Investigation of the Damage Mechanisms Influencing the Short Crack Behavior of Inconel 625 Under Variable Amplitude Fatigue Loading

Abstract

Variable amplitude fatigue loading can result in both accelerated and decelerated fatigue damage due to load interaction effects. Short fatigue cracks in particular exhibit a wide range of crack growth behavior due to multiple damage mechanisms contributing to interaction effects. To investigate this variation in fatigue damage behavior and the influence of causative damage mechanisms, variable amplitude fatigue tests were conducted on an Inconel 625 alloy. Periodic overload, high-low, and repeated block loading patterns were applied, and specimens were analyzed with a surface replication technique during testing to capture crack growth. Fracture surface imaging of failed specimens identified crack face morphology. High stress cycles in the overload and repeated block loadings resulted in increased fatigue life, and evidence of plastic crack closure was noted in periodic overload samples. Crack growth deceleration due to overload was identified in crack lengths as short as 65 µm. This increase in fatigue life differs from other research that demonstrated damage acceleration of short cracks during variable amplitude fatigue. This acceleration was attributed to crack closure and microstructural barriers, whereas the deceleration in this study is attributed to the interaction of plastic crack closure and crack extension caused by the application of an overload.

1. Introduction

Aerospace structures operate under Variable Amplitude Fatigue (VAF) loading, wherein fluctuating stress levels induce progressive damage accumulation, significantly influencing the fatigue life of structural components. Vibrational loads in the form of high cycle fatigue (HCF), such as those during cruise, occur at high frequencies and lower stress levels, resulting in limited cyclic plasticity and many cycles to failure. Under HCF, a large portion of life is consumed by crack nucleation and short crack growth, which influences endurance limit and fatigue strength. Linear elastic fracture mechanics is not valid at this length scale, and damage initiation and propagation are dependent on microstructure. In contrast, scenarios such as takeoffs, landings, maneuvers, and turbulence are less frequent or of a shorter duration and typically cause loading at a higher stress. Characterized as low cycle fatigue (LCF), this loading can cause extensive plasticity at crack tips and fewer cycles to failure. These two types of loading during in-service operating conditions can interact and either accelerate or decelerate fatigue damage.

Overall, HCF and very high cycle fatigue (VHCF) are characterized by a large number of cycles to failure, e.g., 10⁴ to 10⁷, and negligible plastic to elastic strain and energy ratios. Beyond the initial nucleation phase and short crack growth regimes, HCF and VHCF are often modeled by the linear elastic fracture mechanics (LEFM) theory and are stress-based. In contrast, LCF and VLCF often refer to cycle-to-failure counts of about 100 to 1000 and 1 to 20, respectively [1]. The plastic deformation is significant in terms of both plastic strain and energy ratios to their elastic counterparts. Often, strain-based and plastic fracture mechanics (PFM) approaches are used in this regime. In general, the fatigue response of ductile metals is strongly dependent on the stress/strain state, especially for the LCF. For example, Kanvinde (2007) and Wei (2025) discuss mechanisms such as micro-void growth and micro-shear cracking under high triaxiality and shear-dominant loadings, respectively, for VLCF [2,3]. From a modeling perspective, there have been efforts to include such microstructural effects in the fatigue crack growth equations. For example, Zhou (2025) integrates a crystal plasticity (CP) finite element model with fatigue indicator parameters (FIPs) in a two-stage approach to account for microstructure-sensitive fatigue processes such as crack nucleation and microstructurally short crack growth [4]. Recently, machine learning approaches are also used to determine the most important microstructural features and loading parameters that contribute to different stages of fatigue crack growth [5].

Attention is directed to experimental approaches to determine the most important microstructural features and loading parameters that determine fatigue crack growth, particularly for VAF loading. VAF loading can affect fatigue damage in all stages of life, from fatigue crack initiation and subsequent growth until failure [6,7,8]. These changes in fatigue life manifest themselves through sequencing and interaction effects, when fatigue life is affected by the ordering in which the load cycles are applied and when the fatigue damage rate is influenced by the previous loading history [9,10]. Fatigue load interaction effects are caused by a wide variety of mechanisms, including plastic crack closure [11,12,13], compressive crack tip residual stresses [7,14], strain hardening behaviors [15], fatigue coaxing [16,17], single-cycle crack extension [18], and the influence of microstructural barriers [19,20], with both the dominant mechanisms and the magnitudes of their influence varying as fatigue damage progresses [6,7,8].

The influence of these mechanisms and their interactions as damage progresses can lead to a wide range of fatigue damage behaviors under VAF, complicating the analysis of a VAF loading scenario. Therefore, it is critical to understand the engagement of the various mechanisms and their contributions for safe component design and lifetime structural reliability. While significant research is available in the literature on the modeling and analysis of fatigue damage due to variable amplitude effects under a variety of loadings and materials (e.g., [10,21]), gaps remain in our understanding of distinctive aspects, for example, the effects of overload (OL)-induced single-cycle crack extension on fatigue life when short crack behavior is dominant.

Many experimental and analysis techniques have focused on the VAF effects of one dominant mechanism or one damage stage but often fail to consider the influence of interacting and competing mechanisms across the full-length scale of fatigue damage. The fatigue damage stage is classified according to crack length into four main categories: crack initiation (when the crack is being formed by damage and dislocation accumulation at persistent slip bands, grain boundaries, or other barriers [22] and a crack has yet to initiate), microstructurally short cracks (the crack behavior is strongly influenced by local microstructural features), physically short cracks (a high ratio of plastic crack tip zone to crack length necessitates the need for elastic plastic fracture mechanics), and long cracks (linear-elastic crack analysis is applicable). In the case of fatigue overloads, researchers have investigated damage-accelerating behaviors, attributing the life reduction caused by Ols to decreased crack opening loads in short cracks, as well as the OL advancing fatigue damage past a microstructural barrier [23,24,25,26,27,28]. Alternatively, researchers have also observed damage-decelerating behaviors caused by an OL due to increased plastic crack closure in long cracks and cyclic strain hardening or softening [14,15,29,30].

Other research, based on a broader view of variable amplitude effects observed both damage-accelerating and damage-decelerating behaviors in the same study. In a wide range of fatigue tests in stainless steels and aluminum, Collin (2009) attributed load interaction effects due to Ols in both materials to mean stress change and strain hardening from OL cycles [15]. The effects of this cyclic hardening were captured in fatigue life prediction by using a Smith–Watson–Topper damage parameter instead of S-N and ε-N data in damage accumulation. The results indicated strain hardening during OL that decelerated crack growth in stress control tests and accelerated crack growth in strain control tests for a cyclically hardening material. He (2017) mainly observed damage-accelerating behaviors in a stainless steel due to Ols and attributed the behavior to OL interaction with grain boundaries, though some tests with the base level loading above the material endurance limit exhibited increased fatigue life, attributed to a fatigue coaxing effect [27]. Meanwhile, Song (1999) investigated the closure behavior of short fatigue cracks in a steel alloy under Ols, and observed that for shorter cracks, the initial crack opening effect of the OL yielded a more significant initial crack growth acceleration that exceeded the subsequent deceleration due to closure [8]. This trend reversed for longer cracks subjected to Ols, with the closure-induced deceleration instead dominating the net effect of the OL. Meanwhile, Su (2023) observed tensile Ols in short cracks using digital imaging correlation (DIC) measurements and noted both compressive residual stresses at the crack tip following tensile Ols as well as evidence of crack closure leading to slowed or arrested behavior after an OL [31].

