Assessing Creep–Fatigue Interactions in Wrought and LP-DED-Processed 316 Stainless Steel Open Access

The austenitic stainless steel (SS) 316 has been favored in the use of nuclear reactors, turbines, heat exchangers, piping, and other power generation equipment due to its combination of high-temperature corrosion resistance, high ductility and fracture toughness, and fatigue and creep strength [1,2]. Current accepted lifing models and qualification testing are based on wrought alloys supported by decades of industrial experience. However, the opportunity for additive manufacturing (AM) of 316 SS components that can be used to produce novel components to improve the efficiency of power generation systems leads to the question what is the optimum type of acceptance testing required to enable rapid adoption of AM for high-temperature applications? Although AM may appear as a material solution when designing the Generation IV power plants, skepticism is present. AM components have a large scatter in material property and microstructural data [3]. These scatters can arise from different printing methods and parameters used when printing [4]. With no universal standards between suppliers, AM systems, and machines for specific high-temperature use, the qualification of these materials is complex to say the least such that interest in creep–fatigue (CF) life prediction modeling has also increased.

Creep damage in 316 SS arises from the formation and coarsening of chromium carbides (M₂₃C₆) during prolonged exposure to high-temperature environments [5]. Carbide coarsening depletes chromium along grain boundaries, diminishing corrosion resistance and increasing susceptibility to grain boundary void formation, which can lead to intergranular cracking [6–8]. Concurrently, low-cycle fatigue (LCF) damage is induced by cyclic thermal stresses resulting from temperature gradients during startup and shutdown cycles [9,10]. These stresses exceed the material's yield strength, causing cyclic plastic deformation and the accumulation of surface microcracks that propagate transgranularly [11,12]. The interaction of fatigue and creep damage may lead to mixed-mode rupture, where both mechanisms contribute to structural degradation. As Generation IV nuclear reactor designs advance, developing materials capable of enduring these extreme conditions over long service durations remains a critical research priority.

Various nuclear component design codes exist. In each design code, a CF interaction “damage” diagram, constructed using the life fraction approach (Fig. 1), is used to assess the life. The French and US design codes, RCC-MRx and ASME BPVC in Sec. 3, respectively, use similar methods to obtain parameters necessary for CF life fraction analysis. Both design codes calculate creep damage with the Time-Fraction (TF) approach. The codes expect conservative outcomes due to factors of safety used when forming the fatigue and minimum creep design curves. When constructing the CF interaction diagram with the TF approach for 304 or 316 SS, both the ASME and RCC-MRx codes require the use of a bilinear failure envelope with intersection point of (0.3, 0.3) [13].

The R5 nuclear design code used in the UK determines creep damage through the Ductility Exhaustion (DE) approach. Although not implemented as part of the R5 design code, the Stress-modified DE (SMDE) creep damage approach can also be used to determine creep ductility. Better predictions of CF interactions have been shown by the SMDE approach compared to the R5 DE approach [14–17]. A linear failure envelope is used when constructing the CF interaction diagram with either the DE or SMDE approaches [12].

The distinct creep and fatigue damage behaviors in different regions of the CF interaction diagram are illustrated in Fig. 1. Under pure LCF, cracking is predominantly transgranular, while pure creep leads to intergranular cracking. When LCF cycles include dwell periods, CF interactions are promoted, resulting in combined damage mechanisms.

The following three modes of CF interaction have been identified [12]:

1. Case A: Competitive Mode—This weak interaction occurs when fatigue causes transgranular damage, and creep induces intergranular damage, with minimal interaction between the two mechanisms. One typically dominates.

2. Case B: Additive Mode—A stronger interaction arises as independent fatigue and creep damage mechanisms combine. Local creep damage at the crack tip, driven by elevated stresses, accelerates fatigue crack growth.

3. Case C: Worst-Case Interactive Mode—This severe interaction results in significantly accelerated crack growth. Creep-induced cavities along grain boundaries in the bulk material provide multiple paths for intergranular fatigue crack propagation. This mode is the most detrimental, causing rapid structural degradation [12,18].

Type 316 stainless steel is available in variants such as 316L and 316H, distinguished primarily by their carbon content. Alloy 316L is characterized by lower carbon content (≤0.03 wt%), reducing susceptibility to sensitization and intergranular corrosion during welding, making it well-suited for components subjected to welding operations or environments demanding enhanced corrosion resistance. In contrast, alloy 316H contains higher carbon content (typically 0.04–0.10 wt%), enhancing its high-temperature mechanical strength and creep resistance, making it preferable in elevated-temperature nuclear reactor components subjected to long-term exposure. Given the differences in creep and fatigue behavior arising from their carbon content, investigating both alloys provides critical insights for qualifying additively manufactured materials under realistic operating conditions in nuclear applications.

This paper presents new CF data on wrought 316L with the aim of establishing an acceptance test for AM-processed SS to capture the most degrading CF interaction (Case C in Fig. 1). Using the candidate accelerated CF acceptance test condition, both wrought 316H and directed energy deposition (DED) 316H were tested to evaluate the accelerated CF test condition investigating deformation behavior, cracking behavior, and life analysis. The evaluation of the CF interaction measured and observed in DED 316H is compared to wrought 316H.

