Method for visualizing forging process using deformation processng map

Abstract

The present invention discloses a forging process visualization system. More specifically, the present invention relates to a visualization method using an index regarding a deformation process map and cracks in a forging process for processing alloy materials. According to an embodiment of the present invention, by reflecting a deformation process map of a material to which a finite element analysis model is applied, points with a high probability of crack occurrence can be visualized. Furthermore, a new index called the Crack Susceptibility Index (CSI) is presented, which represents plastic instability based on Ziegler parameters using strain sensitivity (m) and power dissipation efficiency (η) values ​​used in hot processes. By reflecting this in a product, there is an effect of accurately estimating plastic instability and the location of crack occurrence.

Description

Technology Field

[0001] The present invention relates to a method for visualizing a forging process, and more particularly to a method for visualizing a forging process using a deformation process map in a hot forging process for processing alloy materials. Background Technology

[0002] A deformation processing map refers to a graph showing the power dissipation efficiency (η) of an alloy material with respect to temperature and strain rate. Since this indicates the high-temperature machinability and forgeability of the alloy material, it is essential in the field of manufacturing and production of products using alloys.

[0003] Figure 1 shows an example of a conventional deformation process map, through which the distribution of the power distribution efficiency (η) of the material can be easily verified.

[0004] However, deformation process maps have limitations in that they cannot sufficiently explain material behavior during hot working. This is because while high power dissipation efficiency brings about positive effects such as dynamic recrystallization, superplasticity, and dynamic recovery that prevent material cracking, it can also lead to negative effects such as void formation and wedge cracking. Therefore, material analysis methods relying solely on deformation process maps carry the risk of predicting inaccurate results.

[0005] Furthermore, deformation process maps are merely controlled data constructed from averaged flow stress data and have the drawback of being unable to reflect the complexity of the product's shape or the process environment. Therefore, if only deformation process maps are utilized for analysis, it becomes difficult to identify differences in machinability based on the material's local area, and it becomes impossible to predict the occurrence of localized cracks that may arise during complex forging processes.

[0006] In particular, the predictability of the deformation process map decreases further when the distribution of temperature or deformation rate varies significantly depending on the product's location, or when there are large changes in boundary conditions occurring during various process steps.

[0007] To address these limitations, it has been recommended to use plastic instability maps based on Ziegler parameters in conjunction with deformation process maps. However, the limitation of being unable to pinpoint the exact locations where cracks may occur in the material remains. Furthermore, since the parameters are expressed in the form of differential equations, they have the disadvantage of being unsuitable for various analyses because even small errors lead to significant deviations. Prior art literature

[0008] Published Patent Application No. 10-2023-0107030 (Date of publication: July 14, 2023) The problem to be solved

[0009] The present invention has been devised to solve the aforementioned problems. The present invention ensures that power distribution efficiency with respect to temperature and deformation rate is reflected in real time in a material undergoing hot working. The objective is to provide a visualization system that analyzes the machinability of the material at a given location in real time through finite element analysis to more accurately predict the possibility of crack occurrence.

[0010] In addition, the present invention has another objective in presenting a new index, the Crack Susceptibility Index (CSI), which is an application of the Ziegler parameter, and providing a visualization system capable of estimating plastic instability and crack occurrence locations by reflecting this in a product. means of solving the problem

[0011] To solve the aforementioned problem, a method for visualizing a forging process using a deformation process map according to an embodiment of the present invention may include the steps of: performing finite element analysis on a material to be hot forged to generate a geometric material model including mesh elements of a three-dimensional shape; using one or more subroutines to connect one or more process parameters occurring during the progress of the hot forging process on the material to the material model to calculate a power distribution efficiency (η) and CSI according to location; and mapping and displaying the power distribution efficiency (η) and CSI calculated according to the local location of the material to the material model.

[0012] The above subroutine includes a first subroutine for calculating the rate of change of stress (Δσ) of the material model according to the progress of the hot forging process, and the rate of change of strain for the material model ( It may include a second subroutine for calculating ) and a third subroutine for calculating strain sensitivity (m) based on data calculated from the first and second subroutines, and calculating power distribution efficiency (η) and CSI according to the strain rate sensitivity (m).

