The Overload-Induced Delay Model of 7055 Aluminum Alloy Under Periodic Overloading
Abstract
1. Introduction
2. Materials and Test Conditions
2.1. Specimens
2.2. FCG Experiments
3. Experiment Results and Discussion
3.1. FCG Behavior Affected by Overload
- (i)
- Stable period before overload: In this stage, the FCG behavior is consistent with that under CA loading. The FCG rate da/dN can still be calculated and predicted by the Paris equation.
- (ii)
- Instantaneous acceleration period: Following the application of overload, the crack tip undergoes blunting, and the crack closure level established under the baseline loading immediately decreases. Concurrently, the applied overload POL, which exceeds the maximum baseline cyclic load Pmax, results in an effective SIF range ΔKeff higher than that before the overload (ΔKeff = Kmax − Kop, where Kop is the SIF at crack opening). Consequently, the crack tip propagates at an increased FCG rate. It is worth noting that the observable portion of this stage, as indicated by the area enclosed by the yellow dashed lines in Figure 8, was generated during a single overload cycle. This is because no fatigue striations were observed in the localized examination of this region, and its characteristics are consistent with those of static fracture. In other words, under a single tensile overload during periodic loading, this stage corresponds to only one overload cycle, after which the subsequent loading transitions directly into Stage iii.
- (iii)
- Delayed retardation period: After the overload is applied, the crack tip enters the overload plastic zone. The compressive residual stresses generated in the crack tip region during the overload process appear in the wake of the crack tip, leading to a rapid increase in the crack closure level. This causes ΔKeff to decrease swiftly, reaching the minimum FCG rate.
- (iv)
- Retardation period: As the crack continues to propagate further within the overload plastic zone, Kop decreases, and ΔKeff gradually increases, resulting in a gradual rise in da/dN. Due to the inherently three-dimensional nature of the crack opening, Kop in the plane strain region at the crack front is lower than that in the plane stress region on the specimen surface [34]. Therefore, the crack initially begins to open at the mid-thickness of the specimen and then extends towards the specimen surface, concurrently propagating forward.
- (v)
- Stable period after overload: Once the crack propagation extends beyond the influence range of the overload, the FCG rate returns to that under CA loading conditions. The hysteretic process induced by the single overload event concludes.
3.2. Delay Distance ad
3.3. Instantaneous Acceleration Period
3.4. Delay Cycles Nd
3.5. Characteristics of the Fracture Surface
4. Conclusions
- 1.
- All specimens of the studied material exhibited an increased FCG life under periodic overload conditions compared to their CA counterparts. The larger the ROL, the greater the relative deviation degree RD of (da/dN)min from the FCG rate before overload. For 7055 aluminum alloy, the average RD values at 1.4 and 1.7 ROL are 50.3% and 94.8%, respectively, while the experimental data reveal that there is no significant correlation between this value and either the specimen thickness B or the crack length at overload aOL.
- 2.
- The experimental results confirm that the crack growth increment aii during the instantaneous acceleration period plays a significant role in the assessment of FCG life under overload conditions. Periodic overload makes the cumulative impact of this period on FCG life more pronounced. An empirical model for the crack growth increment in this FCG was established and successfully fitted the experimental data. Furthermore, it was found that aii increases with the overload ratio ROL and the SIF range ΔK, while there is no significant correlation with specimen thickness B.
- 3.
- In this research, the MAPE between the plastic zone size calculation models proposed by Irwin, Dugdale, Shin and the experimental data for ad was assessed as a function of KOL/σy. The results indicate that ad follows a power–law relationship with KOL/σy, but the exponent bd exceeds 2. The established evaluation model for ad, which accounts for specimen thickness B and overload ratio ROL, demonstrates greater predictive accuracy for ad compared to the plastic zone models. Finally, by incorporating ad and aii into the Wheeler model, a calculation method for Nd was developed. The calculated Nd values under 1.4 and 1.7 ROL conditions show good agreement with the experimental results. Under periodic overload conditions, both ad and Nd exhibit an increasing trend with the elevation of ROL and B.
- 4.
- Specimens with thickness B = 15 mm exhibit a double-peaked crack front morphology under overload conditions, which is inconsistent with the morphology observed in specimens with thicknesses of B = 5 mm and 10 mm. In all three thicknesses, numerous secondary cracks were observed in the fracture morphologies before and after the application of overload at 1.4 and 1.7 ROL. The ductile fracture characteristics within the overload damage zone are significantly weaker than those in regions subjected to fatigue loading, thereby providing a means to distinguish the boundaries of overload initiation and termination.
