The material used for this study was AISI 1025 steel, known for its applications in mechanical components such as drive shafts, construction materials, and tools and dies. An XRF analysis of the chemical composition of AISI 1025 is shown in Table 1 . The material properties such as density, Poisson’s ratio, tensile strength and resistivity are illustrated in Table 2 . The temperature dependent thermal properties, including thermal conductivity and specific heat, are illustrated in Figure 1 .

Table 1. Chemical composition of AISI 1025 from XRF analysis (wt%).

Table 2. Material properties of AISI 1025.

A 3D model, cylindrical in shape of 12.7 mm by 5 mm on a substrate measuring 50 mm by 50 mm by 10 mm, was created in ANSYS Workbench 2024 software. The dimensions were chosen to reflect a typical industrial application, ensuring that the model captures the critical aspects of heat transfer and stress development during heat treatment. A fine mesh was used ( Figure 1(b) ) after a convergence study as shown in Figure 2(a) , to ensure reliability of the model in capturing the steep temperature gradients and stress concentrations. The model was validated with the results from a study by Kik et al. [18] , demonstrating the model’s capability to predict heat treatment outcomes.

The thermal analysis was employed to simulate the temperature distribution during heating and cooling, followed by a structural analysis to compute the resulting residual stresses. The coupled thermal-mechanical analysis allows for an understanding of the interaction between temperature changes and stress development.

The temperature of 850˚C was applied as the maximum heating temperature for the sample to illustrate the heating temperature used in the real furnace. The ambient temperature of was assumed to be 40˚C which was selected to be the lowest temperature of cooling. The basic heat transfer law of temperature field according to Fourier’s law. The three-dimensional heat transfer differential equation also known as conservation law of energy is expressed as shown in Equation 1 [19] .

$\rho c_p\frac{\partial T}{\partial \tau }=\lambda \frac{{\partial }^{2}T}{\partial x_i^2}+{\sigma }_{ij}{\stackrel{\dot{}}{\epsilon }}_{ij}^p-\sum {\rho }_I{l}_I{\stackrel{\dot{}}{\zeta }}_I,$ (1)

where, T is the temperature [K], $l_I$ is the latent heat due to phase transformation [J/Kg ], λ—heat conductivity coefficient [W⋅m⁻¹⋅K⁻¹], C_p—specific heat [J⋅kg⁻¹⋅K⁻¹], and ρ—mass density [kg⋅m⁻³]. Phase transformation during quenching were modeled using the Johnson-Mehl-Avrami-Kolmogorov (JMAK) equation [20] , which describes the kinetics of austenite-to-martensite transformation [20] . The transformed volume fraction on time $f_V$, was calculated by Equation (2).

$f_V=1-\text{exp}\left(-k{t}^n\right)$ (2)

where k is temperature dependent rate and n is the Avrami exponent. The thermal convection and radiation were taken into account as per Newton’s law of cooling and Stefan-Boltzmann law respectively, as shown in Equations (3) and (4) [21] .

$q_c=Ah\left(T-T_a\right)$ (3)

$q_r={ϵ}_r{\sigma }_r\left(T^4-T_a^4\right)$ (4)

where q_c represents heat transferred through convection and q_r heat transfer through radiation. The variable h represents the heat transfer coefficient associated with natural thermal convection, while A denotes the heat transfer area. The value of σ_r corresponds to the Stefan-Boltzmann constant, set at 5.67e−8 W/m∙K. Lastly, the variable ${ϵ}_r$ represents the coefficient of radiation emissivity for the material.

In thermal treatment simulations, plastic flow stress (σ) calculations depend on the flow stress curve of each phase, and can be defined in terms of strain (ε), temperature (T) and strain rate ( $\stackrel{\dot{}}{\epsilon }$) [22] , as illustrated in Equation 5. Whereas the total strain rate is defined by Equation (6).

$\bar{\sigma }=\bar{\sigma }\left(\epsilon ,\stackrel{\dot{}}{\epsilon },T\right)$ (5)

${\stackrel{\dot{}}{\epsilon }}_{ij}={\stackrel{\dot{}}{\epsilon }}_{ij}^t+{\stackrel{\dot{}}{\epsilon }}_{ij}^e+{\stackrel{\dot{}}{\epsilon }}_{ij}^p+{\stackrel{\dot{}}{\epsilon }}_{ij}^{tr}+{\stackrel{\dot{}}{\epsilon }}_{ij}^{tp}$ (6)

where ${\stackrel{\dot{}}{\epsilon }}_{ij}^t,{\stackrel{\dot{}}{\epsilon }}_{ij}^e,{\stackrel{\dot{}}{\epsilon }}_{ij}^p,{\stackrel{\dot{}}{\epsilon }}_{ij}^{tr},{\stackrel{\dot{}}{\epsilon }}_{ij}^{tp}$ are the thermal, elastic, plastic, phase transformation and phase transformation plasticity strain rates.

