Coupled thermo–mechanical modeling and experimental validation of friction stir welding in thin AA2024-T4 sheets

Friction stir welding, pioneered at the Welding Institute in 1991, has transformed the solid-state joining of aluminum alloys through its unique combination of friction-generated heat and severe plastic deformation [1]. This process overcomes critical limitations of fusion welding in precipitation-hardened alloys, such as AA2024, by eliminating defects like hot cracking, porosity, and severe strength degradation [2], [3]. While this alloy is widely used in aerospace fuselage skins and structural panels due to its exceptional strength-to-weight ratio, it poses particular challenges during welding because its strengthening aluminum–copper–magnesium intermetallic compound (Al$_2$CuMg) precipitates are highly sensitive to thermal exposure [4], [5].

Recent advances in the friction stir welding research have significantly expanded the understanding of process mechanics and microstructural evolution in aluminum alloys [6]. Researchers have demonstrated sophisticated approaches to heat source modeling [7] and provided insights into precipitate evolution during thermal cycling [8]. Studies on process parameter optimization [9], [10] have revealed complex interactions between tool geometry, rotation speed, and material flow patterns. However, despite these advances, several critical gaps remain inadequately addressed.

While extensive research has explored the impact of friction stir welding parameters on mechanical properties [11], [12], [13] and microstructural development [14], [15], three fundamental limitations persist in the current understanding. The first is limited quantitative correlation for thin sections. Existing numerical models predominantly focus on thick plates ($>$4 mm), where heat dissipation characteristics differ substantially from thin sheets [16], [17]. In 2 mm sections, through-thickness thermal gradients and heat extraction rates create unique challenges for precipitate stability and grain refinement that remain poorly quantified. The second is the weak linkage between simulation and microstructure. Most studies present finite element analysis-based thermal predictions and experimental microstructural observations separately, without establishing direct quantitative relationships [18], [19]. The critical connection between simulated equivalent plastic strain, thermal exposure time, and resulting grain size distributions lacks systematic validation. The third is the absence of validated predictive frameworks. Current practice relies heavily on empirical trial-and-error approaches for parameter selection [20]. Validated correlations enabling prediction of joint efficiency and mechanical properties directly from process parameters remain unavailable for industrial implementation.

The objectives of this investigation are (i) to develop and validate a high-fidelity coupled Eulerian–Lagrangian finite element model specifically designed for thermal–mechanical behavior during thin-section friction stir welding; (ii) to establish quantitative links between simulated thermal histories, equivalent plastic strain, and experimentally measured grain refinement kinetics; (iii) to identify $\omega / v$ ratios that optimize joint efficiency while maintaining adequate ductility for aerospace structures; and (iv) to formulate physics-based design guidelines and process maps suitable for industrial implementation. Collectively, this integrated experimental–numerical approach advances the friction stir welding research from qualitative parameter exploration to a predictive engineering discipline.

AA2024-T4 with a thickness of 2 mm, supplied in the naturally aged condition, was used as the base material. The T4 designation denotes solution heat treatment followed by natural aging, performed in accordance with the Aerospace Material Specification 2770 standard (solution treatment at 493 ± 5 ℃, quenching in cold water, then natural aging at room temperature for a minimum of 96 hours). The chemical composition and mechanical properties of the material are listed in Tables~\ref{tab1} and \ref{tab2}, respectively.

Friction stir welding experiments were conducted using a five-axis computer numerical control milling machine (DMG Mori DMU 50, DMG Mori Aktiengesellschaft, Bielefeld, Germany) equipped with integrated force and torque monitoring via a Kistler 9257B dynamometer (Kistler Group, Winterthur, Switzerland). The tool was fabricated from H13 hot-work tool steel (hardened to 52–54 HRC by austenitizing at 1020 ℃ followed by air quenching and double tempering at 560 ℃), with a threaded cylindrical pin (diameter: 4 mm; length: 1.8 mm) and a concave shoulder (diameter: 12 mm). Specimens measuring 70 × 100 mm were prepared and cleaned with acetone prior to welding. The welding parameters are presented in Table 3. Rotational speeds were investigated at four discrete levels (1000, 1200, 1400, and 1600 rpm), and traverse speeds at three levels (100, 200, and 300 mm/min), yielding a full 4 × 3 parameter matrix. The 2° tool tilt angle was selected based on prior coupled Eulerian–Lagrangian modeling experience [22] to ensure consistent shoulder contact pressure and material flow without introducing bending forces that could compromise the thin sheet. The plunge depth of 0.1 mm below full penetration was verified by torque monitoring to ensure full-thickness consolidation.

