Investigation of Die Design Influence on Required Forces in Near-Solidus Forging of Complex Components

Abstract

This study investigates the influence of die design parameters on forging forces and thermomechanical responses during near-solidus forging (NSF) of complex steel components. Finite element simulations using Forge NxT analyzed six die configurations varying geometry orientation, gating system design (conical, cylindrical, curvilinear), and draft angles (20° and 30°), with 42CrMo4E steel modeled at 1360 °C. Key responses including punch and lateral forces, temperature distribution, strain localization, and die stress were evaluated to assess design effects. Results showed that the gating system geometry critically controls material flow and load requirements. The conical gating design with a 30° draft angle yielded the lowest punch (141.54 t) and lateral (149.44 t) forces, alongside uniform temperature and strain distributions, which improve product quality by minimizing defects and incomplete filling. Lower lateral forces also reduce die opening risk, enhancing die life. In contrast, the base case with a 20° draft angle exhibited higher forces and uneven strain, increasing die stress and compromising part quality. These findings highlight the importance of selecting appropriate gating systems and draft angles to reduce forming loads, increase die life, and improve uniform material flow, contributing to better understanding of die design in NSF of complex steel components.

1. Introduction

Forging is a widely used metal-forming process in the automotive, aerospace, and heavy engineering industries [1], due to its reliability and cost-effectiveness in producing high-performance parts such as crankshafts, turbine blades, and connecting rods [2]. As manufacturing priorities shift toward sustainability, there is growing interest in processes that reduce material waste, energy consumption, and tooling wear [3].

Near-solidus forging (NSF), a hot forming method carried out close to the solidus temperature of metals, offers such benefits [4]. It enables the production of complex geometries at lower forging loads and often eliminates the need for multiple forming steps [5]. Recent studies highlight the significant advantages of near-solidus forging (NSF) in reducing forming forces and enabling industrial-scale production of complex steel components. Slater et al. [6] demonstrated successful co-forging of a dual-material spindle using a single 280-ton press, confirming process feasibility at near-solidus temperatures. Lozares et al. [7] validated the thixoformability and mechanical performance of 42CrMo4E steel in forging an automotive spindle. Meanwhile, Plata et al. [8] reviewed key developments in NSF, underscoring its industrial readiness and environmental benefits. For instance, Sajjad et al. [9] developed a digital twin model for NSF of 42CrMo4 steel, emphasizing the role of friction modeling, while Sánchez et al. [10] showed how heating rates affect the resulting microstructure.

Despite its advantages, NSF presents significant challenges, particularly related to die durability and process control [11]. The combination of high temperatures (1200–1500 °C), rapid tool-part interaction, and intense contact pressures leads to various forms of tool damage [12]. Lateral forces account for up to 72% of tool wear, especially near radii and contact zones [13]. Additional damage mechanisms include mechanical cracking (25%), thermal fatigue (2%), and plastic deformation (1%) [14]. These issues can also cause die opening and misalignment, which compromise dimensional accuracy and reduce die life.

Addressing these challenges requires careful attention to die design, especially in terms of the gating system geometry, draft angles, and part orientation, which strongly affect how material flows and how loads are transmitted during the process [15]. While FEM-based simulations have been applied to analyze stress and deformation during hot forging, few studies have examined how die geometry influences lateral forces and tooling conditions in the context of NSF.

Gating system design has been studied in casting, where factors like ingate geometry, runner cross-section, and gate placement influence flow behavior, defect formation, and process efficiency [16]. Tools such as computer-aided design systems and modeling techniques have helped optimize these parameters to reduce defects and improve outcomes [17]. These principles are equally relevant to near-solidus forging (NSF), where controlled flow is essential under semisolid conditions. However, these principles have not yet been explored or applied in NSF. This study adapts casting-derived design strategies for use in NSF, evaluating how they influence material behavior, cavity filling, and mechanical loading.

Using Forge NxT, this study numerically investigates the effects of gating geometry (conical, cylindrical, and curvilinear), draft angles (20° and 30°), and part orientation on punch force, lateral force, and thermomechanical behavior during NSF of a T-shaped steel component. This geometry was chosen for its complexity and sensitivity to unbalanced flow, making it ideal for assessing the effectiveness of die design variations. The results provide insight into how die geometry can be tailored to reduce forming loads, limit tooling damage, and improve process stability in industrial NSF applications.