Temperature variation during simulation was conducted according to AMS2759/4 for both annealing and quenching. For annealing, an AISI 1025 sample was subjected to a heating rate of 5˚C/min to a temperature of 850˚C, above the austenitizing temperature. The temperature was then held constant for 2 hours and then cooled down at a rate of 3˚C /min to the ambient temperature [18] . For quenching, the samples were heated the same as annealing, however the cooling rate was rapid at a rate of 99˚C/sec.

A laser system, LENS 850R by Optomec was used for the deposition of samples. A laser power of 270 W, a scan speed of 7.1 mm/s, feed rate of 1.7 g/min and hatch spacing of 0.67 mm were used during the deposition. A total of 18 samples were produced at a laser spot size of 1.4 mm. Heat-treatment experiments were performed in a muffle furnace supplied by Ultra Furn. The samples were subjected to annealing and hardening, as given in the AMS2759/4 standard [23] . All the samples were placed inside the furnace at heating rate of 5˚C/min until a temperature of 850˚C was attained which is above an austenitizing temperature with a soaking time of 2 hours. The annealing samples were then furnace cooled to ambient temperature whereas the samples for quenching were fast cooled via a water bath. The sample were then prepared for characterization as per ASTM E3-11 standard.

Samples for residual stress analysis were prepared through electrochemical etching using Pulstec electro-etching machine to achieve smooth surface finish. Whereas samples for hardness testing and microstructural investigation were initially sectioned using Struers Labotom machine available at CSIR, South Africa, the sectioned samples were subsequently mounted using an Automatic Mounting Machine, a series of grinding and polishing operations using Struers TegraPol-25 machine, were followed to ensure optimal surface quality for analysis according to ASTM E3 standard.

Residual stress measurements were conducted prior to heat treatment in comparison with post-heat treatment results. After sample preparations, the specimens were subjected to hardness test, microstructural and phase analysis as well as residual stresses to ascertain the effects of heat treatment on mechanical properties. Phase analysis on samples was performed using a Bruker D8 powder diffractometer that utilizes X-ray diffraction (XRD). X-ray radiation with a wavelength of 1.54056 A was used, covering a scanning range of 20 to 110 degrees (2θ). The measurement of residual stress was achieved using a XRD µ-x360 Pulstec residual stress analyzer for the heat treated and as built samples as illustrated in Figure 3(a) . The measurements involved employing cos α technique to calculate both in-plane residual stress (σx) and shear residual stress (τxy) on a LENS produced sample illustrated in Figure 3(b) . Vicker’s hardness testing machine of model Zwick/ Roell ZHVm, was used for measuring hardness on both the as built and heat-treated samples. A load of 500 gf for 10 s was applied as per ASTM E92 standard. Microstructural analysis was achieved using Scanning Electron Microscope (SEM), JEOL JSM-6010PLUS/LA after the polished samples were etched using a 2% nital solution as per ASTM E407.

Figure 4 shows the annealing heat treatment simulations during heating, holding and cooling stages. During the heating phase the sample is subjected to elevated temperature over a specified time as is shown in Figure 4(a) , this indicates that the sample has been uniformly heated to 850˚C, to reach a thermal state crucial for subsequent holding stage. The heating stage tends to reduce the thermal gradient which results in minimum stress development. During the holding stage Figure 4(b) , the temperature stabilizes within (330˚C - 540˚C), allowing the material’s structure to rearrange thus aids in prevention of new thermal stresses. In the cooling stage Figure 4(c) , the temperature decreases gradually (22 - 125˚C). The slow cooling process is essential for preventing the development of thermal gradients that could otherwise induce high residual stresses, as seen in quenching process. The gentle cooling allows the material to contract uniformly, leading to a stress-free state. Overall, the annealing process successfully minimizes residual stresses by controlling the temperature distribution throughout all stages, resulting in a more stable material with enhanced mechanical properties and improved resistance to future stress and fatigue. Tooten et al. [15] highlighted that cooling phases plays a critical role in determining both magnitude and distribution of residual stresses.

