Corrosion–fatigue of high-strength aluminium alloys is governed not only by reductions in mean fatigue life but,

more critically, by systematic changes in fatigue-life dispersion that directly affect structural reliability. In this

study, the corrosion–fatigue behaviour of AA 7075-T651 under multiaxial loading is analysed from a dispersion-

centred statistical perspective using a Weibull-based framework to quantify how variability evolves with stress

level, corrosion exposure, and loading mode. Fatigue data obtained under uncorroded conditions and after 7-day

and 14-day NaCl exposure were analysed for bending and torsional loading. Stress-level binning was employed

to ensure statistically robust parameter estimation without extrapolation beyond the experimentally tested

domain. Rather than treating scatter as experimental noise, the Weibull shape parameter is explicitly interpreted

as a stress- and environment-dependent descriptor of fatigue-life variability. The results show that, under

uncorroded conditions, fatigue-life dispersion increases significantly at lower stress levels for both bending and

alone. Instead, dispersion evolves systematically with stress level, environmental degradation, and loading mode,

necessitating stress- and environment-dependent probabilistic descriptions. By explicitly quantifying these

effects, the present study provides a statistical basis for advancing corrosion–fatigue assessment beyond

conventional deterministic and mean-life-based approaches toward reliability-oriented evaluation under

multiaxial loading.

Keywords: Corrosion–fatigue, Weibull distribution, fatigue-life dispersion, multiaxial loading, AA 7075-T651

Corrosion–fatigue of high-strength aluminium alloys is characterised not only by a reduction in fatigue life but

also by a pronounced increase in life scatter. For alloys such as AA 7075-T651, this variability becomes

particularly critical under multiaxial loading conditions, where complex stress states can substantially influence

multiaxial loading introduces non-proportional stress components, competing damage mechanisms, and

heightened sensitivity to microstructural and surface-condition effects [3]–[5]. Under these conditions, scatter is

no longer incidental but represents an intrinsic characteristic of the fatigue response, with direct implications for

reliability-based design and assessment.

Probabilistic approaches provide a natural framework for capturing this behaviour. Among these, the Weibull

distribution has been widely adopted for fatigue-life analysis due to its flexibility and its ability to represent the

right-skewed life distributions commonly observed in metallic materials [6]. Importantly, several studies have

demonstrated that Weibull parameters particularly the shape parameter are not constant material properties but

exhibit systematic dependence on stress level, with fatigue-life dispersion often increasing as stress decreases

[6], [7]. These findings indicate that variability itself evolves with loading conditions and should be treated as a

interaction between environmental degradation and cyclic loading is expected to further amplify variability,

making a systematic statistical characterisation of fatigue-life scatter particularly important.

The objective of the present study is therefore to quantitatively characterise corrosion–fatigue life dispersion in

AA 7075-T651 using a Weibull-based statistical framework. Rather than focusing on mean-life degradation

alone, this work examines how fatigue-life dispersion evolves as a function of stress level, corrosion duration,

and loading mode under multiaxial loading conditions. Emphasis is placed on the interpretation of Weibull

parameters as descriptors of variability, without recourse to mechanistic modelling of corrosion pits or crack

initiation processes. By isolating stress-level-dependent dispersion effects, the study aims to provide a

statistically grounded basis for reliability-oriented assessment of corrosion–fatigue behaviour that extends

beyond conventional mean-life approaches.

condition and immersion in a sodium chloride (NaCl) solution for durations of 7 days and 14 days.

Fatigue tests were conducted under different loading modes, namely bending, torsion, and combined bending–

torsion, in order to capture the influence of multiaxial stress states on fatigue-life behaviour. Fatigue life was

defined as the number of cycles to failure. Run-out data were identified and treated consistently within the

statistical analysis framework, as described explicitly in the methodology, to ensure unbiased estimation of

fatigue-life dispersion.

To enable a unified statistical treatment of results obtained under different loading modes, an equivalent stress

parameter 𝜎

in previous studies based on the same experimental dataset [11]. Detailed descriptions of specimen geometry,

subsequent statistical interpretations remain robust and defensible.

