Zirconium and its alloys (>98% Zr) have hexagonal close packed (hcp) crystal structure and exhibit highly reproducible anisotropic thermal, elastic and plastic properties, due to thermo-mechanical processing route adopted by the industry to fabricate a tube product that meets or exceeds service requirements. Much of the latter credit is due to metal producers and fabricators for their operational culture. Zircaloy-4 (UNS R60804), in particular, is the backbone in-core structural materials in thermal reactors such as CANDU reactors, by virtue of a superior combination of intrinsic properties, such as compatibility with uranium oxide, low neutron absorption cross section, high melting point, good thermal conductivity, low thermal expansion and high temperature creep behavior, Stress-Corrosion Cracking (SCC) resistance, reduced hydrogen uptake and its resulting embrittlement, and oxidation stability.

Pellet-Cladding (sheathing) Mechanical Interactions (PCMI) have been recognized as the cornerstone of major fuel sheathing reliability shortcomings in the form of sheathing service failures since 1970s, at times proving insidious and costly [1] . PCMI origin dates back to the testing of General Electric Vallecitos Boiling Water Reactor using enriched uranium and stainless-steel sheathing material in 1963, and subsequent elucidation that Iodine Stress-Corrosion Cracking (ISCC) was the underlying cause, was published in 1965 [2] . The onset of systemic failures reached a high point, when on-line refuelling in the CANDU-prototype Nuclear Power Demonstration (NPD) reactors and Douglas Point had started in 1969, with further escalation with the start-up of Pickering-1 (the first CANDU full-scale plant) in 1971 [3] . The PCMI has its roots in simultaneous evolution of local chemical and mechanical stresses inside Zircaloy sheathing, physically encapsulating the uranium dioxide fuel (UO₂) pellets, and acting as first full retention barrier between the radioactive fuel and exterior coolants [4] . Under mechanical stress, UO₂ pellet expansion induces a strain-controlled loading on the sheathing at approximately 1 s⁻¹ circumferential strain rate [5] . This phase is referred to as PCMI (Pellet Cladding Mechanical Interaction).

The following synergy of environmentally assisted requirements for the initiation of ISCC in the Zircaloy sheathing have been identified [6] : i) a critical increase in local stress, or strain from UO₂ pellet expansion; ii) a corrosive environment provided by volatile fission products, predominately iodine; iii) a minimum incubation time; and iv) a susceptible material. The spectrum of combined concentration of factors on the ISCC susceptibility of Zircaloy sheathing encompasses a wide range of attributes such as metallurgical state of alloy (composition, strength level, texture, residual stress history in fabrication), in-reactor stress intensity, iodine concentration, oxide layer type and thickness, and irradiation conditions [7] . Iodine escapes from the fuel to the highly radiolytic fuel-sheathing gap through diffusion or thermal cracking and is proportionate to the fission gas release [8] . Iodine isotopes are about 15% of the total U-235 fission isotopes [9] . Both iodine and ZrI₄ are serious ISCC initiating species for Zircaloy-4 [10] . To affect PCMI cracking from the interior, it is generally accepted that volatile fission by-products must be present locally and be above a threshold concentration [11] . The iodine concentration is highest in the fuel-sheathing gap [12] , inducing a subsequent deleterious effect on the mechanical strength of the Zircaloy sheathing [4] [13] . High local iodine concentrations are reported on the sheathing at pellet crack locations [14] . Critical iodine concentrations for causing ISCC were tabulated earlier [15] .

