Crack growth study under thermo-mechanical loads: parametric analysis for 2024 T3 aluminum alloy

A BSTRACT . Due to their severe operating conditions, many industrial components are subjected to complex combinations of cyclic mechanical stresses and thermal pressures. These combinations are responsible for the initiation and propagation of fatigue cracks in these parts, which can lead to failure. Thus, the study of the fatigue strength of these parts in such conditions becomes essential because it allows us to predict the life and safety of components. This study examines the influence of the load ratio and temperature on the propagation rate of long cracks on the outer surface. The propagation of a fatigue crack in ABAQUS was therefore automatically simulated using an identified Paris law of 2024 T3 aluminum alloy. Therefore, the study of these components' fatigue resistance in such conditions becomes essential to predict the service life and safety of the components. This study presents a tool for simulating the crack growth in thermo-mechanically loaded equipment. This tool is based on the crack block concept and aims to minimize the cost of meshing operations, which are prevalent in this type of application.


INTRODUCTION
o determine whether a crack is present in an equipment under thermo-mechanical loads, it is necessary, for obvious safety reasons, to identify accurately its harmfulness degree. When this crack spreads, under thermo-mechanical loads, it is important to quickly assess the evolution of this harmfulness degree and more concretely the residual life of the cracked structure. T The resolution of this type of problem, within the framework of fracture mechanics, is carried out classically using the finite element method. But digital simulation of two-dimensional crack growth is challenging to simulate due to mesh-size reasons [1]. The asymptotic behavior of the displacement field in the vicinity of the crack front requires the local use of an extremely refined mesh size. Since the remeshing of the complete structure at each stage of the front is prohibitive, one solution is to isolate the discontinuity in a crack block, representing the strict vicinity of the crack, whose mesh size depends on the size of the defect and which can be inserted at any time into the rest of the structure, whose mesh size is fixed once and for all. We can mention, among others. Dhondt [2] proposed an alternative solution for local remeshing with a generation of hexahedral elements at the crack passage, within the same framework as the finite element method. More generally, there are so-called "mesh-less" methods, which, in principle, make it possible to get rid of all the difficulties associated with mesh size, but at a higher price. Jordan [3] studied the effect of the additional SDB (Slide Diamond Burnishing) parameters on the fatigue behavior of the 2024-T3 Al alloy has been studied experimentally. Samples of smooth, hourglass-shaped samples were blade-polished using different combinations of additional SDB parameters and then subjected to flexural fatigue tests. Residual stresses, introduced by the SDB, were measured by the X-ray diffraction technique. The microstructure close to the surface of the samples polished on a slide was studied. It has been established that the SDB produces two main effects, which depend on additional parameters of the SDB. The essence of the macro-effect is the creation of residual compressive stresses in the superficial and submarine layers. These constraints delay the formation and growth of fatigue macro cracks and thus increase the life of the polished components per blade. Monotonic tests were performed From KarakaŞ and Szusta [4] to determine the influence of temperature on the mechanical properties of the material. The purpose of the cyclic tests was to acquire the parameters required for the Manson-Coffin equation in order to plot the stress-fatigue life curves. In addition, the stress-strain behavior of the alloy and the cyclic hardening behavior were evaluated using the Ramberg-Osgood equation. The results obtained indicate that the fatigue life is reduced when the operating temperature increases. Punith Gowda [5] reveals the study of the mechanical properties of Al2024-tungsten carbide MMCs (Metal Matrix Composites) containing tungsten carbide (WC) particles. The reinforcing particles in Al2024 alloy ranged from 0% to 5% by weight. The results of this study revealed that as the tungsten carbide particle content increased, tensile strength, hardness, and Young modulus, compressive strength, increased. Significantly, accompanied by a reduction in ductility. Mohammad Zaki [6] reveals the influences of anodizing parameters of Al 2024 T3 in TSA (Tartaric-Sulphuric Acid) on the thickness, the weight and corrosion resistance of the anodized layer are studied. The corrosion resistance test was performed by running a salt spray test for 336 hours and anodic polarization measurements using a potentiostat. The results of showed that the most important factor in determining the thickness and weight of the anodized layer is the temperature, followed by the applied voltage, the voltage-temperature interaction, the temperature and the duration of the layer [6]. This study presents a tool for simulating the crack growth in thermo-mechanically loaded equipment. This tool is based on the crack block concept and aims to minimize the cost of meshing operations, which are prevalent in this type of application. Moreover, this work is based on the creation of a program in Python language using the advantages of the Abaqus calculation codes, chosen for their respective flexibility in terms of mesh size and geometric modeler, in the absence of a versatile tool. The reminder of the article is organized as follows: Section 2 describes the material used to conduct this study. Section 3 discusses the results and, finally, section 4 summarizes the results of this work and draws conclusions.
To study the characteristics of long-standing cracks, all tests were performed in ambient air with a frequency of 10 Hz [7] and under sinusoidal loading of constant amplitude 118 MPa [8], with a load ratio R between 0.1 and 0.7. The purpose of these tests is to characterize the behavior of long cracks in the case of 2024 T3 aluminum alloy plates by determining the propagation threshold and the Parisian law coefficients. Initial crack size a init = 5.08mm capable spread to a critical final size a = 7.18 mm. Fig. 1 shows the sample (30 mm*10 mm*2.29mm) exposed to an initial temperature of 20°C. This study focuses on the behavior of an external crack, since the rate of crack propagation is more severe [9].