Fatigue-life data are typically characterised by right-skewed distributions and substantial scatter, particularly

under multiaxial loading and in corrosive environments where damage mechanisms are inherently

heterogeneous. To capture this variability in a statistically consistent and interpretable manner, the Weibull

distribution is adopted in the present study. The Weibull model is widely used in fatigue reliability analysis due

to its mathematical flexibility and its ability to represent a broad range of dispersion behaviours using a limited

In fatigue applications, the Weibull distribution has been successfully employed to unify the description of

characteristic behaviour and statistical scatter within a single formulation. Unified statistical methodologies for

fatigue modelling have demonstrated that Weibull-based representations can effectively describe experimental

fatigue data across different stress regimes without requiring explicit assumptions regarding underlying damage

mechanisms [14]. This feature is particularly advantageous when the objective is to quantify variability rather

than to infer physical processes.

Previous studies have further shown that scatter in S–N data is not constant but varies systematically with stress

level, especially in the high-cycle fatigue regime. Such stress-dependent dispersion has been linked to changes

in crack initiation dominance and microstructural sensitivity, effects that are naturally reflected through

variations in Weibull parameters [15], [16]. The Weibull distribution therefore provides a statistically robust

framework for analysing fatigue-life dispersion as a function of stress level, corrosion exposure, and loading

Within the Weibull framework, fatigue-life behaviour is characterised using two primary parameters: the shape

parameter β and the scale parameter η. Together, these parameters provide a compact statistical description of

both fatigue-life dispersion and characteristic life, with β governing the degree of scatter and η representing a

characteristic fatigue life corresponding to a defined survival probability.

The Weibull shape parameter β is widely interpreted as a quantitative indicator of fatigue-life dispersion. Lower

values of β correspond to broader life distributions and increased variability, whereas higher values indicate

more concentrated fatigue-life data with reduced scatter. Importantly, β is not a fixed material constant but has

been shown to depend on loading conditions, stress level, and failure probability, particularly when fatigue

behaviour is examined at low probabilities of failure [6]. This sensitivity makes β especially suitable for

assessing how corrosion exposure and multiaxial loading influence fatigue-life variability.

The Weibull scale parameter η represents the characteristic fatigue life at which approximately 63.2% of

specimens are expected to fail. In the present study, η is employed primarily as a reference quantity for

comparing fatigue-life levels across different corrosion conditions and loading modes. Emphasis is placed on

relative changes in η rather than absolute life prediction, in order to maintain consistency with the statistical

focus of the analysis and to avoid extrapolation beyond the experimentally tested stress ranges.

In corrosion–fatigue applications, Weibull parameters have been successfully used to characterise reliability

trends and life variability under environmentally assisted degradation. Previous Weibull-based reliability studies

have demonstrated that both β and η can be significantly influenced by corrosion exposure, reflecting increased

Accordingly, Weibull parameters are extracted in this study for each combination of stress level, corrosion

condition, and loading mode. Their interpretation is intentionally restricted to comparative statistical behaviour

within the tested domain, without extrapolation to untested stress ranges or attribution to specific microstructural

or mechanistic processes, in full agreement with the defined scope of the work.

To examine the dependence of fatigue-life dispersion on stress level in a statistically consistent manner, the

For each corrosion and loading configuration, stress levels were initially divided into low, medium, and high

ranges. To ensure statistically meaningful estimation of Weibull parameters and to limit sensitivity to individual

data points, a minimum of eight failure events per stress bin was targeted. Comparable binning strategies have

been employed successfully in previous Weibull-based fatigue studies to capture stress-dependent dispersion

while avoiding artificial trends associated with over-parameterisation [7].

Where the initial three-bin division resulted in insufficient failure counts for robust statistical inference, adjacent

stress bins were merged to satisfy the minimum sample-size requirement. Consequently, uncorroded conditions

were analysed using two stress groups (low and high), while corroded conditions were analysed using a single

aggregated stress group. This adaptive binning procedure reflects a data-driven compromise between stress

resolution and statistical reliability, ensuring that estimated Weibull parameters remain stable and interpretable.

