Optimizing post-processing procedures to enhance bond quality of additively manufactured aluminum alloy 6061 using multiscale modeling | npj Advanced Manufacturing

npj Advanced Manufacturing volume 2, Article number: 27 (2025) Cite this article Optimizing post-processing procedures, such as hot isostatic pressing (HIP), is crucial for minimizing defects in

npj Advanced Manufacturing volume 2, Article number: 27 (2025) Cite this article

Optimizing post-processing procedures, such as hot isostatic pressing (HIP), is crucial for minimizing defects in additively manufactured aluminum alloy 6061 (6061) components. In this study, we introduce a multiscale modeling framework integrating molecular dynamics, mesoscale reaction–diffusion, and finite-element modeling to optimize the HIP process by identifying optimal parameters. Our findings reveal that bonding criteria are primarily determined by the rate of magnesium diffusion and the thickness of the Al2O3 layer, leading to the formation of a complex spinel phase at the interface. The multiscale model highlights temperature as the most significant factor influencing bond quality. With HIP temperatures exceeding 400 °C, bond interface voids collapse completely, resulting in desirable bond characteristics and strength. Below 400 °C, void closure is challenging, with multiple factors contributing to the process. This approach offers comprehensive strategies for post-processing optimization, improving bond quality and cutting experimental costs, thus advancing the performance of AA6061 in high-demand applications.

Aluminum alloy 6061 is known for its excellent mechanical properties, including strength, weldability, and corrosion resistance1,2, thereby making it the “workhorse” aluminum alloy. It is widely used in automotive, aerospace, nuclear, corrosion control, and other structural applications3,4,5,6,7,8,9,10,11. To achieve optimal forms and joints of 6061 in complex assemblies, an array of advanced fabrication techniques are being proposed and employed12,13,14,15,16. However, additively manufactured (AM) 6061 often suffers from defects such as interface porosity and cracks, which can compromise component integrity and durability17. Therefore, post-processing procedures like hot isostatic pressing (HIP) are essential for refining the microstructure, eliminating porosity, and removing other material defects, thereby enhancing overall material performance18,19,20,21,22,23,24. An optimized and efficient HIP process is crucial as a post-processing step for additively manufactured parts, as it effectively eliminates internal voids, reduces residual stresses, and enhances mechanical properties25,26. This study focuses on optimizing HIP and similar processes to boost the quality and performance of AM parts.

HIP has been extensively applied and recognized as a vital step in post-processing additive manufacturing. Studies have shown its effectiveness in improving the bonding interface across various alloys and polymers, including FeNiCoCr27, Ti–22V–4Al28, PEEK29, stainless steel 316L30,31. During the plate HIP diffusion bonding process, two prepared surfaces are held together at the desired elevated temperature and pressure to achieve a strong and consistent bond. The process temperature is usually selected in the range of 50–99% of the given material’s absolute melting point or solidus temperature. The applied pressure is generally lower than the material yield strength to avoid large-scale deformation or distortion in the components32. However, in some specialized applications, such as U-10Mo fuel assembly cladding, the HIP temperature can reach up to 560 °C, which is around 0.97Tm of 6061 alloy. The applied pressure can exceed the 6061 yield strength, which makes it different from traditional HIP diffusion bonding settings5,33. The HIP diffusion bonding process in an experiment can last from 1 h to more than 20 h. With the presence of the surface amorphous Al2O3 layer or γ-Al2O3 formed at room temperature, different Al alloy constituents will diffuse to the bonding interface to react with the oxide layer during the HIP process. Precipitates such as Mg2Si, Al2Cu, etc., and spinel phases such as MgAl2O4 or complex derived Mg2Al2O5, oxide phase have been observed experimentally during 6061 HIP diffusion bonding under different operating condition5,34. In literature, the formation mechanism of these precipitates along the interface has been proposed, which is shown in Fig. 134. To test those hypotheses and minimize the number of experiments needed to perform this work; we developed a novel multiscale modeling framework that integrates molecular dynamics (MD), mesoscale reaction-diffusion, and finite-element modeling (FEM). The goal of this approach is to identify the optimal HIP processing parameters—time, temperature, and pressure—thereby reducing experimental costs.

Initially, Mg atoms diffuse from the surrounding Al matrix toward the amorphous Al₂O₃ interface. This leads to the formation of Mg₂Al₂O₅ nanoparticles at the Al₂O₃/Al interface. Once the amorphous Al₂O₃ is fully consumed, a Mg₂Si particle begins to form. As the process continues, the Mg₂Si particle undergoes further growth.

