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Review

Numerical Simulation and Hot Isostatic Pressing Technology of Powder Titanium Alloys: A Review

State Key Laboratory of Materials Low-Carbon Recycling, College of Materials Science and Engineering, Beijing University of Technology, Beijing 100124, China
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Author to whom correspondence should be addressed.
Metals 2025, 15(5), 542; https://doi.org/10.3390/met15050542
Submission received: 2 April 2025 / Revised: 6 May 2025 / Accepted: 12 May 2025 / Published: 14 May 2025

Abstract

Titanium and its alloys have been widely used in high-end fields such as aerospace and biomedical engineering due to their excellent corrosion resistance and comprehensive mechanical properties. However, traditional titanium alloy processing technologies suffer from low material utilization and numerous defects. The emergence of near-net shape forming technology for powder titanium alloys via hot isostatic pressing (HIP) has broken through the limitations of traditional casting and forging, significantly improving the mechanical properties of titanium alloy materials, increasing material utilization, and shortening the production cycle of products. The application of numerical simulation technology has provided a scientific basis for the design of capsules and cores of complex high-performance components and has offered theoretical support for the densification of powders under thermomechanical coupling, becoming an essential foundation for achieving controllable shape and properties of components. This paper introduces the characteristics and process flow of HIP technology for powder titanium alloys, summarizes the current development status and research achievements of this technology both domestically and internationally, elaborates on the research progress of numerical simulation of HIP, and concludes with an analysis of the existing technological challenges and possible solutions, as well as an outlook on future development directions.

1. Introduction

Titanium and its alloys are widely used in aerospace, weaponry, medical, and chemical industries due to their excellent properties such as low density, high specific strength, good creep resistance, and corrosion resistance, which has made them important materials of scholarly interest [1,2,3,4,5]. The weight reduction effect brought by the application of titanium alloys can not only further improve the design level and flight performance of aircraft, but also save significant amounts of advanced fuels, which can further reduce the construction and launch costs of weapons and equipment [2]. However, the high raw material cost of titanium alloy, coupled with the complex procedures and low material utilization inherent in traditional processing methods such as casting and forging, significantly limits the mechanical properties and application scope of titanium alloy components. Additionally, defects like porosity, shrinkage, inclusions, and compositional segregation that commonly occur during the casting process further restrict the expansion of titanium alloy applications in industrial field [3]. Take the manufacturing of titanium alloy fuselage frame of Boeing 787 as an example; about 83% of the original material is lost in the form of chips during the cutting process, and the material utilization rate is significantly low, resulting in high manufacturing costs [2]. This high wastage rate is a key problem to be solved in the processing of titanium alloy components.
As a new manufacturing technology, hot isostatic pressing (HIP) near-net shape forming breaks through the limitations of traditional processes. It significantly enhances the comprehensive mechanical properties of titanium alloy components, and improves material utilization while shortening manufacturing cycle times. Near-net shape HIP (NNS-HIP) process takes metal powder as raw material and combines numerical simulation and mold design technology to achieve rapid densification of powder material and workpiece forming with the help of high temperature and high pressure. This technology provides hot blanks with the required shape, size, and organization for subsequent machining, isothermal forging, or heat treatment process, and has become a key research direction in the field of powder metallurgy [6,7,8]. Compared with traditional processing technology, powder titanium HIP technology, as an advanced material preparation method, has significant technical advantages: (1) high product densities with relative densities close to the theoretical value of 100%—the microstructure is highly homogenized, there is no macroscopic segregation, microscopic pores and residual stresses, and the comprehensive mechanical properties can reach, or even exceed, the level of forgings [9]; (2) strong molding ability—through the capsule/core synergistic design and numerical simulation optimization, near-net shape forming of complex geometric structures (including shaped inner cavities) can be achieved, with dimensional accuracy of 0.2 mm and excellent surface quality, while reducing more than 90% of machining; (3) improve material utilization and reduce production costs—compared with the traditional casting and forging process, NNS-HIP technology makes the material utilization rate increase by more than 50%, and at the same time, the process method is simple. In addition to hot isostatic pressing equipment, it does not require other important equipment, which shortens the production cycle [10,11]; (4) high flexibility in material design, support for multiple alloy composition regulation, can meet the special mechanical, corrosion-resistant and functionalization needs.
Although HIP technology has been applied in high-end manufacturing fields, its powder densification process still faces problems of multi-scale synergistic control. During HIP, part forming occurs under the influence of a complex thermal force coupling field. Powder particles achieve densification through the dynamic rearrangement, plastic yielding, and diffusion creep. This process is accompanied by more than 30% of the volume shrinkage in the capsule system. Due to the existence of the “stress shielding” effect between the capsule and powder, the large differences in thermal properties between the internal core and the powder material, as well as the uneven distribution of powder in the capsule, can lead to an overall uneven shrinkage and deformation of the part [12] and local “corner effect” [13]. The traditional “trial and error method” is overly dependent on the experience of technicians. This requires repeated testing, making it difficult to ensure the quality of the product, while also consuming a lot of manpower, material resources, and increasing manufacturing costs. This method is ill suited to meet the growing demands for large-scale, complex, and high-precision HIP parts [14]. Computer numerical simulation technology enables deformation prediction of components, thereby guiding the design of capsules and cores. This approach not only accelerates the testing process and reduces production costs, but also visualizes the densification of powder particles within the capsule. This visualization facilitates a deeper understanding of the densification and deformation mechanisms during hot isostatic pressing, thus advancing the development of HIP process. To this end, this paper introduces the process and theoretical research of NNS-HIP technology for powder titanium alloys and the current development status both domestically and internationally, summarizes the latest research progress in numerical simulation of hot isostatic pressing in recent years, and briefly analyzes the existing problems and the development direction of this process. In this review, we searched using the keywords “Hot Isostatic Pressing (HIP)”, “powder titanium alloy”, and “numerical simulation” through the Web of Science, CNKI, and ScienceDirect databases. To ensure the timeliness and relevance of the references, we focused primarily on research articles published within the last decade and supplemented our discussion with classic literature.

2. Overview of Powder HIP Technology Process

Hot isostatic pressing (HIP) is an advanced manufacturing process that uses inert gases like nitrogen or argon to apply uniform high pressure and temperature to materials in a closed container, achieving sintering and densification [15]. HIP can directly sinter metal powders for molding or repairing internal defects in castings, providing high-quality blanks for further processing. The technology combines the advantages of casting and forging, enabling near-net shape forming of complex parts with high material utilization and excellent mechanical properties [16].