This represents a linear damage summation model when D = 1. The following sections provide a description of some of the most common approaches applied to CF interaction calculations, but it should be noted that there exist many modifications or alternative assumptions in literature. Therefore, CF interaction diagrams (e.g., Fig. 1) are not “material properties” but must be understood within the details of the analysis methodology employed by the analyst and can only be applied to engineering design and life prediction using the same assumptions for damage summation.

The creep damage is typically determined in one of three ways: (i) the time-fraction (TF) method, (ii) ductility exhaustion (DE) method, and (iii) stress-modified DE (SMDE) method.

This simplification is often used due to the lack of intermediate strain-time data for creep tests with extensive rupture times and is generally sufficient [14,15,17,21,22]. When intermediate strain-time data is available, creep ductility data may also be represented in the form of creep ductility against minimum creep strain rate and temperature [23].

Using the Conway analysis, successful stress predictions for hold times up to 100 h have been observed [20,27,28].

However, the assumption that all inelastic strain is creep strain overpredicts the amount of creep damage in the DE and SMDE approaches. During the dwell time, the inelastic strain is composed of two parts, a viscous strain and a creep strain [29]. The rapid drop in stress at the beginning of the strain hold is the viscous back stress influence on the deformation response. The viscous strain is not associated with the increase in creep damage but instead is the result of short-range rearranging of dislocations into lower energy configurations. This viscous strain component is a large percentage of the total stress relaxation response when the loading strain rates are relatively high. The predictions using the DE and SMDE are considerably better, particularly for shorter dwell times, when only the creep strain component is used as the measure of accumulated creep strain [22,29].

The challenge is how to separate the inelastic strain rate into its viscous and creep strain rate components. A few different approaches can be taken. One approach is to calculate the creep strain from an empirical fit of creep data with inputs of current stress, temperature, and time of dwell instead of using the total inelastic strain measured during the dwell [29]. Another approach is to identify a transition stress or time during the dwell separating viscous strain and creep strain. The transition time $t1$ appears to be of the order of 1 min to account for the portion of the relaxation response that is associated with the viscous strain as proposed by Miller et al. [26]. This is readily implemented using the Conway fit, Eq. (20), by setting the initial time for the accumulated creep strain as t₁ = 1 min instead of zero in Eq. (13) for the DE approach and Eq. (17) for the SMDE approach. The amount of viscous strain depends on the prior strain rate with higher prior strain rates resulting in a greater amount of viscous strain [29], and hence it is expected that $t1$ will have some dependence on the prior strain rate, but this influence appears to be small and using the somewhat arbitrary t₁ = 1 min may be acceptable.

Low-cycle fatigue and CF interaction tests were conducted on five variations of 316 SS. One was a wrought 316L SS bar, cold worked and annealed, per ASTM A276-13a [30]. The mean grain size of the 316L SS bar was 14.1 μm, measured on a plane with normal along the loading axis. The second was a hot-rolled 316H plate (ASTM A240/A240M-19). The 316H SS plate underwent a solution anneal heat treatment at 1052 °C for 1 h and then, water was quenched. The mean grain diameter was 40 µm. More details on the microstructure of the same heat of the 316H plates can be found in Ref. [31]. The chemical compositions of these wrought alloys are given in Table 1.

The remaining three variations of 316 SS were additively manufactured blanks built using the Optomec LENS 500 (Albuquerque, NM) Directed Energy Deposition (DED) system that uses a high-powered laser to build structures layer by layer directly from 316H alloy powder used as the feedstock; i.e., a laser powder DED method (LP-DED). The powder characteristics are given in Table 2. Two variations consisted of cylindrical blanks built vertically, one using 550-W laser power and the other 400 W, while the third variation was a rectangular prism built horizontally using 550-W laser power. All other processing parameters were identical across the three variations, as listed in Tables 3 and 4. The chemical compositions of the as-received powder and as-built blanks are given in Table 1.

Prior to machining into fatigue specimens, the blanks were solution annealed (SA) at 1121 °C for 1 h, followed by a water quench. Vertical specimens were loaded along the build direction, while horizontal specimens were loaded perpendicular to it. The as-built DED 316H specimens contained C near the lower bound of the ASME SA240 316H specification and Si slightly greater than the specified maximum (0.75 wt%).

The as-built DED material exhibited substantial microstructural heterogeneity, with large grains (≥500 µm) interspersed among smaller grains. Grains were predominantly elongated along the build direction, with an average aspect ratio of approximately 3. However, they did not show significant crystallographic texture. The SA treatment was insufficient to fully homogenize the material, leading to partial recrystallization, particularly in regions with smaller grains, while the larger grains continued to grow. Intragranular strain was not fully relieved, and the prior cellular structure evolved into a subgrain structure during the SA treatment [31]. The average grain sizes after the SA treatment were 220 µm for V-SA-550, 110 µm for V-SA-400, and 100 µm for H-SA-550 [32].

