# Analysis of Deformation and Prediction of Cracks in the Cogging Process for Die Steel at Elevated Temperatures

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. The Basic Theories of the Thermal-Mechanical Finite Element Model

_{i}is the surface traction, u

_{i}is the velocity, S is the surface, V is the volume of a sample and K is the penalty constant (K = 10

^{6}).

_{n}denotes the heat flux across the boundary surface. The temperature distribution of the workpiece can be received by solving Equation (4).

_{s}is the velocity vector of the workpiece relative to the anvil and u

_{0}is a very small positive number compared to |u

_{s}|.

#### 2.2. Investigated Material and Simulation Procedures

^{−1}. The course of the relationships between true stress and true strain and temperature for two selected strain rates—1.0 and 3.0 s

^{−1}—and also for three temperatures—1123, 1223 and 1473 K—are presented in Figure 1. The determined curves $\overline{\sigma}=f\left(\overline{\epsilon}\right)$ demonstrate the characteristic maximum of true stress, which is observed in the case of true strain amounting to approximately 0.50, whereas the situation of this maximum is not dependent upon temperature.

_{h}= 0.35 and the constant feed rate amounting to l

_{w}= 0.75 in every pass. Forging was conducted in two anvils for preparing—one convex, which had the impression angle of 130° (Figure 2a), and one in a three-radial assembly (Figure 2b)—and also in an anvil with a skew working surface (Figure 2c) for conducting a complete technological process.

_{z}on the free surface, in the middle of the sample height, assumed negative values in all cases (compressive stress). Tensile stress σ

_{Θ}acted in the circumferential direction; hence, the calculated mean stresses on the free surface, in the middle of the upset samples, assumed variable values from tensile to compression. The conducted research allowed to establish the relationships between the threshold effective strain and stress triaxiality and temperature for the X32CrMoV12-28 die steel, which are presented in Figure 3.

_{1}/h, where h and h

_{1}are the height of the initial and deformed billet, respectively); (3) the feed rate amounted to 0.75 in every pass [8,25]; (4) the environment temperature was 293 K; (5) the initial temperature of forging was 1373 K (it resulted from the performed plastometric tests); (6) the initial temperature of the anvils was 573 K (i.e., the anvil heating-up temperature under industrial conditions); (7) the pressing speed of anvils was 20 mm/s [33]; (8) the convection coefficient to environment was 0.02 N/(s mm °C) [27,32,33]; (9) the heat transfer coefficient between the deformed material and anvils was 5 N/(s mm °C) [34].

#### 2.3. Ductile Fracture Criteria

_{m}is the mean stress.

_{s}= 1.0. The calculations assume the constant of the t coefficient in every pass. The unknown value of the index exponent in the polynomial Equation (8) was determined by the method of successive approximations, using the developed computer program. For the investigated die steel, the determined value of coefficient t amounted to 1.485.

## 3. Results and Discussion

_{h}= 0.70) are presented. The anvils applied in investigations demonstrated a favorable influence upon the distribution of effective strain and effective stress in the cogging process. The highest values of effective strain were observed in the areas of a forging situated under the convex surfaces of anvils ($\overline{\epsilon}$ = 1.00, Figure 7a). The central parts of a forging were the area with the moderately smaller values of effective strain $(\overline{\epsilon}$ = 0.85). The advantage of forging in these anvils was a high uniformity of the distribution of effective strain. Even in the corners of a forging, not remaining under a direct impact exerted by anvils, the high value of effective strain, amounting to $\overline{\epsilon}$ = 0.70–0.85, was obtained. The distribution of the effective stress was similar (Figure 7b). A large contact surface between a deformed material and a tool was the reason for a favorable triaxial compression in the central parts of a forging (Figure 7c). The presented distribution of mean stresses indicated the possibility of observing tensile stresses solely in very insignificant areas, not remaining under a direct impact exerted by anvils. The forging process was accompanied by a stable distribution of temperature in the central parts of a forging, brought about by the emission heat of plastic deformation work (Figure 7d). It was solely on the contact surface between a deformed material and anvils that a greater decrease in temperature, amounting to ΔT = 80–120 °C, was observed.

_{m}in the central parts of the deformation valley were compressing, which exerted a significant influence upon the internal quality of the forgings. It was solely in the lateral zones of a forging that it was possible to expect the presence of insignificant tensile stresses.

_{w}= 0.75 up to l

_{w}= 1.20 brought about an increase in effective strain from $\overline{\epsilon}$ = 0.89 to $\overline{\epsilon}$ = 1.05.

_{m}in the central parts of the deformation valley were compressing. It is solely in the lateral zones of a forging that insignificant tensile stresses may be observed.