Another potential mechanism leading to load interaction effects occurs in cases where the fatigue crack experiences significant extension during an OL or high load cycle [18,32,33,34]. This single-cycle crack extension is less common and mainly observed in steel alloys [32,34] and nickel-based alloys [18,33]. This type of extension is believed to be caused by residual crack tip opening from the crack blunting during the OL cycle [32]. Of particular concern in damage analysis, this crack extension during OL can be several orders of magnitude larger than the crack extension during constant amplitude cycling at the same load level [34]. Thus, crack extension during the OL cycle itself further complicates the analysis of load interaction effects when it occurs.

This wide range of observed fatigue behaviors and mechanisms, and the lack of load interaction models that account for these competing features, illustrates the gap in our understanding of VAF effects in short fatigue cracks. This gap is partially due to the lack of physical experimental data quantifying load interaction effects in different material types and damage regimes, especially when OL crack extension is a concern. Specifically, a more rigorous understanding of interaction effects and the influencing damage mechanisms as damage progresses from crack initiation to long crack growth is needed to accurately predict damage in all fatigue regimes due to VAF. Therefore, the goals of this research are to explore the mechanisms responsible for fatigue interaction effects in Inconel 625 (IN625) in the short crack regime and to better understand the effects of OL-induced crack extension on short fatigue crack growth. IN625 was chosen because this material is known to exhibit OL-induced crack extension, complicating the analysis of VAF. Experimental testing was performed for three loading scenarios: high-low (H-L), repeated block, and periodic tensile overloads (POL), to collect fatigue life and short surface crack growth data. Total life, fracture surface analysis, and surface crack length over time were analyzed from initiation to failure for naturally initiating surface cracks, with the data used to investigate the interplay between multiple mechanisms leading to load interaction effects.

2. Materials and Methods

2.1. Material Information

IN625 is a nickel-based alloy (McMaster-Carr, Elmhurst, IL, USA) that is widely used due to its corrosion resistance and high-temperature performance. Wrought IN625 received in sheet form was used for this study, with a grain size of 11–45 µm and a yield stress (${\mathit{\sigma }}_{\mathit{y}}$) of 446 MPa. IN625 exhibits strain softening behavior at 600 MPa cyclic loading [35,36]. Fatigue endurance limit, fatigue crack growth rate, and threshold stress intensity factors have been previously investigated and reported [37]. A summary of IN625 properties is provided in

Table 1. Inconel 625 properties.

Property	Value	Source
Elastic modulus $\left(\mathrm{E}\right)$	207 Gpa	Experimental
Yield stress ${(\sigma }_y)$	446 MPa	Experimental
Ultimate stress $\left({\sigma }_u\right)$	914 MPa	Experimental
Fatigue endurance limit $({\sigma }_e)$	483 MPa	[38]
Paris law (C)	1.38 $\times$ 10−12  $\mathrm{m}/{\left(\mathrm{M}\mathrm{P}\mathrm{a}\sqrt{\mathrm{m}}\right)}^{3.48}$	[37]
Paris law (m)	3.48	[37]
Threshold (∆K)	7.2 MPa $\sqrt{\mathrm{m}}$	[37]
$d_g$	45 µm	Material data sheet

.

Energy dispersive X-ray Spectroscopy (EDS) was performed on four material samples that were polished and unetched. The samples were examined in a Zeiss EVO SEM (30 kV, 500 pA) with Bruker Xflash 6|30 SDD (Zeiss, Maple Grove, MN, USA). Each spectrum was acquired at a random location while the probe was rastored over an area approximately 1000 µm × 750 µm in size. Detector time was constant with a 30 kcps pulse throughput. At these conditions, the incoming EDS count rate was ~30 kcps with 30% dead time. The spectra acquired for 100 s live time. As shown in

Table 2. Chemical composition.

Element	Mass (%) per Sample				Average	St. Dev.
	1	2	3	4
Aluminum	0.2	0.3	0.2	0.2	0.2	0.062
Silicon	0.3	0.3	0.2	0.2	0.3	0.063
Titanium	0.2	0.2	0.2	0.2	0.2	0.023
Chromium	22.1	22.1	22.4	22.1	22.2	0.157
Manganese	0.3	0.3	0.3	0.3	0.3	0.019
Iron	4.4	4.5	4.5	4.4	4.4	0.038
Nickel	56.0	56.2	56.4	55.8	56.1	0.266
Niobium	2.7	2.9	2.9	2.9	2.9	0.103
Molybdenum	9.0	9.5	9.6	9.4	9.4	0.263
Tantalum	0.7	0.7	0.8	0.6	0.7	0.072

, spectra were quantified for Ni, Cr, Mo, Nb, Ta, Fe, Mn, Si, Al, and Ti.

2.2. Specimen Information

The specimen geometry (Figure 1) is a flat bar cut from a 6.35 mm plate. Shallow notches (radius 38.1 mm, depth 0.635 mm) were fabricated on both sides of the specimen using wire electrical discharge machining (EDM) to promote the initiation location of surface cracks and to confine the replication compound for crack observation. The specimen geometry is within the recommended ranges provided by ASTM E466 [39] and E647 [40], and a similar specimen geometry was successfully used with surface replications to observe naturally initiating surface fatigue cracks in a prior study [41]. Specimens were polished along the gauge section and edges by sequential wet sanding with 400, 600, 800, 1000, 2000, and 3000 grit sandpaper to a near mirror finish to aid in surface replica measurement before testing. Specimens were loaded in tension in the L-T direction.

2.3. Experimental Procedure

Experimental testing was performed at two stress levels corresponding to OL and base level (BL) loads at 724 MPa and 586 MPa, respectively. These load levels were chosen to represent high cycle fatigue behavior above the fatigue endurance limit (483 MPa). Loading at a constant 586 MPa stress level corresponds to a fatigue life of approximately 500k cycles, while the 724 MPa stress loading corresponds to a fatigue life of approximately 100k [38]. It is important to note that the 724 MPa stress is above the material’s initial yield strength, and a minimum of three 724 MPa load cycles are applied prior to 586 MPa loading for all VAF loading scenarios. This loading approach ensures that any additional yielding that occurs during later 724 MPa cycles is a result of fatigue cracks or other stress concentrators rather than bulk material yielding.

Fatigue tests were performed as summarized in

Table 3. Summary of loading patterns.