Currently, most existing diffusion bonding models have been developed to deal with the bond line void closure process using pure metal or alloy without explicitly considering the oxide layer on the bonding interface. Some diffusion bonding models focus on the evolution of the bonding surface profile over a given period. and the reduction of those voids would be critical for determining the bonding strength35,36,37,38,39. The theoretical model can have several sub-models that describe the diffusion bonding process at different stages. At initial contact of the materials, asperities on the bonding surface will be deformed, and voids will form between the contact points. This process is modeled by plastic deformation because of the extreme stress at the initial contact of those asperities40. After initial deformation, void closure and subsequent void collapse are driven by power-law creep and diffusion (surface, interface, volume)18,41. When modeling the 6061 plate HIP process, the influence of the Al2O3 oxide layer and precipitates on the bond lines should not be omitted. Those factors potentially can be handled using the meso-scale reaction-diffusion model to study the conversion of the metal/alloy oxide layer42,43,44,45,46. However, most existing reaction-diffusion models cannot incorporate the evolution of the bond interface void shape during the reaction and diffusion process. The myriad of HIP process windows, oxide layer thicknesses, and the coupled reaction-diffusion process make numerical modeling of 6061 HIP a challenging task. Currently, there is a dearth of research conducted on the HIP diffusion bonding of the 6061 process because most of the research investigations are conducted experimentally and also because of the previously mentioned challenges.

Our proposed multiscale modeling approach, informed by HIP experimental data, aims to simulate the 6061 plate HIP diffusion bonding process, thus providing insights into how HIP parameters influence the bond quality and sealing of bond interface voids. As shown in Fig. 2, the framework integrates three distinct models with length and times scales covering the mechanisms at play during HIP.

The multiscale model consists of molecular dynamics (MD), mesoscale reaction-diffusion, and finite-element modeling (FEM). They cover a wide range of time and length scales to enable the study of the bond interface void closure during the HIP process.

At the mesoscale, the FEM was combined with the reaction-diffusion model, thus enabling the investigation of the void closure phenomenon at varying HIP temperatures and pressures. Species diffusion inside the oxide layer, which is critical to understanding the void closure kinetics, was acquired by correlating the diffusion model predictions with actual experimental observations. The acquired diffusion parameters are further cross-validated with MD simulations, which access the species diffusion quantities at atomic scale. Moreover, the impact of the Mg2Al2O5 oxide layer on void elimination has been explicitly incorporated within the numerical model. This inclusion allows for a more nuanced understanding of the oxide layer’s role in the overall bond quality of the resulting samples. Each modeling scale, from MD to the macroscopic FEM, contributes to a systematic understanding of the HIP process, ensuring that the simulation results are robust and predictive of real-world outcomes.

For the as-received 6061 plates, we carried out an exhaustive transmission electron microscopy (TEM) analysis to quantify the surface oxide layer thickness and enrichment of Mg at the oxide interface. The chemical compositions of the 6061 alloy can be found in Table A.1 (Supplementary Information), which is determined using the inductively coupled plasma-optical emission spectrometry (ICP-OES) method. As mentioned earlier, the proposed hypothesis (Fig. 1) relied on the assumption that an oxide layer with an enriched Mg phase is present before the start of the HIP process. Characterizations of the interface microstructure of the HIP-bonded samples and the oxide layer of the as-received 6061 plate were accomplished through a combination of scanning electron microscopy (SEM) and TEM. SEM analysis was carried out using a JEOL JSM-7600 field emission microscope. For TEM analysis, as received 6061-T6 samples were prepared using a FEI Quanta FEG 250 Dual-Beam SEM focused ion beam microscope provided by Thermo Fisher Scientific in USA, operated at 2–30 kV to determine the oxide and interface chemistry. The TEM analysis was performed using an aberration-corrected microscope (JEM-ARM200CF from JEOL, Japan) equipped with high-angle annular dark field (HAADF), scanning TEM (STEM) and an energy-disperse spectroscopy (EDS) system operated at 200 kV.

The Fig. 3 provides a visual representation of the oxide layer microstructure along with TEM-EDS maps. The TEM analysis confirmed the presence of continuous amorphous and crystalline domains measuring between 2 and 5 nm γ-Al2O3 oxide layer with an overall thickness of 7 nm. Furthermore, the TEM-EDS results validated the enrichment of the magnesium beneath the oxide layer. This sets the stage for all the modeling work.

a and (b) TEM microstructures depicting the thickness of oxide, and (c) TEM-EDS maps illustrating the spatial distribution of oxygen (O), magnesium (Mg), and aluminum (Al) within the oxide layer.