2. Materials and Methods

The selected material for the modeling and simulation of the near-solidus forging (NSF) process, as well as the configuration of the kinematics and other simulation parameters, are described in this section as follows.

2.1. Material Selection and Properties

The material used in this study is 42CrMo4E steel, provided by Gerdau I+D Europe (Basauri, Spain) [7], chosen for its high strength, good ductility, and suitability for high-temperature forming operations. This steel is commonly used in industrial forging processes where strength and thermal stability are required. Its chemical composition is presented in

Table 1. Composition of the 42CrMo4E steel alloy in wt.% [7].

Elements	Fe	Cr	Mn	C	Mo	Si	P	S	Ni	V	Cu	Al
42CrMo4E	Bal.	1.06	0.76	0.42	0.20	0.30	0.02	0.02	0.20	0.01	0.03	0.02

. The material behavior at elevated temperatures was modeled using the Hensel–Spittel constitutive Equation (1), with parameters calibrated and validated through prior experimental work by [18].

$$\overline{\sigma }(\overline{\epsilon },\dot{\overline{\epsilon }},T)=Aexp\left(m_{1}T\right){\overline{\epsilon }}^{m_2}{\dot{\overline{\epsilon }}}^{m_3}exp\left({\displaystyle \frac{m_4}{\overline{\epsilon }}}\right)$$

(1)

where $\overline{\sigma }$ is the flow stress (MPa), T is the temperature (°C), $\overline{\epsilon }$ is the equivalent strain, $\dot{\overline{\epsilon }}$ is the strain rate (s⁻¹), and A, $m_1$, $m_2$, $m_3$, and $m_4$ are material-specific constants.

The parameters used for the Hensel–Spittel model are summarized in

Table 2. Hensel–Spittel model parameters for 42CrMo4E steel.

Parameters	A	${\mathit{m}}_1$	${\mathit{m}}_2$	${\mathit{m}}_3$	${\mathit{m}}_4$
Values	23,921.66	−0.0048	0.0120	0.0232	−0.0267

.

2.2. Finite Element Modelling and Simulation

A three-dimensional (3D) model was developed to simulate the NSF of steel billets. In the simulation setup, the billet was modeled as a deformable body, while the dies and punch were set as rigid bodies.

2.2.1. Geometry Modelling

Figure 1 illustrates the billet, punch, and die setup. The billet was a cylinder (Ø60 mm × 40 mm), while the punch was a flat-bottomed cylinder (Ø61.80 mm × 160 mm) designed to apply uniform pressure. The die assembly comprised two symmetrical child dies forming a closed cavity tailored for complete filling under near-solidus conditions, with draft angles included for easy demolding.

2.2.2. Design Variations

To investigate the influence of die configuration on forming behavior in near-solidus forging (NSF), six simulation cases (cases a, b, c, d, e, and f) were developed by systematically varying three critical design parameters: geometry positioning, gating system type, and draft angle. These variations are aimed at understanding their effects on forming forces (particularly punch and lateral forces), material flow behavior, and die stress.

Each design modification was selected based on prior studies and engineering judgment to address specific process limitations such as high die stress, non-uniform filling, and excessive flash formation. The full set of design variations and their configurations are shown in Figure 2, and details are summarized in

Table 3. Design parameters for each simulation case.

Case	Description	Geometry Position Relative to Press Motion	Gating System	Draft Angle
a	Base case	Vertical	Cone	20°
b	Draft angle modified	Vertical	Cone	30°
c	Rotated geometry	Vertical	Cone	20°
d	Flipped geometry	Horizontal	Cone	20°
e	Gating system redesigned I	Vertical	Curvilinear	-
f	Gating system redesigned II	Vertical	Cylindrical	-

.

• Geometry positioning was modified to assess the impact of part placement oriented normal (vertical) to the punch force versus perpendicular (horizontal) to the press force on material symmetry and lateral load distribution.
• Gating system types (conical, cylindrical, and curvilinear) were tested to determine which entry path promotes smoother material flow and reduces pressure buildup.
• Draft angles (20° and 30°) were chosen based on manufacturability constraints and their known influence on die filling and ejection.

2.2.3. Mesh

The child die and punch were modeled as rigid bodies and discretized with a coarser mesh, sufficient to describe their geometry without unnecessary computational cost. The billet and the punch were both assigned an initial global mesh size of 2 mm, while the punch guide and the child dies were meshed with element sizes in

Table 4. Mesh sizes for the parts in Forge NxT.