Loading Type	OL Stress (MPa)	BL Stress (MPa)	Number of Specimens	Description
Constant amplitude, low	-	586	1	Constant amplitude fatigue at 586 MPa
Constant amplitude, high	-	724	1	Constant amplitude fatigue at 724 MPa
High-Low	724	586	3	3 cycles at 724 MPa followed by 586 MPa loading until failure
Block loading	724	586	3	Blocks of 5k cycles at 724 MPa followed by 22.75k cycles of 586 MPa loading, repeated until failure
Periodic Overload	724	586	3	3 cycles at 724 MPa followed by 586 MPa loading for 200k cycles, a single 724 MPa cycle was then applied for every 50k of 586 MPa cycles until failure

and illustrated in Figure 2. All tests were conducted at room temperature in ambient conditions. Cyclic loads were applied as a sine wave at a frequency of $\mathit{f}=$ 15 Hz. The load ratio was R = 0.1 for all tests. Testing was first performed with constant amplitude fatigue loading at ${\mathit{\sigma }}_{\mathit{max}}=$ 724 and 586 MPa maximum stress levels, denoted by constant high (CH) and constant low (CL), respectively. Given that the loading is stress-controlled, the strain rate is not constant. However, the maximum stress rate for a uniaxial cyclic loading in an elastic regime provides a strain rate scale of $\dot{\mathit{ϵ}}\mathit{=}\mathit{2}\mathit{\pi }\mathit{f}\left(\mathit{1}\mathit{-}\mathit{R}\right){\mathit{\sigma }}_{\mathit{m}\mathit{a}\mathit{x}}/$E. The corresponding $\dot{\mathit{ϵ}}$ for ${\mathit{\sigma }}_{\mathit{max}}=$ 724 and 586 are 0.297/s and 0.240/s, respectively, indicating a low fatigue strain rate scenario. The goal of the constant amplitude testing was to establish baseline behavior for comparison to published results. Only one specimen was tested at each loading to confirm that the material behaved according to MMPDS S-N curves [33]. If results aligned, then published material properties data would be used instead of performing a full material characterization effort.

The VAF loading cases were selected for a focused investigation of two scenarios: (1) a single periodic overload (POL) and (2) a sustained OL with both low and high cycles designed to contribute equally to damage accumulation (block loading) when assessed with a linear damage accumulation (LDR) method [42,43]. High and low applied stress levels were constant across all loading conditions for direct comparison of results. An additional VAF case, high-low (H-L) loading, was performed to observe the initial effects of plasticity on the material behavior. The H-L loading case consisted of three OL cycles at 724 MPa followed by 586 MPa cycles until failure. Thus, CL, CH, and H-L loadings were designed to provide comparison data for the more complex POL and block loading patterns.

For block loading, 5k cycles at 724 MPa were applied, followed by 22.75k cycles at 586 MPa, with the total number of cycles per block (high and low stress) chosen such that an estimated 10 total blocks would occur before failure. POL loading began with 3 cycles of 724 MPa loading followed by 200k cycles at 586 MPa. After this initial block, a single 724 MPa cycle was applied prior to 50k cycles at 586 MPa and repeated until failure. For the POL specimens, testing was paused periodically to take surface replicas at various intervals to measure crack length. This data was collected to investigate the length of crack extension due to an OL as well as the crack growth afterwards.

Struers RepliSet-T3 (Struers, Cleveland, OH, USA), a silicone-based compound, was applied to record the specimens’ surface conditions at various stages of crack growth. Repliset surface replication compound has been shown to capture surface defects as small as 10 µm in length [44]. The compound was applied to the notched areas on the front and back surfaces of the specimen while the test was paused for 10 min at a load of 22.2 kN (338 MPa) for curing. Replicas were taken 25k cycles before the OL, 5k cycles before the OL, immediately before the OL, immediately after the OL, 5k cycles after the OL, and 25k cycles after the OL. After testing, the replicas were imaged to measure surface crack lengths using an optical microscope (Olympus BX60M (Olympus, Center Valley, PA, USA) at magnifications ranging from 5× to 50×. It should be noted that these measurements represent an average value for crack length. More detailed investigation would consider the three-dimensional shape which could potentially affect the interpretation of crack growth rates and acceleration factor values. For all VAF cases, specimen fracture surfaces were imaged via scanning electron microscope (SEM) to investigate fracture surface morphology. Imaging was performed with a ThermoFisher Helios 5 Hydra CX (ThermoFisher Scientific, Waltham, MA, USA) with an Everhart-Thornley detector. Each crack was imaged along the crack length to identify transitions and other features, resulting in 9–18 images depending on the crack length. Based on these images and estimates of transition locations, specific regions of interest were imaged in greater detail. Representative regions of interest were then chosen if they demonstrated a typically observed behavior, particularly at an overload or behavior transition location.

3. Results

3.1. Fatigue Life

Fatigue life information for each load case is provided in

Table 4. Fatigue life results.

Specimen ID	OL Cycles	BL Cycles	Total Cycles	Average	Coefficient of Variation (%)
CH-1	103,249	-	103,249	103,249	-
CL-1	-	470,302	470,302	470,302	-
HL-1	3	353,656	353,659	329,947
HL-2	3	369,619	369,622		16.8
HL-3	3	266,556	266,559 *
B-1	69,577	295,750	365,327	364,052
B-2	70,708	318,500	389,208		7.1
B-3	60,000	277,521	337,621
POL-1	6	314,172	314,178	366,078
POL-2	7	381,820	381,827		12.6
POL-3	8	402,222	402,230 **

* Corner crack may have caused premature failure. ** Edge crack was the primary crack to failure.

. As shown in Figure 3, the constant amplitude tests at 724 and 586 MPa maximum stress agree with published fatigue life data for IN625 in the tested L-T direction [38]. Therefore, published material properties for IN 625 were used for analysis and comparison instead of performing a full material characterization effort. In the case of the high-low loading, the three cycles of 724 MPa reduced the fatigue life of the remaining 586 MPa cycles by roughly 30% relative to constant amplitude data. This reduction in total expected life is commonly observed in high-low loading scenarios [22,23]. This reduction has been attributed to the initial high cycles significantly contributing to crack initiation, causing the following low cycles to more rapidly induce damage propagation. For both the block and POL loading cases, fatigue life was increased relative to the H-L loading. This change in the average is notable given the number of Ols and large blocks of 724 MPa cycles in the POL and block loading cases, respectively. While fatigue testing three specimens per condition is common, the sample size is low from a statistical perspective. However, when considering that a specimen in each of the H-L and POL groups exhibited failure at locations other than the specimen center, the results are consistent.

The fatigue life results were analyzed using LDR (Equation (1)) [42,43] with the results quantified in

Table 5. LDR damage values at failure. Total damage > 1 corresponds to a longer than expected fatigue life as predicted by linear damage summation, while total damage < 1 corresponds to shorter than expected fatigue life.

