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Implications of recent developments in the plastic fracture mechanics field to the pci stress corrosion problem
Journal of Nuclear Materials 95 (1980) 285-289 D North-Holland Publishing Company
IMPLICATIONS OF RECENT DEVELOPMENTS TO THE PC1 STRESS CORROSION PROBLEM
IN THE PLASTIC FRACTURE
MECHANICS FIELD
E. SMITH Joint Manchester University/UMISTMetalIurgy Department, Grosvenor Street, Manchester, MI 7HS, UK Received 8 April 1980
Fractographic observations on irradiated Zircaloy cladding stress corrosion fracture surfaces are considered against the background of recent developments in the plastic fracture mechanics field. Dimples have been observed on the fracture surfaces of failed cladding, even though the cracks in metallographic sections are tight, i.e., crack propagation is associated with a low crack tip opening angle. This result is interpreted as providing evidence for an environmentally assisted ductile mode of fracture. The presence of this fracture mode forms the basis of an argument, which adds further support for the view that power ramp stress corrosion cladding failures are caused by stress concentrations that produce stress gradients in the cladding.
display evidence for the operation of a ductile fracture process. If this crack propagation process were to be purely ductile, i.e. the environment has no effect, one would have expected a significant CTOA (-lo’), even though irradiated Zircaloy deforms inhomogeneously by channel mechanisms; such a CTOA is observed with the fracture of materials such as stainless and ferritic steels, which have a ductility similar to irradiated Zircaloy. The author accordingly believes that when Zircaloy fracture is associated with dimple formation and also a low CTOA, the likely explanation is that the conditions for ductile fracture initiation are satisfied, whereas the conditions for purely ductile fracture propagation are not satisfied. Instead, the environment, in this case iodine, enables the crack to grow by a timedependent environmentally assisted ductile fracture mode, which is associated with a low CTOA. Recent work in the plastic fracture mechanics field has focused particularly on the difference between initiation and propagation of ductile fracture. It is now recognized that for a crack to propagate by a purely ductile fracture mechanism, the J integral, or equivalently the crack tip opening displacement (CTOD), must exceed critical values which increase progressively with the amount of crack
1. Introduction When irradiated Zircaloy cladding tubes are subjected to an internal pressure in an iodine environment, the radial stress corrosion cracks observed in metallographic sections are always tight [ 11, i.e. crack propagation is associated with a very small crack tip opening angle CTOA (-1’ or less). (CTOA is the angle between the opposite faces of the crack, as measured near its tip.) Despite the tightness of the cracks, fracture surfaces exhibit large areas of ductile failure. The cracks found in fuel rod cladding that has been subject to a sufficiently severe power ramp are similarly tight; in this case the fission product iodine is generally believed to be a vital ingredient in the cracking process. Furthermore, a recent detailed fractographic examination [2-43 of incipient cracks in power ramped fuel rods has clearly distinguished between a region of elongated dimples associated with cracking during the ramp, and another more equiaxed dimpled region which is associated with the non-environmentally assisted breaking-open of the cladding for examination. The preceding observations allow one to conclude that cracks can propagate in irradiated Zircaloy with a low crack tip opening angle and produce minimal thinning of the cladding, yet 285
286
6. Smith / I\‘ecetlt dewlopmet~ts in the plastic fbacture mechanics field
growth (51. (CTOD is the relative displacement of the opposite faces of the crack, as measured near the tip, required for the onset of fracture.) If the system loading does not allow the material’s J or CTOD resistance curve to be met during growth, i.e. it is impossible to maintain a critical CTOA (characteristic of the material) during growth, purely ductile crack growth cannot occur; in l~articular, unstable ductile fracture cannot occur. With irradiated Zircaloy tubes that are internally pressurized, the author therefore believes that the sequence of events at a prescribed stress level commences with intergranular fracture. This is followed by environmentally assisted cleavage fracture (plus fluting) until the crack attains a sufflcient depth for dimpled fracture to be initiated at the crack tip. However, the system loading is such that unstable ductile fracture, associated with a large instead environmentally CTOA, cannot occur; assisted ductile fracture, associated with a small CTOA, proceeds in a stable manner across the cladding thickness until a through-thickness crack is formed. This paper develops this viewpoint quantitatively, and the implications are discussed with regard to the general problem of Zircaloy stress ‘corrosion cracking, caused by the power-ramping of watercooled reactor fuel rods. The next section analyses models that are essentially continuu~~l based, though recognizing that plastic deformation proceeds in an inhomogeneous manner by channel mechanisms; this behaviour is averaged in the models.