The main factor influencing ISCC is the chemical composition of Zircaloy sheathing, culminating in changes in the structure, mechanical and physical properties of the alloy system. The changes in strength and resulting resistance to ISCC are the primary by-products of the Zircaloy chemical makeup [16] . The experimental data and analyses [17] [18] have correlated the texture of non-irradiated Zircaloy-4, more than its chemical composition (for variations within the ASTM specification), with a strong effect on ISCC. The in-reactor structural integrity such as yield strength, fatigue and SCC are strongly correlated with the characteristic final texture in the finished Zircaloy sheathing product. The texture is affected by the tool design as well by the tube reduction parameters [19] . This further reinforces a conclusion that the Zircaloy tube manufacturing process is a significant factor in ISCC [20] . Residual stresses in materials arise in not only operational use, but stem from many a priori mechanical manufacturing and processing methods involving material deformation, heat treatment and machining. Almost every step of many machining processes can induce a wide variety of residual stresses with beneficial or detrimental effects. Particularly, the introduction of subsurface residual stresses in these operations, in terms of their depth, sign and magnitude may be the most influential factor in fatigue life, dimensional stability, brittle fracture and corrosion resistance. Since residual stresses are in self-equilibrium, both positive tensile, and negative compressive values must exist if residual stresses are present. These can be uniaxial, biaxial, or triaxial [21] [22] .

Seamless Zircaloy-4 sheathing in CANDU reactors are manufactured in an incremental compression forming process called pilgering, where the sheathing tube is subject to a complex stress system. These stresses are not necessarily subject to continuous quality control assessment and monitoring, and unfortunately, in too many cases, residual stresses and their potential to improve or damage components subjected to repeat load cycles may be overlooked, or it is assumed that additional treatment either has eliminated them or introduced beneficial compressive stresses. The residual stresses persist as long as the sum of residual stress and applied external stress does not exceed the pertinent 0.2% yield stress (σ_y0.2) of the materials. The stresses required to cause SCC are small, usually below the macroscopic σ_y0.2, and are tensile in nature. When superimposed to repeated applied external stresses, residual stresses at the proper surface play a crucial role in the structural integrity of components and structures [22] [23] . This is critical in the nuclear field, where highly favourable (sub)surface residual compressive stresses in the Zircaloy sheathing, efficiently retard the applied PCMI loading and overcome formation and propagation of cracks, thus enhancing fatigue resistance. Whereas residual tensile stresses are generally harmful and decrease the SCC resistance. Adequate depth and magnitude of the compressively stressed layer is important, in order to mitigate the initiation of cracks. Corrosion fatigue is often considered a subset of SCC [23] . During normal operations, high thermal conductivity in the fuel and sheathing, in conjunction with high sheathing strength and adequate creep resistance in the latter components are desired to withstand stress buildup in the sheathing [24] . Creep is deformation occurring as a constant volume process, normally at low stresses below the usual yield strength (σ_y0.2). Detailed thermo-mechanical analysis was able to show that during slow power ramping the sheathing and the pellet will creep, reducing the stress state of the former [25] .