_{σ}

_{,}significant for forging technologies.

_{σ}and the deformation damage factor Ψ

_{S}in the function of reduction ratio in the course of the cogging process in investigated anvils is presented in Figure 13, Figure 14 and Figure 15. It was demonstrated that a reduction ratio exerted a significant influence upon the values of effective strain at particular points in the deformation valley. The specific character of the preparatory forging process in convex anvils, and in the three-radial ones, brought about moderately varied local strains on the cross-section of a deformed material; however, maximum plastic deformations were obtained simultaneously in a limited workability zone. The application of interoperational rotating of the billet and repeating deformation brought about a significant increase in the uniformity of effective strain in a cogging. For that very reason, preparatory forging in convex anvils and in assembly of three-radial anvils ensured intensive and uniform plastic deformation (Figure 13a and Figure 14a).

_{σ}, in the function of reduction ratio at the selected points of the cross-section in the course of forging a sample of the X32CrMoV12-28 die steel in three investigated anvils, are presented. The convex shape of the working surfaces of convex anvils, and of the assembly of three-radial ones, brought about the concentration of significant compression stresses in the central parts of the deformation valley, on insignificantly small areas, not significant for forging technologies, subjected to the impact exerted by tensile stresses. The stress triaxiality, accompanied by an increase in reduction ratio, particularly for applied anvils, adopted favorable negative values.

_{h}= 0.15–0.35, it was transforming entirely into compressing stress, whereas the intensity of these changes was determined, in addition to that, by the shape of the applied anvils. The most favorable conditions for reforging the particular zones of a forging were obtained in assembly of three-radial anvils, where, at a reduction ratio of 0.15 in the lateral zones of a forging, a favorable change from tensile stresses into the compressing ones was obtained (Figure 14b).

_{S}in the function of reduction ratio for three characteristic points—the center (A), lateral surface (B) and the internal point (C)—in the course of forging a sample of X32CrMoV12-28 die steel in three investigated anvils are presented. The presented values demonstrate significant differences in the values of deformation damage factor for the analyzed areas of the cross-section of a forging. The analysis of the results of the investigations, after the first pass (reduction ratio of 0.35), failed to demonstrate significant differences in the values of factor Ψ

_{S}in particular investigated tools. The scope of the values of deformation damage factor for the analyzed points of the cross-section amounted to Ψ

_{S}= 0.05–0.13. For samples deformed in convex anvils and anvils with skew working surfaces, the highest values of the deformation damage factor were observed in the central parts of a forging (point A). On the lateral surfaces (point B), lower values of the deformation damage factor were observed. For samples deformed in assembly of three-radial anvils, the highest values of the deformation damage factor were observed in the lateral zones of a forging (point B). In the central parts of a forging, the lowest values of the deformation damage factor (Ψ

_{S}= 0.05) were obtained. In the zone determined by point C, the mean values of factor Ψ

_{S}were observed. In the distributions of the deformation damage factor, it is possible to observe a close connection with a local distribution of the values of effective strain, accompanied by increase in reduction ratio; the varied local values of effective strain, and also the values of deformation damage factor, were more and more visible.

_{h}= 0.70) brought about an intensive increase in the values of the deformation damage factor, Ψ

_{S}= 0.30–0.35, in the particular zones of plastic deformation represented by points A, B and C, whereas the character of these changes for particular investigated anvils was similar to the results obtained after the first technological pass (ε

_{h}= 0.35). A further increase in the total reduction ratio up to the value of ε

_{h}= 1.40 (after the fourth technological pass) in the course of forging in anvils with skew working surfaces brought about a proportional increase in the deformation damage factor at particular points of the cross-section (Figure 15c). Nevertheless, reaching the threshold value of the deformation damage factor and the formation of discontinuities in the course of forging in anvils with skew working surfaces originated significantly later for the higher values of reduction ratio. The possibility of prediction of the ductile fracture of a shaped material during the cogging process is an indispensable element of designing the best possible technological process.

## 4. Conclusions

_{S}) in the course of cogging were the shape of anvils and the value of reduction ratio. The investigated changes in the deformation damage factor in the course of forging in different investigated anvils were the source of data on the values of factor Ψ

_{S}in particular zones of plastic deformation and rendered it possible to predict the situation and the phase of deformation in which the loss of cohesion of a deformed material will occur. At the initial stages of forging, it is proposed to apply highly effective convex anvils or assembly of three-radial ones; further, and also finally, forging may be conducted in universal anvils with skew working surfaces.