Temperature monitoring was performed using K-type thermocouples (accuracy ±1.5 ℃, calibrated against a National Institute of Standards and Technology (NIST)-traceable reference prior to experiments) positioned at distances of 10 and 20 mm from the weld centerline on the retreating side, inserted into 1.5 mm diameter blind holes drilled to the mid-thickness of the sheet (1.0 mm depth from the bottom surface). This ensured direct contact with the material without protruding into the weld zone. Data acquisition was performed at a 10 Hz sampling rate using a National Instruments NI USB-6211 data acquisition system. Temperature measurements were used for validation of the finite element model predictions.

A combined Eulerian–Lagrangian formulation was adopted in ABAQUS/Explicit: the workpiece was modeled in an Eulerian framework to accommodate large deformations, while the tool was treated as a Lagrangian rigid body with prescribed rotational and translational motion. Heat generation included both frictional heating at the tool–workpiece interface and plastic dissipation in the deformation zone. Temperature-dependent material properties for the aluminum workpiece and the H13 steel tool were sourced from established literature [23]. A constant friction coefficient of 0.4 was applied, consistent with prior friction stir welding simulation studies [22]. It should be noted that this constant value is an assumption of the model; in reality, the friction coefficient varies with temperature and contact pressure. Sensitivity analysis conducted in a related study on friction stir welding of copper [24] showed that ±20\% variation in the friction coefficient produces approximately ±5\% change in peak temperature, indicating moderate sensitivity. A temperature-dependent friction model of the form $\mu$($T$) = 0.45 - 0.0002T (for $T$ $<$ 500 ℃) and $\mu$ ($T$) = 0.35 (for $T$ $\geq$ 500 ℃) was therefore explored in sensitivity runs, confirming that the constant value of 0.4 represents a reasonable mean approximation for the AA2024-T4 system within the operating temperature range.

The thermo–mechanical response of AA2024-T4 was described using the Johnson–Cook constitutive model [25], which captures the coupled effects of strain hardening, strain rate sensitivity, and thermal softening through the flow stress relation: $\sigma=\left[A+B(\varepsilon)^n\right]\left[ 1+C \cdot \ln \left(\dot{\varepsilon} / \dot{\varepsilon}_0\right)\right\}\left[ 1-\left(\left(T-T_0\right) /\left(T_m-\mathrm{T}_0\right)\right)^m\right\}$. For AA2024-T4, the Johnson–Cook parameters A = 352 MPa, B = 440 MPa, C = 0.0083, $n$ = 0.42, and $m$ = 1.7 were adopted from the study by Lesuer et al. [26], which are widely validated for high-temperature and high strain-rate deformation of this alloy. This model is particularly appropriate for friction stir welding simulation as it effectively characterizes material behavior under the elevated temperatures (up to ~490 ℃) and high strain rates ($\dot{\varepsilon}$ $>$ 10 s$^{-1}$) prevailing in the deformation zone.

The mesh was refined near the tool to capture steep thermal gradients and coarsened in peripheral regions for efficiency. A mesh sensitivity analysis was performed using five element sizes (0.5, 0.4, 0.3, 0.2, and 0.1 mm) in the tool-adjacent zone. Convergence was confirmed at 0.3 mm, where peak temperature and maximum von Mises stress varied by less than 1\% relative to the finest mesh, while computational time remained manageable. The selected mesh size of 0.3 mm was therefore adopted for all production simulations. The coupled system was solved using automatic time-stepping to ensure numerical convergence and to accurately capture the transient thermal–mechanical response during tool traversal.

The principal assumptions and limitations of the model are as follows: (i) the tool is treated as a rigid body, neglecting tool deformation and wear; (ii) a constant friction coefficient is assumed as a simplification, as discussed above; (iii) the model is calibrated for 2 mm AA2024-T4 sheets and may require recalibration of boundary conditions and friction parameters before application to other thicknesses or alloy systems; and (iv) microstructural features such as precipitate dissolution kinetics are inferred from simulated thermal histories and not modeled explicitly within the finite element method framework.