Zircaloy failure under the ISCC regime emerges from PCMI conditions, when the synergy of existing tensile hoop stress and stress imposed on the sheathing by fuel thermal expansions during steep power ascension rates, and corrosion reaction by high iodine concentration at the inner surface, are combined in tandem [4] [26] [27] . Initially, ISCC cracks proceed along the grain boundaries, and then propagate across the grains to leave a fracture pattern as a rupture during the ISCC process [4] . PCMI conditions and the associated ISCC process, as a by-product of sudden power ramping, can limit the lifetime and safety of the Zircaloy-4 sheathing [1] . Zircaloy sheathing has demonstrated a high probability of brittle fracturing due to PCMI, during severe power ramping in test reactors [28] and water-cooled reactors [29] . Ramp rates above 3% hour⁻¹ [30] in fuel rods with extended service life over 10 GWd·t(U)⁻¹ [31] , culminate in increased UO₂-pellet thermal expansion. The ensuing aggressive fission-gas product accumulation above a threshold concentration [11] [32] [33] and gap closure, generates local tensile hoop stresses on the inner surface of the sheathing, near radial fuel cracks or pellet-pellet interfaces [8] [34] , at or above a stress threshold value. A sudden power increase that sets up such magnification of stresses plays a key role in the creation of PCMI conditions, normally leading to crack growth and failure in detectable ISCC. The crack propagates in the radial direction under a hoop stress. Crack growth rate has been expressed as a function of stress intensity [35] . The stress state in the sheathing then becomes a direct function of UO₂-pellet swelling during large power transitions, with higher burnups, therefore increasing the tensile stress state of the former [4] [36] . The burnup trials at 20 GWd·t(U)⁻¹ at the Bruce Power Reactor (Tiverton, ON) revealed a high failure rate due to PCMI conditions [32] [37] . Dynamic operations can cause considerable strains in CANDU fuel sheathing. For instance, the minimum strain predicted to initiate SCC cracking (0.1% - 0.5% [38] ) is generally exceeded during power ramping in CANDU fuel, wherein the hoop strain in the sheathing can reach values of 0.8% - 1.3% and drop by 0.6% during a shutdown condition. Furthermore, the highest strains occur at fast ramp rates (1 kW·m⁻¹·min⁻¹), because they reduce the time available for fuel densification [39] . Under a power ramp regime, PCMI is minimized with high strength sheathing and its ability to accommodate pellet expansion via creep, to delay sheathing ballooning and burst [40] . Threshold values of stress [41] , stress intensity factor, iodine concentration for detectable ISCC [42] , and iodine levels of PWR rods at normal and high burnups [43] [44] have been documented. A surplus of iodine over cesium reaches the sheathing in a power ramp [45] but is independent of fuel burnup [33] .

PCMI conditions and the resulting ISCC failures remain a licencing concern for water reactors, including CANDU reactors, accommodating a multitude of power manoeuvrability events, higher discharge burnups and non-standard fuel designs, in a less conservative and more financially incentivized state of operation [3] . Although PCMI/ISCC mechanism accounted for very isolated failure rates of Zircaloy sheathing in all Pressurized Heavy Water Reactors (PHWR) surveyed during 2006-2015 [46] , new safety requirements now include consideration of the effects of power cycling at high burnups [47] , and development of reliable sheathing to mitigate PCMI conditions under these operating parameters [48] - [50] . The stresses induced by dynamic thermo-mechanical equilibrium under a PCMI scenario amplifies the fact that residual stress state of the sheathing above a certain threshold is highly correlated to the failure in SCC process. Residual compressive stresses protect the integrity of sheathing material from PCMI related ISCC, whereas residual tensile stresses promote ISCC in tests of Zircaloy in iodine vapors at 300˚C [51] . The Cold-Worked, Stress-Relieved (CWSR) microstructure and texture for CANDU fuel sheathing have been better controlled in the ensuing decades [52] .

Multitude of obstacles inherent with in-reactor PCMI tests, have prompted considerable efforts in simulation of these conditions in the laboratory [26] [53] - [55] . A variety of different sample geometries have been examined (C-ring, standard tensile samples, and tube sections) using different methods for inducing stress (internal pressure tests, expanding mandrels, tensile and compression tests). Stress-Corrosion Cracking (SCC) in Zircaloy-4 fuel sheaths has previously been investigated by static loading of slotted ring samples [51] [56] [57] . At 300˚C, slotted Zircaloy rings crack in iodine vapour at applied hoop stresses greater than 217 MPa, where the failure time depends critically on whether the iodine concentration exceeds 3 mg I₂·cm⁻² of Zircaloy material [51] . In addition, the applied stress continuously relaxes during the test, which means that the stress could decay below the threshold stress for SCC during a long incubation period. These are disadvantages that make interpreting results difficult [4] . PCMI models provide reasonable failure predictions at low sheathing stresses (<1%) in test ramp data. In situations when fission product release is significant [58] , general sheathing stresses are maintained well below yield by creep relaxation. In contrast, fuel rod codes that treat PCMI as a predominantly mechanical interaction [59] must resort to the assumption of unrealistically large stress concentration factors from the fuel pellet in order to raise the sheathing stress to its 0.2% yield strength (σ_y0.2) failure limit.