Specimen ID	724 MPa LDR Damage	586 MPa LDR Damage	Total LDR Damage	Average Total LDR Damage	Coefficient of Variation (%)
HL-1	3 × 10−5	0.75	0.75	0.70
HL-2	3 × 10−5	0.79	0.79		16.7
HL-3	3 × 10−5	0.57	0.57
B-1	0.67	0.63	1.30	1.28
B-2	0.68	0.68	1.36		7.6
B-3	0.58	0.59	1.17
POL-1	6 × 10−5	0.67	0.67	0.78
POL-2	7 × 10−5	0.81	0.81		12.6
POL-3	8 × 10−5	0.86	0.86

. Damage, D, is the fatigue damage normalized by the predicted cycles to failure, such that D = 0 is undamaged material, and at D = 1 failure is predicted. The damage contributions of the 724 MPa and 586 MPa cycles during VAF loading are calculated as the number of applied cycles at that stress before specimen failure during VAF loading divided by the cycles to failure during the constant amplitude test at the same stress level. These LDR damage values provide a point of comparison to demonstrate that the H-L and POL specimen groups experienced load sequence and interaction effects resulting in a net effect of accelerating fatigue damage. Meanwhile, the block loading specimen group experienced load interaction effects that decelerated damage [42,43].

$$D={\sum }_i{\displaystyle \frac{N_{i,app}}{N_{i,failure}}},$$

(1)

where $N_{i,app}$ is the number of cycles for the phase $i$ of VAF, and $N_{i,failure}$ is the number of cycles to failure that is computed based on a representative initial crack length $a_0$ growing to critical crack length $a_c$ for the specific loading of the VAF phase $i$; see [22] for more details.

3.2. Crack Length Measurements for Periodic Overload Tests

Surface replicas were used to measure surface crack length at various cycle counts during the POL tests to observe crack growth behavior before and after tensile Ols. The total surface crack length of each specimen’s primary crack as a function of cycle count is shown in Figure 4. Surface crack behavior exhibited tortuous crack paths and microcrack coalescence, consistent with prior observations [41,45]. One specimen, POL-2, failed due to a single dominant crack that propagated in the gauge section, while the other two specimens, POL-1 and POL-3, failed due to the coalescence of several smaller cracks. While the crack recorded via surface replications on the POL-3 specimen occurred on the front face of the specimen, the dominant crack that led to failure initiated at the specimen edge within the gauge section. This crack was not fully measured as it was outside the notched region where surface replications were performed.

Surface cracks typically initiated immediately after the first three 724 MPa load cycles, with initial defect lengths ranging from 7 to 20 µm. After crack initiation, the crack growth rate slowly increased until the first OL was applied at 200k cycles. Upon application of the OL, several phenomena were typically, but not always, observed. During the OL cycle the crack extended, and after the OL cycle crack growth was either reduced or temporarily arrested.

The extension experienced during the applied Ols is shown in Figure 5. The crack extension due to a single OL cycle does not appear to be correlated to the crack length at the time of the OL, but rather stays consistently under 35 µm, roughly corresponding to the characteristic microstructural dimension. An outlier in the length of crack extension is seen for the OL applied to the longest crack length of 900 µm, with crack extension of over 125 µm during the OL. This longer extension length is likely due to the crack approaching failure at the time of the OL, causing unstable crack growth. OL extension was previously observed in a nickel-based alloy [18,33] and other materials as previously discussed.

3.2.1. General Fracture Surface Observations

Fracture surfaces were imaged with SEM after ultrasonic cleaning in acetone and ethanol to observe crack propagation behavior and crack face morphology. Observed features were compared to the IN625 literature examples of fatigue fracture surfaces [46]. Regions of the fracture surface were identified corresponding to the mechanism of crack growth: crack initiation/Stage I (single-slip) crack growth, Stage II (multi-slip) crack growth, Stage III (unstable) crack growth, and ductile failure/fast fracture. An illustration of these different regions is shown in Figure 6 with example images displayed in Figure 7. Magnification factor (mag), working distance (WD), and horizontal field width (HFD) were optimized for each image. These values are provided along the bottom of all SEM images.

Near the fatigue crack initiation point, the fracture surface exhibits a relatively rough, faceted fracture surface. Due to the nature of single-slip fatigue, the fatigue crack propagates on a single-slip plane in the crystal, leading the crack path to follow the local crystal geometry. It is difficult to distinguish between an initiating flaw and stage I fatigue in this region due to their similar faceted appearance. Further away from the crack initiation point, the fatigue crack grows via multiple slip planes, according to stage II behavior. This growth is characterized by fatigue striations, with each line perpendicular to the crack growth direction representing one cycle of crack extension. The stage III region of fatigue consists of elements of both stage II and ductile failure. Finally, the region of fast fracture as the specimen fails and completely separates on the last load cycle is characterized by a ductile pitting texture. These textures are consistent with those observed in the literature examples of IN625 fracture surfaces [46]. Several features on the fracture surface were specifically identified: (1) the fatigue initiation point and any contributing flaws, (2) the transition point between stage I (single-slip) and stage II (multi-slip) fatigue crack propagation, (3) the transition between fatigue and ductile failure/fast fracture, and (4) changes in load level.

Fatigue cracks appeared to initiate via cleavage, with a rough, faceted texture similar to that seen in single-slip fatigue crack propagation. Crack initiation points were located using the origin point of beach/clam shell marks on the fatigue surface. Occasionally, for specimens with surface replications, the initiation point was occluded by remnants of the surface replication compound, which could be removed via the ultrasonic cleaning in solvent before imaging. These initiation characteristics are shown in Figure 8.

The transition between single- and double-slip fatigue crack growth behavior proved more difficult to identify. As shown in Figure 9, the observed fracture surface features of single-slip and multi-slip fatigue are similar, both showing striation markings perpendicular to the crack growth direction. The difference between stage I and II can then be identified by the underlying surface texture, as well as by the intensity and shape of the striations themselves. In stage I growth, the striations lie on a faceted, quasi-cleavage surface [46] following the crystallographic orientations most likely to experience cyclic deformation (with some regions of rough texture where the crack propagated via cleavage between slip planes, and no striations are observed). In stage II growth, the fatigue crack is propagating via slip on multiple planes, allowing the crack growth to lie along the plane normal to the applied stresses instead of aligning with the most favorable orientation of the local crystal. Therefore, the observed fatigue striations in stage II are more consistent, relatively straighter, easier to identify, and more uniform than those observed in stage I fatigue. While stage II fatigue is typically assumed to occur after stage I propagation (once the crack tip driving force is high enough to activate multiple slip planes), the variability of single-slip behavior due to local microstructure means that the transition between stage I and II fatigue crack growth occurs somewhat gradually rather than at a specific crack length. Therefore, the transition between stage I and II fatigue is provided as a range from multi-slip texture initiation to the end of single-slip behavior. These ranges for each specimen group are provided in

Table 6. Slip transition length for each specimen group. Transition is displayed as a range from the first evidence of multi-slip texture to the end of observed single-slip behavior.

Loading	Single-Multi Slip Transition Region (µm)
CA, 724 MPa	900–1200
CA, 586 MPa	1200–1800
H-L	900 *–1500
POL	900–1200
Block	500–1200

* The first evidence of multi-slip propagation in H-L samples varied between 900 and 1200 µm. All other specimens exhibited insignificant variation in start and end values within a group.

.

