# Phenomenological Models and Peculiarities of Evaluating Fatigue Life of Aluminum Alloys Subjected to Dynamic Non-Equilibrium Processes

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

_{max}from 340 to 440 MPa, cycle asymmetry coefficients R = 0.1 and load frequency f = 110 Hz. The main model parameters are the initial alloy hardness HV and the limiting parameters of scatter of hardness values m. These parameters are evaluated in the process of cyclic loading with fixed maximum stresses of the cycles. Relative values me are also considered. For the alloys in the initial state, the proposed models are shown to be in good agreement with the experimental results. Conversely, structural changes taking place in alloys after DNP complicate the prediction of their fatigue life.

## 1. Introduction

_{1}coefficient is 1.43 for surface defects and 1.56 for subsurface defects and the C

_{2}coefficient is 120 for a wide class of materials.

## 2. Materials and Methods of Research

#### 2.1. Methods of Mechanical Tests

_{max}of 440, 400, 370 and 340 MPa.

_{imp}during the realization of DNP. The simplicity and advantages of this procedure have been time and again noted in [12,13,14]. In addition, this procedure makes it possible to easily assess the effect caused by the intensity of introducing impulse energy on the fatigue life of the alloy at a given variable load [13,14].

#### 2.2. Evaluation Methods of Physical-Mechanical Properties of Surface Layers of Aluminum Alloys

_{i}calculated from hardness characteristics at different stages of loading the specimen from the structural material. We can also load the structure itself, provided it has the initial value of homogeneity coefficient m

_{init}. Knowing or predicting limiting values of m

_{lim}under a certain type of loading is also helpful.

_{e}) were determined on fractured specimens in the transverse direction in areas close to the fracture surface. A similar technique was then used for all specimens fractured under cyclic loading preceded by the realization of DNPs of different intensities.

#### 2.3. Materials and Specimen for Test

## 3. Analysis of Experimental Results of Fatigue Testing in the Initial State

#### 3.1. Physical-Mechanical Models for Predicting the Fatigue Life of Aluminum Alloys in the Initial State

_{e}when the current value of the homogeneity coefficient m

_{i}refers to the original m

_{init}.

_{e}and two coefficients, C

_{1}and C

_{2}, which are determined based on the results of experimental studies with the minimum number of pre-set variable loading conditions.

_{1}= −1.39 × 10

^{7}; C

_{2}= 1.04 × 10

^{5}; HV = 2.84 MPa; σ

_{ys}= 328.4 MPa.

_{1}= −6.89 × 10

^{7}; C

_{2}= 2.33 × 10

^{5}; HV = 2.67 MPa; σ

_{ys}= 348.7 MPa.

_{max}). For this purpose, it is enough to plot a σ

_{max}versus m

_{e}graph with the minimum number of pre-set variables loading conditions. The article does not propose a prediction method based on a probabilistic approach, estimates of probability, errors, etc. We developed a deterministic, engineering approach to assessing the conditions of the materials.

_{max}= 350.6·m

_{b}+ 150

_{max}value, we determine the corresponding m

_{e}value by Equation (5) or the graph shown in Figure 4 and, substituting it in Equation (3), we obtain the required number of cycles to fracture N

_{cycle}of the alloy.

#### 3.2. Physical-Mechanical Model for Predicting Fatigue Life of Aluminum Alloy after Preliminary Introduction of Impulse Energy of Optimal Intensity

_{imp}= 3.7%, 5.4% and 7.7% cover the entire range of maximum cycle stresses under the cyclic deformation studied [13]. Unfortunately, the previous experimental data for alloy 2024-T351 taking into account the influence of the DNP at the low values of ε

_{imp}= 1.5% and 5.0%, at which the maximum increase in the number of cycles to fracture of the alloy was attained in subsequent cyclic tests, do not cover the entire range of maximum cycle stresses [14]. Therefore, in later experiments, the authors limited themselves to the analysis of the data obtained for alloy D16ChATW only.