Average Mesh Size	Billet	Punch Guide	Punch	Child Die
Fine region (mm)	2.00	2.00	2.00	2.00
Coarse region (mm)	-	22.82	-	13.82

. An illustration of the meshed components is shown in Figure 3, highlighting the mesh density distribution applied to each tool and the billet.

In regions of interest, particularly near the billet-die interfaces and sharp corners of the die cavity, local mesh refinement was applied automatically by the software to improve solution accuracy.

2.2.4. Thermo-Mechanical Properties of the Material

The billet material, 42CrMo4E steel, was modeled using the Hensel-Spittel constitutive law as previously defined in Section 2.1. The calibrated parameters were implemented into the simulation to accurately represent material behavior under high-temperature deformation. Thermal and mechanical properties such as thermal conductivity, specific heat, density, and Young’s modulus were assigned based on literature values and are summarized in

Table 5. Thermal and mechanical material properties, data from [9,12].

Property	Density (kg/m3)	Specific Heat (J/kg/K)	Thermal Conductivity (W/m/K)	Young’s Modulus (GPa)	Poisson’s Ratio
Billet (42CrMo4E)	7850.0	778.0	35.5	210.0	0.3
Dies and punch (tool steel)	7800.0	460.0	-	200.0	0.3

.

The dies and punch were modeled as rigid bodies with elastic behavior, neglecting thermal expansion to reduce computational cost. Heat transfer between the billet, dies, and surrounding environment was considered through specified thermal contact and convection coefficients.

2.2.5. Press Kinematics

The forging was modeled using a single-acting vertical press, where only the upper die (punch) was allowed to move. A constant downward velocity of 200 mm/s was applied in the negative Y-direction until full cavity filling. All other dies were fixed to replicate industrial die constraints. The punch displacement was used to track forming stages and monitor press force evolution.

2.2.6. Initial Conditions

The billet was assigned an initial temperature of 1360 °C according to [7,19], which corresponds to the near solidus range of 42CrMo4E steel, allowing partial solid deformation during forging. The dies and punch were assumed to be at a constant initial temperature of 50 °C, representing typical tool preheating conditions to reduce thermal shock and premature wear. No initial stresses or strains were applied to the billet or tooling. The simulation assumes thermal equilibrium at the start of deformation, and no preloading or residual stress conditions were included.

2.2.7. Boundary Conditions

The mechanical press movement was simulated using a velocity vs. height control mode with a constant press speed of 200 mm/s. The heat transfer coefficient was obtained from the Forge database [20], and friction conditions were obtained from the previous work by [21]. The key boundary parameters applied in the simulation are summarized in

Table 6. Summary of boundary conditions and process parameters [21,22].

Parameter	Value	Description
Press type	Mechanical	Velocity-controlled
Press speed	200 mm/s	Constant throughout stroke
Friction model	Coulomb	Water + graphite lubrication
Friction coefficient ($\mu$)	0.1500	-
Shear friction factor (m)	0.3000	-
Heat transfer coefficient (die interface)	10,000 W/m2·K	Billet–die contact
Heat transfer coefficient (air interface)	10 W/m2·K	Billet–air contact
Tool effusivity (W.s1/2/m2·K)	11,763.62	Based on material thermal inertia

.

3. Model Validation

The reliability of the numerical model was assessed by comparing simulation results with experimental data from Plata et al. (2018) [23], which involved the near-solidus forging of an automotive spindle shown in Figure 4a.

3.1. Geometry and Process Description

The displacement–time profile used in the simulation was extracted from the experimental study (Figure 4b in [23]). This profile was applied as a kinematic input to drive the punch movement. Other conditions, such as initial temperature, die temperature, and frictional contact definitions, were matched to those reported experimentally to ensure a consistent thermomechanical environment.

3.2. Force-Time Comparison for the Experimental and Numerical Model

The simulation output was evaluated in terms of punch force and forming time. The predicted maximum punch force was 271.14 tons, which occurred at 0.72 s, closely matching the experimental results of 275.28 tons at 0.79 s as presented in

Table 7. Comparison of the experimental model with simulation parameters.

Parameter	Simulation	Experimental	Deviation
Max punch force (tons)	271.14	275.28	1.5%
Forming time (s)	0.72	0.79	8.9%

The experimental data in this table were adapted from Figure 4b in [23].

. This corresponds to a 1.5% force deviation and an 8.9% time deviation, which are considered acceptable in forging simulations given the inherent approximations in material behavior and heat transfer modeling.