While the transition between fatigue and ductile fracture can be identified with a naked eye and at low magnifications on the fracture surface, finding the exact point of transition using high-resolution imaging is more challenging. In theory, stage II fatigue should be easily identifiable with fatigue striations and fast fracture with its ductile pitting texture. However, for this material, the fatigue surface exhibited elements of particle separation similar to pitting, and slip lines were visible in the ductile fracture region [46], thus confounding the exact point of transition. Examples of the transition between stage II fatigue and ductile fracture are shown in Figure 10, at both low and high magnifications. In general, the ratio between ductile damage and fatigue damage can be deduced by inspecting ductile damage-induced regions from the SEM images. While this ratio was not calculated for the present study, we refer the reader to [3] for further discussion on fatigue and ductile damage, as well as the sensitivity of ductile damage to loading paths or histories.

3.2.2. Fracture Surface Observations for Load Level Changes

Areas on the fracture surface corresponding to load level changes were noted for both low to high load (586 to 724 MPa) and high to low load (724 to 586 MPa) changes. Locating the first load level transition in the H-L and POL specimens is challenging, as is differentiating the damage caused by the three initial load cycles at 724 MPa versus that from the subsequent 586 MPa cycles. When examining the difference between crack initiation and the start of short crack growth in the constant amplitude specimens, no general differences in texture were observed. This challenge also applies to identifying load level transitions elsewhere in the region of stage I fatigue. Transitions in load level are much easier to observe once the fatigue crack is propagating in stage II when transitions are distinguished by a change in striation spacing [47,48]. An example is provided (Figure 11) for a low to high load change in a block loading specimen.

Due to the nature of stage I fatigue that typically occurred at a lower driving force (e.g., ΔK) than stage II fatigue, transitions from multi-slip to single-slip fatigue that are consistent across the crack front can be interpreted as changes from high to low loading (Figure 12). Several instances of HL to BL (724 to 586 MPa) load level changes were observed. The block loading specimen (B-2) exhibited the formation of a distinct ridge at the transition from the low 586 MPa load to the higher 724 MPa load (Figure 13). The texture in the area immediately after the load was similar to that observed in the ductile/fast fracture region, showing regions of ductile pitting. Several other fracture surfaces exhibited texture changes due to the single-cycle 724 MPa tensile Ols during the POL testing. Explicit differences at load changes were identified at crack lengths ranging from 680 to 1800 µm (Figure 14). The texture created during the OL itself demonstrated plastic stretching, possibly indicative of crack tip single-cycle crack extension or blunting, with longer regions exhibiting ductile pitting (Figure 15). Notably, this texture of plastic deformation was also observed when the crack length was short and growing in the stage I/single-slip regime (Figure 16).

Determining the exact point on the fracture surface corresponding to the OL is challenging at crack lengths shorter than 600 µm. Crack growth rate variability in the single-slip/stage I regime signifies that the crack front growth rate is dependent on the local microstructure, which varies across the crack front. As the crack grows and a higher driving force is manifested, an increased number of slip planes are activated and the crack front growth rate is stabilized, leading to a more uniform crack front shape. This microstructure dependence is also noted in other studies [49].

4. Discussion

4.1. Overall Trends and Comparisons to Linear Damage Accumulation

The fatigue life results, (Table 4 and Table 5), provide a comparison of observed fatigue lives to those predicted by LDR. Though the LDR prediction is inaccurate in the case of this study, both over-predicting and under-predicting fatigue lives by 28–30%, respectively, it serves as a point of comparison for the fatigue data to determine if load sequencing or load interaction effects are present. The direction of the error in the LDR prediction allows us to determine whether the load sequence or interaction effects have a net accelerating damage or net decelerating damage behavior.

The H-L samples exhibited failure 30% earlier on average than predicted by LDR. This demonstrates that the initial cycles of the 724 MPa OL significantly decreased fatigue life, even though the linear damage contribution of the 724 MPa cycles was minimal. This drop in life can be explained by load sequence effects common in H-L loading scenarios [10,22], and is often accounted for and shown though a damage-curve method [50,51]. The initial high load cycles cause the rapid initiation of a fatigue crack that is propagated by subsequent low load cycles. Evidence of this mechanism is present in this study from the crack initiation length of 7–20 µm following the initial three 724 MPa cycles determined from the surface replicas.

The block loading tests exhibited an average fatigue life 28% longer than that predicted by LDR. Therefore, load interaction effects caused the net effect of decelerating fatigue damage. Meanwhile, the POL specimens exhibited an average life that is 22% shorter than the LDR prediction. While this demonstrates that load sequence and interaction effects are present and cause a net reduction in fatigue life, a comparison of the POL group to the H-L group shows a relative increase in fatigue life of 11% for the POL specimens. This shows that while the POL and H-L specimens are both influenced by load sequencing effects (due to the same initial three cycles of 724 MPa in each), an additional load interaction effect is present due to the applied OLs causing this increase in fatigue life. This load interaction effect from the OLs results in a net deceleration in fatigue damage, as observed in the block loading specimens.

4.2. Fatigue Damage Regime

As previously discussed, multiple fatigue damage regimes dictate damage mechanisms and behaviors. Several definitions for a crack length that is considered short or small ($a_s$) exist in the literature based on varying criteria (

Table 7. Short crack definitions. Values for short crack transition lengths are computed using the material properties listed in Table 1 at both 586 MPa and 724 MPa load levels where applicable.

Formula	Basis	Value
$a_s\le 5-10 d_g$ [40,52]	Crack is shorter than the characteristic microstructural dimension	225–450 µm
$r_y\le 2-3 d_g$	Plastic zone size is too small to apply smeared/homogeneous material properties in fatigue crack growth	144 µm (@586 MPa) 91 µm (@724 MPa)
$a_s\le {\displaystyle \frac{1}{\pi }}{\left({\displaystyle \frac{{∆K}_{th}}{{\sigma }_e}}\right)}^2$ [53]	Transition behavior is dictated by endurance limit vs. threshold SIF	142 µm
observed	Stage I to stage II crack growth transition	900–1200 µm (@586 MPa) 500–1200 µm (@724 MPa)

). From shortest to longest, these are: a short crack based on the size of the crack tip plastic zone ($r_y$) relative to the microstructure, the crack length at which the fatigue damage threshold is controlled by endurance limit stress (${\sigma }_e$) becomes controlled by the threshold stress intensity factor (${∆K}_{th}$), the short crack length is defined as a multiple of the microstructure dimension (grain size $d_g$), and the crack length when the fatigue crack growth transitions from single-slip to multi-slip crack propagation.