ISCC is not the dominant mode of failure for CANDU reactors. Improved reactor operating procedures to preclude severe power ramps, in addition to the introduction of CANLUB graphite coating used exclusively in CANDU reactors to protect Zircaloy-4 fuel sheathing [57] , have been the cornerstone of reliability of power generation in Canada. Although a comprehensive review of ISCC processes has been presented earlier [60] , a detailed examination of the most recent literature reveals the noticeable absence of ISCC investigations pertaining to the post-production stress history of Zircaloy-4, prior to the experimental undertaking in this work.

The test programme described here has primarily focused on determining the dependency of PCMI-ISCC on inherent residual stress within a wide range of non-irradiated, stress-relieved commercially available CANDU Zircaloy-4 sheathing and ubiquitous influence of iodine. A historical context is provided in terms of Zircaloy-4 sheathing from two independent sources, and their associated post-production stress state. In a first study of its kind, a more defining relationship between ISCC and the nature and magnitude of indigenous residual stress and the resulting changes in the mean stress to a constant hoop tensile stress, at or near the maximum 0.2% yield strength (σ_y0.2) of 400 MPa, by static loading of slotted Zircaloy-4 ring samples in corrosive conditions in iodine-methanol has been investigated.

The axial slitting to effect slot openings in narrow rings (5.00 ± 0.05 mm), releases the residual stress distributed relatively uniformly in the entire length of the original Zircaloy-4 sheathing (≈490 mm). A quantitative relationship between the slot opening and residual stress has been formulated (Equation (3)) [64] , based on the elasticity of the slotted C-ring. The purely elastic deflection behaviour of the C-rings is verified for before and after the fixed mass-load (100.00 ± 0.01 g), in the Zr-alpha and Zr-beta C-ring series, respectively. The displacement in the form of positive slot openings ( Figure 4 and Figure 5 ) is categorically predictive of the universal presence of hoop tensile stress in the rings. Residual tensile stress data for Zr-alpha and Zr-beta C-ring series ( Figure 6 and Figure 7 ) were quantitatively determined (Equation (3)) [64] prior to Stress-Corrosion trials. Zr-alpha series incorporate residual tensile stresses of 49.84 ± 4.55 MPa across the vintage years 2008-2016. For Zr-alpha series, coefficient of variation of 9.13%, from a production and quality control management process, reflects lower dispersion and highly consistent residual stress properties [72] , and hence the ability to effectively combat the fuel sheathing failure for various reactor conditions (e.g., power ramps, increased linear power, etc.), and to further support higher burnups in advanced fuel cycles [56] [73] . This is further amplified by comparatively the lowest average maximum tensile stress value of 56.10 MPa in a vintage year and batch ( Figure 6 ; 2014-A1). This is in clear contrast to quantitatively higher average post-production residual tensile stress of 87.63 ± 29.75 MPa for Zr-beta series across the vintage years 1988-2017. Zr-beta sample series integrate distinctively higher standard deviation and resulting coefficient of variation of 33.95%, reflecting unfavourably high dispersion and inconsistent residual stress profile. The highest average maximum value of 151.41 MPa, in a vintage year and batch ( Figure 7 ; 1992.V6-1), exemplify the measurably higher residual tensile stresses in the Zr-beta series. The higher average post-production residual tensile stresses inherently mask the riskiest cases in the Zr-beta series.