The discrepancy in time is attributed to factors such as simplified friction conditions, assumptions of perfect heat transfer, and material property idealizations in the simulation model. However, the general shape and trend of the force curve are consistent, indicating that the model captures the primary mechanical behavior of the process. The result of the temperature profile of the spindle after complete filling and the comparison of the punch force from the simulation with the experimental press force are presented in Figure 5.

4. Results

The results of the finite element simulations for the different die design variant cases (a–f) presented in Table 3 are summarized in terms of maximum press force and peak lateral force acting on the child dies. These force values were extracted at the moment of complete cavity filling for each case.

4.1. Press and Lateral Force Analysis

Figure 6 presents a comparative bar chart of the punch force and lateral force exerted on the child dies for each design case in the near-solidus forging (NSF) process. The punch force reflects the load required to fully fill the cavity, while the lateral force corresponds to the reactive stress transmitted to the die walls. Excessive lateral force can induce die opening, misalignment, or premature wear. This graphical comparison enables a clearer evaluation of which design variants reduce forming load and minimize die stress, which are critical for process efficiency and tool durability.

Figure 6 shows the effect of design variations on punch force and lateral force on child dies required for complete cavity filling. Cases a–f explore the effects of geometry positioning, gating system type, and draft angle. The 30° cone design case b and curvilinear entry case e showed significant reductions in both press and lateral forces, while rotated and flipped geometries cases c and d increased the load response, indicating less efficient force transmission and higher lateral stress on the dies.

To streamline further analysis and avoid redundancy, a discriminatory selection was made based on the combined behavior of press force and lateral force. Cases c and d were excluded due to their relatively higher lateral or press forces, which may lead to increased die stress, energy consumption, or poor forming efficiency. The remaining cases b, e, and f exhibited favorable balances between forming load and die reaction forces, making them more suitable for optimized forming. These three were therefore selected for detailed thermo-mechanical analysis in the next section.

4.2. Thermomechanical Analysis of the Selected Cases

This section presents the contour plots of temperature, equivalent strain, and strain rate to evaluate material flow, cavity filling, and potential recrystallization behavior. Only cases a, b, e, and f were retained for this analysis.

4.2.1. Temperature Distribution Profile

Figure 7 presents the temperature distribution profiles for the four selected cases (a, b, e, and f). Each subfigure displays two views: the left-hand side shows the surface temperature of the forged part, while the right-hand side presents a cross-sectional view that reveals the temperature distribution within the internal core of the geometry.

The overall distribution is similar across all cases, but differences in minimum temperatures reveal distinct heat retention behavior. Case (b) exhibited the most favorable thermal retention, with a minimum of 864.05 °C, followed by case (e) at 804.77 °C and case (a) at 781.59 °C, while case (f) demonstrated the least favorable thermal performance with the lowest minimum temperature of 761.13 °C, indicating higher heat loss during forming.

4.2.2. 3D Equivalent Strain Profile

Figure 8 presents the equivalent strain distribution profiles for the selected cases (a, b, e, and f). Each subfigure consists of two views: the left-hand side displays the surface strain distribution of the forged component, and the right-hand side shows a cross-sectional view highlighting the internal strain distribution. Case (f) exhibits the highest peak strain, 12.47, indicating more intense localized deformation. Case b also shows significant strain accumulation (7.82), while cases a and c display lower and more uniformly distributed strain levels across the geometry.

4.2.3. 3D Strain Rate Profile

Figure 9 illustrates the strain rate distribution for the selected designs at representative time steps during the cavity filling process. The analysis focuses on three key stages observed across all cases (a, b, e, and f), with time points selected based on the moment each case reached specific filling milestones:

• Stage I (Initial filling∼0.05 to 0.15 s): A sharp rise in strain rate is observed at the transition between the vertical and horizontal walls, particularly as the material enters the gating system. This effect is most pronounced in case (f), due to the radius of the cylindrical gating of the child die.
• Stage II (Wing region filling∼0.15 to 0.30 s): A notable increase in strain rate occurs as the material spreads into the lateral wing areas of the cavity.
• Stage III (Full cavity filling∼0.30 to 0.45 s): The strain rate intensifies again at the cavity corners and near sharp features, where the material flow decelerates and is redirected. Localized peaks are evident in all cases, though cases (b) and (e) show a smoother distribution due to more balanced flow paths.