Samples were sectioned perpendicular to the welding direction, mounted in cold-setting epoxy resin, ground through 800–2000 grit silicon carbide (SiC) papers, polished to 0.05 $\mu$m colloidal silica finish, and etched with Keller’s reagent (2 mL hydrofluoric acid (HF) + 3 mL hydrochloric acid (HCl) + 5 mL nitric acid (HNO$_3$) + 190 mL water (H$_2$O), 10 s immersion). Optical microscopy was performed using a Zeiss Axio Imager M2m equipped with AxioVision image analysis software for grain size measurements according to the ASTM E112 standard.

Vickers microhardness measurements were conducted across the weld cross-section using a Zwick/Roell ZHV30 hardness tester (Zwick/Roell Group, Ulm, Germany), applying a 50-gf load with a 20-second dwell time in accordance with the ASTM E384 standard. Measurements were taken at 0.5 mm intervals to produce detailed hardness maps across the full weld cross-section.

Tensile specimens were prepared according to the ASTM E8M standard and tested using a Zwick/Roell Z100 universal testing machine (Zwick/Roell Group, Ulm, Germany) at a constant crosshead speed of 1 mm/min. Three specimens were tested per condition to ensure statistical reliability; mean values and standard deviations are reported.

Comparison between simulated and experimentally measured thermocouple data shows excellent agreement. The maximum deviation between predicted and measured peak temperature, as depicted in Figure 1, was below 3.2% across all parameter combinations, confirming the reliability of the proposed thermo–mechanical model.

Peak temperatures ranged from 415 ℃ to 496 ℃ (69–82% of the aluminum solidus at 638 ℃), confirming solid-state processing throughout. Higher $\omega / v$ ratios systematically increased peak temperatures and broadened thermal profiles, indicating elevated heat input per unit weld length. A recent study by Seleman et al. [7] on AA2024 reported similar temperature ranges of 420–485 ℃ with comparable parameters, supporting the measurements of this study. The relatively steep through-thickness thermal gradient observed in the thin-sheet configuration highlights the dominant effect of backing plate conduction, which differs significantly from thick-plate friction stir welding conditions [27]. A temperature deviation of just 10 ℃ near 480 ℃ can alter precipitate dissolution kinetics by approximately 15%, demonstrating the sensitivity of microstructural evolution to thermal accuracy. Thin sheets typically exhibit through-thickness thermal gradients on the order of 50 ℃/mm; thus, maintaining prediction accuracy within 1–3% is essential to ensure that precipitate stability remains within acceptable limits. From an industrial standpoint, consistent joint properties require process control within a ±15 ℃ tolerance window, a requirement that the present model satisfies.

Within this context, the relationship between the $\omega / v$ ratio and heat input per unit length was quantified using a power-law regression of the following form:

$ H=k_1(\omega / v)^a+k_2\left(\omega^2 / v\right)^\beta $

where, $H$ is heating input per unit length (J/mm). The constants $k_1$ = 42.5, $k_2$ = 0.0185, $\alpha$ = 0.65, and $\beta$ = 0.23 were determined by nonlinear least-squares regression (MATLAB Curve Fitting Toolbox, Isqnonlin solver) applied to the 12 experimental heat input data points derived from measured torque and traversal speed using the relation $Q=2 \pi \eta T N / v$ [24], where $\eta$ = 0.9 is the heat partition factor, $T$ is the measured tool torque, $N$ is the rotational speed, and $v$ is the traverse speed. The goodness of fit (R$^2$ = 0.964) confirms that the relationship adequately captures the nonlinear dependence of heat input on both rotational and traversal speeds within the parameter space investigated. These constants are specific to the present material system (AA2024-T4, 2 mm sheet, H13 tool with 12 mm shoulder) and should be recalibrated for different thicknesses, alloys, or tool geometries.

The predicted temperature distribution, as shown in Figure 2, during friction stir welding of 2 mm AA2024 sheets demonstrates asymmetric heat concentration around the tool shoulder due to combined rotational and translational motion. Peak temperatures occur slightly behind the tool centerline on the advancing side, consistent with well-established thermo-mechanical behavior during friction stir welding. In the figure, the asymmetric heat distribution around the tool shoulder and the peak temperature zone slightly trailing the tool on the advancing side are clearly visible.