All bars, plates, and DED blanks were machined into uniaxial smooth LCF specimens as prescribed in ASTM E606-21 [33]. The gage section diameter was 6.35 mm (0.25 in.), and the gage section length was 13.2 mm (0.52 in.). After machining, the specimen gage section was ground and polished using a succession of SiC abrasive paper finishing with 4000 grit with residual grinding marks along the axis of the specimen. Uniaxial round bar creep samples were fabricated with a gage section diameter of 6.35 mm (0.25 in.) and a gage length of 31.8 mm (1.25 in.)

The LCF tests with no dwells were conducted in strain control per ASTM E606-21 [33]. The specimens were heated and maintained at test temperature using induction heating. The temperature within the gage section was within 1% of the testing temperature as required by ASTM E606-21. A uniaxial high-temperature extensometer with ceramic extension rods with a nominal gage length of 12.7 mm (0.5 in.) was used to measure gage section displacement. Additional testing details can be found in Ref. [34]. Creep-rupture testing was conducted per ASTM E139 using lever-arm creep machines with continuous strain monitoring affixed to the specimen shoulders outside the gage.

Three different types of CF interaction tests were conducted: (i) standard strain-controlled isothermal CF tests (ASTM E2714-13 [35]), (ii) force-dwell (FD) ratcheting CF tests, and (iii) FD non-ratcheting CF tests. Dwell periods are introduced either at peak tensile or peak compressive strains. For the FD non-ratcheting CF tests, cycling is conducted in strain control and the dwell in force control at the maximum strain of the cycle. The target maximum and minimum strains during the loading and unloading sequences are kept fixed and the strain is allowed to increase during the force-controlled dwell period. This results in a total strain range greater than the difference between the target strains. For the FD ratcheting CF tests, cycling is also performed in strain control and dwell in force control. In contrast to the FD non-ratcheting CF test, the strain range is fixed, resulting in ratcheting of the strain with cycling.

The loading and unloading ramps for all tests were conducted at a strain rate of 2.0 × 10⁻³ 1/s. All LCF and strain-controlled CF tests were conducted at a strain ratio of −1. The FD tests had varying strain ratios due to the additional creep strain during the dwell. For all tests, the failure criterion was defined as a 20% reduction in maximum stress from a linear extension of the maximum stress evolution during the quasi-stable regime on a linear-log plot of maximum stress versus cycles. Most tests were stopped prior to complete specimen separation after the failure criterion was met. However, for the FD ratchetting CF tests, the continually increasing strain resulted in the extensometer reaching its upper limit, and hence, those tests were stopped prior to meeting the failure criterion.

Tests conducted on the 316L bar material consisted of temperatures from 550 °C to 700 °C, strain ranges from 0.4% to 1.0%, and dwell times from 1 min to 30 min. In one test, the dwell occurred in compressive at the minimum strain. All the tests conducted on 316H, both wrought and DED processed, were conducted at 650 °C, strain range of either 0.6% or 1.0%, and either no dwell (i.e., LCF) or 30-min dwell at the maximum tensile strain.

After LCF and CF testing, several specimens were sectioned longitudinally through the gage section to examine damage and cracking behavior. The sectioned samples were mounted and polished using a stepwise procedure. Final preparation involved polishing with a 1-µm colloidal diamond suspension from Struers, followed by a final step using a 0.05-µm polycrystalline acidic alumina slurry from Pace Technologies. The specimens were immediately rinsed with tap water after the final polishing step to remove any residue. Damage and crack morphology were imaged using a Keyence UHX7000 digital microscope (Itasca, IL).

The life data from all tests are plotted in two ways, in terms of the total strain range and in terms of the inelastic strain range, in Fig. 2. The data used to generate these plots are summarized in Tables 5–7 for 316L bar, wrought 316H plate, and DED 316H, respectively. The total and inelastic strain ranges are taken at half-life. The ASTM E2714-13 definition of inelastic strain range, width of hysteresis loop at zero stress, is used [35]. As a reference, the design curve specified in ASME BPVC Sec. III, no. 5 for T < 705 °C, $ε˙=10−31/s$ for 316 SS [36] is shown in Fig. 2(a). All wrought data lives, including LCF and CF and both 316L and 316H, exceed the design curve by an order of magnitude in life.

The 316L tests were conducted first to determine the test condition that promotes a CF interaction most rapidly (i.e., promote Case C in Fig. 1). This was assessed by comparing the cyclic response and cracking behavior between LCF and the various CF tests, shown in Fig. 3. When the hold times were 10 min or less, whether the dwell was in tension or compression, the cracking behavior was similar to what was observed in LCF. The cracks formed from the surface and propagated inwards similar to the LCF tests (Figs. 3(a) and 3(b)). Crack initiation and propagation were primarily transgranular. Secondary cracks were observed near the crack tips at the end of life, but no clear creep voids along grain boundaries were observed near the primary crack [34]. The presence of these cracks suggests some creep damage had occurred. However, the absence of grain boundary damage around the primary crack and the primarily transgranular crack propagation suggests a weak, competitive creep–fatigue interaction mode, or no creep–fatigue interaction. As the intergranular cracks are only found at the crack tips, it is likely that these cracks formed near the failure cycle. Near the end of life, the stress intensity range promoting crack growth is considerably reduced in strain-controlled tests, and crack propagation is likely halted, resulting in nucleation of the secondary cracks during the dwell.