2. Analysis Scanning electron microscope (SEM) observations [l] on the fracture surfaces of irradiated Zircaloy tubes that have been pressurized in an iodine environment, show that cracks have an approximately semi-elliptical shape at each stage of crack propagation. The major axis is parallel to the tube axis and the minor axis is parallel to the thickness direction, whiIe a hoop tensile stress acts perpendicular to the crack plane. It will first be demonstrated that plastic deformation must spread across the ligament between the crack front and the outer surface, in order for ductile fracture to be initiated at the crack front. Thus, consider the model (fig. 1) of a panel of width h (simulating the tube wall thickness) containing an
(I
a
t
t_
4--c-
a-
*
4
h
L
--
Fig. 1. The two-dimensional model of a pane1 of width h containing an edge crack of depth c; the panel is subject to a tensile stress 0.
edge crack of depth c; the panel is subject to a tensile stress u, which simulates the hoop stress in the tube. For the purposes of this part of the paper’s analyses, the crack is assumed to be in~nitely long in the direction of the figure normal; the problem therefore becomes two-dimensional, and the Bilby-CottrellSmith-Swinden (BCSS) results [6] for a periodic sequence of coplanar cracks contained within an infinite solid should be adequate. Plastic yield is represented by a strip yield zone ahead of the crack tip (see fig, 1). If the stress within this zone is maintained at a constant value Y, representative of the material’s tensile yield stress, the BCSS analysis shows that the maximum crack tip opening displacement + max that can be sustained at the crack tip without the yield zone spreading across the ligament, is @ max -7
Y I:
h
where E is the Young modulus of the cladding. With typical values for irradiated Zircaloy at -600 K: 700 MN/m2 (-100 ksi), 70 X IO3 MN/m2 (-lo4 ksi), and h = 700 pm, eq. (1) gives G,, - 7 pm. Since the grain size is typically lo-20 ym, the crack tip displacement @rc required to initiate dimpled ductile
E. Smith /Recent
devebpments
287
in the plastic fracture mechanics field
-2bFig. 2. The model of a pit-through
crack and associated strip yield regions.