2024-T3 alloy
he 2024 alloy is a copper magnesium aluminum alloy with a high copper content of up to 4% by mass. Generally, impurities such as iron and silicon are always present in the composition. In addition to the precipitation hardening, fine particles of size ≈ 100 nm formed during heat treatment, alloy 2024 also contains intermetallic particles. These particles are much larger than the hardening precipitates; they are formed during processing and have no effect in the curing process. On the other hand, they have an important role in the phenomena of localized corrosion. Baog et al. [10] estimated that the density of intermetallic is in the order of 300,000 particles/cm 2 . The microstructure of these alloys becomes very complex given the difference in composition and the different forms of this intermetallic, which are of two types: • The particles S (Al2CuMg): according to Bechet et al. [11], the particles S represent 60% of the intermetallic particles present in the alloy 2024-T3. They have a rounded shape, with sizes ranging from 1 to 5 µm [12]. •The particles of Al-Cu-Fe (Mn): several authors have worked on the characterization of these particles according to their size and their chemical composition [10, 11, and 13]. Al-Cu-Fe (Mn) particles are generally larger than S-phase particles, with sizes ranging from 10 to 25 µm and irregular shapes. Tab. 1 summarizes the intermetallic particles of this type present in the 2024-T3 alloy.  [11] Al20 (Cu, Fe, Mn) 5Si [10] Tab. 3 provides the 2024T3 aluminum alloy chemical compositions [4].

RESULTS AND DISCUSSION
aris and Erdogan have constructed a quantitative framework of fatigue fracture mechanics, which correlates the fatigue crack growth rate to the range of stress intensity factor as follows [16]: where C and m are empirical material constants, ∆K = Kmax -Kmin is the stress intensity factor range in fatigue loading, N is number of cycles, and da is crack extension length.
The following correlation gives the relation between C and m parameters: a and b 0  where: a is the ordinate at the origin and b is the slope of the regression line. Or Coordinates of the pivot point [17].  P When the crack extends over ten or more grains, the influence of the material structure on the growth of the crack becomes negligible and the theory of mechanics of linear elastic fracture can be applied later [19]. In this simple form, the presence of a growth threshold of fatigue cracks and a limit greater than ∆K (stress intensity factor range) for the fracture are not shown, although, if appropriate, expressions taking into account these limits, as well as the influence of the load ratio of the cycle R = Pmin / Pmax can be easily found in the literature.

LOAD RATIO INFLUENCE
ig. 2 shows the curves representing the cracking rate versus the stress intensity factor range for the different load ratios studied. Fig. 2 indicates that the propagation rates vary according to the load ratio.    The results show that the number of cycles increases with the load ratio, that is the higher the load ratio, the greater the cracking resistance at the same maximum stress. We also note that: The paper presents a computational model for determining the lifetime of crack propagation for 2024 T3 aluminum alloy. The fatigue process is divided into crack initiation (Ni) and crack propagation (Np) periods, which allows the total lifetime to be determined as

INFLUENCE OF TEMPERATURE
hese results present a digital calculation of the plate. Thermal and mechanical results are exposed respectively.  These results show that the thermal gradient in the thickness continues by conduction and decreases during the inner face of the plate. the temperature field in the plate has been well estimated by our calculations.

