research Laboratory.
References 1. D. J. Michel and H. H. Smith, Effect of hold time on elevated temperature fatigue crack propagation in Types 304 and 316 stainless steel, in Creep Fatigue Interaction, MPC-3 (R. M. Curran, ed.), American Society for Mechanical Engineers, New York (1976), pp. 391-415. 2. D. J. Michel and H. H. Smith, Observations of the dislocation substructure produced by elevated temperature fatigue crack propagation in Type 316 stainless steel, Eng. Fracture Mech. 9:925-930 (1977). 3. C. Bathias and R. M. Pelloux, Fatigue crack propagation in martensitic and austenitic steels, Met. Trans. 4:1265-1273 (1973). 4. A. G. Pineau and R. M. Pelloux, Influence of strain-induced martensitic transformation of fatigue crack growth rates in stainless steels, Met. Trans. 5:1103-1112 (1974). 5. G. T. Hahn, R. G. Hoagland, and A. R. Rosenfield, Local yielding attending fatigue crack growth, Met. Trans. 3:1189-1202 (1972). 6. J. Lankford, D. L. Davidson, and T. S. Cook, Fatigue crack tip plasticity, cyclic stressstrain and plastic deformation of fatigue crack growth, ASTM STP 637, American Society for Testing and Materials, Philadelphia (1977), pp. 36-55. 7. H. H. Smith and D. J. Michel, The effect of irradiation on the fatigue and flow behavior of TZM alloy, J. Nuclear Mater. 66:125-142 (1977).
Received March 1982; accepted May 1982