_{imp}= 3.7% and 5.4% (see Figure 5a,b), the DNP is represented by inflections on the curves at the maximum cycle stress σ

_{max}= 400 MPa. It is noteworthy that σ

_{max}= 400 MPa practically corresponds to the new yield strength of alloy D16ChAT subjected to the DNP of different intensities followed by static tension [13]. It was found that, with ε

_{imp}= 3.7% at the three cycle stresses σ

_{max}= 400 MPa, 370 MPa and 340 MPa, the fatigue life of the alloy improves and, at σ

_{max}= 440 MPa, a positive effect is not achieved (see Figure 5a). Similarly, with ε

_{imp}= 5.4% at the two cycle stresses σ

_{max}= 440 MPa and 400 MPa, the fatigue life of the alloy either improves or does not change, compared to the initial state (see Figure 5b). However, at the low cycle stresses σ

_{max}= 370 MPa and 340 MPa, the fatigue life of the alloy decreases (see Figure 5b). With high values of ε

_{imp}= 7.7%, the fatigue life of the alloy decreases at almost all values of σ

_{max}(see Figure 5c). Moreover, the inflection on the curve occurred at σ

_{max}= 370 MPa. The regularities found in the effect of DNP on the fatigue life of alloy D16ChATW clearly indicate specific changes in the structural state of alloy surface layers, as well as in the volume of the material, depending on the intensity of impulse energy introduced into the alloy. Since after impulse loading of different intensity we are dealing with completely different physical and mechanical properties of the aluminum alloy compared to the initial state, then, in the process of subsequent cyclic loading with different maximum stresses of the cycle, we can expect significant changes in the curve showing the scatter of alloy hardness m or its relative values m

_{e}.

_{max}= 400 MPa to estimate changes in the relative hardness values HV

_{e}and relative scattering parameters m

_{e}, depending on the intensity of the impulse energy introduction. For clarity, the data are presented in the following form (Figure 7).

_{e}is very complex. Moreover, it should be noted that the nature of the changes in the relative parameter HV

_{e}, depending on the intensity of the impulse energy introduction by parameter ε

_{imp}, is also very complex.

_{e}during the realization of DNPs of different intensities in aluminum alloys is problematic at this stage of research [40]. Even when trying to predict the number of cycles to failure by the relative values of the limiting parameters m

_{e}for the data shown in Figure 7, there are many difficulties (see Figure 8).

_{imp}= 3.7%, 5.4% and 7.7%) with the experimental values of the limiting relative parameters m. It should be noted that, in this case, the critical values of parameter m were selected as a damage parameter of the surface layers of the alloy. As shown in standard [36], it is allowed to choose either parameter m

_{e}or parameter m for a specific type of loading.

_{imp}= 3.7% (intensity of introducing impulse energy). The previous realization of DNP in the alloy is most helpful in increasing the number of cycles to fracture under subsequent cyclic loading (see Figure 5a). To this end, an additional C

_{3}coefficient was introduced into the structural and mechanical model.

_{1}= 2.96 × 10

^{4}; C

_{2}= 1.86 × 10

^{10}; C

_{3}= 18.18; HV = 2.84 MPa; σ

_{ys}= 448.7 MPa. In this case, a new yield strength of the alloy after the realization of DNP is substituted in Equation (6) [13].

## 4. Discussion

_{e}and m parameters can be used as basic parameters in structural and mechanical models for estimating the number of cycles to fracture. In this case, this refers to the investigated alloys in the initial state. When, by virtue of sudden additional impulse loads, DNPs are realized in the process of cyclic loading of the structural material, the previous dependences of the number of load cycles on the relative or absolute values of m

_{e}and m change dramatically. This is because the phase composition in the surface layers of alloys changes radically, along with the physical and mechanical properties of the surface layers of the alloys. Therefore, with further cyclic loading, we have a completely different dependence of the number of cycles to fracture of alloys on the relative values of the m

_{e}parameters or absolute values of the m parameters. Moreover, it turned out that maximum cycle stresses of the subsequent cyclic loading have the greatest effect on the changes in dependence of the number of cycles to fracture of alloys on the relative values of the m

_{e}parameters or absolute values of the m parameters after the realization of the DNP.

_{imp}with the same value m, we can obtain two or even three values of the number of cycles to fracture. Thus, using the parameters m or m

_{e}in the author-proposed structural and mechanical models for predicting the number of cycles to fracture of aluminum alloys after the realization of DNP becomes problematic. Since earlier models for predicting fatigue life similar to those proposed by Murakami Y. have never been tested under the realization of DNPs in materials, significant changes can be expected in the damage accumulation patterns that occur in the surface layers of alloys after the realization of DNPs of different intensities—one of the main parameters of the model proposed by Murakami Y.