fracture should not be as low as 7 pm. indeed the Krc value corresponding to this displacement is “’ 15 MPa 9 ml’* (-15 ksi din), KIC - (~Y~lC) which is unrealistically low for a material that is as inherently ductile as irradiated Zircaloy, It is therefore concluded that yield must have spread across the ligament between the crack front and the outer surface, for ductile fracture to be initiated at the crack tip. In the model in fig. 1, it has been assumed that the crack is infinitely long in the direction of the figure normal, which simulates the tube axis. It will now be shown that the actual crack length in this direction must exceed a critical length for ductile fracture to be initiated at the crack front. To demonstrate this point, the part-through crack and associated strip yield regions are modelled as in fig. 2, remembering that it has already been shown that plastic deformation must have spread across the ligament. If the restraining force provided by the yielded ligament is smeared across the surface of a throu~-thic~ess crack of length 2b, the average restraining stress is Y(l y c/h). Application of the Bilby-CottrellSwinden (BCS) results [7] for a throu~~rack in an infinite panel then gives the displacement # at the crack centre as:
earlier in this section. These results clearly show that crack tip displacements sufficient for the initiation of ductile (dimpled) fracture can be attained, provided the crack is sufficiently long in the direction of the tube axis, i.e. provided b is sufficiently large. For example, with a critical crack tip opening displacement 20 pm, ductile fracture will be initiated at low stress levels (o/Y - 0.4), if the crack length is five times the cladding thickness; much shorter crack lengths are required at higher stress levels. The preceding simple analyses therefore provide quantitative support for the view that ductile (dimpled) fracture can be initiated at a propagating stress corrosion crack tip before the crack traverses the cladding thickness. To assess whether or not the crack then immediately becomes unstable by a purely ductile mechanism in the constant pressure situation, use is made of Paris and co-workers’ results [5]. When the applied stress u is less than the yield stress Y, as it is with the irradiated tube experiments [ 11, they have shown that a deep part-through cracks should not propagate unstably. Their arguments are based on calculations which show that the applied dJ/dc value for ductile crack propagation across the remaining
77 o- Y(1 -c//z) 8Yb cash-’ set 2’ y _ Y(l _ cam) . at - I&
Table 1 ~/(2~/~) for various applied streses fo) and crack depths (c); 9 is the crack tip displacement
(2)
This value can be used [5] as an estimate for the displacement at the tip (position C) of a part-through crack of depth c. Noting that o a Y(l - c/h) for ligament yield, relation (2) gives (b for different applied stress levels and for various crack depths (c) and lengths (b). Table 1 shows the results, using the same input values of Y, E and h as have been used
0.8 0.6 0.4
0.4
0.6
0.8
4 _
9 6 -
16 13 9
ligament is appreciably less than ti/dc values obtained from J versus crack growth resistance curves for ductile materials. Assuini~?g that this bellav~our is applicable to part-through cracks in irradiated Zircaloy cladding tubes, it follows that while ductile fracture is able to initiate at the front of a partthrough stress corrosion crack, purely ductile fracture instability should not ensue. This viewpoint accords, of course, with the expe~nlent~ observation [l] that crack propagation is not associated with a large crack tip opening angle. Instead, the author believes that propagation procee,ds stably via an environmentally assisted ductile fracture mode, which is associated with a low crack tip opening angle. The crack presumably grows faster than if there had been no ductile fracture initiation until the crack front reaches the outer surface and a through-thickness crack is formed. In concluding this section, it is worth observing that i~nmediately prior to the initiation of ductife (dimpled) fracture in internally pressurized irradiated tubes, crack propagation proceeds by a mixture of environmentally assisted transgranular cleavage and fluting [l]. In some respects, this fracture mode is similar to the mode already discussed in this section, since fluting refers specificalfy to the plastic rupture of crystals whose basal plane normals are inclined at a large angle to the hoop stress direction, and are therefore unable to cleave so readily [8]. The fluting displacement is expected to be lower than that for dimpled rupture and, from an assessment of experimental results 191, the author has used a value of 4 pm in previous analyses [ 10,l l] . Crack propagation by this mixture of cleavage and fluting is believed to proceed by preferentially oriented grains cleaving, with the remaining ligaments eventually failing by fluting; this gives a damaged region of partially cohesive material at the crack front [ 1 I]. in this respect the fracture is different to environmentally assisted dimpled rupture, for which a combination of two essentially different fracture processes is not anticipated.