To calculate the Mg diffusion speed inside the Mg2Al2O5 layer, we compared the layer thickness predicted by the reaction–diffusion model to the measurement obtained experimentally. As shown in Fig. 4a, the color contour map visualizes the Mg2Al2O5 layer thickness with different HIP time (tHIP) predicted by the reaction–diffusion model.

a The Mg2Al2O5 layer thickness (L) plot with respect to the HIP time calculated from the numerical solutions. b Calculation of the Mg diffusion coefficient correlation from the experimental data. The yellow region represents the diffusion coefficient boundary estimated from the experimental data with diffusion–reaction model.

The contour line represents the log-scale Mg2Al2O5 layer thickness using Mg diffusion coefficient DMg at different temperatures. The blue rectangular patch region stands for the Mg2Al2O5 layer thickness measured experimentally. Because the total amount of the Al2O3 supply is limited, the actual Mg2Al2O5 layer thickness cannot grow indefinitely and is confined in a limited region along the y-axis. In the experiment, the HIP time is predetermined. However, the actual reaction time (tReact) to form the Mg2Al2O5 layer can be shorter than the designated HIP time, especially at high-temperature conditions, if all the Al2O3 is consumed before the HIP procedure is finished. Therefore, the width of the blue patch in Fig. 4a represents the tReact range in the experiment, which starts from 1 min to the whole length of the HIP time tHIP at the T = 450 °C. By examining the overlapped regions, the Mg diffusion coefficient range can be calculated for given temperature conditions. Repeating the same procedure for the cases at the temperature of T = 350, 450, and 560 °C, the Mg diffusion coefficient correlation with respect to temperature can be estimated as shown in Fig. 4b. The yellow area represents the possible DMg range at different HIP temperatures. The lower boundary stands for the DMg calculated for each temperature by assuming that tReact = tHIP. At 350 °C, with a sufficient supply of the Al2O3, the reaction time would be equal to the HIP time, and the Mg diffusion coefficient can be calculated as DMg = \(5.3\times {10}^{-21}\) (m2/s).

As the temperature surpasses 400 °C, the tReact becomes significantly shorter than tHIP. This discrepancy introduces substantial uncertainty when attempting to quantify the Mg diffusion coefficient using the reaction-diffusion model only. To determine the effective Mg diffusion coefficient, we conducted MD simulations at temperatures of 450, 500, and 550 °C. Our goal for these simulations was to measure the Mg diffusion rate within the Mg2Al2O5 layer. Combined with data obtained from the MD simulations, the diffusion coefficient curve for Mg calculated using Eq. (1) is depicted as a red line in Fig. 4b:

where the pre-exponential factor D0 = \(1.6\times {10}^{11}\) m2/s and activation energy Q = 375.4 kJ/mol are determined. Given the diffusion coefficient, we ascertain that the actual reaction time at 400 °C is around tReact = 1 min, which is considerably shorter than the entire HIP process. The red dashed line in Fig. 4b shows the upper and lower bound of DMg with a ±10% variation in the activation energy Q. This covers the MD-predicted Mg diffusion coefficient within the 450–550 °C range.

After applying pressure on the 6061 plates, the existing void will initially experience plastic deformation, which we investigated using FEM. The applied pressure ranges from 50–108 MPa at six different levels. Fig. 5a–d shows examples of the remaining void shape after applying 50 MPa pressure at four different temperatures. Voids are assumed to distribute periodically along the bonding interface with a similar shape. Therefore, we selected a representative region with the middle void for subsequent void closure modeling. We noticed that all the voids remained elliptically shaped but decreased in size. The resulting void profiles after peak pressure were used as the input for the beginning of the HIP process and their heights are summarized in Fig. 5e. At T = 350 °C, the void height remains around 1.7 nm after applying pressure at 108 MPa. As the temperature was increased to 380 °C, the remaining void height decreased to 0.7 nm at 108 MPa. When the temperature reached 400 °C, the void height dropped below 1 nm at a relatively low pressure of 60 MPa.

a T = 350 °C, p = 50 MPa, (b) T = 360 °C, p = 50 MPa, (c) T = 380 °C, p = 50 MPa, (d) T = 400 °C, p = 50 MPa. e The height of voids was simulated using the FEM study conducted at the beginning of the HIP process.