2.1. Process Flow of Hot Isostatic Pressing Technology for Powders

Powder metallurgy is an advanced manufacturing technology that uses metal powder or its mixture as raw material to realize near-net shape forming of materials or parts through pressing and sintering processes. Through precise control of powder particle size, morphology, and process parameters, the technology can create complex-shaped parts and high-performance materials, with high material utilization and excellent microstructure uniformity [17]. Hot isostatic pressing (HIP) technology is an important means for the production and preparation of high-quality materials. It involves placing a capsule or casting containing metal powder in a hot isostatic press, using inert gas as the pressure medium, so that the capsule and casting are uniformly pressurized in a high-temperature environment [18]. The HIP equipment mainly consists of a heating furnace, a high-pressure gas system, a vacuum treatment device, and a water cooling system [19]. The key parameters of the HIP process include pressure, temperature, and time, in which the heating temperature is usually chosen to be 0.6–0.7 Tm, the pressure is usually set at 100–200 MPa, and the complete cycle is about 2–5 h [20].Through the synergistic effect of high temperature and high pressure, the internal defects such as pores and microcracks are eliminated, thus significantly enhancing material density and overall mechanical properties [21].
Powder hot isostatic pressing technology is a product of the combination of powder metallurgy and HIP processing, which inherits and develops the advantages of the two processes, not only significantly improving the overall performance of the product, but also significantly shortening the production cycle. The main process steps include: powder preparation; design and manufacture of the capsule and core according to the size of the molded part; leakage checking of the capsule; filling with metal powder and vibration compaction; vacuum pumping and sealing welding of the capsule; removal of the capsule through machining or pickling after the completion of the hot isostatic pressing process; and, finally, local finishing to obtain the finished part [5]. Figure 1 shows the HIP manufacturing process for simplified turbine disc. It should be noted that the sealing and vacuuming process needs to ensure a high vacuum inside the capsule to prevent the oxidation of the alloy powder at high temperatures, thus safeguarding the performance of the product [22].
In this process, powder quality and capsule design and manufacturing are particularly important. The quality of metal powder determines the mechanical properties of powder metallurgy components, so powder preparation is a key link in the hot isostatic pressing process. The mainstream methods for preparing titanium alloy pre-alloyed powder are gas atomization (GA) and centrifugal atomization (CA). In addition, there are other methods, such as the elemental mixing method and the hydrogenation–dehydrogenation (HDH) method. Figure 2 shows the schematic diagrams of the two main powder production processes.
The GA method involves pulverizing the molten titanium alloy into small droplets in an atomization chamber by means of a high-speed gas stream (e.g., argon), and forming metal powder after cooling. This method has high production efficiency and is suitable for large-scale production with a wide powder size distribution (50–300 μm), but it is prone to form hollow powder, which affects the powder densification and the final product properties [23]. The CA method utilizes the centrifugal force generated by the metal liquid at high rotational speeds to condense into a powder [24], with the plasma rotating electrode atomization (PREP) method being the most widely used. The powder prepared by this method has high sphericity, good fluidity, high densification, and narrow particle size distribution (150–250 μm) [25], but the low production efficiency and high cost of equipment limit its use primarily to high-end fields such as aerospace. The elemental mixing method involves mechanically mixing titanium with other alloying element powders. While it is low cost, it suffers from poor mixing uniformity. The HDH method involves hydrogenation to make titanium alloy friable, followed by crushing and dehydrogenation to produce powder; this method is also low cost, but the resulting powders have low purity, non-uniform particle size, and poor sphericity. These characteristics make it difficult to meet the precision requirements for HIP near-net shape forming [26].
The capsule acts as a gas-tight container to prevent pressure medium infiltration and control the size and shape of the preformed part. For the complex-shaped titanium alloy components, cores are also needed to further control the size and shape. Common core materials internationally include carbon steel, graphite, and ceramics, while carbon steel and graphite are more widely used in China. Carbon steel and stainless steel are usually used for the external capsule [27]. The design of the capsule is critical to the mechanical properties, dimensional accuracy, and cost control of powdered titanium alloy products. The surface quality of the product directly affects its fatigue performance, which is mainly determined by the capsule material. For demanding workpieces, high-strength materials should be selected for the capsule to ensure high product quality and performance [2].

2.2. Mechanism of Powder Densification

Powder densification is a complex multi-stage process involving the transition from loose particles to a dense continuum. In the HIP process, the densification behavior of powder is synergistically affected by high temperature and high pressure, and this process involves both macroscopic volume contraction and density change, as well as microscopic particle interaction and deformation mechanisms [28]. Its mechanism can be elucidated at both macroscopic and microscopic levels for a comprehensive understanding of the deformation and densification behavior of metal powders under the action of high temperature and high pressure, and its mathematical model is shown in Figure 3.

2.2.1. Macroscopic Model of Powder Densification

The hot isostatic pressing densification process of metal powders can be regarded as a special type of pressurized sintering or high-temperature pressing process. During this process, the work-hardening effect generated by the deformation of metal powders can be promptly eliminated through continuous dynamic restitution and dynamic recrystallization mechanisms. This significantly reduces the influence of work-hardening on the densification process [29], allowing the complexity caused by work-hardening to usually be ignored in mathematical modeling and theoretical analysis of the HIP densification process. However, the simultaneous presence of two key variables, temperature and pressure, in the HIP process makes the study of its kinetic behavior and volume shrinkage law more challenging than those of simple sintering or high-temperature pressing processes. Therefore, it is necessary to simplify the problem based on reasonable assumptions and appropriate mathematical models so as to provide the necessary theoretical basis for the mathematical analysis and numerical simulation of the process [30].
From the macroscopic perspective, the powder densification process can be regarded as a volume change process of a porous continuum, and it is considered that the powder body consists of a granular phase and a pore phase, which is an incompressible solid with specific physical properties and yield limit, while the pore phase has no mass, strength, density, or deformation resistance. In the HIP process, plastic deformation under external pressure is involved, causing the pores between the particles to be gradually filled. This results in the volume contraction of the powder body and the reduction in the compression blank volume, while the mass remains unchanged and the density increases. Specifically, the deformation behavior of powder particles follows the plastic flow characteristics of non-Newtonian fluids, namely the Bingham body deformation model [31]. This model assumes that the powder particles will flow plastically only when the shear stress exceeds the critical shear stress. As the temperature increases, the critical shear stress of the powder particles decreases, thus accelerating the densification process.
The macroscopic mechanism focuses on the overall densification behavior of the powder body under external pressure and temperature, emphasizing the rearrangement of the powder particles and the pore-filling process, which can be obtained as a function of density versus time and deformation at each site [16]. Quantifying the densification rate through changes in relative density requires establishing an intrinsic equation that links the strain increment to the stress and experimentally determining the coefficients of the intrinsic equation. Compared with microscopic methods, numerical simulations based on macroscopic methods require fewer parameters to be determined, have more mature theoretical development, and are widely used in predicting the shape changes of complex geometrical parts [32]. However, the macroscopic mechanism cannot reveal the microscopic interactions between powder particles and deformation mechanisms in detail.