3. Discussion The focused
preceding section’s considerations have on pressurized tube experiments in which
irradiated Zircaloy cladding is subjected to a unifornr hoop stress in an iodine environment. The important conclusion is that when tight cracks arc associated with dimpled fracture surfaces, these cracks propagate by an environmentally assisted mechanism and not by a purely ductile mechanism. Crack propagation should be faster than for the cleavage plus fluting mode, although it will not be as rapid as for purely ductile unstable fracture. Because such fracture should be relatively fast, its presence will have only a minor effect on the failure time in tube experiments; indeed, the author believes that the major proportion of the failure time is associated with the early stages of the cracking process, prior to propagation via the fluting and transgranular cleavage mode. However, evidence of environmentally assisted dimpled fracture on fracture surfaces is important, in that it can be used to provide an estimate of the stress levels attained by fuel rod cladding during a power ramp. A recent SEM examination [2--41 of incipient cracks in power-ramped fuel rods has clearly shown two different dimpled regions: a region of elongated dimples, associated with crack propagation during the power transient, and another region of more equiaxed dimples, which is associated with the nonenvironmentally assisted breaking-open of the cladding for examination purposes. The incipient cracks in metallographic sections are tight. In the light of this paper’s considerations, it is therefore concluded that the elongated dimples are a manifestation of stable environmentally assisted ductile crack growth. The elongated dimples appeared when the cracks had propagated to a depth of --11/4 (h is the cladding thickness) by intergranular fracture followed by transgranular cleavage plus fluting fracture. If one proceeds on the basis that the power ramp generates a un~forIn cladding stress, the pr-eceding section’s analysis suggests that plastic deformation must have spread across the ligament between the crack front and the outer surface; more imporantly, the hoop stress must have been high -Y(i - l/4) - SY/4. However, fuel rod code predictions for cladding subjected to ramps simiiar to those used for the incipiently cracked rods, give uniform stresses that are considerably smaller than -3 Y/4; these predictions are based on the assumption that there are no stress concentrations. In the light of this apparent inconsistency, the idea of a uniform cladding stress must be
E. Smith /Recent
developments
abandoned. It is therefore concluded that locally high regions of stress play a major role in the formation of dimples, i.e. the initiation of ductile fracture, on fuel rod fracture surfaces. This conclusion reinforces the author’s earlier view [lo] that power ramp cladding failures are generally associated with high local stresses. Stress concentrations will arise from pellet relocation effects, cladding ridges associated with pellet-pellet interfaces, and also fuel-pellet cracks. The latter are expected to be a particularly important source of cladding stress concentrations, provided the fuel-cladding interfacial friction coefficient is sufficiently large. The existence of stress concentrations has important implications for the development of a cladding failure criterion and its incorporation within an integrated fuel rod code. Thus, the present paper’s observations provide further support for the view that a failure criterion should take into account throughthickness stress gradients associated with stress concentrations. Indeed these concentrations ought to be a central feature of a power ramp cladding failure criterion.
4. Conclusions The paper has discussed certain metallographic features of iodine stress corrosion cracks in internally pressurized tubes of irradiated Zircaloy cladding, against the background of recent developments in the plastic fracture mechanics field. When the cracks are tight, and there are dimples on the fracture surfaces of failed cladding, it is concluded that fracture propagation proceeds by an environmentally assisted ductile mode. The presence of this fracture mode in fuel rods provides further support for the view that power ramp cladding failures’are associated with stress con-
in the plastic fracture mechanics field
centrations which produce gradients in the cladding.
289
through-thickness
stress
Acknowledgement This work was conducted as part of the Electric Power Research Institute Light Water Reactor Fuel Rod Performance Programme, and the author thanks colleagues at EPRI and elsewhere, for fruitful discussions on the PC1 phenomenon over the past few years.