After the initial plastic deformation, the void shape will further evolve due to the formation of the Mg2Al2O5 layer during the HIP process. We analyzed this Mg2Al2O5 growth effect on the void shape change with the reaction–diffusion model by importing void profiles from the FEM models. Affected by the void shape, the Mg diffusion distance from the Al/Mg2Al2O5 to the Mg2Al2O5/Al2O3 interface will vary at different void locations. The Mg concentration and diffusion flux speed can also vary spatially. Those differences will further change the shape of the voids. We used the 2-D reaction–diffusion model to track void shape evolution as depicted in Fig. 10c. An example of a simulated final void shape after the HIP process is shown in Fig. 6a.

a Simulation of Mg diffusion and Mg2Al2O5 layer formation during the HIP process. The color bar stands for the Mg concentration inside the Mg2Al2O5 layer, and the streamlines represent the Mg diffusion path. b–d Evolution of void height and Mg2Al2O5 layer thickness during the HIP time under different temperature and pressure conditions.

The color-coded region represents the formed Mg2Al2O5 layer after 300 min HIP at 360 °C and 60 MPa. The color scale shows the concentration of the Mg inside the Mg2Al2O5 layer, with red being the highest concentration and blue the lowest. The streamline visualizes the diffusion pass of the Mg. At the top boundary, the Mg concentration is kept as a constant supplied by the Al alloy matrix. The Mg concentration decreases gradually to the bottom, where it is consumed by reacting with Al2O3 to form the Mg2Al2O5. By tracking bottom moving boundary shape change, the Mg2Al2O5 layer thickness and void height profiles can be plotted during the HIP process. Three examples are shown in Fig. 6b–d at different HIP temperatures with a pressure of 60 MPa. For T = 360 °C, the Mg has a very low diffusion speed of DMg = 1.6 × 10−20 m2/s. The Mg2Al2O5 layer grows only 2.6 nm, with no significant void height change over the 300-minute HIP period. By increasing temperature by 20–380 °C, the Mg2Al2O5 layer thickness reaches 9 nm at the end of the HIP process. The void height shows a noticeable change from 2 to 0.5 nm. At T = 400 °C, the Mg diffusion coefficient (DMg = 1.0 × 10−18 m2/s) becomes two orders of magnitude larger compared to the value at 360 °C. The amorphous Al2O3 layer is all consumed at 150 min before the end of the HIP process. Therefore, the Mg2Al2O5 layer thickness stops growing after 150 min. The void height drops to below 0.1 nm, indicating that the void is fully collapsed at this temperature.

HIP parameters can largely affect the characteristics of the precipitates at the bond line interface. In this study, we focused our investigation on the Mg2Al2O5 particle size, which is closely related to the void shape change and bond strength after the HIP process. The Mg2Al2O5 oxide layer thickness is measured from the HAADF-STEM images as shown in Fig. 7a. The Mg2Al2O5 oxide layer thickness is about two times larger than that of the Mg2Al2O5 nanoparticle size. Assuming a symmetric distribution of Mg2Al2O5 particles at both the top and the bottom of the Al plate interface, the Mg2Al2O5 layer thickness on one side of the plate can be represented using the measured nanoparticle size. Figure 7b–g shows the nanoparticle size distribution at various HIP temperature, time, and pressure conditions. As observed by Song et al.34 at a low temperature of 350 °C, very few Mg2Al2O5 particles formed at the bonding interface, and the particle size was measured to be around 3.5 nm. A high HIP pressure of p = 206 MPa does not facilitate the formation of particles at such a low temperature. The slow diffusion speed and reaction rate of Mg with the Al2O3 limited the formation of the particles, and the voids at the interface would stay almost unchanged. When the temperature is increased above 400 °C, the Mg2Al2O5 becomes denser along the bonding interface with an average particle size of 19.0 nm. However, further increasing the temperature does not increase the particle size. This is limited by the total amount of available surface Al2O3 layer formed at room temperature before the HIP process is initiated. After all the Al2O3 is consumed, the growth of the Mg2Al2O5 particle stops, and the Mg2Al2O5 layer thickness will reach a plateau after 400 °C, regardless of the HIP time and pressure applied. Figure 7e–g further confirmed this conclusion with three repeated tests at 560 °C. Particle sizes averaged between 17.2 and 19.8 nm, which are close to the sizes measured at 400 and 450 °C.

a STEM-HAADF image showing the Mg2Al2O5 band at the bonding interface with T = 560 °C. b–g Distributions of Mg2Al2O5 particle size (correlated to layer thickness) after the HIP process.