The equivalent plastic strain ($\varepsilon_p$) distribution reveals strong localization within the stir zone, with maximum values occurring beneath the tool shoulder edge. At the lowest $\omega / v$ ratio investigated (Figure 3a), the microstructure exhibits a heterogeneous distribution with coarser grains and increased porosity, indicated by dark voids dispersed throughout the matrix, suggesting insufficient heat input and inadequate material flow. Increasing the rotational speed (Figure 3b) yields a more refined and homogeneous microstructure with significantly reduced void content, consistent with adequate frictional heating and improved plastic deformation. However, at the highest rotational speed of 1600 rpm (Figure 3c), the microstructure displays evidence of excessive heat input: grain coarsening and darker phase regions are observed. These darker contrast regions are tentatively attributed to coarsened Al$_2$CuMg precipitate fragments or oxide particles dispersed during stirring; however, definitive identification would require scanning electron microscopy and energy-dispersive X-ray spectroscopy analysis, which is beyond the scope of the present study and is explicitly acknowledged as a limitation. As shown in the figure, optical micrographs were acquired at the weld centerline and mid-thickness position using a constant magnification corresponding to a 50 $\mu$m scale bar.

The stir zone exhibited fine equiaxed grains ranging 3–8 $\mu$m, as measured by the linear intercept method per the ASTM E112 standard on a minimum of five fields per sample, resulting from dynamic recrystallization under combined high temperature (460–490 ℃) and severe plastic deformation ($\varepsilon_p$ $>$ 5). Recent work by Sun et al. [28] on 3 mm AA2024 reported grain sizes of 5–12 $\mu$m at similar $\omega / v$ ratios, slightly coarser than the 3–8 $\mu$m observed in this study. This difference is attributed to faster cooling rates in thinner (2 mm) sheets, which limit grain growth time after recrystallization [27].

Grain size plays a critical role in determining the mechanical performance of the stir zone. A finer grain structure contributes to Hall–Petch strengthening, which helps counteract the softening associated with precipitate dissolution [29]. It also promotes more homogeneous deformation, thereby improving ductility, and enhances fatigue resistance—a key requirement for aerospace structural components.

The relationship between $\omega / v$ ratio and joint efficiency (defined as $U^{\text {LoINt}} / U T S^{\text {KaLN}}=U T S$ / 467 MPa) is shown in Figure 4 and presented numerically in Table 4, achieving a maximum efficiency of 88\% at $\omega / v$ = 4.67 ($\omega$ = 1400 rpm, $v$ = 300 mm/min). This optimum represents a critical balance between adequate material consolidation and controlled thermal exposure.

The reduction in ultimate tensile strength observed above $\omega$ = 1400 rpm is attributed to three interacting mechanisms. First, at $\omega$ = 1600 rpm, excessive heat input raises peak temperatures beyond 495 ℃, facilitating abnormal grain growth. Grain size increases from the optimal 4–6 $\mu$m to 8–12 $\mu$m after more than 15 seconds above 480 ℃, diminishing the Hall–Petch strengthening contribution. Second, the prolonged thermal exposure accelerates dissolution of Al$_2$CuMg strengthening precipitates and broadens the heat-affected zone, which expands from 8.2 mm at 1400 rpm to 11.5 mm at 1600 rpm, increasing the softened region that governs tensile failure location. The heat-affected zone boundaries were identified on hardness contour maps as the regions where hardness falls below 110 HV (representing $>$15\% reduction from base metal hardness of 126 HV), consistent with established heat-affected zone identification criteria for AA2024 [12]. Third, decreased material viscosity at high heat input promotes void nucleation and incomplete consolidation, creating defect sites that act as crack initiation points during tensile loading.

The graphical analysis of ultimate tensile strength and elongation as functions of $\omega$ under varying $v$ (100, 200, and 300 mm/min) is presented in Figure 5. Hanif et al. [13] reported similar ultimate tensile strength degradation above 1500 rpm in AA2024 sheets and attributed it primarily to heat-affected zone softening, consistent with the present findings. Feddal et al. [2] documented an optimal $\omega$ range of 1200–1400 rpm for thin AA2024 sections, in agreement with the results of this study.

Ductility is maximized when the peak temperature remains within 460–490 ℃, the material experiences 8–15 s above 450 ℃, and cooling rates are maintained between 15–25 ℃/s. Deviations from these conditions either restrict consolidation at lower temperatures or cause over-softening at higher temperatures, reducing elongation in both cases.

The hardness profiles presented in Figure 6 exhibit the characteristic W-type pattern, with minimum values in the heat-affected zone (85–95 HV) and partial recovery in the stir zone (100–115 HV), consistent across all parameter combinations. The heat-affected zone minimum is located approximately 6–8 mm from the weld centerline, coinciding with the region of maximum thermal exposure without the beneficial grain-refining effect of severe plastic deformation. This pattern can be attributed to the competing effects of precipitate dissolution and grain refinement. Yang et al. [30] showed that the size and distribution of coarse secondary particles decrease within the stir zone, and the present results corroborate this finding. Increasing rotational speed widens the precipitation-free zone in the heat-affected zone, while simultaneously promoting re-precipitation within the stir zone that partially restores hardness. The net result, governed by the dominance of the stir zone response, determines the final joint mechanical properties.