2.2.2. Microscopic Model of Powder Densification

From the microscopic standpoint, the powder densification process involves microscopic interactions and deformation behaviors between powder particles. The large pores between powder particles lead to large deformation and volume contraction, and the numerous nonlinear situations make it difficult to study the densification mechanism of powder. Although there is no unanimous conclusion on the microscopic mechanism of powder densification during HIP, the existing literature [32,33,34] generally suggests that the densification process involves the following three main stages:
(1)
Particle proximity and rearrangement
During the initial heating and pressurization stage, the relative density of powder titanium alloy is about 65%, with large numbers of pores between particles, mostly in point contact, and with no significant stress and strain. When an external force is applied, the powder particles approach each other by translating or rotating. Smaller particles are squeezed into the neighboring pores, and larger pores collapse, thus significantly reducing the number of pores and rapidly increasing the relative density of the powder body to about 90% [2]. This stage is mainly driven by particle rearrangement and proximity, with the effective contact area between particles gradually increasing and deformation resistance decreasing.
(2)
Plastic deformation
As the process enters the pressure holding stage, the relative density of the powder body continues to increase, and the contact area between the particles expands further, the particles collide or wedge into each other, and the larger gaps between the powder particles tend to close. When the compressive stress endured by the powder body exceeds its yield shear stress, the particles begin to deform plastically in a slip mode. Some powder atom groups are squeezed into the neighboring pores, resulting in a significant reduction in the pore volume and a substantial increase in density [35]. During this process, smaller powder particles are more prone to plastic deformation than larger ones, which drives the larger particles to rotate or move further into the proper positions [36]. This stage is the key to powder densification and contributes the most to the final density.
(3)
Diffusion creep
In the late stage of heat preservation and pressure reduction, the powder particles carry out extensive plastic flows, the relative density of the powder body rapidly approaches the theoretical value, the particles are basically linked together, with the residual tiny pores no longer being connected to each other, but diffusely distributed in the powder matrix. These pores gradually become spherical under surface tension, reducing their volume share and increasing the contact area between particles. At the same time, the effective stress on the powder body cannot exceed the critical shear stress, and the plastic deformation mechanism, which is dominated by atom group slip, no longer plays a dominant role. The densification process is mainly achieved through the mechanisms of power-law creep, grain boundary diffusion, and inter-particle dislocation creep and recrystallization, which eventually converge to the maximum terminal density value. At this stage, power-law creep is the main densification mechanism [37].
In practice, these three mechanisms are not strictly separated, but dominated different stages of densification. In the early stage of HIP, particle rearrangement and proximity are the main densification drivers; in the middle stage, plastic deformation mechanism dominates and significantly increasing the density of the powder body; and in the late stage, diffusion creep mechanism further improves the densification by eliminating the residual pores. Although the plastic deformation mechanism contributes most significantly to densification throughout the process, the particle rearrangement and diffusion creep mechanisms also play important roles in the early and late stages [2]. The synergistic effect of multiple mechanisms enables titanium alloys to transform from loose particles to dense materials. However, many assumptions of the microscopic model do not reflect the actual working conditions, such as the difficulty of maintaining uniform particle size and constant temperature and pressure. In addition, the microscopic method does not establish the interrelationship between strain and strain rate with density and densification rate, and its theoretical development is still incomplete. The accuracy of the simulation results needs improvement, making it challenging to accurately predict the overall shape change of the part [38].
In summary, the macroscopic and microscopic mechanisms complement each other and describe the densification behavior of the powder body under both external pressure and temperature. The macroscopic mechanism focuses on the overall shrinkage and density change in the powder body, making it suitable for studying capsule deformation and overall densification behavior. The microscopic mechanism focuses on the microscopic interactions between powder particles and deformation behavior, and is able to calculate the relationship between the HIP process parameters and densification rate, which is suitable for studying the microstructure and mechanical behavior of the powder particles [16]. The two synergistically construct a theoretical framework for the preparation of high-performance HIP parts.

3. Research Progress on HIP for Powder Titanium Alloys

Hot isostatic pressing (HIP) technology first appeared in 1955, when the Battelle Institute in the United States successfully developed the world’s first hot isostatic pressing equipment, marking the official birth of the technology. Its initial research and development goal was to provide a new means for the diffusion bonding of nuclear reactor fuel elements, which is a new technology integrating powder molding, sintering, and heat treatment [33]. However, in the early stage of development, HIP faced limitations due to the lack of systematic theoretical support and mature test methods, and the research focus was concentrated on the development of equipment engineering. This changed in the 1960s when the technology was introduced in Europe. The Swedish ASEA company optimized the equipment structural design and developed a miniaturized, highly reliable HIP system, for the subsequent promotion of the technology to lay a key foundation. In 1977, the China Iron and Steel Research Institute in Beijing successfully developed the first domestic HIP machine, whose core parameters reached the international advanced level [39]. Although the research on HIP forming of titanium alloy powder started later, over the past 20 years this technology has become a cutting-edge hotspot in the field of precision manufacturing of titanium alloy due to its unique advantages in near-net shape forming, integrated preparation of complex components, and diffusion connection of composite materials, realizing the leapfrog development from the special technology of the nuclear industry to the key process of high-end equipment manufacturing.

3.1. Foreign Research Status

Since its introduction, the powder hot isostatic pressing technology has rapidly attracted extensive attention from the international academic community because of the advantages of its high material utilization and comprehensive mechanical properties close to those of forgings. However, due to the limitations at the technical level, the core part of the technology is mainly concentrated in developed countries such as Europe, the United States, and Japan, as well as a few countries like Russia and China.
The United States, as a pioneer in the field of powder titanium alloy HIP technology, has been in a leading position globally in both the research and application of this technology. In 1956, General Electric Company in Boston successfully produced GET73 turbojet engine bearing housing blanks by using the method of hot-pressing sponge titanium powder, which reduced the cost by 25–30% compared with the traditional forging process [40]. This achievement marks the initial success of powder titanium alloy hot isostatic pressing technology in practical application. In the 1970s, the U.S. government and military to sought to reduce the procurement cost of aircraft engines and airframes and other components, and actively promote the powder metallurgy process to replace the traditional forging process. In this context, Crucible in NY introduced powder metallurgy ceramic mold technology by drawing on the investment casting process, and successfully developed a variety of complex titanium alloy components for military engines and aircraft [41]. Entering the 21st century, Synertech PM in CA has made the leap from fine process testing to high-volume marketable production with its advanced equipment and technology, including vacuum powder making, non-polluting vacuum loading, high-performance capsule preparation, hot isostatic pressing equipment, and computer simulation design [3]. Two components produced by the company are shown in Figure 4. In terms of titanium alloy powder preparation, the PREP method and gas atomization method in the United States are technologically advanced, capable of preparing powders with high sphericity, good fluidity, and excellent quality, which provide high-quality raw materials for hot isostatic pressing technology [5].
European countries have their own focus on the research of HIP technology for powdered titanium alloys and the results are fruitful. Switzerland-based ABB has rich technical reserves in the field of hot isostatic pressing equipment design and manufacturing, and it has established a complete set of HIP production line in 1990. The equipment produced by the company has excellent safety and operational reliability, diversified product specifications, and its technology successor Avure in OH, USA has long held a dominant position in the global hot isostatic pressing equipment suppliers [42]. Germany’s Krupp company in Essen used ceramic mold NNS-HIP technology, successfully produced a thin-walled variable surface titanium alloy impeller, with mechanical properties comparable to casting alloy and cost reduced by 40%, fully demonstrating the advantages of this technology in the manufacture of complex components [43]. France’s Safran aircraft engine company in Courcouronnes developed ISOPREC® powder titanium hot isostatic pressing technology, innovative in its approach. This technology enables the development of low-temperature titanium alloy impellers that can operate stably at −253 °C and 550 m/s, in extreme low-temperature, high-speed environment. It replaces the traditional forging and five-axis machining processes, shortening the processing cycle from nearly a year to a few weeks, greatly improving production efficiency [44]. The finished product is shown in Figure 5. Rolls-Royce company in London, UK, in close cooperation with Xinhua Wu’s team at the University of Birmingham, successfully produced an aero-engine compressor housing using advanced computer simulation and simulation and NNS-HIP technology. This is the largest powder titanium alloy NNS-HIP aerostructural part reported so far [45].
Russia also has a deep research foundation and rich practical experience in HIP technology for powdered titanium alloys. The large-size HIP compressor stage 9 disk developed by the All-Russian Light Alloy Research Institute in Moscow using hot isostatic pressing technology is used in the PD14 civil aviation engine. The disk body adopts near-net shape forming design with small machining allowance, and the capsule shape and final product are shown in Figure 6. The strength was tested to be comparable to forgings of the same specification, while the plasticity was improved by about 2.0–2.5 times [46]. The Russian Research Institute of Chemical Machinery in Moscow has conducted a systematic study of the hot isostatic pressing process for centrifugal impellers of large-size engine crown-top blades of various powdered titanium alloys, such as VT3-1, VT5-1, and VT25U, covering various aspects, including the design of the capsule for near-net shape forming, diffusion of the core material of the bore and the alloy powder, the relationship between the hot isostatic pressing regime and the performance, etc. The study also includes the removal of the capsule and the partial internal core material and the alloy powder, and issues such as capsule removal and reuse of part of the inner control were also explored [47].