References [l] R.F. Mattas, F.L. Yaggee and L.A. Neimark, in: Proc. ANS Topical Meeting on Light Water Reactor Fuel Performance, Portland, OR, USA (Am. Nucl. Sot. 1979) p. 128. [2] H. Mogard, U. Bergenlid, S. Djurle, E. Larsson, G. Lysell, G. Ronnberg, K. Saltvedt and H. Tomani, in: Proc. ANS Topical Meeting on Light Water Reactor Fuel Performance, Portland, OR, USA, p. 128. [3] Report Studsvik Inter-Ramp Project, STIR-53, AB Atomenergi, Studsvik, Sweden (1979). [4] G. LyselI and S. Birath, Report Studsvik Inter-Ramp Project, STIR-51 (1979). [5] P.C. Paris, H. Tada, A. Zahoor and H. Ernst, Report US Nucl. Regulatory Commission, NUREO311 (1977). [6] B.A. Bilby, A.H. Cottrell, E. Smith and K.H. Swinden, Proc. Roy. Sot. (London) A279 (1964) 1. [7] B.A. Bilby, A.H. Cottrell and K.H. Swinden, Proc. Roy. Sot. (London) A272 (1963) 304. [B] I. Aitchison and B. Cox, Corrosion 28 (1972) 83. [9] D. Cordall, R.M. Cornell, J.W. Jones and J.S. Waddington, Nucl. Technol. 34 (1977) 438. [lo] E. Smith, Paper C4/4 presented at the SMIRT V Conference, Berlin (1979). [ll] E. Smith and A.K. Miller, J. Nucl. Mater. 80 (1979) 291. [12] B. Cox, in: Coatings and Corrosion (Freund, Tel Aviv, 1974) p. 366.
IMPLICATIONS OF RECENT DEVELOPMENTS TO THE PC1 STRESS CORROSION PROBLEM
IN THE PLASTIC FRACTURE
MECHANICS FIELD
E. SMITH Joint Manchester University/UMISTMetalIurgy Department, Grosvenor Street, Manchester, MI 7HS, UK Received 8 April 1980
Fractographic observations on irradiated Zircaloy cladding stress corrosion fracture surfaces are considered against the background of recent developments in the plastic fracture mechanics field. Dimples have been observed on the fracture surfaces of failed cladding, even though the cracks in metallographic sections are tight, i.e., crack propagation is associated with a low crack tip opening angle. This result is interpreted as providing evidence for an environmentally assisted ductile mode of fracture. The presence of this fracture mode forms the basis of an argument, which adds further support for the view that power ramp stress corrosion cladding failures are caused by stress concentrations that produce stress gradients in the cladding.
display evidence for the operation of a ductile fracture process. If this crack propagation process were to be purely ductile, i.e. the environment has no effect, one would have expected a significant CTOA (-lo’), even though irradiated Zircaloy deforms inhomogeneously by channel mechanisms; such a CTOA is observed with the fracture of materials such as stainless and ferritic steels, which have a ductility similar to irradiated Zircaloy. The author accordingly believes that when Zircaloy fracture is associated with dimple formation and also a low CTOA, the likely explanation is that the conditions for ductile fracture initiation are satisfied, whereas the conditions for purely ductile fracture propagation are not satisfied. Instead, the environment, in this case iodine, enables the crack to grow by a timedependent environmentally assisted ductile fracture mode, which is associated with a low CTOA. Recent work in the plastic fracture mechanics field has focused particularly on the difference between initiation and propagation of ductile fracture. It is now recognized that for a crack to propagate by a purely ductile fracture mechanism, the J integral, or equivalently the crack tip opening displacement (CTOD), must exceed critical values which increase progressively with the amount of crack
1. Introduction When irradiated Zircaloy cladding tubes are subjected to an internal pressure in an iodine environment, the radial stress corrosion cracks observed in metallographic sections are always tight [ 11, i.e. crack propagation is associated with a very small crack tip opening angle CTOA (-1’ or less). (CTOA is the angle between the opposite faces of the crack, as measured near its tip.) Despite the tightness of the cracks, fracture surfaces exhibit large areas of ductile failure. The cracks found in fuel rod cladding that has been subject to a sufficiently severe power ramp are similarly tight; in this case the fission product iodine is generally believed to be a vital ingredient in the cracking process. Furthermore, a recent detailed fractographic examination [2-43 of incipient cracks in power ramped fuel rods has clearly distinguished between a region of elongated dimples associated with cracking during the ramp, and another more equiaxed dimpled region which is associated with the non-environmentally assisted breaking-open of the cladding for examination. The preceding observations allow one to conclude that cracks can propagate in irradiated Zircaloy with a low crack tip opening angle and produce minimal thinning of the cladding, yet 285