To investigate the influence of HIP parameters on void closure, we divided the discussions into two parts based on the HIP temperature. For HIP temperatures of 400 °C and above, the temperature plays the most dominant role in dictating the void closure process. At the beginning of the HIP process, the applied pressure causes significant plastic deformation of the voids along the bond interface. Specifically, at a 50 MPa pressure, the initial void height rapidly decreases from 5 nm to ~1.5 nm (Fig. 5e). For a HIP pressure of 60 MPa, the voids shrink to below 1 nm even before the onset of magnesium diffusion, which subsequently accelerates void closure. As the HIP process progresses, the significantly enhanced Mg diffusion at T ≥ 400 °C further promotes rapid void elimination. The numerical model predicts that after just 1 h of HIP at 400 °C and 50 MPa, the final void height decreases to about 0.2 nm. Extending the HIP duration to 2 h results in final void heights below 0.1 nm across all tested pressures, indicating nearly complete void collapse and the formation of strong interfacial bonds. This suggests that at HIP temperatures ≥400 °C, the 6061 plates can achieve ideal bond quality in a short period, with pressure having a comparatively minor influence. Furthermore, the enhanced Mg diffusion at elevated temperatures facilitates the rapid conversion of Al₂O₃ to Mg₂Al₂O₅, contributing to the full void collapse and improved bond strength. This outcome is confirmed by experimental images shown in Fig. 8e, which display a fully bonded interface with no visible voids after 5 h of HIP at 400 °C. This is consistent with our model’s predictions.

a–c Final void heights after given HIP time and temperature. d SEM and STEM-HAADF images showing the voids at the bonding interface with T = 350 °C and tHIP = 25 h. e SEM and STEM-HAADF images showing the fully bonded interface at T = 400 °C and tHIP = 5 h.

For HIP temperatures below 400 °C, voids are more difficult to collapse. In these cases, the influence of HIP time and pressure should also be considered. Void heights were calculated over HIP durations ranging from 1 to 10 h at four different temperatures, as shown in Fig. 8a–c. At a HIP temperature of 360 °C, the Mg diffusion speed is significantly reduced, and the void shape remains largely unchanged throughout the HIP process. Even after extending the HIP time to 10 h, the final void height at 108 MPa is 0.8 nm. This is only a modest improvement compared to the 1.36 nm void height after 1 h. Therefore, it is not cost-effective to extend the HIP time under low-temperature conditions. For a HIP temperature of 380 °C, increasing both tHIP and pressure has more noticeable changes to void height. For example, at tHIP = 1 h, increasing the pressure from 50 to 108 MPa can reduce the void height by 1 nm. Extending HIP time from 1 to 10 h leads to near full collapse of voids. A longer HIP duration becomes more effective in void elimination at this temperature level. Figure 8d shows an experimental observation of the bond interface at HIP temperatures of T = 350 °C. We observed several elliptically shaped voids at the bonding interface ranging from ~2 to 10 nm, even after 25 h of HIP. It is important to note that the initial void height of 5 nm used in the numerical model represents a typical pre-HIP void size in the 6061 plates. The exact initial void size may vary at those post-HIP imaging locations in the experiment. However, the persistence of voids at T \(\le\) 360 °C is consistent between the numerical predictions and experimental results.

To further demonstrate the capability of our model in studying additively manufactured materials, we applied it to predict interlayer void shape changes during the post-ultrasonic additive manufacturing (UAM) HIP process. The developed FEM model was used to simulate void structure behavior in UAM-fabricated aluminum parts, and the predictions were compared with experimental observations that were performed by Gussev et al.12. The Fig. 9a (adapted from ref.12) shows an optical microscopy of as-built UAM specimens before HIP, with voids in chains at multiple bonding layers. After HIP, all voids collapse, leaving no cavities or pores as depicted in Fig. 9b. To simulate void geometry changes, the as-built image was pre-processed into binary images to extract void shapes, which were directly imported into the FEM model. Figure 9d shows the computational domain, extended at the top and bottom to avoid boundary effects. The temperature was set to 580 °C and pressure was set to 100 MPa to match the experimental conditions. Figure 9e displays the simulation results after HIP, where a significant void collapse can be observed. The inset provides a zoomed-in view of a section, illustrating the localized stress distribution and void collapse.

Structures of the UAM-produced part. a As-built, and (b) after HIP conditions (adapted from ref. 12). c Image processed to extract the voids formed during the UAM process. d Finite element method (FEM) model setup for simulating the void shape evolution during HIP. e FEM prediction of the UAM part structure after HIP.

Both the experimental and simulated results confirmed that voids in UAM-fabricated parts collapse after HIP, consistent with the improved strength and ductility observed in the z-direction specimens. This successful application of our FEM model underscores its predictive capability and utility in optimizing post-processing treatments in additive manufacturing technologies.