The depth and particularly the magnitude of post-production subsurface residual tensile stresses of Zircaloy-4 sheathing in CANDU reactors, manufactured in pilgering process, are influential in fatigue life, dimensional stability, brittle fracture and corrosion resistance. The synergy of existing higher residual tensile stress, and stresses at or near the maximum 0.2% yield strength (σ_y0.2) imposed on the C-rings are generally harmful and decrease the ISCC resistance [4] [26] [27] . The samples from Zr-alpha series comprised of 40 C-rings with decisively lower original residual tensile stresses of 49.84 ± 4.55 MPa across the vintage years ( Figure 6 ), did not suffer a single fracture failure post 400 (±2%) MPa stress, in iodine-methanol solution at room temperature ( Figure 4 ). C-rings prepared from Zr-beta series suffered fracture failure spread across the vintage years, resulting in complete splitting of the C-ring into two sections. The five failed groups from Zr-beta series comprised of 20 C-ring samples ( Figure 5 ; missing data points), possessed the highest average original residual tensile stresses, ranging from 68.95 to 151.41 MPa, across all 88 samples from Zr-alpha and Zr-beta series ( Figure 6 and Figure 7 ). The latter values and the higher group average of 87.63 ± 29.75 MPa in the Zr-beta series, exemplify the measurably higher residual tensile stresses synonymous with larger mean stresses, resulting in cracking and fracture failure post 400 (±2%) MPa stress, in iodine-methanol solution at room temperature. The latter failed sample groups are indicated by missing data points in Stress-Corrosion trial results in iodine-methanol at 400 (±2%) MPa in Figure 5 . Depending on metallurgical conditions, the aforementioned stress condition lies at or near the maximum 0.2% yield strength (σ_y0.2) for non-irradiated, stress-relieved Zircaloy-4 sheathing of 414 - 565 MPa [66] .

Original post-production residual stress can raise or lower the mean stress experienced over a fatigue cycle. The Goodman relation is particularly helpful in determining the effectiveness of a material, because a residual tensile stress increases the mean stress [74] . Mean stress values incorporating higher residual tensile stresses are more likely to promote ISCC than residual compressive stresses. Larger mean stress values promote ISCC in tests of Zircaloy in iodine vapours at 300˚C [51] and may trigger static fracture during fatigue.

The Zr-beta sample series displayed the more pronounced post ISCC effects from pitting to ductile fracture ( Figure 10 ), diametrically across the slot zone (i.e., point A, Figure 2(a) ). In contrast, the Zr-alpha sample series, with lower mean stresses, displayed the more mitigated post ISCC effects in the same zone, including the complete absence of cracking in the inner surface, and cracking without pitting ( Figure 9 ). The iodine-methanol Stress-Corrosion medium had been observed earlier as the most aggressive, in terms of penetration depth [71] .

The resulting average slot openings post iodine-methanol Stress-Corrosion trials are 6.009 mm (±1.322) and 5.963 mm (±1.791) for Zr-alpha and Zr-beta series, respectively; the failed C-rings from Zr-beta excepted. This degree of experimental scatter is common in ISCC experimental campaigns, and the 0.77% difference between average slot openings between the two series amplifies the notion that iodine-methanol medium consistently replicates Stress-Corrosion effects. Fractures obtained in internal pressure tests for SCC in iodine vapors at T = 350˚C and in an iodine-methanol medium at room temperature are largely identical [70] .

The slotted C-rings were weighed (±0.02 mg) prior and post Stress-Corrosion testing, during which the chemical as well as the mechanical conditions for cracking are satisfied [4] [75] . Zr-beta C-ring series possessing larger mean stress, that did not suffer complete fracture failure, registered a 1.71 % average weight loss as compared to a 0.90% weight loss for a group average for Zr-alpha series with lower mean stress. The extent of intergranular cracking is greater in statically loaded tests particularly for iodine solutions in organic solvents, resulting in dissolution, removal of material and larger weight loss during cracking from the grain boundaries [76] . Increasing the original slot openings for all C-rings in the range of 6.40-10.00 mm (Equation (3)) to deliver a constant hoop tensile stress of 400 (±2%) MPa, at or near the maximum 0.2% yield strength (σ_y0.2) for non-irradiated, stress-relieved Zircaloy-4 sheathing of 414 - 565 MPa [66] , induces a strain between 0.7 to 1.1% [73] . This is comparable to the strains induced by power ramps in CANDU nuclear reactors (0.8% - 1.3%) [39] and exceeds the minimum strain range for inducing SCC in Zircaloy-4 sheathing (0.1% - 0.5%) [17] . During power ramps and increased linear power operations in water-cooled reactors, Zircaloy sheathing has demonstrated a high probability of brittle fracturing due to PCMI and associated ISCC process [29] .