In contrast, when hold times increased to 30 min, the cracking behavior became notably more tortuous from the early crack growth to near the end of the test (Fig. 3(c)). This suggests that a creep–fatigue interaction significantly contributes to crack formation and growth.

The cracking behavior for the force-controlled dwell (FD) non-ratcheting CF test, shown in Fig. 4, was transgranular suggesting minimal CF interaction. Similar to LCF and strain-controlled CF tests, the force-control dwell non-ratchetting CF test initiated a crack at the surface which propagated inwards transgranularly. At the crack tip near the end of the test, crack blunting is observed. This feature was not observed in the LCF or conventional isothermal strain-control CF tests suggesting plastic deformation at the crack tip is larger due to force-control dwell periods. There is little evidence of creep voids forming on grain boundaries away from the crack.

A sampling of the hysteresis loops for both LCF and CF tests is shown in Fig. 5. The hysteresis response at half-life is similar for 316L and 316H. The addition of dwells at either the maximum or minimum strain increases the cyclic inelastic strain range commensurate with the amount of relaxation. In the non-ratcheting force-dwell (FD) test, the total cyclic inelastic strain increases to compensate for the creep strain during the dwell.

The unconstrained ratcheting test with a fixed strain range did not promote a CF interaction. Instead, it resulted in a tensile overload failure. No true fatigue or creep damage was apparent. Therefore, this test resulted in a failure mechanism that will not be represented by most component designs being accessed and could be evaluated simply from a strength consideration.

The CF lives of 316L were all within a factor two of the LCF life. The FD non-ratcheting CF test on the other hand produced a much larger inelastic strain range than all other tests as observed in the hysteresis response (Fig. 5). A factor of two decreases in cyclic life was seen from these tests with respect to LCF tests. Yet, even in this case, the plotted point generally correlates with the Coffin–Manson relation (Fig. 2(b)), indicating that life is also primarily controlled by cyclic inelastic strain amplitude with the creep contribution reflected in the small increase in the inelastic strain amplitude.

For a fixed total strain range, the inelastic strain range increases as temperature increases due to the reduction in strength with temperature [37]. Even with these differences in temperatures and dwell periods, the 316L LCF and CF data points are within a factor of two of the strain-life relation curves (Fig. 2(b)). The decrease in life with increasing temperature or dwells is simply captured by the increase in the inelastic strain range generated at higher temperatures and longer dwells.

Therefore, the life can be predicted solely from the inelastic strain range without additional frequency or dwell effect. Dwells less than 10 min, while accelerating the test time by minimizing the dwell time, are not sufficient to promote a discernable CF damage interaction in 316 SS. In addition, force-controlled dwells do not promote a strong CF damage interaction either, particularly when the strain range is 1.0%. In these tests, the large strain range promoted the fatigue damage to dominate. It is possible that a lower strain range with force dwell or imposing the force-control dwell at a stress lower than the maximum stress may promote a CF interaction [38,39]. However, this was not further pursued since lowering the strain range will lengthen the test time. In summary, of all the tests conducted on 316L, only the 0.6%, 30-min dwell test promoted a true CF damage interaction. Therefore, for the CF tests on wrought and DED 316H, the CF test condition selected was 0.6% with 30-min dwells as our reference CF damage interaction condition.

The wrought 316H LCF and CF lives are considerably greater than those of the 316L bar. The hysteresis responses at half-life are similar (Fig. 5). However, the evolution of the maximum stress of wrought 316H and 316L is different, as shown in Fig. 6. The stress evolution response generally exhibits three distinct regimes: initial cyclic hardening, followed by stable or quasi-stable maximum stress with a gradual decline in maximum stress, and finally rapid stress decline. For 316L, the initial cyclic hardening reached saturation in 20 cycles when the strain range was 1.0% and in 100 cycles when the strain range is smaller, 0.6%. In contrast, for the 316H, the initial hardening regime saturated near cycles 70 and 300 for $Δε=1.0$ and 0.6%, respectively. All CF tests had a lower maximum stress than the LCF tests after the saturation of the initial cyclic hardening. The wrought 316H, which was annealed, had a much lower initial yield strength and a much larger increase in stress during this initial cyclic strain hardening stage compared to 316L.

In comparison to wrought 316H, the DED 316H LCF lives were more comparable to the 316L lives, all generally within a factor of two, and still well above the ASME design curve (Fig. 2). However, the lives of the accelerated CF interaction test (0.6%, 30-min dwell) conducted on two of the variations of DED 316H (H-550 and V-400) are considerably below the mean curve for 316L in contrast to the CF tests conducted on 316L and wrought 316H, though still lying above the conservative ASME design curve.

The stress relaxation responses during the dwell at half-life are shown in Fig. 6(c). For the 30-min dwell, the 316L exhibits the largest amount of stress relaxation in comparison to the 316H wrought suggesting a higher creep rate. Therefore, the 316H wrought retains a higher lower relaxation value than the 316L. The DED 316H V-400 and H-550 had the highest maximum stress at the beginning of the dwell, comparable to wrought 316L and 316H, but having a greater stress relaxation than 316H and lesser stress relaxation than 316L. The maximum stress at half-life for the DED 316H V-550 was considerably smaller.