In summary, this study proposes an integrated multiscale model aimed at optimizing post-processing HIP procedures to enhance the bonding quality of additively manufactured aluminum alloy 6061 under various processing conditions. The HIP temperature was identified as the most influential factor that dictates bond strength and Mg2Al2O5 layer formation. For temperatures >400 °C, the faster Mg diffusion speed will provide sufficient reactants for forming the Mg2Al2O5 layer at the interface and yielding a higher bond strength. We determined the Mg diffusion speed inside the Mg2Al2O5 layer and cross-validated the results using reaction-diffusion and MD models at different scales. Void closures were modeled by integrating the FEM with the reaction-diffusion model. The evolution of the Mg2Al2O5 layer thickness and void height changes were tracked over the whole HIP process. From this study, we determined that for high HIP temperature cases (T > 450 °C), it is possible to reduce the current HIP time to within 1 h without compromising bonding quality.

The HIP pressure is not a critical factor at high process temperatures. For low temperature (T \(\le\)360 °C) conditions, extending the HIP time and increasing the process pressure have marginal effects on closing bond interface voids, and the overall bonding quality achieved under those conditions is not desirable due to the slow Mg diffusion speed. For a HIP temperature range [380–400 °C], it is possible to fully collapse the voids and provide good bonding quality by applying high pressure and an extended HIP time.

A total of 12 HIP experiments were performed to investigate how HIP processing parameters affect plate bond strengths and the interface microstructures47,48. Before the experiment, surface treatment was performed to remove oxides and impurities from aluminum. This process involved several steps: applying an acidic solution, rinsing with deionized water, etching in sodium hydroxide, and drying with nitrogen gas. These steps are standard for removing oxides, including the natural aluminum oxide layer (Al₂O₃), which forms rapidly when aluminum is exposed to air. The literature49,50 confirms that Al₂O₃ forms almost immediately due to aluminum’s strong affinity for oxygen, even after thorough cleaning. This re-oxidation can impact the HIP process and is modeled in this study. The interval between cleaning and the HIP process, ranging from hours to days, allows sufficient time for the native Al₂O₃ layer to re-form. In a controlled experiment, a TEM sample was prepared and kept at room temperature under atmospheric conditions. The results confirmed the presence of the Al₂O₃ layer, consistent with the conditions under which it was bonded (Supplementary Information, Fig. A.1).

The HIP temperature ranged from 350 to 560 °C, and the HIP process time was selected at 1, 1.5, 5, and 25 h. A detailed experimental test matrix and the HIP experiment setup can be found in the work performed by the current authors34. The outer HIP can be assembled with low-carbon steel that is to be evacuated to eliminate the internal pressurized gas that would negatively affect the diffusion bonding process. Multiple 6061 plates were alternately sandwiched between mild steel plates (strong backs) within the HIP can. The assembled can be then placed inside the HIP chamber for the diffusion bonding process. Inert argon gas is used for pressurizing the HIP can assembly within the HIP chamber. At the beginning of the test, the HIP chamber temperature was elevated at a given heating rate until the designated HIP temperature was reached. The sample was then held at a given temperature and pressure for a designated period. After that, the HIP chamber was depressurized and cooled at a given furnace cooling rate (CR)51. For each HIP condition, peel testing was repeated four times to determine the average bond strength according to the equation Sbonding = F/W, where F is the peeling force, and W is the width of the HIP-bonded specimens. The peel test procedures had been set up according to the ASTM B1021-21 standard. From these tests, we determined that temperature has the strongest effect on the ultimate bonding strength. With T = 350 °C, the HIP-bonded claddings have consistently low bond strength below 2 N/mm. After increasing the temperature above 400 °C, the bond strength reached over 6 N/mm for all specimens. We observed a uniform band of Mg2Al2O5 nanoparticle phase along the bond line, which forms at a HIP temperature of 450 °C and higher.

The diffusion speed of Mg from the Al matrix to the reaction front is one of the most important factors that determines the formation of the complex spinel Mg2Al2O5 phase at the interface and the speed at which the reaction occurs. During the HIP process, it has been hypothesized that Mg2Al2O5 is expected to nucleate initially between the Al matrix and amorphous Al2O3 following the reaction described below34:

To model the formation of the Mg2Al2O5 layer, the diffusion-reaction process is summarized in Fig. 10.

a Model of initial condition setup based on the TEM image observation, (b) during the formation of Mg2Al2O5 with moving boundary and no voids, (c) during the formation of Mg2Al2O5 with 2-D moving boundary and voids.