## 5. Conclusions

_{e}are the main model parameters. The models were tested under specified conditions of variable loading at maximum cycle stresses σ

_{max}= 340–440 MPa, approximate load frequency of 110 Hz and cycle asymmetry coefficient R = 0.1 on specimens from alloys in the initial state and after the realization of DNPs at ε

_{imp}= 3.7%, 5.4% and 7.7%.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 3.**Comparison of experimental results on the number of cycles to failure of aluminum alloys in the initial state (D16ChATW (blue dots); 2024-T351 (red triangles)) at given variable loading conditions (m

_{e}parameter) with analytical results of the structural and mechanical models proposed (dashed line 1, Equation (3); dashed curve 2, Equation (4)).

**Figure 4.**σ

_{max}versus m

_{e}graph for alloy D16ChATW taking into account cyclic deformation conditions realized.

**Figure 5.**Cyclic durability of alloy D16ChATW in the initial state ( ) and after DNP: (

**a**) εimp = 3.7% ( ); (

**b**) εimp = 5.4% ( ); (

**c**) εimp = 7.7% ( ).

**Figure 6.**The effect of the intensity of the impulse energy introduction on the number of cycles to fracture of alloy D16ChATW (σ

_{max}= 400 MPa): indicates the alloy condition after the DNP and exposure for 6–7 months; indicates the initial state of the alloy; blue lines indicate data scatter in the initial state date form [13].

**Figure 7.**The effect of the intensity of the impulse energy introduction into alloy D16ChATW depending on parameter ε

_{imp}, which causes changes in the relative value of parameter HV

_{e}(

**a**) and relative value of parameter m

_{e}(

**b**) (maximum cycle stress σ

_{max}= 400 MPa).

**Figure 8.**Dependence of cycles to fracture of alloy D16ChATW at different intensities of additional impulse loading applied (ε

_{imp}= 3.7%, 5.4% and 7.7%) and in the initial state on the limiting values of m

_{e}(maximum cycle stress σ

_{max}= 400 MPa).

**Figure 9.**Results of experimental comparison of the number of cycles to fracture of alloy D16ChATW in the initial state and after DNPs of different intensities with the experimental values of limiting parameters m: 1, initial state; 2, ε

_{imp}= 3.7%; 3, ε

_{imp}= 5.4%; 4, ε

_{imp}= 7.7% at all variable cyclic loading conditions investigated (σ

_{max}= 340, 370, 400 and 440 MPa).

**Figure 10.**Comparison of experimental results on the number of cycles to fracture of aluminum alloy D16ChATW in the initial state (red dots) and after introducing impulse energy ε

_{imp}= 3.7% into the alloy (brown characters) at specified conditions of variable loading with analytical results obtained using the proposed structural and mechanical models (line 1, Equation (3); line 2, Equation (6)).

Alloys | E (MPa) | ${\mathit{\sigma}}_{\mathit{y}\mathit{s}}$(MPa) | ${\mathit{\sigma}}_{\mathit{u}\mathit{s}}$(MPa) | $\mathit{\delta}$(%) |
---|---|---|---|---|

2024-T351 | 0.72·10^{5} | 342 | 462 | 20.5 |

D16 ChATW | 0.71·10^{5} | 322 | 452 | 21.5 |

Alloy 2024-T351 (%) | |||||||

Si | Fe | Cu | Mn | Mg | Cr | Zn | Ti |

0.05 | 0.13 | 4.7 | 0.70 | 1.5 | 0.01 | 0.02 | 0.04 |

Alloy D16ChATW (%) | |||||||

Si | Fe | Cu | Mn | Mg | Cr | Zn | Ti |

0.11 | 0.18 | 4.4 | 0.63 | 1.4 | 0.01 | 0.01 | 0.07 |

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**MDPI and ACS Style**

Chausov, M.; Pylypenko, A.; Maruschak, P.; Menou, A.
Phenomenological Models and Peculiarities of Evaluating Fatigue Life of Aluminum Alloys Subjected to Dynamic Non-Equilibrium Processes. *Metals* **2021**, *11*, 1625.
https://doi.org/10.3390/met11101625

**AMA Style**

Chausov M, Pylypenko A, Maruschak P, Menou A.
Phenomenological Models and Peculiarities of Evaluating Fatigue Life of Aluminum Alloys Subjected to Dynamic Non-Equilibrium Processes. *Metals*. 2021; 11(10):1625.
https://doi.org/10.3390/met11101625

**Chicago/Turabian Style**

Chausov, Mykola, Andrii Pylypenko, Pavlo Maruschak, and Abdellah Menou.
2021. "Phenomenological Models and Peculiarities of Evaluating Fatigue Life of Aluminum Alloys Subjected to Dynamic Non-Equilibrium Processes" *Metals* 11, no. 10: 1625.
https://doi.org/10.3390/met11101625