The reliability of the finite element model was evaluated through quantitative comparison with experimental data for peak temperature, heat-affected zone width, stir zone hardness, and ultimate tensile strength under identical processing conditions. As summarized in Table 4, the model demonstrated strong predictive accuracy, with all deviations below 5%. Coefficients of determination ($R^2$) exceed 0.985 and p-values are below 0.001 for all parameters, confirming that the simulations capture experimental variability across the full parameter space.

This level of accuracy represents a significant improvement over existing thin-sheet friction stir welding models, which typically report 5–10% deviation in predicted mechanical properties [12], [13], [14], [15], [16], [17], [18], [19]. The ultimate tensile strength error of less than 2% is particularly relevant for aerospace certification, where strength predictions must meet tight tolerances. The validated correlation between equivalent plastic strain and grain size enables direct microstructural prediction from the finite element method outputs without empirical recalibration for each new parameter set.

The integrated experimental–numerical investigation identified an optimal operational window for friction stir welding of 2 mm AA2024-T4 sheets. The $\omega / v$ ratio is the dominant parameter governing joint quality [31], with maximum efficiency at $\omega / v$ = 4.67 (1400 rpm, 300 mm/min). At this condition, peak temperatures of 460–490 ℃ promote fine equiaxed grain formation while preventing excessive precipitate dissolution. Heat input per unit length should be maintained within 180–220 J/mm. $\omega / v$ ratios below 3.0 produce insufficient material flow; ratios exceeding 8.0 cause grain coarsening, precipitate dissolution, and metallurgical defects.

Joint efficiency follows the predictive Gaussian function:

$ \eta=0.95 \times \exp \left[-0.08 \times(\omega / v -4.67)^2\right] $

This relationship demonstrates symmetric Gaussian degradation of mechanical properties for deviations in either direction from the optimum $\omega / v$ ratio of 4.67. The process parameter map in Figure 7 delineates the recommended operational envelope centered at 1300–1400 rpm and 100–300 mm/min, within which both strength and ductility are simultaneously optimized.

This study addresses key knowledge gaps in thin-section friction stir welding by introducing the following contributions:

(i) Quantitative strain–microstructure correlations: By linking simulated $\varepsilon_p$ values exceeding 5 to experimentally measured grain sizes of 3–8 $\mu$m (measured per the ASTM E112 standard), this work demonstrates that microstructural evolution in thin AA2024-T4 sheets can be predicted directly from validated thermal–mechanical simulations, without requiring separate empirical calibration.

(ii) Thin-section model accuracy: The coupled Eulerian–Lagrangian model achieved 1.4–3.2% deviation from experimental data for all key parameters (peak temperature, heat-affected zone width, stir zone hardness, and ultimate tensile strength), with $R^2$ $>$ 0.985 and $p$ $<$ 0.001. This precision is critical for aerospace-grade materials where small temperature fluctuations significantly influence precipitate dissolution and joint strength.

(iii) Predictive design framework: A Gaussian joint efficiency function and a comprehensive process map were derived, enabling systematic parameter selection without extensive experimental trials. The optimal condition ($\omega$ = 1400 rpm, $v$ = 300 mm/min, $\omega / v$ = 4.67) achieves 88\% joint efficiency and an ultimate tensile strength of 401 MPa.

The specific quantitative conclusions are as follows:

• The model accurately predicted peak temperature with less than 3.2% deviation from experimental measurements across all 12 parameter combinations.

• Equivalent plastic strain localized within the stir zone ($\varepsilon_p$ $>$ 5), directly explaining the grain refinement to 3–8 $\mu$m and the associated hardness recovery to 100–115 HV.

• Minimum hardness (85–95 HV) and tensile fracture consistently occurred in the heat-affected zone at 6–8 mm from the weld centerline, confirming its dominant role in determining joint efficiency.

• Predicted joint efficiency agreed with experiments within 1.5% error, validating the Gaussian predictive function.

• The proposed framework provides a reliable, physics-based predictive tool for process optimization of thin aluminum alloy friction stir welding, with direct applicability to aerospace manufacturing.