Initially, at room temperature, the Al matrix is covered by a thin layer of amorphous Al2O3 formed, resulting in an enriched magnesium and silicon region below the interface. As the temperature in the HIP chamber increases, the Mg will diffuse faster from the Al/Al2O3 interface to the amorphous Al2O3. During the formation of the Mg2Al2O5, the travel distance of Mg from the Al matrix to the moving reaction front will increase accordingly. The diffusion process can be described by Fick’s second law as

where Ci denotes the concentration of species i. In this study, Ci would be the Mg because it is the limiting factor that dictates the growth speed of the oxide layer. The boundary conditions of the computational domain are given in Fig. 10b as

where x = 0 stands for the location Al/ Mg2Al2O5 interface and the concentration of the Mg will be constant at 0.9% according to the 6061 constituents, which are measured following the ASTM B209-14 standard. At the boundary x = L, the Mg2Al2O5/Al2O3 interface is moving with the formed Mg2Al2O5. The Mg diffusion flux \({D}_{{\rm{Mg}}}\frac{\partial C\left(L,t\right)}{\partial x}\) should be equal to the Mg consumption rate (Ri) following the reaction described in Eq. (2). The reaction front (x = L) move speed v1 can then be correlated to the Mg diffusion flux inside the Mg2Al2O5 as

The volume fraction of Mg2Al2O5 in the computational domain is calculated as α = 78.3%. Therefore, the Mg mole density inside the computational domain is \({\rho }_{{\rm{M}}{\rm{g}},{\rm{o}}{\rm{x}}{\rm{i}}{\rm{d}}{\rm{e}}}=2{\rho }_{{{\rm{M}}{\rm{g}}}_{2}{{\rm{A}}{\rm{l}}}_{3}{O}_{5}}\alpha =3.26\times {10}^{4}\) mol/m3. The materials properties used for the reaction–diffusion model are listed in Table A.2 (Supplementary Information). Following the formula of the Arrhenius equation, the Mg diffusion coefficient can be expressed as a function of temperature as

where DMg,0 is the pre-exponential factor and QMg stands for the activation energy. The R and T terms are the universal gas constant and temperature, respectively. Because DMg in the Mg2Al2O5 layer is not directly available from the literature, this correlation needs to be calculated using the experimental data, which is discussed in the “Results” section.

To validate and benchmark the Mg diffusion speed calculation, we performed MD simulations using the Large-scale Atomic/Molecular Massively Parallel Simulator package52. Mg2Al2O5 structures from the Materials Projects database53 were used in the simulation setup. A supercell of size 9 × 9 × 9 nm3 containing around 80,000 atoms was created and periodic boundaries were used in all three directions. The simulation box is energy minimized by the conjugate gradient algorithm with an energy tolerance of 10−15 eV and a force tolerance of 10−15 eV/Å. The system is equilibrated at 450, 500, and 550 °C, under the microcanonical ensemble (NVE) for 100 ps with a Berendsen thermostat for maintaining the temperature. Atomic positions and velocities with respect to time were recorded for 50 ps and diffusion coefficients, while both materials were in the solid phase, as done in previous works54,55. D was calculated using the slope of the linear mean square displacement curve as56 \(D=\frac{1}{6}\partial \left(\frac{1}{N}{\sum }_{i=1}^{N}\left\langle {\left({x}_{i}\left(t\right)-{x}_{i}\left(0\right)\right)}^{2}\right\rangle \right)/\,\partial t\). Here, N is the total number of atoms, and \({x}_{i}(t)\) is the position of ith atom at time t.

We employed reactive force field (ReaxFF)57 parameters developed by Yeon et al.58 to simulate the γ-Al2O3 and Mg2Al2O5 systems. ReaxFF is a type of force field that is designed specifically to model chemical reactions and the behavior of molecules in a reactive environment. Unlike traditional force fields that rely on fixed parameters for atoms and molecules, ReaxFF incorporates a reactive potential energy surface that can change as atoms move and interact with each other57. This allows ReaxFF to describe bond breaking and formation, as well as other chemical reactions, within an MD simulation. The potential was validated by comparing the bond distances and lattice constants with the density functional theory (DFT) obtained values. The lattice constant obtained from this potential was 8.86 Å, which compares well with the 8.88 Å value obtained from DFT, and the Al-O bond length for γ-Al2O3 obtained in this work was 1.88 Å, which compares well with the 1.90 Å obtained from DFT53. The density obtained for γ-Al2O3 is 3.88 g/cm3, which is in excellent agreement with the 3.87 g/cm3 result from DFT.