3.2. Chinese Research Status

Although the research on powder titanium alloy HIP technology in China started late, with a growing demand for high-performance titanium alloy parts in aerospace and military fields, the relevant research work had been carried out rapidly. In recent years, Beijing University of Aeronautics and Astronautics, the Institute of Aerospace Materials and Technology, the Institute of Metals, Chinese Academy of Sciences, Huazhong University of Science and Technology, and other scientific research institutions in the field of powder metallurgy HIP have carried out extensive research work, some of their achievements have reached international advanced levels [5].
The Institute of Aerospace Materials and Technology (IAMT) in Beijing is one of the early research units in China to carry out the research on powder titanium alloy NNS-HIP technology. During the “Ninth Five-Year Plan” period, the institute has been committed to the research on high-performance titanium alloy powder metallurgy NNS-HIP process, and after years of accumulation, it has successfully developed aerospace parts of various grades (e.g., TC4, TC11, TA7, and TA15). Three major product systems have been formed, including rudder wing skeleton, complex structure thin-walled cabin, and thin-walled shaped surface structure, and the scale production of some products has been realized [2]. Figure 7 shows some of the products developed by the institute.
The Institute of Metals and Materials, Chinese Academy of Sciences in Shenyang, has continued to carry out research on titanium alloy powder near-net shape forming technology since 2003, and undertook the development of the impeller for the hydrogen pump of Long March 5. The key technology of powder metallurgy for the hydrogen pump impeller was successfully overcome, which laid the foundation for China to make a major breakthrough in this field. In addition, Xu Lei’s team at the Institute of Metals has achieved remarkable research results in high-temperature titanium alloys and titanium–aluminum intermetallic compounds, developed near-net shape forming products of various grades of titanium alloys, and formed the production capacity of small batches [48,49].
Huazhong University of Science and Technology (HUST) in Wuhan has achieved outstanding results in the research of HIP technology for powdered titanium alloys. The team of Yusheng Shi and Qingsong Wei has thoroughly studied the optimal design rules for capsules, the densification and organization structure evolution mechanism of powder materials under high temperature and high-pressure coupling, and the deformation law of the densification process of parts under multiple constraints [50,51]. Meanwhile, the State Key Laboratory of Forming and Molding Technology of the university has cooperated extensively with European universities and enterprises, leveraging its advantages in computational simulation near-net shaping. It made important breakthroughs in the simulation and forming of titanium alloy integral blisks (one-piece molded construction of blades and disk), turbines, and magazine parts and successfully prepared key parts of aerospace engines with mechanical properties superior to those of products made in ordinary casting processes, and with high part accuracy [52,53]. Figure 8 shows the Gearbox capsule parts and trial production samples.
The research team of Lang Lihui at Beijing University of Aeronautics and Astronautics (BUAA) in Beijing has carried out a lot of fruitful research work on the design of the overall capsule for HIP and quasi-isostatic pressing for the preparation of complex components [54]. The team has obtained several patents on the electroforming of outer capsule, and has provided important technical support for the application of HIP technology in the manufacture of complex components through the study of different materials and process parameters [55,56,57].
At present, China’s powder titanium alloy HIP technology has been widely used in the aerospace field. In the manufacture of some key components, the mechanical properties of the products reach the index of forgings, and the dimensional accuracy can be controlled at a high level. However, in terms of the scope of popularization and application of the technology, there is still some room for improvement compared with foreign countries. In the process, stability and product quality consistency needs to be further improved, the development of civil applications also needs to be strengthened, so as to fully use the advantages of the technology and promote the development of related industries.

4. Research Progress on Numerical Simulation of HIP of Powder Titanium Alloys

During the hot isostatic pressing (HIP) forming process, the densification behavior of the powder body is a nonlinear process involving the coupling of heat and force multi-fields. This complexity primarily arises from the stress shielding effect of the capsule and the internal pressure gradient distribution, which makes the forming process difficult to be directly observed. For many years, the powder metallurgy field relied heavily on the traditional “trial and error method”, which involved repeatedly adjusting the capsule size design and increasing the machining allowance in complex areas, gradually approaching the geometric accuracy requirements of the target component [5]. With the development of computer simulation technology, numerical simulation has gradually become a key tool for optimizing the forming process and predicting the performance of components, which is of great engineering value for realizing the quantitative control of the HIP process [58,59,60].
Finite element method (FEM) is the mainstream method for numerical simulation of the HIP of titanium alloy powder. By establishing a thermal-force coupling model, researchers can theoretically visualize and analyze the powder densification process, as well as the deformation and stress distribution during the HIP process. This provides a theoretical basis for the design of the capsule structure and the optimization of process parameters. Currently, mainstream commercial software (such as ANSYS, Abaqus, MSC. Marc, DEFORM, etc.) has integrated powder HIP simulation module, the basic principle is to discretize the continuum into finite units and reconstruct the macroscopic molding process by solving the deformation, temperature, density, and stress state of each unit. In recent years, multi-scale modeling methods have received increasing attention, and discrete element–finite element (DEM-FEM) coupled simulations have been gradually applied to characterize the discrete properties of powder particles, which further improves the prediction accuracy of shrinkage deformation of HIP parts [61].
The metal powder used in HIP consists of a large number of fully dense particles at the micrometer scale with a large number of inter-particle pores, forming a complex discontinuity [34]. Plastic deformation occurs during the densification process, which no longer follows the principle of volume invariance, but the forming process is similar to that of a sintered material. In order to describe the compressible viscoplastic deformation of porous powders and to take into account the effect of hydrostatic pressure on the material, the powder body is usually regarded as a “compressible porous continuum” in the finite element simulation [62]. After a long period of research and accumulation, several mathematical models have been established to consider factors such as grain boundary diffusion and particle morphology, which have laid a theoretical foundation for the accurate simulation of the HIP process.