286
6. Smith / I\‘ecetlt dewlopmet~ts in the plastic fbacture mechanics field
growth (51. (CTOD is the relative displacement of the opposite faces of the crack, as measured near the tip, required for the onset of fracture.) If the system loading does not allow the material’s J or CTOD resistance curve to be met during growth, i.e. it is impossible to maintain a critical CTOA (characteristic of the material) during growth, purely ductile crack growth cannot occur; in l~articular, unstable ductile fracture cannot occur. With irradiated Zircaloy tubes that are internally pressurized, the author therefore believes that the sequence of events at a prescribed stress level commences with intergranular fracture. This is followed by environmentally assisted cleavage fracture (plus fluting) until the crack attains a sufflcient depth for dimpled fracture to be initiated at the crack tip. However, the system loading is such that unstable ductile fracture, associated with a large instead environmentally CTOA, cannot occur; assisted ductile fracture, associated with a small CTOA, proceeds in a stable manner across the cladding thickness until a through-thickness crack is formed. This paper develops this viewpoint quantitatively, and the implications are discussed with regard to the general problem of Zircaloy stress ‘corrosion cracking, caused by the power-ramping of watercooled reactor fuel rods. The next section analyses models that are essentially continuu~~l based, though recognizing that plastic deformation proceeds in an inhomogeneous manner by channel mechanisms; this behaviour is averaged in the models.
2. Analysis Scanning electron microscope (SEM) observations [l] on the fracture surfaces of irradiated Zircaloy tubes that have been pressurized in an iodine environment, show that cracks have an approximately semi-elliptical shape at each stage of crack propagation. The major axis is parallel to the tube axis and the minor axis is parallel to the thickness direction, whiIe a hoop tensile stress acts perpendicular to the crack plane. It will first be demonstrated that plastic deformation must spread across the ligament between the crack front and the outer surface, in order for ductile fracture to be initiated at the crack front. Thus, consider the model (fig. 1) of a panel of width h (simulating the tube wall thickness) containing an
(I
a
t
t_
4--c-
a-
*
4
h
L
--
Fig. 1. The two-dimensional model of a pane1 of width h containing an edge crack of depth c; the panel is subject to a tensile stress 0.
edge crack of depth c; the panel is subject to a tensile stress u, which simulates the hoop stress in the tube. For the purposes of this part of the paper’s analyses, the crack is assumed to be in~nitely long in the direction of the figure normal; the problem therefore becomes two-dimensional, and the Bilby-CottrellSmith-Swinden (BCSS) results [6] for a periodic sequence of coplanar cracks contained within an infinite solid should be adequate. Plastic yield is represented by a strip yield zone ahead of the crack tip (see fig, 1). If the stress within this zone is maintained at a constant value Y, representative of the material’s tensile yield stress, the BCSS analysis shows that the maximum crack tip opening displacement + max that can be sustained at the crack tip without the yield zone spreading across the ligament, is @ max -7
Y I:
h
where E is the Young modulus of the cladding. With typical values for irradiated Zircaloy at -600 K: 700 MN/m2 (-100 ksi), 70 X IO3 MN/m2 (-lo4 ksi), and h = 700 pm, eq. (1) gives G,, - 7 pm. Since the grain size is typically lo-20 ym, the crack tip displacement @rc required to initiate dimpled ductile
E. Smith /Recent
devebpments
287
in the plastic fracture mechanics field
-2bFig. 2. The model of a pit-through
crack and associated strip yield regions.