A plot of crack length data for the POL specimens, as compared with the short crack definitions, is provided in Figure 17. This plot shows that for the POL group, the majority of the fatigue life and crack growth occurred where at least one definition of a short crack, based on stage I vs. stage II crack growth, was applicable. Though the rest of the short fatigue crack definitions are applicable for smaller fractions of the total fatigue life than the slip-based transitions, they remain valid for at least 50% of the total life. This finding is consistent with other high cycle fatigue data, where crack initiation and short crack growth regimes constitute the majority of fatigue life [22]. Additionally, most of the applied OL cycles occurred at crack lengths where many of the smaller short crack definitions (such as those based on microstructure size or threshold behavior transition) are applicable. Due to the large portion of fatigue life spent in the short crack regime, we can assume that any of the load interaction effects present in the block and POL sample groups affected damage in the short fatigue crack growth regime. Some observations on the crack growth behavior with respect to the short crack definitions is that post-OL crack arrest is seen in cracks as long as 330 µm, within the short crack range based on characterizing microstructure dimensions, and that pre-OL crack arrest was not observed at crack lengths longer than 130 µm, just before the plastic zone/grain size for 586 MPa loads and the threshold behavior transition point.

4.3. Quantification of Overload Effects

Several measures have been used to quantify the effects of an individual OL or load level change on fatigue damage. The most basic and widely used method for both experimental analysis and modeling is an acceleration or retardation factor (AF). The AF is a ratio of crack growth rates before and after an OL or a change in load level (Equation (2)). An AF >1 indicates acceleration, while an AF < 1 indicates deceleration. This particular measure is applied in methods such as the Wheeler model [14] and in block loading [54],

$$AF={\displaystyle \frac{{\left(da/dN\right)}_{post-OL}}{{\left(da/dN\right)}_{pre-OL}}},$$

(2)

where ${\left(da/dN\right)}_{pre-OL}$ and ${\left(da/dN\right)}_{post-OL}$ are the crack growth rates before and after the application of the OL.

Care must be taken in measuring growth rate, as crack growth rates after an OL can quickly change as factors such as crack closure and crack tip geometry evolve. Therefore, selection of regions/timesteps to measure crack growth rate is important given the potential for multiple behaviors in a short timestep; for example, differentiating the crack extension during the OL cycle from subsequent crack growth. A potential problem with the AF approach for microstructurally short cracks is the possibility of crack arrest before OL application, resulting in an undefined AF.

Several measures of AF were used to quantify OL effects in this study (

Table 8. Crack length, OL extension, and acceleration factor measures for the POL specimen group. Undefined values of AF indicate that the crack was arrested before the OL application.

Specimen	Overload	aOL-1	Δa	5k AF	25k AF	25k AF (w/OL)
POL-1	200k **	140	42	0.346	0.311	0.771
	250k	249	16	0.000	1.118	1.520
	300k	880	124	1.823	N/A *	N/A *
POL-2	200k	65	30	0.083	0.045	3.035
	250k	96	29	undefined	undefined	undefined
	300k	195	7	0.571	1.389	1.494
	350k	496	29	0.667	4.166	4.315
POL-3	200k	98	0	undefined	undefined	undefined
	250k	124	0	undefined	undefined	undefined
	300k	159	27	0.096	1.675	2.431
	350k	327	28	0.042	1.493	1.831

* Specimen failed within 25k cycles of overload. ** two microcracks coalesced to form primary crack.

). The metrics are the 5k acceleration (the ratio of the crack growth 5k cycles after the OL to the crack growth 5k before the OL), the 25k acceleration (the ratio of the crack growth during the 25k cycles after the OL to the crack growth 25k before the OL), and the 25k acceleration that includes the crack extension during the OL. Actual crack growth rate data and predicted crack growth rate based on a Paris model are shown in Figure 18. The calculated Paris model crack growth rate (Equation (3)) does not account for load interaction effects and is included to differentiate between load interaction effects and the increase in growth rate due to increasing crack length. Paris growth constants are shown in Table 1 above, and a geometry factor of 0.73 was applied to the calculation of the stress intensity factor range to represent a semi-circular surface crack.

Crack growth rate $da/dN$ is calculated from the total crack length on each specimen,

$${\displaystyle \frac{da}{dN}}=C{(∆K)}^m,$$

(3)

$$∆K=0.73 ∆\sigma \sqrt{\pi a}$$

(4)

From the acceleration measures, all but one of the applied OLs caused a reduction in crack growth when looking at the 5k AF. The final OL of the POL-1 specimen was the longest crack length observed and contained evidence of unstable stage III crack growth on the fracture surface (Figure 14). The AF measures taken over the wider 25k cycle windows, however, show more variance. The tendency of the AF to be higher (more acceleration) for the 25k cycle window can be partially attributed to cracks simply growing faster because they are longer (higher ΔK (Equation (4)) driving force at the same applied load level). The comparison of the experimental crack growth to the Paris model predictions (Figure 16) shows that while the Paris model does not account for the OL effects, it clearly indicates an increase in growth rate due to the increasing crack length alone.

4.4. Mechanistic Analysis

Correlation of the fatigue damage mechanisms to the damage-decelerating load interaction effects observed in the block and POL specimen groups is now addressed. Section 4.4.1, Section 4.4.2, Section 4.4.3, Section 4.4.4 and Section 4.4.5 discuss potential fatigue load interaction mechanisms individually, and their interactions are discussed in Section 4.5.

4.4.1. Mean Stress Rearrangement and Cyclic Hardening/Softening

Potential contributing mechanisms to fatigue load interaction effects are mean stress rearrangement and cyclic hardening/softening due to load level changes. Mean load rearrangement was observed by [15,55], where POLs applied to a 304 L stainless steel caused repeated cyclic hardening. This cyclic hardening causes an increase in stress range ($\Delta \mathit{\sigma }=2{\sigma }_a$) for strain-controlled tests and a decrease in strain range ($\Delta ϵ=2{ϵ}_a$) for load control tests, as well as changes in cyclic mean stress (${\mathit{\sigma }}_{\mathit{m}})$.

Because the application of the overload adjusts the range and mean of stress or strain for strain-controlled or stress-controlled loadings, respectively, a fatigue life model that includes all such values is sought to predict the effect of the overload. This combined effect of mean and range values is included in Smith–Watson–Topper (SWT) life estimation [56], given by Equation (5).

$${\sigma }_{\mathrm{m}\mathrm{a}\mathrm{x}}{ϵ}_a={\sigma }_a\left[{\displaystyle \frac{{\sigma }_f^{\prime }}{E}}{\left(2N_f\right)}^b+{ϵ}_f^{\prime }{\left(2N_f\right)}^c\right]$$

(5)

where ${\sigma }_{\mathrm{m}\mathrm{a}\mathrm{x}}= {\sigma }_m+ {\sigma }_a$ is the maximum stress in the cycle and $N_f$ is the number of full cycles to failure. The terms ${(\sigma }_f^{\prime }/E){ \left(2N_f\right)}^b$ and ${ϵ}_f^{\prime }{\left(2N_f\right)}^c$ represent the elastic and plastic parts of the half-strain range (${ϵ}_a$), each individually related to $N_f$. Thus, the equation captures the combined effect of elastic and plastic strains on $N_f$. ${\sigma }_f^{\prime }$  is the fatigue strength coefficient, which is close to the true fracture strength ${\sigma }_f$. Similarly, ${ϵ}_f^{\prime }$ is the fatigue ductility coefficient, which is close to the true fracture ductility ${ϵ}_f$ (true strain corresponding to ${\sigma }_f$). The ordering of powers $c<b< 0$ ($b\approx$ −0.12, c $\approx$ −0.75 for Inconel [17]) ensures a dominant elastic strain contribution for long fatigue lives [17]. Finally, the terms ${ \sigma }_{max}$ and ${\sigma }_a$ on the two sides of the equation account for the mean stress effects [56].