4.1. Foreign Research Status

Hot isostatic pressing (HIP) technology has become a research hotspot in the field of powder metallurgy due to its unique advantages in the preparation of high-performance powder alloys, such as organization uniformity and excellent mechanical properties. Foreign research in HIP numerical simulation is more systematic and in-depth. A variety of ontological models have been proposed to describe the densification behavior of powder in the HIP process and are now widely used in the numerical simulation of the HIP process.
In the early 1970s, Kuhn and Downey [63] learned the relationship between plastic Poisson’s ratio and relative density through iron powder sintering experiments, and established the yield criterion for ellipsoidal yield surfaces. Green et al. [64] proposed a sphere model for rigid-plastic materials based on the pure shear theory and the hydrostatic pressure assumption and established the yield criterion for porous body materials. They regarded the metal powder body as a continuous medium and established the theory of plastic mechanics of porous metallic materials, determining the yield criterion and the intrinsic relationship of porous metallic materials. Based on Kuhn’s theory, Doraivelu et al. [65] established the relationship between the yield stress of porous materials and the matrix using empirical corrections and conducting compression experiments with different initial densities of materials. Park et al. [66] introduced strain-strengthened and geometrically-strengthened powders as two factors to establish different constitutive equations based on Kuhn’s model, and corrected the data based on uniaxial compression experiments in order to solve the error problem of the model for multi-directional force cases.
Japanese scholars Mori et al. [67] used the elastic-plastic intrinsic model of porous body materials to analyze the stress change and density distribution of sintered cylinders during upsetting, and their simulation results were in high agreement with the experimental data. Subsequently, Mori’s team [68] further combined the rigid-plastic intrinsic model and the yield theory of porous body materials to investigate the density distribution, stress and strain, and other changes in the unit tensor of the sintered products during the rolling process, which provided theoretical support for the processing of porous body materials. Laptev et al. [69], from the former Soviet Union, proposed a comprehensive model for the rate of powder densification as a superposition of power rate creep, particle boundary diffusion, grain boundary diffusion, and lattice diffusion, and analyzed the effects of temperature, pressure, and holding time on the HIP process accordingly.
Shima and Oyane [70] proposed a continuum medium plasticity theory for general metal powders in the 1970s through experimental studies of copper-powder sintered bodies and concluded that the theory is applicable to most metal powder densification processes. It has been widely used in the field of powder metallurgy due to its relatively simple parameter acquisition, and it was implanted in the large-scale nonlinear finite element software MSC. Marc. Nohara et al. [71] numerically simulated the hot isostatic pressing of MERL 76 nickel-based powder high-temperature alloy by using the Shima model, and found that the temperature distribution and stiffness of the capsule have a significant effect on the powder densification process. The modeling and numerical simulation and validation of its turbine disk are shown in Figure 9.
Yuan from the University of Birmingham in the UK and Samarov from LNT et al. [11] developed a new plastic model based on Green’s model and predicted the shrinkage deformation of titanium alloy powder in the hot isostatic pressing process by using ABAQUS/CAE simulation based on Green’s model. They developed a TC4 alloy magazine scale model, whose simulation results deviated from the actual dimensions within 2%, providing important theoretical guidance for HIP molding of complex parts. Teraoku T et al. [72] further modified the Shima model, and after high-temperature uniaxial compression tests on Ti6Al4V compression samples with different densities, finite element simulations of TC4 powder hot isostatic compression of the turbine blade were carried out with the obtained parameters, and the results of the simulation were very close to the actual part dimensions.
In the further improvement of the model, French scholars L Sanchez et al. [73] took into account the importance of capsule stiffness in the HIP process and obtained a more accurate intrinsic relationship through repeated iterative optimization of the simulation and experimental results. They compared it with the complex structural parts of powder Ti-6AI-4V and found that the simulation accuracy was significantly improved. YOU et al. [13] carried out numerical simulations and experimental studies on the HIP process of milled and atomized Ti-6Al-4V powders using the Shima model to simulate the powder flow process and relative density changes during the forming process. Comparison of the simulation results with the experimental results shows that the deformation trend and densification behavior of the two powders are in good agreement, and the maximum relative error between the experimental and simulated values is only 2.66%.
In terms of diversified development of models, Ales Svoboda et al. [74] assumed the porous body material as a continuum medium and proposed a viscous-elastic-plastic intrinsic model in conjunction with creep, which was successfully applied to the simulation of the HIP forming process of cylindrical parts. The viscoplastic model, proposed by Abouaf et al. [75] in 1988, laid an important foundation for the numerical simulation of HIP, which has been successfully applied in the HIP process simulation of various materials, such as nickel-based high-temperature alloy turbine discs, and the simulation results are in high agreement with the experimental results. In addition, the Abouaf model has been widely used in industrial production—for example, it is embedded in the PreCAD software developed by CEA-CEREM in France, which is used for the numerical simulation of powder metallurgy materials [76].
In addition, Chung et al. [77] applied the Abouaf model in finite element analysis to optimize the capsule structure and investigated the HIP densification process of 316 L stainless steel powder. Kim’s team [78] from Pohang University of Science and Technology in South Korea utilized the Abouaf model to investigate the densification behavior of Ni-Cr-Co alloy powder during the HIP process. The results of the finite element calculations for the shape change were basically consistent with the experimental data obtained, as illustrated in Figure 10, which verified the validity of the model in predicting the deformation of the press blank. C. Van Nguyen et al. [79] from RWTH Aachen University in Germany, used the Abouaf model to simulate the shrinkage process of 316 L stainless steel powder during HIP. They found that the error between the simulated and experimental values was within 0.55%. This minor error confirmed the model’s accuracy in predicting the densification behavior of metal powders.
The plastic model described by Shima focuses on the elastic and plastic deformation of the powder body, with pure plastic deformation as the primary densification mechanism. It requires few parameters and minimal computational time, making it a better predictor of the shape change of parts during HIP, as demonstrated by sybsewuent studies. However, it deviates from experimental results because it ignores high-temperature mechanisms like creep and diffusion. In contrast, the viscoplastic model described by Abouaf incorporates the effect of high-temperature creep on the densification and deformation of the powder body, which requires more material parameters but offers more accurate predictions. However, the error of parameter measurements also affects the accuracy of the simulation results. The defect of this model is that it cannot adequately describe the densification of the powder body at low temperatures and densities, because the main mechanism of powder densification in this stage should be rearrangement and plastic deformation.
In recent years, many scholars have developed a new combined model based on the plastic and viscoplastic models, in which the inelastic deformation of materials includes plastic and viscoplastic mechanisms and is integrated into a unified numerical model, which more realistically reflects the deformation of the parts and the densification of powders during the entire hot isostatic pressing process. Xue et al. [80] used the “Fleck/Gurson hybrid model” to simulate the HIP densification process of powdered TC4 alloys, and found that the hybrid model was superior to the Abouaf power-law creep model in predicting relative density, as shown in Figure 11. The team of C. Van Nguyen from RWTH Aachen University in Germany [81] developed a comprehensive constitutive model by combining the plasticity theory and creep mechanism to analyze the effects of the initial relative density and temperature field distribution on the HIP process.
In general, a more perfect theoretical system has been formed in the numerical simulation of HIP abroad. The characteristics of some typical simulation models have been summarized in Table 1. The proposed constitutive model can better describe the complex behavior of powder materials in the HIP process, and the simulation results have a high degree of agreement with the experimental data, which provides important technical support for the industrial production of complex parts.