All cases display a similar overall distribution pattern, with average strain rates ranging from 20–50 s⁻¹. However, cases (b) and (e) demonstrated smoother flow behavior and more uniform strain rate distribution compared to cases (a) and (f), indicating better material deformation and die-filling characteristics.

5. Discussion

This section discusses the influence of die design variations on the near-solidus forging (NSF) process based on the selected cases: (a) base design, (b) cone gating with 30° draft, (e) curvilinear gating, and (f) cylindrical gating. Cases (c) and (d) were excluded due to excessive forming forces and prolonged cavity filling times. Forming forces, particularly press and lateral forces, are crucial for evaluating die stress and forming efficiency. Case (a) exhibited the highest lateral force (318.39 t), indicating significant resistance to material flow and increased risk of die wear or failure. Case (b) showed the most favorable response, with the lowest lateral force (149.44 t) and press force (141.54 t), suggesting efficient material feeding with minimal expansion of the die cavity. Case (e) offered a balanced force response, while case (f), despite its low lateral force, showed signs of flow irregularity, raising concerns about final part integrity.

Temperature distribution plays a vital role in maintaining material deformability in NSF. Case (b) retained the most favorable temperature profile, with a high and uniform distribution ranging from 864.05 to 1351.76 °C, which promotes steady plastic flow. Case (e) also exhibited good thermal retention. In contrast, Case f experienced the lowest minimum temperature (761.13 °C), which may result in restricted flow during the final filling stages. Case (a) presented moderate thermal behavior but with uneven distribution.

Equivalent strain analysis reflects the degree and uniformity of deformation across the part. Case (b) showed a maximum strain of 7.82, with a uniform distribution that supports consistent mechanical properties. Case (f) reached the highest strain value (12.47), particularly concentrated near cavity corners, indicating localized over-deformation that may lead to tool damage or material defects. Cases (a) and (e) demonstrated moderate strain levels, with case (e) offering better deformation uniformity due to its smooth curvilinear profile.

Strain rate behavior followed a three-stage evolution: initial flow through the gating system, expansion into the wing regions, and final filling of the cavity corners. Across all cases, average strain rates ranged between 20 and 50⁻¹. Case (b) provided the smoothest transition between stages, minimizing abrupt changes that could cause stress accumulation. Case (e) also showed stable progression. Conversely, case (f) exhibited concentrated strain rate peaks at cavity corners, indicating irregular filling behavior despite low force demands. Case (a) presented a typical transition but with less control over material flow.

In summary, case (b) proved to be the most effective configuration, achieving low forming resistance, stable thermal and mechanical behavior, and smooth material flow, which collectively enhance die life and part quality. Case (e) is also a promising alternative due to its consistent strain and temperature profiles. Cases (a) and (f) were less favorable overall, reinforcing the importance of optimizing gating geometry for successful NSF applications.

6. Conclusions

This study analyzed the influence of die design parameters on the forging response of complex steel geometries under NSF conditions. Using finite element simulations in Forge NxT, six die configurations were evaluated, varying geometry orientation, gating system shape, and draft angles. The goal was to understand how these design modifications affect punch force, lateral force, material flow, and thermomechanical behavior. Cases c and d, which involved rotating the base geometry by 90°, were excluded due to poor material filling and excessively high lateral loads that could compromise die integrity and part quality. The analysis therefore focused on four configurations: a base geometry (a) with a 20° draft angle, (b) a conical gating system with a 30° draft angle, (e) a curvilinear gating system, and (f) a cylindrical gating system. The simulation results led to the following key conclusions:

• Case b, featuring a conical gating system with a 30° draft angle, delivered the best overall performance with the lowest punch 141.54 t and lateral forces 149.44 t, a uniform temperature distribution (864.05–1351.76 °C), and a maximum equivalent strain of 7.82, indicating efficient deformation and lower risk of die damage.
• Case e curvilinear design also showed promising thermomechanical behavior, providing smoother material flow and better strain distribution compared to the base and cylindrical designs, although it generated slightly higher lateral forces than Case b.
• Case f cylindrical gating resulted in localized over-deformation, reaching a peak strain of 12.47, which could lead to internal defects and reduced part integrity.
• The base design, case (a), exhibited the highest lateral force, 318.39 t, and uneven strain distribution, suggesting high stress concentrations in the die and reduced product quality.

These findings highlight the importance of optimizing gating geometry and draft angles to minimize tooling loads, improve material distribution, and enhance the quality and reliability of forged components under NSF conditions.