The cracking behavior of wrought and DED 316H under LCF and CF conditions at $Δε=0.6%$ and 650 °C is compared in Fig. 7. In all cases, cracks initiated at the surface and propagated inward. Under LCF, cracks propagated transgranularly for all variations of 316 SS, with a slightly more tortuous crack path in DED 316H due to its larger grain structure, which can be observed in the etched images (Fig. 7(c)). Minor secondary cracking along the main crack was observed in all process variations under LCF.

In CF conditions, the crack propagation was intergranular for all process variations, with distinct differences in the extent and distribution of damage. The better-performing wrought 316H, which exhibited a CF life nearly an order of magnitude higher than DED H-550 and V-400, showed widely distributed creep cavities along grain boundaries (Fig. 7(b)). This uniformly distributed cavity formation and extensive secondary cracking likely shielded the primary crack tip, reducing the driving force for crack growth.

In contrast, DED 316H demonstrated less extensive and less uniformly distributed creep cavitation, attributed to its larger grains and fewer grain boundaries (Figs. 7(d) and 7(e)). The reduced creep cavitation in DED 316H was likely a result of faster fatigue crack growth, which limited the time for cavity formation. The damage in DED 316H tended to concentrate on crack-like features away from the primary crack, increasing the stress intensity at the crack tip and promoting both fatigue and creep crack growth.

The mesostructure characteristic of DED processing, including the elongated grains and anisotropic grain boundary network formed by the weld pool solidification, likely influences both LCF and CF crack propagation behavior. In particular, the H-550 specimen, which exhibited the poorest CF performance, featured a greater number of grain boundaries oriented normally to the loading direction compared to the vertically built specimens. This grain boundary orientation can facilitate intergranular crack growth during dwell periods promoting faster crack propagation. Although detailed quantitative characterization of the mesostructure was not performed in this study, the observed differences in cracking behavior and fatigue life across the DED specimens support the conclusion that mesostructure contributes to the observed variability in CF damage evolution.

Further, the DED 316H material exhibited lower creep ductility at higher stress levels in creep tests (Table 8). The stress levels during the dwells in CF tests tended to be closer to these higher stress levels in the creep tests, suggesting that the local fracture toughness is reduced in the DED process. At lower stress levels in the creep tests, the creep ductility was comparable between DED and wrought 316H. Among the DED conditions, V-400 showed even less distributed cracking under CF conditions (Fig. 7(e)), likely exacerbating its reduced creep ductility.

Overall, CF interactions were only observed under $Δε=0.6%$ and a dwell time of 30 min. The coupling of creep cavitation and fatigue crack growth was particularly detrimental in DED 316H, as its larger grains and less uniform damage distribution limited the beneficial load-shedding effects seen in wrought 316H.

The other way $tc$ was estimated was using the sinh relationship, Eq. (11). The parameters for this model are given in Table 9. They were determined from a regression analysis of the 316H data obtained from Refs. [40–47].

Creep ductility–creep rupture time data was extracted from multiple sources and heats of 316H [40–47]. Using Eq. (14) to determine the average creep strain rate, the creep ductility as a function of the average creep strain rate for 650 °C data was plotted (Fig. 9). The upper and lower-shelf ductility for the piece-wise function, Eq. (15), was each defined. The minimum creep-rupture elongation of all creep tests was set as the lower-shelf ductility. Upper-shelf ductility was defined based on both the maximum rupture elongation found from tensile tests conducted at 650 °C which generally correlated with the creep ductility reported in these shorter creep tests.

Regression fits were used to determine the creep ductility in the creep strain rate–dependent regime. For the ductility exhaustion (DE) model, the parameters of Eq. (16) were determined (Table 10), and for the SMDE creep ductility equation, the parameters for Eq. (18) were determined (Table 11). Plots of these fits are shown in Fig. 9. Considering the large variation in the creep ductility, the correlations have considerable uncertainty embedded in them. Using the SMDE approach, the stress values of 100 and 200 MPa tend to bind the lowest and highest stress measured during stress relaxation in the CF tests on the DED 316H (Fig. 6).

The DED data does not follow the trend of reducing creep ductility with a reduction in creep strain rate (i.e., lower stress), as seen in Fig. 9. Two of the DED processed 316H, V-400 and H-550, exhibited a lower ductility than the majority of the wrought 316H when the stress was greater than 170 MPa. Therefore, the DE approach is not able to represent the strain rate–dependent behavior of the DED correctly. The SMDE approach that includes a stress dependence provides a better correlation to the creep ductility but still, it does not capture the stress dependence on the creep ductility particularly when the creep stresses are high.

The creep ductility values for DED 316H lie within the scatter of the wrought 316H data (Fig. 9), though closer to the lower end of the scatter, suggesting that there may be some reduction in creep ductility for the DED processed material compared to wrought 316H. However, as shown in Fig. 10, the average creep strain rates measured in the DED 316H all lie within the scatter band of wrought 316H and in fact, for V-500 and H-550, lie near the lower bound indicating increased resistance to creep deformation. Research by Snitzer et al. [31] on the same process and materials used to produce these DED samples showed similar trends in graded samples with DED having improved creep resistance (reduced minimum creep rates) but lower ductility as a function of heat input and heat treatment when compared to wrought. Since there is minimal creep data on the DED, using the mean creep rate response of the wrought 316H data, shown in Fig. 10, is justified for analyzing and predicting the CF life of DED 316H.