4.2. Chinese Research Status

Compared with other countries, China’s numerical simulation research on the HIP process of metal powders started relatively late, but with the rapid development of computer technology and the wide application of finite element simulation in industry, domestic scholars have made remarkable progress in this field in recent years. Domestic research mainly focuses on the introduction and improvement of foreign classical models, as well as numerical simulation research for specific materials and processes. The major domestic organizations conducting research on HIP forming include China Steel Research Technology Group Corporation, Beijing Institute of Aeronautical Materials Research, the Institute of Metals of the Chinese Academy of Sciences, the Institute of Aerospace Materials and Processes, University of Science and Technology Beijing, Beijing University of Aeronautics and Astronautics, Huazhong University of Science and Technology, and others [83].
China Steel Research Technology Group Co., Ltd. [84] in Beijing conducted an in-depth study on the NNS-HIP process of metal powder, developed powder high-temperature alloy parts with excellent performance, and successfully applied them to the core parts of a certain type of engine, including turbine disks, drum shafts, and wind guide wheels. Beijing Institute of Aerospace Materials [85] combines the HIP process with the forging process, utilizing the HIP equipment to press the metal powder into a blank, and then manufacturing small engine discs through the isothermal forging process. The Institute of Aerospace Materials and Technology [86], through the analysis of hot isostatic pressing near-net shape forming process of Ti-6Al-4V alloy powder, developed a sample of automotive connecting rod, whose mechanical properties are significantly better than those of castings with the same organization, which can reach the level of conventional forgings.
Since 2003, Xu Lei’s team at the Institute of Metals, Chinese Academy of Sciences, has been researching the finite element densification process of titanium alloy powder. They established a simulation prediction and calculation database for titanium alloys, successfully realizing the simulation of simple rotary bodies, complex thin-walled shaped structural parts, and complex closed cavity symmetric parts of the size of the simulation. The key dimensional error range is less than 2% [1]. The team also found that the electric field-assisted HIP (FAHIP) technology can significantly reduce the densification temperature and improve the performance of the parts, which has been successfully applied to the manufacturing of the impeller of the hydrogen pump of the Long March 5, so that its energy consumption is reduced by 20%, and the tensile strength of the parts is close to the level of forgings.
Jun He [87] from University of Science and Technology Beijing investigated the densification behavior of ceramic powder during cold isostatic pressing by using finite element simulation, and found that the shape and size of the capsule had a significant effect on the densification process by studying the deformation behavior of the press blanks and the relative density distribution law. Lang Lihui et al. [54,57,88] from Beijing University of Aeronautics and Astronautics simulated the HIP process of titanium and tungsten alloy parts using the Shima model. The dimensional errors were controlled within 4.9% and 1.4%, respectively, which verified the applicability of the model in domestic research. Yu Si et al. [89] designed two schemes, powder-solid diffusion joint forming and powder net forming, using metal powder HIP process to numerically simulate the titanium alloy TC11 powder material. The results showed that the powder net forming resulted in larger capsule deformation and non-uniform relative density distribution, while the powder-solid diffusion connection forming resulted in more uniform relative density distribution and higher compact density. Li Shaobo et al. [90] optimized the process parameters of the hot isostatic pressing process of ceramic materials by establishing a HIP diagram through the densification mathematical model, and the error range between the simulation results and the experimental data was below 0.35%.
Lin Guangke et al. [51] from Huazhong University of Science and Technology combined CAD/CAE technology with MSC. Marc finite element simulation to study the densification behavior and deformation law during HIP near-net shape forming of titanium alloy powder. They proposed an optimization plan for the shape control mold of the inner core scheme, which achieved high precision forming without error in the internal dimensions. Figure 12 shows the design, finite element simulation, and comparative test of the titanium engine brake capsule at the university. The results show that the simulation is highly consistent with the test. Jun Huang et al. [91] proposed a two-step HIP forming method in order to solve the issue of non-uniform relative density distribution of high-temperature alloy parts formed by conventional HIP process. By combining numerical simulation with experimental studies, they identified key process parameters. The results indicated that the parts obtained by the two-step forming method have uniform organization, strong metallurgical bonding of powder particles, and better tensile properties than the conventional HIP process. Wang Min et al. used numerical simulation software to investigate the HIP forming process of titanium alloy powder, examining the effects of temperature and pressure on the forming quality through cross-simulation combined with experimental verification [6]. Yin Yajun et al. [92] modified the traditional Shima yield criterion by performing uniaxial experiments on porous specimens with different initial densities. The numerical simulations results based on the modified yield criterion were within 5% error from the experimental results, which was extremely reliable.
Guo Ruipeng et al. [53] from Northeastern University in Shenyang chose two materials, Ti-6Al-4V and Ti-5Al-2.5Sn, and used finite element simulation to comparatively analyze the densification process and the shrinkage and deformation of the capsule, and the simulation results were in good agreement with the test results. Zhao Qinyang’s team from Chang’an University [93] in Xi’an combined powder bed fusion additive manufacturing with HIP process and proved that HIP post-treatment can effectively eliminate the residual porosity and unfused defects in additive manufacturing, and improve the fatigue life of titanium alloy parts by more than 30%. The group of Liu Dehui from South China University of Technology [62] in Guangzhou selected the Shima yield criterion to numerically simulate the hot isostatic pressing densification process of Ti6Al4V powders in MSC. Marc, and the results showed that the powders were first subjected to thermal expansion and then contracted and densified in the process of densification, and the deformation trend of the compression billet in the actual experiments was close to the simulation results.
Although important progress has been made in HIP numerical simulation in China, it is still in the research stage compared with other countries. At present, Chinese research mainly focuses on the introduction and improvement of the classical model, for the overall HIP forming of large-size and complex parts still cannot fully realize industrial production, and the performance of HIP forming parts needs to be further improved. In the future, Chinese scholars need to further optimize the numerical simulation technology, combined with advanced experimental means, to improve the simulation accuracy, in order to promote the wide application of HIP technology in the manufacture of complex parts.