Mechanical results
This section presents the results of the calculation with a model in which the mechanical behaviour of each phase is of the elasto-plastic type with linear cinematic hardening. The axial displacement variations follow the thickness are represented by the Figs. 5 < A (a=5.08mm); B (a=5.50mm); C (a=6.34mm); D (a=7.18mm)> for differing temperatures at crack widths ranging from 5.08 to 7.18. On the one hand in Fig. 5: -we note that for each x-position in thickness, when the temperature increases from + 30°C to +60°C, the changes in the very high axial displacement is more apparent for crack widths greater than 7.18 mm.
-On the other hand, for a x-position in thickness and constant temperature, with an increase in crack width from a=5.08mm to 7.18mm, the changes in axial displacement increase. Deformation variations according to thickness are illustrated in Fig. 6 < A (a=5.08mm); B (a=5.50mm); C (a=6.34mm); D (a=7.18mm)> to differentiate temperatures at crack widths ranging from 5.08 to 7.18 mm. These results also indicate that: -The overall deformations of the plate increase significantly, when the thermal and mechanical aspect are coupled.
-Overall, compared to the thermo-mechanical growth cases presented above, the overall deformations of the plate are less well simulated in this case.

T
The equivalent stress variations according to Vos-Mises follow thickness are represented by the Figs. 7 < A (a=5.08mm); B (a=5.50mm); C (a=6.34mm); D (a=7.18mm)> to differ from temperatures at crack width between 5.08 and 7.18 mm. We also note that: Maximal value of the Von-Mises stress due to the thermo-mechanical effect is located at the level of the crack axis. Stress distribution is very different with singularities at the x-position in the thickness. In an aluminum alloy plate, the stresses range from 0 MPa to 100 MPa. The difference is quite significant, around 20 MPa, so we can observe the good thermal and mechanical behavior.

Decrease in stress on the inside edge.
If the temperature increases, the equivalent stress increases at any temperature, which validates the published results. Variations in equivalent stress according to Vos-Mises as a function of axial displacement are represented in Figs. 8 < A (a=5.08mm); B (a=5.50mm); C (a=6.34mm); D (a=7.18mm)> at different temperatures for crack width between 5.08 and 7.18. 5,0x10 3 1,0x10 4 1,5x10 4  C D Figure 8: Variations in equivalent stress according to Von-Mises as a function of axial displacement at different temperatures CONCLUSIONS he obtained results reveal a difference in behaviour at the selected node levels relative to the conditions imposed by the proposed model. Thermo-mechanical input was found to show a significant increase in stress relative to the elasticity threshold of this 2024 T3 aluminum alloy, relative to mechanical input. The following conclusions can be made: -The proposed model is used to determine the number of Ni loading cycles required to initiate fatigue damage through certain loading cycles and the introduction of adequate material fatigue parameters. The method used for numerical T modelling and the possibility of predicting the initiation of fatigue damage in mechanical elements following a cyclic contact solicitation represent this contribution to the problems examined.
-The qualitative effect of load ratio is to shift a growth rate curve along a line passing through the inflection points. The observation that this shift is not horizontal forms the basis for stress ratio modeling with the hyperbolic sine When the curve is completed.
-The use of the appropriate mechanical behavior laws for the different phases of thermo-mechanical growth plays an important role in the mechanical results, in particular on the distribution of residual stresses in the structure. Thus, the increase in temperature leads to an increase in the equivalent stresses of Von-Mises, axial displacements and total deformation of the plates. -The Thermo-mechanical effect occurring at the conditions of the performed tensile , depends on the temperature and the direction of sampling concerning the plate rolling direction. The effect occurs even at such low temperature as 30°C and is most in-tense in the temperature range 50 -60°C.
-Von-Mises stresses and overall deformations and plate contact pressures increase significantly when the thermal and mechanical aspect is coupled.
-The effect of temperature on crack propagation is presented, giving the best lifetime prediction.
-The damage becomes more pronounced with higher temperature Finally, it is important to note that the "strong" coupling between temperature and mechanical variables (stress, strain, strain, and damage) is very important. Temperature considerations in plastic or visco-plastic models allow the behaviour of structures to be well represented without complex loads. Additional analyses should be conducted to assess the applicability and limitations of the methodology for studying cases in which significant behavior of plastic deformation is involved.