## Funding

## Conflicts of Interest

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**Figure 1.**The relationships between true stress and true strain for X32CrMoV12-28: (

**a**) strain rate 1.0 s

^{−1}; (

**b**) strain rate 3.0 s

^{−1}.

**Figure 2.**Shape of anvils: (

**a**) convex; (

**b**) assembly of three-radial; (

**c**) with skew working surfaces.

**Figure 3.**Relationship between the threshold effective strain and stress triaxiality and temperature for the X32CrMoV12-28 die steel.

**Figure 4.**Schematic illustration of the cogging process: (

**a**) finite element model for the forging experiment; (

**b**) the hitting sequence for the cogging process (l/w

_{d}= 0.70; l/D

_{0}= 0.75); (

**c**) pass sequence for the cogging process.

**Figure 5.**Distribution of effective strain (

**A**) and effective stress (

**B**) after the cogging process in convex anvils with an angle of 130°: (

**a**) after first pass; (

**b**) after the second pass (reduction ratio 0.70).

**Figure 6.**Distribution of mean stresses (

**A**) and temperature (

**B**) after the cogging process in convex anvils with an angle of 130°: (

**a**) after first pass; (

**b**) after the second pass (reduction ratio 0.70).

**Figure 7.**Distribution of the effective strain (

**a**), effective stress (

**b**), mean stresses (

**c**) and temperature (

**d**) after the cogging process in the assembly of three-radial anvils after the second pass (reduction ratio 0.70).

**Figure 8.**Distribution of the effective strain after the cogging process in anvils with skew working surfaces: (

**a**) after the second pass (reduction ratio 0.70); (

**b**) after the fourth pass (reduction ratio 1.40)

**.**

**Figure 9.**Distribution of mean stresses after the cogging process in anvils with skew working surfaces: (

**a**) after the second pass (reduction ratio 0.70); (

**b**) after the fourth pass (reduction ratio 1.40).

**Figure 10.**Distribution of effective strain after the cogging process in anvils with skew working surfaces after the second pass (reduction ratio 0.70): (

**a**) feed rate of 0.75; (

**b**) feed rate of 1.20.

**Figure 11.**Distribution of mean stresses after the cogging process in anvils with skew working surfaces after the second pass (reduction ratio 0.70): (

**a**) feed rate of 0.75; (

**b**) feed rate of 1.20.

**Figure 12.**The influence of reduction ratio (

**a**) and feed rate (

**b**) on the effective strain $\overline{\epsilon}$ during the cogging process of the X32CrMoV12-28 die steel specimens in anvils with skew working surfaces: (

**a**) feed rate of 0.75; (

**b**) reduction ratio of 0.70.

**Figure 13.**The variation in effective strain $\overline{\epsilon}$ (

**a**), stress triaxiality T

_{σ}(

**b**) and the deformation damage factor Ψ

_{S}(

**c**) at selected points A, B and C during the cogging process of the X32CrMoV12-28 die steel specimens in convex anvils with an angle of 130°.

**Figure 14.**The variation in effective strain $\overline{\epsilon}$ (

**a**), stress triaxiality T

_{σ}(

**b**) and the deformation damage factor Ψ

_{S}(

**c**) at selected points A, B and C during the cogging process of the X32CrMoV12-28 die steel specimens in the assembly of three-radial anvils.

**Figure 15.**The variation in effective strain $\overline{\epsilon}$ (

**a**), stress triaxiality T

_{σ}(

**b**) and the deformation damage factor Ψ

_{S}(

**c**) at selected points A, B and C during the cogging process of X32CrMoV12-28 die steel specimens in anvils with skew working surfaces.

**Figure 16.**Comparison of theoretical and experimental results after the cogging process in anvils with skew working surfaces: theoretical (

**a**) and experimental (

**b**) distributions of effective strain (l

_{w}= 0.75, ε

_{h}= 0.35); (

**c**) temperature on the surface of the specimens.

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**MDPI and ACS Style**

Kukuryk, M.
Analysis of Deformation and Prediction of Cracks in the Cogging Process for Die Steel at Elevated Temperatures. *Materials* **2020**, *13*, 5589.
https://doi.org/10.3390/ma13245589

**AMA Style**

Kukuryk M.
Analysis of Deformation and Prediction of Cracks in the Cogging Process for Die Steel at Elevated Temperatures. *Materials*. 2020; 13(24):5589.
https://doi.org/10.3390/ma13245589

**Chicago/Turabian Style**

Kukuryk, Marcin.
2020. "Analysis of Deformation and Prediction of Cracks in the Cogging Process for Die Steel at Elevated Temperatures" *Materials* 13, no. 24: 5589.
https://doi.org/10.3390/ma13245589