This article was originally published in December 2013.

Hot-forging dies should display high strength, toughness and low wear. Plastic deformation and wear of the dies lead to their costly refitting or disposal. This article analyzes the role of circumferential press-fit rings on the plastic deformation and wear of a die employed in the production of spherical milling bodies.


Hot closed-die forging involves the pressing of an adequately heated metal blank between two dies with cavities corresponding to the desired shape of the part. These dies must display high wear resistance as well as adequate toughness and compressive strength.

    This article discusses the hot forging of a cylindrical blank into a spherical shape. Figure 1 is a schematic view of the bottom die utilized in the operation. This is where the compressive forging loads impose radial and circumferential stresses on the die. The press-fit (interference-fit or shrink-fit) mounting of a ring around the die (Fig. 1) is commonly employed in order to decrease the imposed tensile stresses during forging.

    With each forging cycle, the pressure on the internal surface of the die, coupled with the relative movement between the material and the die, lead to wear. The complex stresses acting on the die, in addition to its lowered strength due to heating, may cause plastic deformation in the die. This situation may lead to unacceptable dimensional problems in the product as well as the potential of expensive scrapping or reworking of the dies. An even more drastic situation – the partial or complete cracking of the dies – could also result.

    Researchers have verified that abrasive wear associated both with hard oxide particles between the blank and the dies and with direct contact between them predominates during forging. The Archard generalized equation (Equation 1) is utilized to describe the wear: where W is the volume of material removed by wear; P is the local load applied normally to the die surface; V is the relative speed between the two contacting bodies; H is the surface hardness; t is time; a, b and c are constants; and K is a wear coefficient that depends on various conditions.

    Here we try to present a numerical analysis of the effect of an interference ring on the abrasive wear and plastic deformation of the die used in the production of spherical milling bodies.



The dies with and without press-fit rings are displayed in Figure 2. The spherical milling body material was AISI 1045 steel with a diameter of 90 mm (3.5 inches). Its forging led to the formation of flash around the sphere. The cylindrical blank was 120 mm (4.7 inches) long with a diameter of 76.2 mm (3 inches). The die material was H13 tool steel, with an initial average hardness of 52 HRC. The external ring was made with AISI 1020 steel.


Finite-Element Method

The initial calculation of interference between the outer ring and the die itself was based on the DIN 7190 standard, subject to equations beyond the scope of this article. Based on the specific parameters of this project, however, interference between them was calculated to be close to 3 mm (0.12 inches).

    The DEFORM 2D software package from Scientific Forming Technologies Corp. of Columbus, Ohio, was used for the simulation of the forging and the wear. The software utilizes an implicit formulation for the integration with time, where the solution of the equation governing equilibrium is obtained through the consideration of the moment of time,t+Δt.

    Once the displacement (U) and speed (U) at time (t) are known, an initial estimate of these values is made for the time t+Δt. These are then adjusted through a numerical solution of the force equilibrium equation (Equation 2), based on the minimization of the residue R(t+Δt):

    The incremental Newton-Raphson method is usually employed in non-linear situations in order to obtain the value of Ü(t+Δt). The displacement of the upper die, for example, is divided into small increments, and the displacement vectors are calculated for each increment. This method demands the preparation and inversion of the rigidity matrix for each new increment, leading to extended processing times. Since the lower and upper dies, interference ring and material have an axisymmetric geometry, the situation was simplified as illustrated in Figure 3.

    The material of the spherical milling body (AISI 1045 steel) was considered an isotropic and rigid-plastic material whose constitutive equation (considering variations on strain, strain rate and temperature) and thermal properties were taken from the software library.

    The lower and upper dies (H13 tool steel) and the interference ring (AISI 1020 steel) were also modeled as isotropic and rigid plastic materials and displayed 700 and 250 square elements, respectively. A region with smaller elements (0.75 mm-dimension) was utilized in the regions of the dies in contact with the material in order to reach an adequate convergence of results. A coarser mesh (5-mm elements) was considered for the rest of the die, without loss of quality in the results. The elements in the interference ring also had a size of 5 mm (0.2 inches), and a friction factor of 0.3 was taken for the contact between the dies and the material.


Heat Transfer

The thermal evolution of the dies and pressure rings involves the heat generated by the plastic deformation of the material and the die/material friction. Additionally, the heat transfer from the blank to the dies and the heat loss to the atmosphere was considered by the DEFORM program. Room temperature was taken as 25°C (77°F); the thermal conductivities of the materials were taken from the software library; and the coefficient of convective heat transfer was 50 watt/m2K. The initial temperature of the spherical body material in each forging cycle was 950°C (1742°F); 250°C (482°F) for the dies; and 150°C (302°F) for the interference ring.