fracture should not be as low as 7 pm. indeed the Krc value corresponding to this displacement is “’ 15 MPa 9 ml’* (-15 ksi din), KIC - (~Y~lC) which is unrealistically low for a material that is as inherently ductile as irradiated Zircaloy, It is therefore concluded that yield must have spread across the ligament between the crack front and the outer surface, for ductile fracture to be initiated at the crack tip. In the model in fig. 1, it has been assumed that the crack is infinitely long in the direction of the figure normal, which simulates the tube axis. It will now be shown that the actual crack length in this direction must exceed a critical length for ductile fracture to be initiated at the crack front. To demonstrate this point, the part-through crack and associated strip yield regions are modelled as in fig. 2, remembering that it has already been shown that plastic deformation must have spread across the ligament. If the restraining force provided by the yielded ligament is smeared across the surface of a throu~-thic~ess crack of length 2b, the average restraining stress is Y(l y c/h). Application of the Bilby-CottrellSwinden (BCS) results [7] for a throu~~rack in an infinite panel then gives the displacement # at the crack centre as:
earlier in this section. These results clearly show that crack tip displacements sufficient for the initiation of ductile (dimpled) fracture can be attained, provided the crack is sufficiently long in the direction of the tube axis, i.e. provided b is sufficiently large. For example, with a critical crack tip opening displacement 20 pm, ductile fracture will be initiated at low stress levels (o/Y - 0.4), if the crack length is five times the cladding thickness; much shorter crack lengths are required at higher stress levels. The preceding simple analyses therefore provide quantitative support for the view that ductile (dimpled) fracture can be initiated at a propagating stress corrosion crack tip before the crack traverses the cladding thickness. To assess whether or not the crack then immediately becomes unstable by a purely ductile mechanism in the constant pressure situation, use is made of Paris and co-workers’ results [5]. When the applied stress u is less than the yield stress Y, as it is with the irradiated tube experiments [ 11, they have shown that a deep part-through cracks should not propagate unstably. Their arguments are based on calculations which show that the applied dJ/dc value for ductile crack propagation across the remaining
77 o- Y(1 -c//z) 8Yb cash-’ set 2’ y _ Y(l _ cam) . at - I&
Table 1 ~/(2~/~) for various applied streses fo) and crack depths (c); 9 is the crack tip displacement
(2)
This value can be used [5] as an estimate for the displacement at the tip (position C) of a part-through crack of depth c. Noting that o a Y(l - c/h) for ligament yield, relation (2) gives (b for different applied stress levels and for various crack depths (c) and lengths (b). Table 1 shows the results, using the same input values of Y, E and h as have been used
0.8 0.6 0.4
0.4
0.6
0.8
4 _
9 6 -
16 13 9
ligament is appreciably less than ti/dc values obtained from J versus crack growth resistance curves for ductile materials. Assuini~?g that this bellav~our is applicable to part-through cracks in irradiated Zircaloy cladding tubes, it follows that while ductile fracture is able to initiate at the front of a partthrough stress corrosion crack, purely ductile fracture instability should not ensue. This viewpoint accords, of course, with the expe~nlent~ observation [l] that crack propagation is not associated with a large crack tip opening angle. Instead, the author believes that propagation procee,ds stably via an environmentally assisted ductile fracture mode, which is associated with a low crack tip opening angle. The crack presumably grows faster than if there had been no ductile fracture initiation until the crack front reaches the outer surface and a through-thickness crack is formed. In concluding this section, it is worth observing that i~nmediately prior to the initiation of ductife (dimpled) fracture in internally pressurized irradiated tubes, crack propagation proceeds by a mixture of environmentally assisted transgranular cleavage and fluting [l]. In some respects, this fracture mode is similar to the mode already discussed in this section, since fluting refers specificalfy to the plastic rupture of crystals whose basal plane normals are inclined at a large angle to the hoop stress direction, and are therefore unable to cleave so readily [8]. The fluting displacement is expected to be lower than that for dimpled rupture and, from an assessment of experimental results 191, the author has used a value of 4 pm in previous analyses [ 10,l l] . Crack propagation by this mixture of cleavage and fluting is believed to proceed by preferentially oriented grains cleaving, with the remaining ligaments eventually failing by fluting; this gives a damaged region of partially cohesive material at the crack front [ 1 I]. in this respect the fracture is different to environmentally assisted dimpled rupture, for which a combination of two essentially different fracture processes is not anticipated.