Referring to Equation (5), the possible effects of the OL on fatigue life can be discussed, from the perspective considered herein; that is, the adjustment of the mean and range of relevant values for the stress-controlled fatigue loading considered in our experiments. Referring to the aforementioned effects of the POL from [15,55], for a cyclic hardening effect of the overload, both ${ϵ}_a$ and ${\mathit{\sigma }}_{\mathit{m}}$ decrease after the OL. Given that ${\sigma }_a$ is fixed, this results in a net increase in fatigue life ($N_f$) upon the application of the OL. Thus, by reversal of these effects (increase of ${ϵ}_a$ and ${\mathsf{\sigma }}_{\mathit{m}})$ for a cyclic-softening material, it is reasoned that POLs applied in stress control accelerate damage in cyclically softening materials, while decelerating damage in cyclically hardening ones.

With such a predictive model, the possible effect of mean stress rearrangement on our fatigue life experiments will be discussed. The cyclic behavior of IN625 shows an initial period of cyclic hardening for the first 10–100 cycles, followed by cyclic softening until failure [35]. Based on this cyclic behavior, the material used in this study reached its cyclic softening stage prior to the application of both the POLs and high stress blocks. An increase in the strain range of cycles following the OL or high stress block should therefore have been observed. This increase in strain range for the low-stress cycles would then correspond to an increase in fatigue damage per cycle as predicted by Equation (5), and thus a shorter fatigue life. However, the load-controlled OLs and high stress blocks resulted in damage deceleration, indicating that cyclic softening and mean stress rearrangement had a minimal effect on fatigue life.

4.4.2. Microstructural Barriers

Microstructural barriers, such as grain boundaries (GBs), play a significant role in short crack growth rate variability [57] as well as fatigue endurance limit behavior [58,59]. Damage propagation, including at the physical crack tip as well as in regions of cyclic plasticity ahead of the crack tip, can be arrested or slowed by a grain boundary or other barriers if the applied loading and driving force are not sufficiently high to advance the crack tip through the barrier, resulting in variable and slowed short crack propagation under constant, low amplitude fatigue. Acceleration can occur across a grain boundary if a high-amplitude load cycle generates a driving force sufficient to advance the crack tip or the damage process/plastic zone past the barrier (Figure 19). This damage-accelerating behavior of VAF and OLs at microstructural barriers has been investigated using modeling techniques [19,54] and observed in experimental testing [27]. This damage acceleration is significant in cases where lower amplitude fatigue loads are below the material endurance limit, and barriers would arrest crack growth without the OL growing the crack or damage zone past the grain boundary.

In this study, the majority of the applied OLs and high stress blocks occurred in the short crack regime, where significant variability in growth rates was observed, indicating that the effects of the local microstructure at the crack tip were significant. The acceleration from high load cycles pushing past barriers as described above was not observed in the POL or block specimen groups.

4.4.3. Plastic-Induced Crack Closure

Plastic deformation that forms at a crack tip can subsequently cause contact in the wake of crack tip advancement as the crack grows, reducing the range of the load cycle at the crack tip when the crack tip is open. This plasticly induced crack closure (PICC) is often represented as U, the ratio of the applied stress while the crack tip is open over the total applied stress cycle range (Equation (6)). A U value of 1 indicates that the crack is open for the entirety of the load cycle (no closure effects), and low values of U indicate crack closure/crack face contact. PICC behavior can occur during both constant amplitude and variable amplitude fatigue. In constant amplitude fatigue, yielded material from each load cycle accumulates in the wake of the crack tip, causing a steady-state crack closure once a sufficient accumulation has formed. In VAF, additional PICC is caused by the asperity (or bump) of yielded material formed during an OL or HL block, causing contact on the crack surface at the location corresponding to the OL application. As the crack tip grows away from this plastic asperity, its effect of increasing PICC is slowly reduced until it returns to its steady-state value.

PICC has been attributed as the primary mechanism for load interaction effects from OLs applied to long cracks [13,30]. Plastic crack closure explains both the overall retardation of crack growth after the OL due to the plastic asperity and the initial crack growth acceleration observed directly after OL application, often seen in long crack OL data. This initial jump in crack growth rate is caused by the crack tip opening while still located in the region of deformed material caused by the OL, relieving any steady-state levels of crack closure built up during constant amplitude fatigue. The effective stress intensity factor range $\Delta K_{\mathrm{e}\mathrm{f}\mathrm{f}}=U\Delta K$ is used to determine fatigue life,

$$U={\displaystyle \frac{∆{\sigma }_{\mathrm{e}\mathrm{f}\mathrm{f}}}{∆\sigma }}={\displaystyle \frac{{\sigma }_{\mathrm{m}\mathrm{a}\mathrm{x}}-{\sigma }_{\mathrm{o}\mathrm{p}\mathrm{e}\mathrm{n}\mathrm{i}\mathrm{n}\mathrm{g}}}{{\sigma }_{\mathrm{m}\mathrm{a}\mathrm{x}}-{\sigma }_{\mathrm{m}\mathrm{i}\mathrm{n}}}},$$

(6)

where $\Delta {\sigma }_{\mathrm{e}\mathrm{f}\mathrm{f}}= {\sigma }_{\mathrm{m}\mathrm{a}\mathrm{x}}- {\sigma }_{\mathrm{o}\mathrm{p}\mathrm{e}\mathrm{n}\mathrm{i}\mathrm{n}\mathrm{g}}$ is the effective stress range from the instant of crack opening to the maximum stress, and $\Delta \sigma = {\sigma }_{\mathrm{m}\mathrm{a}\mathrm{x}}- {\sigma }_{\mathrm{m}\mathrm{i}\mathrm{n}}$ is the total stress range.

The relationship between plastic crack closure and fatigue interaction effects on short fatigue cracks has been debated [60,61]. Because crack closure requires deformed material to cause contact on the crack face in the wake of the crack tip growth, closure therefore requires a change in crack length to engage. This requirement led some researchers to discount the role PICC plays in short fatigue cracks. The reasoning is that there is not significant crack growth for deformed material to accumulate in meaningful quantities on the crack face [60] or that, due to the shear dominant mechanism of stage I, crack propagation does not deform the material in such a way that PICC is possible [61].

The accumulation of deformed material as a short crack propagates was experimentally investigated in an aluminum alloy [6], where plastic crack closure was used to explain some of the short crack load sequencing effect. Song (1999) tracked short crack growth rates and opening levels in an alloy steel, with OLs applied at crack lengths ranging from 0.58 mm to 3.20 mm [8]. Initial acceleration of crack growth immediately after OL application due to an increase in U, with deceleration following afterwards due to a decrease in U, was observed during tests (behavior characteristic of plastic crack closure). However, the crack growth acceleration immediately after the OL had a larger effect than the subsequent deceleration, leading to a net increase in damage. This effect is depicted in Figure 20, illustrating how the ratio of acceleration to deceleration periods of crack growth influences the net change in fatigue damage, and how this applies to the difference between PICC effects in long and short cracks. Measurements of closure levels have confirmed this observation [31].