5. Problems and Countermeasures of HIP of Powder Titanium Alloy

5.1. The Problems Faced

In the field of powder titanium HIP technology, there are many problems restricting its further development and wide application. In terms of cost, the high price of pre-alloyed powder, the use of hot isostatic pressing equipment, and maintenance costs contribute to the overall high cost of near-net shape forming products. To remain competitive, the BTF value usually needs to be reduced to 7 or less [3]. For titanium alloy components with complex structures, capsule design and production costs account for more than 50% of the total cost, making it a key factor in the high overall cost [2].
Currently, the level of process control of powdered titanium alloys is limited, resulting in some volatility in product performance. Different powder states and HIP forming processes can cause differences in alloy’s density, oxygen content, and organization and morphology, which can affect the mechanical properties of HIP near-net shape forming titanium alloy parts [2]. Because the requirements for product safety and reliability are extremely high in aerospace and other fields, flight needs to be absolutely safe, which makes the product entry threshold is extremely high, limiting the application of powder titanium hot isostatic pressing products in these fields. In the 20th century, The United States invested a lot of research funds to carry out related projects; although the test results are significant, due to the fluctuation of performance problems, the actual application is still relatively limited [3].
Product size control is also a major challenge–in the hot isostatic pressing of powdered titanium production process, the product size depends on the precise control of the capsule. However, in the high-temperature and high-pressure environment of HIP, both the capsule and the powder will shrink. Although the degree of shrinkage can be estimated theoretically, in actual production, it is difficult to accurately calculate and control the degree of shrinkage due to the influence of a variety of complex factors, such as the characteristics of the material of the capsule, the characteristics of the powder, and the parameters of the hot isostatic pressing process, making it difficult to satisfy the demand for high-precision product production [4].
At the same time, powder titanium alloy HIP technology preparation links are numerous, from powder preparation, capsule design and production, powder loading, degassing, sealing to hot isostatic pressing treatment, each link is critical to the final product quality. During the HIP process, the densification mechanism of powder is complex, involving particle proximity and rearrangement, plastic deformation, diffusion creep, and other mechanisms, which are intertwined with each other and difficult to control precisely. Any deviation in any part of the process may cause product quality problems, which increases the difficulty and complexity of process control. In addition, the impact and influence of the electrochemical corrosion process used in the mold removal process on the environment is also an urgent problem to be solved in the development of this technology [1].

5.2. Solutions

To address the above problems, the industry has explored a range of appropriate solutions. Cost reduction can be achieved in various ways. With technological progress and increased raw material production, the price of pre-alloyed powder, especially PREP powder, has dropped significantly. In the future, we should pay continuous attention to the powder market dynamics, and make full use of the furnace space of the hot isostatic pressing equipment to reduce the unit cost of hot isostatic pressing by means of increasing the unit loading capacity and optimizing the loading method [3]. For non-fatigue application components with low performance requirements, the hybrid powder method can be used for production, and the process cost can be reduced under the premise of meeting the service performance index [2]. At the same time, the focus should be on increasing the investment in the research and developing domestic hot isostatic presses, mastering the key technologies, and striving to reduce the dependence on foreign imported equipment, which will reduce the cost of equipment procurement and maintenance, and enhance the economic efficiency and competitiveness of the industry. Besides, finite element simulation and batch production of workpieces can also significantly reduce the process cost.
In terms of quality control, the whole process of powder production should be strictly controlled. First of all, it is necessary to ensure that the powder production environment and equipment are very clean. The particle size distribution and shape of the powder need to be precisely controlled, the stability of the quality between batches should be ensured [4]. For different application scenarios, suitable powder manufacturing processes should be selected. For example, oxygen-sensitive materials are best processed using the PREP method or GA methods. Under the cost constraints, the HDH method can be used, supplemented by post-processing to improve the performance of the powder [2]. Secondly, computer numerical simulation technology can aid in the optimal design of the capsule, allowing for the prediction of geometric deformation and microstructure evolution during the hot isostatic pressing process. This enables precise reverse design of the capsule size, improving forming efficiency and product qualification rates. In addition, it is essential to develop low-cost shaped capsule manufacturing technology, improve the welding process, and improve the quality of the capsule to reduce the negative impact of the capsule-related factors on product quality [3]. Powder filling needs to be carried out in a clean environment, with vacuum sealing, automated unmanned operation, and other processes to reduce the risk of contamination by foreign impurities. Non-destructive testing technologies, such as ultrasound and industrial CT, should be used to detect and reject defective products, ensuring product quality and safety [3].
In order to solve the size control problem, it is necessary to optimize the HIP process, combine the material science theory and actual production data, and establish a more accurate theoretical model. With the help of advanced tools such as finite element analysis, in-depth research on the shrinkage behavior of powder and capsule under high temperature and high pressure is conducted to predict the shrinkage law. At the same time, we increase the scale of test samples, make precise records and in-depth analysis of each test data, summarize the shrinkage law, and closely combine theoretical calculations with test results to continuously improve the control accuracy of product forming dimensions. After the products come out of the furnace, we use high-precision measuring equipment to calibrate the product size again and ensure that the product size meets the design requirements [4].
In terms of process optimization, the HIP process should be strictly standardized, and the key process parameters such as temperature, pressure and time should be precisely controlled to improve the densification and uniformity of the product through process optimization. This will ensure the stability of the product performance, dimensions, and shape, and improve the fatigue performance, durability, and damage tolerance of the product [3]. During the HIP process, suitable process control methods are used, such as certain pre-pressing at the early stage of sintering, to obtain large strain energy and refine the organization and improve the product performance. For NNS-HIP parts, the alloy organization can be changed to obtain better mechanical properties through reasonable post-process heat treatment, such as “Broken-up structure (BUS)” treatment or hydrogen heat treatment of the formed powder titanium alloy [2].

6. Conclusions and Outlook

After nearly 70 years of development, the HIP technology of powdered titanium alloy has realized a wide range of applications in high-end fields such as aerospace and complex component manufacturing. This technology has become an important means of manufacturing high-performance titanium alloy parts by virtue of its high material utilization rate, excellent product performance and near-net shape forming capability for complex components. However, despite its great potential for development, the process still faces many challenges:
(1)
The introduction of numerical simulation technology and batch production has reduced the cost of the process, but the preparation of small quantities of components still incurs a high cost. This is especially true for the design and manufacture of complex components, capsule design and manufacturing, the use of HIP equipment, and high-purity powder production, which limits its widespread application in the civilian market.
(2)
Computer finite element modeling and simulation technology have lowered the technical threshold of capsule design; however, how to closely integrate it with the actual production and further reduce costs remains a key area of future research. At the same time, the research on powder metallurgy densification mechanism and models is insufficient, restricting the further development of the technology.
(3)
As HIP parts continue to move towards large-scale, complex, and high-precision designs, the role of numerical simulation in process design is becoming increasingly important, but the current finite element simulation software is mainly focused on the prediction of capsule deformation. Reverse design for target sizes still requires secondary development or the use of other software, making the process cumbersome.
For the further development of powder titanium alloy HIP technology, future breakthroughs and innovations are needed in several key directions:
(1)
In order to realize large-scale commercial application, it is necessary to carry out systematic engineering application research, focus R & D on the upgrading of equipment, reduce the cost of powder production and enhancement of process technology, strengthen the degree of participation in computationally-assisted design technology, and to reduce the cost of pre-development while enhancing the automation level of the production process.
(2)
The introduction of additive manufacturing technology will further broaden the choice of capsule materials. The “reverse design + additive manufacturing + hot isostatic pressing” multi-technology composite mode is expected to realize the integration of high-performance complex parts of the homogeneous capsule near-net shape forming and become the mainstream of the future direction of the NNS-HIP technology [61].
(3)
The development of integrated simulation software will help the transformation from single deformation prediction to reverse design optimization, and the combination of advanced technologies such as machine learning and multi-objective genetic algorithms with the establishment of a parts and materials database will significantly improve the accuracy and efficiency of reverse design.
In summary, in the future, through in-depth study of the mechanism of powder densification, the development of integrated simulation software, the strengthening of process control, and the promotion of engineering applications, it is expected to further reduce the process cost, improve the quality of products and production efficiency, so as to promote the wide application of HIP technology in the field of aerospace and civil applications and provide a strong support for the manufacturing of high-end equipment.