3. Discussion The focused
preceding section’s considerations have on pressurized tube experiments in which
irradiated Zircaloy cladding is subjected to a unifornr hoop stress in an iodine environment. The important conclusion is that when tight cracks arc associated with dimpled fracture surfaces, these cracks propagate by an environmentally assisted mechanism and not by a purely ductile mechanism. Crack propagation should be faster than for the cleavage plus fluting mode, although it will not be as rapid as for purely ductile unstable fracture. Because such fracture should be relatively fast, its presence will have only a minor effect on the failure time in tube experiments; indeed, the author believes that the major proportion of the failure time is associated with the early stages of the cracking process, prior to propagation via the fluting and transgranular cleavage mode. However, evidence of environmentally assisted dimpled fracture on fracture surfaces is important, in that it can be used to provide an estimate of the stress levels attained by fuel rod cladding during a power ramp. A recent SEM examination [2--41 of incipient cracks in power-ramped fuel rods has clearly shown two different dimpled regions: a region of elongated dimples, associated with crack propagation during the power transient, and another region of more equiaxed dimples, which is associated with the nonenvironmentally assisted breaking-open of the cladding for examination purposes. The incipient cracks in metallographic sections are tight. In the light of this paper’s considerations, it is therefore concluded that the elongated dimples are a manifestation of stable environmentally assisted ductile crack growth. The elongated dimples appeared when the cracks had propagated to a depth of --11/4 (h is the cladding thickness) by intergranular fracture followed by transgranular cleavage plus fluting fracture. If one proceeds on the basis that the power ramp generates a un~forIn cladding stress, the pr-eceding section’s analysis suggests that plastic deformation must have spread across the ligament between the crack front and the outer surface; more imporantly, the hoop stress must have been high -Y(i - l/4) - SY/4. However, fuel rod code predictions for cladding subjected to ramps simiiar to those used for the incipiently cracked rods, give uniform stresses that are considerably smaller than -3 Y/4; these predictions are based on the assumption that there are no stress concentrations. In the light of this apparent inconsistency, the idea of a uniform cladding stress must be
E. Smith /Recent
developments
abandoned. It is therefore concluded that locally high regions of stress play a major role in the formation of dimples, i.e. the initiation of ductile fracture, on fuel rod fracture surfaces. This conclusion reinforces the author’s earlier view [lo] that power ramp cladding failures are generally associated with high local stresses. Stress concentrations will arise from pellet relocation effects, cladding ridges associated with pellet-pellet interfaces, and also fuel-pellet cracks. The latter are expected to be a particularly important source of cladding stress concentrations, provided the fuel-cladding interfacial friction coefficient is sufficiently large. The existence of stress concentrations has important implications for the development of a cladding failure criterion and its incorporation within an integrated fuel rod code. Thus, the present paper’s observations provide further support for the view that a failure criterion should take into account throughthickness stress gradients associated with stress concentrations. Indeed these concentrations ought to be a central feature of a power ramp cladding failure criterion.
4. Conclusions The paper has discussed certain metallographic features of iodine stress corrosion cracks in internally pressurized tubes of irradiated Zircaloy cladding, against the background of recent developments in the plastic fracture mechanics field. When the cracks are tight, and there are dimples on the fracture surfaces of failed cladding, it is concluded that fracture propagation proceeds by an environmentally assisted ductile mode. The presence of this fracture mode in fuel rods provides further support for the view that power ramp cladding failures’are associated with stress con-
in the plastic fracture mechanics field
centrations which produce gradients in the cladding.
289
through-thickness
stress
Acknowledgement This work was conducted as part of the Electric Power Research Institute Light Water Reactor Fuel Rod Performance Programme, and the author thanks colleagues at EPRI and elsewhere, for fruitful discussions on the PC1 phenomenon over the past few years.
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