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In this paper a theoretical model was developed to predict the fatigue crack growth behavior under the constant amplitude loading with single overload. In the proposed model, crack growth retardation was accounted for by using crack closure and plastic zone. The virtual crack annealing model modified by Bauschinger effect was used to calculate the crack closure level in the outside of retardation effect region. And the Dugdale plastic zone model was employed to estimate the size of retardation effect region. A sophisticated equation was developed to calculate the crack closure variation during the retardation area. Model validation was performed in D16 aluminum alloy and 350WT steel specimens subjected to constant amplitude load with single or multiple overloads. The predictions of the proposed model were contrasted with experimental data, and fairly good agreements were observed.

The damage tolerance concept is widely used in modern aircraft design to ensure flight safety, which has made the prediction of fatigue crack propagation lives of aircraft components under service loading necessary [

The paper is organized as follows. First, the fatigue crack growth model and the modified virtual crack annealing crack closure model are briefly reviewed. Second, our proposed model for crack growth retardation behavior estimation is discussed in detail. The model is derived based on plastic zone and crack closure variation. And then model validation is performed using the experimental data in D16 aluminum alloy and 350WT steel from the literature. Finally, some conclusions and future work are given based on the current study.

A general fatigue crack growth model can be expressed as (

In this paper the virtual crack annealing model is employed to avoid considering the complex contact of crack closure [

As shown in Figure

Schematic illustration of real crack and virtual crack model.

Since the crack overlapping length is very small compared with the true crack length (i.e.,

There are two possible solutions for the opening stress level under the proposed virtual crack annealing model. One solution is

Retardation caused by overloads is a typical phenomenon of loading interaction effect. A great number of papers were presented to investigate the single overload [

Schematic illustration of CA load interspersed with single-cycle tensile overload.

The crack growth behavior is shown in Figure

Schematic of delayed retardation due to single tensile overload.

The crack tip plastic zone associated with the application of a single overload is shown in Figure

(a) Crack-tip plastic zone due to single tensile overload; (b) the mathematical derivation of

A function of

The horizontal ordinate of point

Based on the discussion above, the new crack closure model is established as (

The cycle by cycle algorithm is used to implement the above model. The flow chart for fatigue crack growth prediction based on the modified crack closure model is shown in Figure

Flow chart for fatigue crack growth calculation.

The experimental data for model validation are from the literature [^{0.5}, and percentage elongation = 12%.

Standard chemical composition [

Chemical composition of D16 aluminum alloy | ||||||
---|---|---|---|---|---|---|

Element | Cu | Mg | Mn | Si | Fe | Zn |

Weight % | 3.8–4.9 | 1.2–1.8 | 0.3–0.9 | 0.5 | 0.5 | 0.3 |

Before any predictions can be made, there are several unknown parameters (see (

Then additional two sets of

The model predictions are compared to the experimental data in Figure

More detailed information can be obtained in the

Additional set of testing data is used for the model validation in the same material and similar specimen configuration [

In this section, the model validation will extend to 350WT steel. The experimental data are given by Taheri et al. [

Similarly, the parameters are calibrated by the

Figure

In Figure

In this investigation, a theoretical model is developed to predict the fatigue crack growth behavior under the constant amplitude loading with single overload. The crack growth retardation was accounted for by using crack closure concept and plastic zone. Model was validated in D16 aluminum alloy and 350WT steel subjected to several different loading spectra, and the predictions matched experimental data well. The following conclusions can be drawn based on the current investigation.

Fatigue crack growth is slowed down by application of single overload cycle. A convincing reason for this retardation phenomenon is that after the overload a large plastic zone will form ahead of the crack tip, which can increase the crack closure level within this region. And as the crack grows through the large plastic zone, the crack closure level will gradually decrease which can be described as a linear function. The retardation effects disappear after a certain characteristic crack length extension from the overload position. This extension is approximately equal to monotonic plastic zone size caused by the overload.

The proposed model is derived from fatigue crack growth mechanisms (such as crack closure, plastic zone, and Bauschinger effect), and it does not require any additional parameters which has no physical meaning.

The above statement is only valid under the current investigated loading spectrums and materials. In the future, the whole frame work should be extended to other materials. Additionally, branching and bifurcation caused by overload can also retard the crack growth rate, which should be investigated in the future.

Crack length

Crack growth in one cycle

Infinitesimal crack increment

Fatigue crack growth rate per cycle

Minimum and maximum stress in one loading cycle

Stress level at which the crack begins to grow

Stress level of single overload

Stress ratio

Overload ratio

Maximum/minimum stress intensity factor

Stress intensity factor range

Stress intensity factor at which the crack begins to grow

Effective stress intensity factor range

Monotonic plastic zone size

Forward plastic zone size

Reverse plastic zone size

Material yield strength

Bauschinger effect factor in loading process

Bauschinger effect factor in unloading process

Bauschinger effect factor.

The authors declare that there is no conflict of interests regarding the publication of this paper.

The research is financially supported by the specialized research fund for the doctoral program of higher education funding under the contract no. 20131102120047.