The influences of PICC in this study are evident in the crack growth before and after OL application in the POL specimens (Figure 4 and Figure 18). Deceleration of crack growth, and in some cases, temporary crack arrest, are observed after OL application. This behavior aligns with PICC behavior documented in the literature for both long and short cracks, though notably, the initial period of crack acceleration after OL application was not observed. This finding is reinforced by the total-life data for the block and POL specimens, which show an increase in fatigue life, counter to the expected behavior of short crack closure, predicting a decrease in life. The implications of this observation are discussed below in relation to other mechanisms that cause interaction effects, notably the crack extension due to a single high stress OL cycle or the first high stress cycle of an OL loading block.

4.4.4. Compressive Residual Stresses (Crack Tip Shielding)

Compressive residual stress, considered the cause of crack tip shielding, is another mechanism that potentially contributes to load interaction effects. Such stresses occur when fatigue cycles transition from high to low load levels, and the crack propagates through the compressive plastic zone caused by the previous, higher loading. The degree to which compressive residual stress plays a role through crack tip shielding versus that of crack closure is debated. Fatigue crack growth often accelerates immediately after a tensile OL [13], as mentioned above in the discussion of PICC, which is counter to the expected effect that compressive residual stresses would decelerate crack growth. This observation has led some researchers to discount the effects of compressive residual stress as a mechanism for load interaction effects, instead concluding that PICC is the dominant mechanism leading to slowed crack growth after OL application. Deceleration immediately after OL application has, however, been observed in some cases [7]. DIC and X-ray diffraction measurements demonstrated crack tip shielding, which was separated from plastic crack closure. Su (2023) also observed crack tip shielding in short crack growth during an OL using a DIC technique [31]. This shielding effect, along with significant crack tip blunting, led to the complete arrest of some shorter cracks, though in some cases cracks propagated past the initial blunting and shielding, where plastic crack closure was observed. In the current study, immediate growth deceleration after OL application was noted in the crack growth data for the POL specimens, similar to [7,31]. This observation could indicate residual stress interaction effects, though this behavior could also be attributed to PICC or crack tip blunting mechanisms.

4.4.5. Crack Tip Blunting

Crack tip blunting occurs when a high stress cycle causes significant yielding at the crack tip, converting a previously sharp crack into a more open/rounded notch, reducing the crack tip stress intensity and growth rate [31]. As with crack tip shielding, the degree to which this blunting plays a role after an OL or high cycle application is debated, as blunting should immediately slow crack growth after an OL but growth acceleration after OL is often observed instead [13].

4.5. Mechanistic Basis for Observed Crack Growth Behavior

PICC was investigated as a potential primary mechanism of fatigue interaction effects, as it is the most often attributed mechanism in the literature and is observed in both short and long cracks [13]. However, the behavior observed in this study differs from the literature examples of PICC-induced interaction effects in short cracks in several ways. The first difference between the behavior in this study to others [8,31] is the absence of an initial period of crack growth acceleration due to the brief increase in U immediately after an OL. This difference could be partially due to the effects of a single OL cycle crack extension on the crack closure process, which was not present in [8,31]. It is possible that the deformed material created during the OL extension caused immediate contact between crack surfaces, given the significant crack extension during the OL, rather than a delay while the crack grows past the initial location corresponding to the OL for the crack faces to begin contact. The single OL cycle extension negates the need for some length of crack growth after the OL or high stress cycle for reduced growth rates to begin, therefore bypassing the period of accelerated crack growth due to a reduction in closure levels and increase in U. This partially explains why the crack growth behavior observed experimentally is closer to what we would expect in a long crack for PICC than the closure effects typically seen in short cracks. An illustration of this concept is provided in Figure 21.

The total load interaction effect mechanisms can be summarized as follows: H-L samples experienced life-reducing load sequence effects from crack initiation due to the initial high cycle loads. Block loading and POL samples both experienced damage-decelerating interaction effects. Several mechanistic processes were considered to explain this overall deceleration. First, mean-stress rearrangement results in deceleration or acceleration for cyclic hardening or softening material. Since earlier experimental works indicate the softening behavior for IN625 at cycle numbers at which the OL was applied in our experiments, a crack acceleration is expected from this perspective. Accordingly, this process is deemed to be insignificant in this work, given the contrary deceleration observed. Second, OL stress is high enough that it is expected to facilitate a sufficient driving force to pass through microstructural barriers. Third, PICC is expected to decelerate crack growth for long cracks. For short cracks, both acceleration and deceleration are reported. In our case, a deceleration response similar to long cracks was observed, indicating a higher effect of the crack closure than the initial acceleration after the application of the OL. PICC is likely to have such a significant effect because the OL extension grows the crack sufficiently to engage PICC. Fourth, compressive residual stresses have a similar effect to PICC, although PICC is deemed to have a more dominant role in the deceleration case. Fifth, crack tip blunting is expected to immediately result in crack growth deceleration, whereas an initial acceleration was observed after the OL.

5. Conclusions

Fatigue tests were conducted on Inconel 625 specimens at three VAF load patterns (H-L, block, and POL) consisting of varying patterns of 586 MPa low-level loads and 724 MPa high-level loads. Fatigue life for the H-L exhibited reduced fatigue life, while the results for the block and POL showed that the OL cycles increased the fatigue life of the specimens, indicating load interaction effects. Surface replicas from the POL specimens demonstrated that crack extension occurred during the high-amplitude cycles applied to microstructurally short cracks, followed by slowed or completely arrested crack growth immediately after the OL. Fractography of the fatigue specimens exhibited deformation/extension during load level changes, which was especially clear at longer crack lengths. Evidence of OLs or load transitions for short crack lengths was more difficult to discern due to the torturous path of the crack front. Several mechanistic processes were considered to explain the crack deceleration of POL and block loadings relative to H-L loading. This overall deceleration and the observed crack extension, followed by immediate deceleration of the crack growth rate, indicate a combination and interaction of PICC with a single-cycle crack extension mechanism. Crack growth and total life data also suggest a significant net decelerating effect of PICC to overcome the accelerating effect of single-cycle crack extension, in contrast to some of the literature examples of PICC damage acceleration in short cracks.

This focused study isolated the effects of a periodically applied single OL and a sustained OL at fixed values of low and high applied stress levels. The results clearly indicate load interaction and sequencing effects. Future work should consist of a more comprehensive study that investigates varying values for low and high stress levels and combinations of more than two stress levels. Additionally, the effect of R ratio should be studied. Such test data will not only elucidate load sequencing and interaction effects but also provide validation data for advanced computational models, such as crystal plasticity. Such computational models can also provide insight into damage mechanism effects and enable rapid evaluation of varying parameters (stress levels, number of cycles, R values, etc.) once validated.