Using the Abaqus code, we developed a FEM to simulate void collapse between two 6061 plates that were influenced by varying pressures and temperatures. A schematic of the two-dimensional (2-D) FEM representing this void collapse process, complete with specified boundary conditions, is shown in Fig. 11.

a Setup and boundary conditions for void collapse model using the FEM simulations, where the red arrows are the applied pressure. The sides of the assembly are fixed in the horizontal direction and the bottom of the assembly is fixed in the vertical direction. b FEM mesh of the 2-D void collapse model.

The model consists of three 10 nm wide, 5 nm tall voids that are 10 nm apart. We selected the initial void shape to be elliptical, which is consistent with experimental observations59. Each plate has a node spacing of 0.5 nm and is modeled with CPE4R elements. The material properties used in this model were obtained from the literature and are presented in Table A.3 and Fig. A.2 in Supplementary Information. The true stress versus true plastic strain correlation is directly used in the basic elastic–plastic constitutive model. Linear regression is assumed for higher temperatures, and geometric nonlinearity also was assumed. The 6061 plates are fixed in the horizontal direction along the sides to mimic the conditions within the HIP can. The bottom plate is fixed in the vertical position. Pressure was applied across the top of the top plate. Temperatures ranging from 350 to 560 °C were investigated. The pressure range was selected according to the HIP experimental conditions described in the section “Results”. The resulting deformed void geometry for a given pressure and temperature then was extracted from the model to be used for the reaction–diffusion model. A total of 20 different temperature and pressure cases were evaluated in this FEM study.

To accurately and efficiently capture the void collapse based on various temperatures, a 2-D model is optimal because of the high mesh resolution demand. To ensure the accuracy of the 2-D model, we compared its simulation results with those of a three-dimensional (3-D) model, as illustrated in Fig. 12a and b. For this comparison case, one 5 × 10 µm elliptical void is modeled in the middle of the assembly. The temperature of each model is set to 400 °C and the applied pressure at the top of the assembly is 50 MPa. C3D8R elements are used for the 3-D model, and CPE4R elements are used in the 2-D model. The resulting void height for the 3-D model and 2-D model are shown in Fig. 12c.

a Isometric view of the half-symmetry 3-D model used for justification of the 2-D model. b Front view of the 3-D model with red arrows indicating the applied pressure. Resulting in void height at a temperature of 400 °C and a pressure of 50 MPa for the (c) 3-D model and (d) 2-D model.

There are minor differences in stress profile between the 3-D model and the 2-D model, where the 3-D model experiences more of a butterfly-shaped stress response than that of the 2-D model. Despite these slight differences, the 2-D model can predict the resulting void height within a 1% difference from that of the 3-D model. Therefore, the 2-D model is used for the evaluation of void collapse during the HIP diffusion bonding process.

The raw/processed data required to reproduce these findings cannot be shared at this time as the data also are part of an ongoing study.

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This work was conducted at Pacific Northwest National Laboratory, which is operated by Battelle for the U.S. Department of Energy under contract DE-AC05-76RL01830. This work was funded by the National Nuclear Security Administration Office of Material Management and Minimization. The authors would like to thank everyone directly or indirectly associated with producing the results. This manuscript was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

Pacific Northwest National Laboratory, Richland, WA, 99352, USA

Yucheng Fu, C. J. Taylor Mason, Rajib Kalsar, Ankit Roy, Miao Song, Kenneth I. Johnson, Zhijie Xu, Kriston P. Brooks, Naveen K. Karri, Matthew J. Olszta, Curt Lavender, Ayoub Soulami & Vineet V. Joshi

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Y.F., C.J.T.M., A.R., and Z.X. developed the multiscale model. R.K., M.S., K.I.J., N.K.K., M.J.O., and C.L. performed the experiments and conducted material characterization and analysis. Y.F., C.J.T.M., R.K., and A.R. wrote the manuscript draft. K.P.B., A.S., and V.V.J. provided supervision and project management. All authors reviewed the manuscript.

Correspondence to Yucheng Fu or Vineet V. Joshi.

The authors declare no competing interests.

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Fu, Y., Mason, C.J.T., Kalsar, R. et al. Optimizing post-processing procedures to enhance bond quality of additively manufactured aluminum alloy 6061 using multiscale modeling. npj Adv. Manuf. 2, 27 (2025). https://doi.org/10.1038/s44334-025-00037-w

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Received: 04 December 2024

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Published: 30 June 2025

DOI: https://doi.org/10.1038/s44334-025-00037-w

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