The Conway stress relaxation model, Eq. (20), was used to approximate the stress relaxation response required to compute the creep damage fraction. The fitting parameters from various CF stress relaxation data at half-life are given in Table 12 with fits shown in Fig. 6(c). The inelastic strain rate during the dwell is determined from Eq. (24). The computed minimum creep strain rates at the end of the 30-min dwell are reported in Table 12.

The life predictions for CF with different tensile dwell times are shown in Fig. 11 for each of the variations of 316 illustrate how these models predict the reduction in life as dwell time increases. The data points with arrows on the left part of each plot represent the LCF lives used to establish the fatigue damage fraction for each material and strain range. The creep damage fraction was calculated in several ways. Each prediction curve represents one of the approaches: (1) time fraction using either LM (Eq. (8)) or the hyperbolic sine function (Eq. (11)) to determine the creep-rupture time, $tc$⁠, (2) DE without any adjustment to account for viscous strain and two approaches for accounting for viscous strain, Miller (assume first minute of inelastic strain is a viscous (non-damaging) strain) and Takahashi (Eq. (26)), and (3) stress-modified DE (SMDE) without any adjustment for viscous strain and also computed using the Miller and Takahashi approaches to account for viscous strain. Since the creep behavior of the DED 316H fell within the data for wrought 316H, the creep damage fraction predictions for DED 316H used the model parameters for the wrought 316H response.

For the CF life predictions for the wrought 316L, Figs. 11(a) and 11(b), the SMDE (Miller) approach tends to perform better than the others for both the lower and higher strain range. All the predictions are overly conservative for the wrought 316H (Fig. 11(c)) with the DE and SMDE approaches accounting for viscous strain being closer to the observed CF test life.

In contrast to the wrought 316L and 316H, the life predictions for the DED 316H (Figs. 11(d)–11( f)) tended to be all non-conservative with H-SA-550 being highly non-conservative no matter which creep damage approach was used (Fig. 11( f)). This is attributed to the lower stresses during stress relaxation resulting in reduced inelastic strain during dwell, but perhaps more significantly, because the stress is low, the predicted creep ductility is higher, reaching the upper shelf in the case of SMDE.

To assess the impact of the upper-shelf ductility on the long-term dwell predictions, the DED 316H H-SA-550 predictions were recalculated using either $εf,max=0.1$ or 0.03, with the latter being the lower-shelf value and will provide the most conservative prediction (Fig. 12). The actual life lay between these two predictions suggesting that the creep ductility to predict the DED 316H is smaller than that for the wrought 316H. The creep experiments conducted on the same material processed the same way indicate that the creep ductility is lower for the DED, particularly the H-550 and V-400, compared to the annealed wrought 316H (Fig. 9).

Creep–fatigue life with short dwells is predicted to be much lower than observed when the viscous strain is not accounted for in the DE and SMDE models (Figs. 11(a) and 11(b)). Even though the creep damage fraction depends only on the upper-shelf ductility, the amount of stress relaxation and corresponding inelastic strain is larger upon the initial part of the dwell, which has the effect of increasing the creep damage contribution in the early parts of each dwell. This demonstrates the necessity to account for the viscous strain in the DE and SMDE methods to improve the predictions of ductility exhaustion approaches.

For the TF method, the inflection point observed in the life curves in Fig. 11 is associated with the CF interaction diagram's bilinear failure envelope. As dwell time increases, the computed damage summation transitions from one slope of the bilinear envelope to another. The inflection point is formed when the failure locus' intersection point is crossed. Therefore, the inflection point represents the dwell time when the damage fraction transitions from LCF-dominated to creep-dominated, with the greatest CF interaction predicted to occur near the transition. However, the predictions using the TF method generally are poor being particularly overly conservative for high $Δε$ because the maximum stress at the beginning of the dwell is high resulting in a short $tc$ greatly magnifying the creep damage fraction.

In contrast to the TF method, the inflection points observed in the DE and SMDE predictions in Fig. 11 are associated with creep ductility value when transitioning from the strain rate–dependent regime to either the upper or lower shelf. The predictions are controlled by the upper-shelf ductility when dwell periods are shorter than 0.1 h for the 0.6% and 1.0% strain range, regardless of the DE or SMDE models used.

The CF damage interaction diagrams for the $Δε=0.6%$⁠, 30-min dwell condition are shown in Fig. 13. The damage fractions per cycle used to generate these plots are summarized in Table 13. Fatigue damage fractions are based on the LCF lives for each alloy pedigree, while creep damage fractions are determined from the half-life stress relaxation behaviors, fitted to the Conway expression. These are calculated using various approaches for creep damage evaluation, applying the creep deformation response of wrought 316H as a reference. This choice is justified because the variations in creep strain rates and ductility among all alloy pedigrees lie within the range of the large wrought 316H database (Figs. 9 and 10).