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
a | crack length, mm |
ad | delay distance, mm |
an | machined notch length, mm |
aOL | crack length at overload application, mm |
aii | the amount of crack propagation during instantaneous acceleration, mm |
aiii | the amount of crack propagation during the delayed retardation period, mm |
aiv | the amount of crack propagation during the retardation period, mm |
B | specimen thickness, mm |
C | coefficient in the Paris formula |
Cd | coefficient in the ad expression |
Cp | retardation parameter in the Wheeler formula |
CODd | delay crack opening distance, mm |
da/dN | crack growth rate, mm/cycle |
(da/dN)min | minimum crack growth rate after overload application, mm/cycle |
(da/dN)BL | crack growth rate before overload application, mm/cycle |
(da/dN)OL | instantaneous accelerated crack growth rate after overload, mm/cycle |
f | load frequency, Hz |
K | stress-intensity factor, MPa·m1/2 |
KOL | overload stress intensity factor, MPa·m1/2 |
Kop | crack opening stress intensity factor, MPa·m1/2 |
m | exponent in the Paris formula |
m′ | exponent in the Cp expression |
md | exponent in the ad expression |
N | number of loading cycles |
Nb | number of overload interval cycles |
Nd | number of delay cycles |
Nf | number of cycles to failure |
Nj | number of cycles of the increment polynomial’s window center |
NOL | number of cycles elapsed when overload applied |
Ns | number of overload cycles applied |
P | applied load, kN |
Pmax | applied baseline maximum load, kN |
Pmax,i | maximum value of cyclic load at stage i during pre-cracking, kN |
Pmin | applied baseline minimum load, kN |
POL | applied overload, kN |
rp | plastic zone dimensions, mm |
rp,OL | plastic zone dimensions under the applied overload, mm |
R | stress ratio (σmin/σmax) |
R2 | coefficient of determination |
ROL | overload ratio (σOL/σmax) |
sN | standard deviation of experimental FCG life data, cycles |
V | crack opening displacement, mm |
W | dimension relative to the width of the specimen, mm |
Δai | increment of crack propagation in stage i of pre-cracking, mm |
ΔK | range of stress-intensity factor (Kmax − Kmin), MPa·m1/2 |
ΔKBL | range of baseline stress-intensity factor, MPa·m1/2 |
α | normalize crack length (a/W) |
α0 | coefficient related to the stress state in rp calculations |
β(a) | shape factor related to the specimen’s geometric characteristics |
εtrue | true strain, mm/mm |
σ | stress applied, MPa |
σa | stress amplitude, MPa |
σb | ultimate tensile stress, MPa |
σy | tensile yield stress, MPa |
σmax | stress under applied baseline maximum load, MPa |
σmin | stress under applied baseline minimum load, MPa |
σOL | stress under applied overload, MPa |
σtrue | true stress, MPa |
Al | aluminum |
ASTM | American society for testing and materials |
CA | constant amplitude |
CV | coefficient of variation |
C(T) | Compact-tension specimen |
EDM | electrical discharge machining |
FCG | fatigue crack growth |
ICP-MS | inductively coupled plasma mass spectrometry |
L-T | longitudinal-transverse |
MAPE | mean absolute percentage error |
RD | relative deviation between (da/dN)min and (da/dN)BL |
VA | variable amplitude |
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TC Id | Overload Ratio, ROL | Interval Cycles, Nb (Cycles) | B = 5 mm | B = 10 mm | B = 15 mm | |||
---|---|---|---|---|---|---|---|---|
(Cycles) | CV | (Cycles) | CV | (Cycles) | CV | |||
TC1 | N/A | N/A | 71,610 | 7.23% | 83,654 | 6.07% | 97,057 | 9.25% |
TC2 | 1.4 | 10,000 | 75,150 | 0.11% | 128,633 | 6.07% | 134,903 | 3.03% |
TC3 | 1.7 | 10,000 | 101,421 | 2.48% | 112,691 | 7.99% | 170,000 | 8.32% |
Thickness B | Cd × 103/mm·m−b/2 | md | R2 | |||
---|---|---|---|---|---|---|
TC2 | TC3 | TC2 | TC3 | TC2 | TC3 | |
5 mm | 36.825 | 13.771 | 4.1032 | 3.6625 | 0.9842 | 0.9637 |
10 mm | 48.856 | 14.095 | 4.1532 | 3.6267 | 0.9200 | 0.9369 |
15 mm | 67.952 | 30.847 | 4.1694 | 3.8014 | 0.9879 | 0.9716 |
Thickness B | lnC | m | R2 |
---|---|---|---|
5 mm | −14.536 | 2.553 | 0.977 |
10 mm | −14.106 | 2.325 | 0.948 |
15 mm | −12.833 | 1.885 | 0.947 |
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Liu, Z.; Cao, J.; Liu, S.; Yang, Y.; Yao, W. The Overload-Induced Delay Model of 7055 Aluminum Alloy Under Periodic Overloading. Metals 2025, 15, 644. https://doi.org/10.3390/met15060644
Liu Z, Cao J, Liu S, Yang Y, Yao W. The Overload-Induced Delay Model of 7055 Aluminum Alloy Under Periodic Overloading. Metals. 2025; 15(6):644. https://doi.org/10.3390/met15060644
Chicago/Turabian StyleLiu, Zuoting, Jing Cao, Shilong Liu, Yuqi Yang, and Weixing Yao. 2025. "The Overload-Induced Delay Model of 7055 Aluminum Alloy Under Periodic Overloading" Metals 15, no. 6: 644. https://doi.org/10.3390/met15060644
APA StyleLiu, Z., Cao, J., Liu, S., Yang, Y., & Yao, W. (2025). The Overload-Induced Delay Model of 7055 Aluminum Alloy Under Periodic Overloading. Metals, 15(6), 644. https://doi.org/10.3390/met15060644