Figure 5 illustrates simulation of quenching process at various stages of cooling after the heating phase. During heating ( Figure 5(a) ), the samples reach a peak temperature of 850˚C. When the samples were subjected to cooling, just after 2 seconds as illustrated in Figure 5(b) , the temperature dropped significantly to 645˚C, within the next 15 seconds ( Figure 5(c) ) and 38 seconds ( Figure 5(d) ), the

temperatures dropped further to 330˚C and 125˚C respectively before cooling down to room temperature. As demonstrated in Figure 6 , the cooling rate for both annealing and quenching plays a crucial role in the formation of residual stresses. Specifically, the annealing process, which involves a slower cooling rate, leads to lower residual stresses compared to the quenching process, which features rapid cooling. The annealing sample shown in Figure 7(a) supports this, displaying considerably lower residual stresses with a maximum value of 34.72 Mpa. This finding is consistent with the study by Lu et al. [24] , which indicated that slower cooling reduces residual stress and strain. Annealing involves slow cooling rates, contributing to a uniform thermal contraction that results in low magnitudes of residual stresses. The distribution appears uniform compared to the quenched sample, with stress values nearing zero as portrayed by the contour map. This uniform distribution demonstrates that annealing effectively alleviates residual stresses, thus reducing the likelihood of material failure due to cracking.

Figure 7(b) shows residual stress distribution of a quenched sample, a significant high residual stress of 407 Mpa is observed mostly near the edges of the deposited part, this is as a result of rapid cooling process, which induces steep temperature gradients that contributes to uneven contraction within the material leading to tensile stresses at the edges and compressive stresses at the center, which can lead to cracking if not properly managed [25] . Similar patterns of residual stress distribution have been observed in [10] .

The numerical results were validated against experimental data. Figure 8 compares residual stresses under varying heat treatment conditions both experimental and simulation. As per experimental results, the as built and annealing samples exhibited residual stress of 144 ± 20 Mpa and −3 ± 16 MPa respectively. However, the quenching process resulted in an increase in residual stress of 425 ± 14 MPa. These observations indicate that residual stresses in LENS fabricated AISI 1025 can be decreased by annealing, tensile stresses reduced into compressive stresses. The reduction of tensile stresses into compressive stresses is beneficial, as compressive stresses can enhance fatigue resistance and prevent crack initiation, improving the overall structural property of the material. The close agreement between the numerical and experimental results further validates the ANSYS model’s capability, with minimal error of 4.24% observed between the two sets of data, confirming its reliability for simulating residual stresses in AISI 1025 steel.

The evaluation of the microstructure further explains the behaviour of AISI 1025 during heat treatment. Figure 9 shows SEM micrographs for as-built and heat treated AISI 1025 samples. The annealed sample in Figure 9(b) indicates enlarged grains consisting mainly of ferrite as the main phase as illustrated in Figure 10 . The evenly distributed homogenized grains can be attributed to the slow cooling which causes transformation of austenite to soft pearlite, displayed by the laminar structure. Coarser grains are mostly associated with improved ductility and toughness as was demonstrated by Hang et al. [26] . Additionally, the grain structure contributes to low residual stress magnitudes as observed with the annealing simulation. However, the hardness is reduced considerably to 126 ± 4 HV, compared to 169.17 ± HV recorded on the as built sample. The reduced hardness can be attributed to slow rate of cooling which refines previously formed grains. This agrees with Rahman et al. [27] who reported that annealing enhances the ductility of a material at the expense of hardness and removes internal stresses. Figure 9(c) illustrates a microstructure from the quenched sample, a fine highly strained grain structure is observed indicating that the grains had limited time to undergo growth due to the rapid cooling rate which contributed to high residual stresses as was depicted by the simulation.

The quenched microstructure further consists of a tempered martensite with retained austenite structure as displayed in XRD results in Figure 11 . The rapid cooling rate prevents the complete conversion of austenite into ferrite structure; thus, the residual austenitic structure subsequently undergoes a transformation

into martensite. In steels, due to recrystallization and formation of martensite, a hard and brittle phase, which is known to increase strength and hardness but also induce significant residual stresses as Aversa et al. [28] also reported. High hardness of 205.21 ± 13.2 HV was recorded after quenching, which was related to rapid martensitic transformation [8] .