The CF damage interaction diagrams reveal notable trends in damage fraction predictions. For most cases, the predictions for LP-DED 316H alloys are highly non-conservative, while those for wrought 316L and 316H are overly conservative, falling well outside the failure envelopes. An exception occurs with the DED 316H V-550 condition under the DE approach (Fig. 13(b)), where the predictions are consistently conservative across all creep damage evaluation methods. Among the three DED process conditions studied, the V-550 condition demonstrates superior performance, exhibiting both longer LCF and CF lives. However, the TF approach fails to account for this improved behavior, likely due to the underprediction of creep damage caused by the lower stresses during the dwell period. Incorporating the non-damage viscous strain component in the DE and SMDE approaches reduces the predicted creep damage fraction but does not change the overall trend; predictions for wrought 316L and 316H remain conservative.

The non-conservative CF life predictions for DED 316H alloys are driven by several factors. One key issue is the underprediction of creep damage, which arises from the lower maximum stresses observed during the dwell periods of DED 316H tests (see Fig. 6). This leads to longer times to rupture when using the TF approach and an overprediction of creep ductility in the DE and SMDE approaches. Additionally, microstructural differences play a significant role. The large grain sizes characteristic of DED 316H, as shown in Fig. 7, result in less distributed creep cavitation through the microstructure and is concentrated along the fewer grain boundaries. This localized cavitation produces crack-like features that, under cyclic loading, promote fatigue crack growth. Consequently, the DED 316H alloys exhibit greater susceptibility to CF interactions compared to their wrought counterparts. These combined effects highlight the limitations of current damage fraction approaches in accurately capturing the CF behavior of DED 316H materials.

The results highlight that CF lives for DED 316H alloys cannot be reliably predicted from LCF and creep data alone using current damage fraction approaches. Most predictions are highly non-conservative. This underscores the need for acceptance testing to include test conditions specifically designed to promote CF interactions. Relying solely on LCF and creep data, as outlined in lifting methodologies like ASME and R5 design codes, is insufficient for predicting CF behavior in DED 316H alloys.

One of the primary motivations for this work was to identify a cycle type to promote the severe Case C CF interaction in 316 SS to use as an accelerated test for worse-case CF interaction and lowest life. The challenge remains that short dwell times do not promote a severe CF interaction, but long dwell times result in tests that can go on for several days or even months. Although significant life reduction is seen from dwell periods less than one hour from each strain range, these tests can take as long as 3 months to complete, rendering them impractical for accelerated qualification and acceptance testing. However, one feasible approach involves conducting CF tests with an intermediate dwell time (e.g., 30 min) for a specified number of cycles to confirm minimal survivability. This approach would ideally be coupled with an analysis of maximum stress evolution versus cycles to evaluate stability, as well as a metallurgical analysis to quantify the severity and extent of fatigue and creep damage. A possible test at 650 °C is $Δε=0.6%$ with 30-min dwell at maximum strain using the test method ASTM E2714-13 [35]. As shown in the tests conducted here, this cycle promotes a CF interaction that is highly sensitive to the microstructures susceptible to CF interactions.

The large variability in the creep-rupture data introduces considerable uncertainty in life predictions. To isolate the impact of this variability on life estimation, the ±95% CI associated solely with the measured creep ductility was established using a comprehensive database for wrought 316H and applied within the DE and SMDE methods. When these extreme values were used to predict life for tests with a $Δε=0.6%$⁠, 30-min dwell periods, the difference in CF lives spanned a factor of six [34]. This discrepancy increased further with longer dwell times.

It is important to note that this calculation does not account for other sources of uncertainty, such as model form errors, variations in fatigue life, and microstructural heterogeneity. Incorporating these additional factors would likely compound the uncertainty, emphasizing the need for robust methods to quantify and mitigate their impact. Furthermore, future work could focus on reducing variability in creep ductility measurements, exploring probabilistic modeling approaches, and linking microstructural features directly to creep damage mechanisms to enhance predictive accuracy.

For longer dwells, the uncertainty with extrapolating the stress relaxation response is significant. This uncertainty can be reduced to some extent by imposing an extreme strain dwell (say, 100 h) in the CF test program after the CF cyclic response using shorter dwells (e.g., 30 min) has reached a quasi-stable condition. If a 100-h dwell is imposed, then the predictions of CF cycles with up to 100-h dwells will not involve extrapolation of the stress relaxation response significantly reducing the uncertainty extrapolating the dwell stress versus time response to longer times. In addition, other modeling approaches, incorporating refined constitutive modeling, may provide improved extrapolated predictions [48].

A large difference in LCF life is observed between the 316L and 316H evaluated in this study. The evolution of maximum stress reveals important trends (Fig. 6(b)). Annealed 316H, with initially lower strength, reaches a lower saturated maximum stress compared to the 316L bar, which experienced some work hardening during shaping into the bar and hence add less capability of further cyclic hardening. Even though the DED 316H processed were also solution annealed, all had a higher initial yield strength and a higher saturated maximum stress than wrought 316H. One possible explanation for this behavior is the presence of a persistent subgrain structure in the DED material, formed during solidification and partially retained after annealing. These subgrains, which are not typically present in the wrought 316H after annealing, may limit the mean free path of dislocations and thus contribute to the elevated strength. Other factors, such as residual dislocation structures or compositional segregation at subgrain boundaries, may also play a role. The increase in strength is therefore likely due to a combination of factors, with the subgrain structure being a particularly viable contributor.