Author Contributions

Conceptualization, J.C. and H.F.; methodology, H.F.; formal analysis, J.C. and X.L.; investigation, J.C. and X.L.; data curation, J.C.; writing—original draft preparation, J.C. and X.L.; writing—review and editing, H.F.; visualization, J.C.; supervision, H.F.; project administration, H.F.; funding acquisition, H.F. All authors have read and agreed to the published version of the manuscript.

Funding

This research received no external funding.

Conflicts of Interest

The authors declare no conflict of interest.

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Figure 1. HIP manufacturing process for simplified turbine disc reprinted with permission from Ref. [6]. Copyright 2025 Jianxin Zhou. (a) Parts simplified model; (b) HIP scheme; (c) HIP near-net shape processing.
Figure 1. HIP manufacturing process for simplified turbine disc reprinted with permission from Ref. [6]. Copyright 2025 Jianxin Zhou. (a) Parts simplified model; (b) HIP scheme; (c) HIP near-net shape processing.
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Figure 2. Schematic diagrams of two typical processes for the preparation of pre-alloyed powders of titanium alloys reprinted with permission from Ref. [1]. Copyright 2025 ACTA METALLURGICA SINICA. (a) Gas atomization (GA); (b) plasma rotating electrode process (PREP).
Figure 2. Schematic diagrams of two typical processes for the preparation of pre-alloyed powders of titanium alloys reprinted with permission from Ref. [1]. Copyright 2025 ACTA METALLURGICA SINICA. (a) Gas atomization (GA); (b) plasma rotating electrode process (PREP).
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Figure 3. Schematic diagram of the mathematical model of powder HIP reprinted with permission from Ref. [16]. Copyright 2025 Powder Metallurgy Industry. (a) Microscopic model; (b) macroscopic model.
Figure 3. Schematic diagram of the mathematical model of powder HIP reprinted with permission from Ref. [16]. Copyright 2025 Powder Metallurgy Industry. (a) Microscopic model; (b) macroscopic model.
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Figure 4. Synertech PM production of (a) rocket motor impellers and (b) large frame components for motors reprinted with permission from Ref. [3]. Copyright 2025 Powder Metallurgy Industry.
Figure 4. Synertech PM production of (a) rocket motor impellers and (b) large frame components for motors reprinted with permission from Ref. [3]. Copyright 2025 Powder Metallurgy Industry.
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Figure 5. ISOPREC® powdered titanium HIP technology for the preparation of high-performance components for gas turbines reprinted with permission from Ref. [44]. Copyright 2025 Elsevier.
Figure 5. ISOPREC® powdered titanium HIP technology for the preparation of high-performance components for gas turbines reprinted with permission from Ref. [44]. Copyright 2025 Elsevier.
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Figure 6. Near-net shape forming capsule and samples of HIP compressor disks prepared by the All-Russian Research Institute of Light Metals reprinted with permission from Ref. [46]. (a) Capsule; (b) sample. Copyright 2025 Powder Metallurgy Industry.
Figure 6. Near-net shape forming capsule and samples of HIP compressor disks prepared by the All-Russian Research Institute of Light Metals reprinted with permission from Ref. [46]. (a) Capsule; (b) sample. Copyright 2025 Powder Metallurgy Industry.
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Figure 7. Powdered titanium alloy products developed by the IAMT reprinted with permission from Ref. [3]. Copyright 2025 Powder Metallurgy Industry.
Figure 7. Powdered titanium alloy products developed by the IAMT reprinted with permission from Ref. [3]. Copyright 2025 Powder Metallurgy Industry.
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Figure 8. Titanium engine lock capsule and samples from HUST reprinted with permission from Ref. [51]. Copyright 2025 Qingsong Wei.
Figure 8. Titanium engine lock capsule and samples from HUST reprinted with permission from Ref. [51]. Copyright 2025 Qingsong Wei.
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Figure 9. MERL 76 alloy turbine disk: (a) modeling and (b) HIP deformation simulation vs. test reprinted with permission from Ref. [71]. Copyright 2025 John Wiley & Sons-Books.
Figure 9. MERL 76 alloy turbine disk: (a) modeling and (b) HIP deformation simulation vs. test reprinted with permission from Ref. [71]. Copyright 2025 John Wiley & Sons-Books.
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Figure 10. Simulation of densification process of Ni-Cr-Co alloy powder by Abouaf model reprinted with permission from Ref. [78]. Copyright 2025 Elsevier. (a) Finite element meshing; (b) comparison between experimental data and finite element calculation results.
Figure 10. Simulation of densification process of Ni-Cr-Co alloy powder by Abouaf model reprinted with permission from Ref. [78]. Copyright 2025 Elsevier. (a) Finite element meshing; (b) comparison between experimental data and finite element calculation results.
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Figure 11. Comparison of relative density results simulated by different models with experimental data reprinted from Ref. [80].
Figure 11. Comparison of relative density results simulated by different models with experimental data reprinted from Ref. [80].
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Figure 12. The design, finite element simulation, and comparative test of the titanium engine brake capsule from Huazhong University of Science and Technology reprinted with permission from Ref. [51]. Copyright 2025 Qingsong Wei.
Figure 12. The design, finite element simulation, and comparative test of the titanium engine brake capsule from Huazhong University of Science and Technology reprinted with permission from Ref. [51]. Copyright 2025 Qingsong Wei.
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Table 1. International HIP numerical simulation model characteristics.
Table 1. International HIP numerical simulation model characteristics.
Research PrincipalVintageMain Features
Perzyna [82]1966Describes viscoplastic behavior under dynamic loading considering strain rate and temperature effects.
Kuhn and Downey [63]1971Based on an elliptical yield surface, it describes the plastic deformation behavior of powder materials.
Green [64]1972Proposes a rigid-plastic spherical model and establishes the yield criterion for porous materials.
Shima and Oyane [70]1976A continuum plasticity theory suitable for metal powder densification, with simple calculations.
Doraivelu [65]1984Considers the effects of initial density and microstructure of powder particles on the deformation behavior.
Abouaf [75]1988A viscoplastic model that considers high-temperature creep, offering high prediction accuracy.
Park [66]1995Introduces strengthening factors to improve model errors under multi-directional loading.
Yuan [11]2007Introduces a step-by-step iterative method to modify the capsule dimensions for optimization.
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Cui, J.; Lv, X.; Fu, H. Numerical Simulation and Hot Isostatic Pressing Technology of Powder Titanium Alloys: A Review. Metals 2025, 15, 542. https://doi.org/10.3390/met15050542

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Cui J, Lv X, Fu H. Numerical Simulation and Hot Isostatic Pressing Technology of Powder Titanium Alloys: A Review. Metals. 2025; 15(5):542. https://doi.org/10.3390/met15050542

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Cui, Jianglei, Xiaolong Lv, and Hanguang Fu. 2025. "Numerical Simulation and Hot Isostatic Pressing Technology of Powder Titanium Alloys: A Review" Metals 15, no. 5: 542. https://doi.org/10.3390/met15050542

APA Style

Cui, J., Lv, X., & Fu, H. (2025). Numerical Simulation and Hot Isostatic Pressing Technology of Powder Titanium Alloys: A Review. Metals, 15(5), 542. https://doi.org/10.3390/met15050542

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