Beyond facilitating parameter estimation, the stress-level binning strategy also defines the scope of statistical

inference in the present work. By restricting the analysis to experimentally tested stress ranges and avoiding

extrapolation beyond the available data, the study does not attempt to infer endurance limits, threshold stresses,

or long-term service behaviour. Instead, Weibull parameters are interpreted as local descriptors of fatigue-life

variability within defined stress groups, fully consistent with the objective of statistically characterising

dispersion rather than predicting fatigue performance outside the experimental domain.

The variation of the Weibull shape parameter with loading mode under uncorroded conditions highlights that

fatigue-life dispersion is inherently influenced by stress state, even in the absence of corrosion. As illustrated in

Fig. 1, torsional loading consistently exhibits higher β values than bending across the investigated stress range,

confirming lower intrinsic variability under torsion. Together, these results establish a quantitative statistical

seven days of NaCl exposure. The corresponding Weibull shape (β) and scale (η) parameters are reported in

Table 1, while overall trends relative to the uncorroded condition are illustrated in Fig. 1, enabling assessment

of the early statistical effects of environmental degradation on fatigue behaviour.

parameter for both bending and torsional loading compared with the uncorroded baseline. For bending, the

secondary or long-term effect.

The observed increase in dispersion with short-term corrosion exposure is consistent with previous corrosion–

fatigue reliability studies, which have shown that environmental degradation amplifies fatigue-life variability by

Although the present study does not explicitly account for corrosion pit geometry or crack initiation mechanisms,

Under torsional loading, the amplification of dispersion is even more pronounced. The Weibull shape parameter

decreases further to β ≈ 0.52 after fourteen days of corrosion (Table 1), indicating a highly dispersed fatigue-life

distribution. As illustrated in Fig. 1, torsional loading consistently exhibits lower β values than bending under

corroded conditions, demonstrating that shear-dominated stress states are particularly sensitive to corrosion-

broader life distributions and reduced predictability even when mean-life trends remain comparatively smooth

[7]. These findings indicate that prolonged corrosion exposure primarily degrades the predictability of fatigue

The combined influence of corrosion duration and loading mode on fatigue-life dispersion aligns with reliability-

based corrosion–fatigue frameworks that emphasise the dominant role of statistical variability under sustained

environmental exposure [2]. Within this context, the fourteen-day corrosion condition represents a regime in

which variability becomes a controlling factor in fatigue behaviour, reinforcing the necessity of explicitly

accounting for environment- and loading-dependent dispersion in probabilistic assessment of corrosion–fatigue

performance.

Under uncorroded conditions, torsional loading exhibits consistently higher Weibull shape parameters than

underscores the importance of explicitly incorporating loading-mode effects in statistical and reliability-based

assessments of corrosion–fatigue behaviour.

transitions from being dominated by relatively deterministic crack growth to initiation-controlled processes that

This combined effect of stress level and environmental degradation aligns with modified Weibull

parameterisations proposed for fatigue reliability analysis, in which the shape parameter is explicitly treated as

stress-dependent rather than constant [25]. Similar stress-sensitive behaviour has also been reported in multiaxial

In the presence of corrosion, the interaction between stress level and dispersion becomes more pronounced.

Probabilistic corrosion–fatigue studies have shown that Weibull shape parameters are highly sensitive to both

Overall, the results demonstrate that fatigue-life dispersion in AA 7075-T651 cannot be adequately characterised

using a single Weibull shape parameter across stress levels. Instead, stress-dependent Weibull parameters are

Under uncorroded conditions, the systematic reduction of the Weibull shape parameter at lower stress levels

confirms that fatigue-life dispersion increases as stress decreases. This trend is consistent with Weibull-based

fatigue analyses reporting enhanced variability in regimes where fatigue life becomes increasingly governed by

initiation sensitivity rather than deterministic crack propagation [29]. In such regimes, small variations in

maintains or intensifies this elevated dispersion. These observations are consistent with corrosion–fatigue

reliability studies demonstrating that environmental degradation often manifests more strongly through increased

The coupled influence of stress level, corrosion exposure, and loading mode further highlights the limitations of

deterministic fatigue models for corrosion–fatigue assessment, particularly under multiaxial stress states [31].

The present results demonstrate that dispersion varies systematically with stress level and is amplified by both

environmental degradation and loading-mode complexity. In this context, probabilistic models that assume

stress-independent scatter or constant Weibull parameters are unlikely to provide reliable descriptions of