In wrought 316H, the higher fatigue ductility coefficient associated with its lower initial strength contributes to improved LCF life, as the microstructure can accommodate cyclic plastic deformation with less damage accumulation; i.e., less cracking and debonding of particles or weak interfaces. The enhanced life of wrought 316H is likely due to its greater cyclic and creep ductility compared to both wrought 316L and DED 316H. To improve the CF performance of DED 316H, optimizing microstructures to lower initial strength and increase ductility would be beneficial, as this also reduces applied stress levels and mitigates creep damage.

The creep strains to failure for the two of the DED processed 316H (V-400 and H-550) are lower than the majority of the wrought 316H when the stress is greater than 170 MPa (Table 8 and Fig. 9). Since the CF predictions are highly non-conservative due in part that we are not predicting enough creep damage in the DE and SMDE models, the predictions improve by using a lower creep ductility (Fig. 12), though they still are non-conservative even when the measured creep ductility values are used (0.1 is minimal measured in creep tests) suggesting that the cyclic ductility is also an important consideration. The microstructure needs to be able to withstand cyclic strain without generating crack-like damage, typically observed along grain boundaries.

It should also be noted that despite differences in chemistry and processing, all the process variations tested had creep-rupture lives within the wrought scatterband. While wrought 316H showed improved creep–fatigue resistance to 316L and 316H DED, this work suggests this is most likely due to processing and microstructure with yield strength and elevated-temperature ductility being more important than chemistry. 316H has a higher minimum C content compared to 316L, but macro analysis of long-term creep data shows that C + N and austenite stability, which is similar for all the materials in this study, is likely more important to high-temperature creep performance [49] supporting the important role of ductility and microstructure over chemistry.

Based on the current analysis, a sensible acceptance test program for additively manufactured stainless steels for demanding creep–fatigue conditions should include: (1) creep tests at component temperature, (2) LCF at component temperature, and (3) CF interaction tests conducted at a low strain amplitude $(Δε/2=0.3%)$ with sufficiently long tensile dwell times (30 min or greater) for a specified number of cycles for which susceptibility materials will exhibit discerning cracking which should be verified by post-test metallography consistent with recommendations in Ref. [33].

This study comprehensively evaluated the low-cycle fatigue (LCF) and CF behavior of wrought and additively manufactured (AM) 316 stainless steel, aiming to develop acceptance criteria for accelerated CF testing of AM materials. The key findings are as follows:

1. Influence of Testing Parameters: Temperature, control mode, and dwell time were assessed across 550 °C to 700 °C. Dwell times shorter than 10 min did not significantly promote CF interaction, with cracking behavior resembling LCF. Force-controlled dwell tests also failed to effectively induce a CF interaction, especially at higher strain ranges. A clear CF interaction was only observed with 30-min dwells at $Δε=0.6%$ among the test conditions considered.

2. Comparison of Wrought and AM-processed Stainless Steel: Annealed wrought 316H demonstrated superior fatigue and CF life compared to 316L, with enhanced cyclic and creep ductility attributed to its lower initial strength and greater ability to accommodate cyclic plastic deformation. In contrast, laser powder-directed energy deposition (LP-DED) 316H had comparable LCF life to 316L but significantly shorter CF life. Damage fraction models failed to provide conservative life predictions for DED 316H, unlike wrought materials.

3. Cracking Behavior: Both wrought and DED 316H exhibited CF-induced intergranular cracking. In DED 316H, faster fatigue crack growth limited the formation of creep cavities, resulting in less distributed damage but greater susceptibility to crack propagation. This behavior indicates reduced fracture resistance in this specific LP-DED process for the sample orientations tested, underscoring the importance of optimized microstructures to enhance CF resistance. Differences in DED build orientation and the associated loading direction led to mesostructural variations that influenced cracking behavior and CF performance. Specifically, specimens tested under horizontal loading exhibited shorter CF lives compared to vertically loaded specimens, likely due to a higher number of grain boundaries oriented perpendicular to the loading axis, which facilitated intergranular crack propagation.

Special thanks are due to the institutions and team members who were part of the “Technical Basis of Microstructure Criteria & Accelerated Testing for Qualifying Additively manufactured 316H Stainless Steel for High-temperature Cyclic Service” NEUP Project (Dr. Xiaoyuan Lou and John Snitzer from Purdue University, Dr. Jian Wang and Bingqiang Wei from University of Nebraska-Lincoln, and Dr. Bart Prorok from Auburn University). Dr. James Collins and Jonathan Jean-Louis assisted with the LCF and creep–fatigue testing in the Mechanical Properties Characterization Facility (MPCF) at Georgia Tech. Stefan DeBates, Neil Jackson, and Brian Naing helped with data analysis and life modeling.

• The U.S. Department of Energy (DOE) Nuclear Energy University Program (NEUP); Award No. DE-NE0009193.

There are no conflicts of interest.

The datasets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request.