For Archard’s equation, the software suggests a = 1, b = 1 and c = 2 for tool steels. K is usually experimentally calibrated, and it was taken as K = 300 for the forging of all the 950 parts in the present case.


Results and Discussion

The variation of the applied effective stress and wear were plotted between the corner (P0) and the bottom of the die (Pf), as indicated in Figure 4. The die profile was divided into three areas: Region I refers to the bottom of the die; Region II refers to the initial contact region between the material and the blank; and Region III refers to the upper part of the die, including the flash-forming region.

    Figure 5 displays the predicted distribution of the effective stress on the die at the moment of maximum displacement of the upper die, with and without the press-fit ring and after 950 forging cycles.

    For the situation without the press-fit ring, the highest effective stress was located at the die corner (Region III). In addition, the stress first increases up to around 560 MPa and then decreases to 450 MPa as one progresses toward Regions II and I of the die. In contrast, the presence of the press-fit ring leads to a displacement of the maximum effective stress to Region II (with a value of only 450 MPa), decreasing markedly in the directions of Regions I and III.

    Figure 6 displays the simulated distribution of effective strain along the die surface. The press-fit die underwent appreciably lower strains than the die without the interference ring. The maximum strain (≈ 0.075) for the ring-mounted die strain occurred in Region II, close to where the blank first contacts the die. The press-fit die exhibited a maximum strain at point P0 (Region III, with a strain of ≈ 0.05).

    Figure 7 compares the experimentally measured with the predicted dimensional changes in the die, both for the press-fit case and without the press-fit ring. The former situation clearly leads to a lower dimensional loss in the die after the 950 forging cycles. On the other hand, there are appreciable differences between the numerically predicted and the experimental dimensional changes for Region I of the die (with and without the press-fit ring) and for Region II of the die when no press-fit ring is mounted.

    The finite-element simulations allow one to evaluate the effect of various press-fit mountings on the wear of the die. Figure 8 exhibits the predicted effective strain distributions for ring/die interferences of 4 mm (0.16 inches), 5 mm (0.2 inches) and 6 mm (0.24 inches) after the 950 forging cycles. The curve for the 3-mm (0.12-inch) interference (taken from Figure 6) is also included for comparison. The increase in the interference values clearly decreases the effective strains in the dies.

    Table 1 indicates the temperatures at which the ring would have to be heated before the interference mounting for the various interferences. The necessary temperatures for the 5-mm (0.2-inch) and 6-mm (0.24-inch) interferences cannot be used because they are quite close or beyond the melting temperature of steel.

    Figure 9 shows the dimensional change of the die associated exclusively with wear. The highest damage (≈ 0.88 mm) occurred in Region III (point P0), but appreciable damage was also observed close to the initial contact point between the die and the blank (≈ 0.56 mm).

    It is noteworthy that between the positions corresponding to distances 7.5-25 mm (0.3-1 inch), a somewhat higher wear is predicted for the die with the press-fit ring than for the die without it. A comparison with the values for dimensional changes in Figure 7 (total dimensional changes in the die) and Figure 9 (dimensional changes associated only with wear) indicates the utilization of the present wear parameters in Archard’s equation should be viewed with caution and should be calibrated in relation to experimentally measured values.



The simulations presented here led to the following conclusions:

• Wear damage to the dies occurred basically on the upper corner of the dies and in the region of initial contact between the blank and the dies.

• Press-fit rings appreciably decrease the applied effective stress on the dies during forging, leading to a decrease in the effective strain and corresponding plastic deformation of the dies.

• Interference-mounted rings had a negligible influence on the wear of the dies.

• A quantitatively adequate prediction of the geometrical damage in closed forging dies depends on an initial calibration of the parameters involved in Archard’s equation.



The authors thank CAPES, CNPq, FAPEMIG, the Graduate Program in Metallurgical and Mining Engineering of UFMG and the Graduate Program in Mechanical Engineering of UFMG for the financial support.

This article was derived and edited from a paper given at the 65th Annual Congress of the Brazilian Society of Metals, Materials and Mining, July 2010 in Rio de Janeiro, Brazil. Co-author Frederico de Castro Magalhães is in the post-doctoral graduate program in metallurgical and materials engineering at the Federal University of Minas Gerais (UFMG). He can be reached at Co-author Antônio Eustáquio de Melo Pertence is associate professor of mechanical engineering at UFMG; co-author Haroldo Béria Campos is associate professor of mechanical engineering at UFMG; co-author Maria Teresa Paulino Aguilar is associate professor, department of construction and materials at UFMG; and co-author Paulo Roberto Cetlin is professor of mechanical engineering at UFMG.