The positive slot opening remains purely a function of the individual post-production residual tensile stress (Equation (3)) [64] across the vintage year, batch and the tube sample number for Zr-alpha and Zr-beta series ( Figure 6 and Figure 7 ). In spite of the fact that axial slitting to effect slot openings may have relieved the original residual tensile stress to the largest extent possible, the unfavourably higher and irregular original residual tensile stress profile of Zr-beta series (87.63 ± 29.75 MPa) and associated mean stress of 400 (±2%) MPa, at or near the maximum 0.2% yield strength (σ_y0.2), are evidently manifested in Zr-beta series having suffered wide spread brittle fracture failure under the ISCC regime in this investigation. This would be potentially limiting the lifetime and safety of the Zircaloy-4 sheathing in power maneuverability events.

The positive initial slot openings, based on individual SEM measurements, allows for determination of the indigenous residual tensile stresses for individual C-rings from Zr-alpha and Zr-beta series. The Zircaloy-4 sheathing tubes from Zr-alpha series clearly exhibit a lower group average residual tensile stress (49.84 MPa), incorporating a substantially lower scatter (±4.55 MPa) across the vintage years examined. The higher group average of 87.63 MPa, exemplifies the measurably higher residual tensile stresses in the Zr-beta sample series, in addition to the much larger scatter (±29.75 MPa) in the vintage years under examination. The Coefficient of Variance of residual tensile stresses for Zr-alpha and Zr-beta series measures 9.13% and 33.95%, respectively. Zr-beta sample series reflect unfavourably high dispersion and inconsistent inherent residual stress profile. The two-sample t-test provides a decisive case for the inferiority of Zr-beta in its inherent residual tensile stress.

It has been demonstrated that Zircaloy-4-based C-rings stressed at or near the maximum 0.2% yield strength (σ_y0.2) of 414 - 565 MPa [66] , for non-irradiated, stress-relieved Zircaloy-4 sheathing, in iodine-methanol, subject to the original residual tensile stress and the resulting changes in the mean stress, are susceptible to Stress-Corrosion Cracking and fracture. The samples from Zr-alpha series composed of 40 C-rings with decisively lower original residual tensile stresses across the vintage years did not suffer a single fracture failure post 400 (±2%) MPa stress. In contrast, the 48 C-rings from the Zr-beta series suffered fracture failure spread across the vintage years, resulting in complete failure and splitting of 20 C-rings into two sections. Zr-beta C-ring series possessing larger mean stress, registered a 1.71 % average weight loss, reflecting a greater intergranular cracking as compared to a 0.90% weight loss for a group average for Zr-alpha series with lower mean stress.

The presence of higher residual tensile stress as a structural element in commercially available Zircaloy-4 has been established to considerably undermine corrosion resistance and enhance brittle fracture. The future advancement of Zircaloy sheathing production should embrace the stress state of the latter and its inevitable changes during reactor power transitions. Considerable advantage can be realized by engineering beneficial residual compressive stress in the sub-surface layers of the Zircaloy substrate to mitigate origination and propagation of deleterious Stress-Corrosion Cracking and increase wear resistance. It is noteworthy that the findings of this particular investigation are not exactly representative of Zircaloy-4 sheathing performance inside a CANDU reactor and complimentary studies incorporating sheathing condition properties like irradiation damage, oxide layer thickness, hydride concentration and a more superior siloxane coating, would further enhance the forecasting of sheathing behaviour in a reactor environment.

Clarence McEwen, Senior Technologist, Department of Chemistry and Chemical Engineering, Royal Military College, Canada, precision-machined individual Polyether Ether Ketone (PEEK) blocks (6.40 - 10.00 ± 0.01 mm).

This work was partially funded by Natural Sciences and Engineering Research Council of Canada (NSERC-CRDPJ-436050-12).