[0013] The step of calculating the power distribution efficiency (η) and CSI according to position by connecting one or more process parameters occurring during the progress of the hot forging process for the material to the material model using the above one or more subroutines comprises the current time (t) at which the first subroutine is input to the material model.k A step of loading parameters regarding stress at ), wherein the first subroutine, according to the parameters, at the current time (t k ) or, previous time (t k-1 From ) to current time(t k Stress (σ) of the material model up to ) von-mises A step of calculating ), a step in which the second subroutine loads a parameter regarding the current strain rate of the material model, and a step in which the second subroutine calculates the current time (t) according to the parameter k ) or, previous time (t k-1 From ) to current time(t k Strain rate of the material model up to ) A step of calculating ), wherein the third subroutine calculates the stress (σ von-mises ) and strain rate( A step of calculating sensitivity (m) using ), a step in which the third subroutine calculates the power distribution efficiency (η) and CSI using the sensitivity (m), a step in which the third subroutine stores parameters regarding the power distribution efficiency (η), and, depending on the progress state of the forging process, the first subroutine calculates stress (σ von-mises Previous time (t) for ) calculation k-1 Stress (σ) at ) old ) stores, and the second subroutine is the strain rate ( Previous time (t) for ) calculation k-1 Strain rate at ) It may include a step of storing ) and, according to a preset interval, a step of sequentially repeating from the step of loading parameters regarding current stress to be input into the material model until the end of the forging process to the step of storing the calculated strain rate.

[0014] The above stress (σ von-mises ) can be calculated as Von mises stress.

[0015] The strain sensitivity (m) above is given by the following mathematical formula,

[0016]

[0017] It can be calculated as (where 'UVARM1' and 'UVARM2' are the output values ​​of the first and second subroutines, respectively)

[0018] The above power distribution efficiency (η) is given by the following mathematical formula,

[0019]

[0020] It can be calculated as.

[0021] The above CSI is, according to the following mathematical formula,

[0022]

[0023] It can be calculated as.

[0024] The above subroutine can be implemented in ABAQUS. Effects of the invention

[0025] According to an embodiment of the present invention, by reflecting a location-specific deformation process map of a material to which a finite element analysis model is applied, it is possible to visualize points with a high probability of crack occurrence.

[0026] In addition, according to an embodiment of the present invention, by displaying the degree of plastic instability of the material during the process in the form of a graphic image, there is an effect of quantifying and visualizing the possibility of crack occurrence according to process variables such as temperature, time, and speed. Brief explanation of the drawing

[0027] Figure 1 is a diagram showing an example of a conventional deformation process map. FIG. 2 is a diagram showing a deformation process map and a forging process visualization method using CSI according to an embodiment of the present invention. FIG. 3 is a diagram showing a method for calculating power distribution efficiency (η) and CSI included in a method for visualizing a forging process using a deformation process map and CSI according to an embodiment of the present invention. FIG. 4 is a diagram illustrating a finite element analysis model provided by a forging process visualization method using a deformation process map according to an embodiment of the present invention, and a screen showing stress and CSI values. FIG. 5 is a diagram comparing a conventional deformation process map and a map of CSI values ​​according to an embodiment of the present invention. FIG. 6 is a diagram illustrating a screen in which a subroutine is applied to a finite element analysis model according to an embodiment of the present invention. FIG. 7 is a diagram comparing a map of conventional Ziegler parameters and CSI values ​​according to an embodiment of the present invention. Specific details for implementing the invention

[0028] The present invention as described above will be explained in detail through the attached drawings and embodiments.

[0029] It should be noted that the technical terms used in this invention are used merely to describe specific embodiments and are not intended to limit the invention. Furthermore, unless specifically defined otherwise in this invention, the technical terms used in this invention should be interpreted in the sense generally understood by those skilled in the art to which this invention pertains, and should not be interpreted in an overly broad or overly narrow sense. Additionally, if a technical term used in this invention is an incorrect technical term that fails to accurately express the concept of the invention, it should be replaced with a technical term that can be correctly understood by those skilled in the art. Moreover, general terms used in this invention should be interpreted according to their prior definitions or the context, and should not be interpreted in an overly narrow sense.

[0030] Furthermore, singular expressions used in the present invention include plural expressions unless the context clearly indicates otherwise. In the present invention, terms such as "composed of" or "comprising" should not be interpreted as necessarily including all of the various components or steps described in the invention, and should be interpreted as meaning that some of the components or steps may not be included, or that additional components or steps may be included.

[0031] Additionally, terms including ordinal numbers, such as first, second, etc., used in the present invention may be used to describe components, but the components should not be limited by these terms. The terms are used solely for the purpose of distinguishing one component from another. For example, without departing from the scope of the present invention, the first component may be named the second component, and similarly, the second component may be named the first component.

[0032] Furthermore, in describing the present invention, detailed descriptions of related prior art are omitted if it is determined that such descriptions may obscure the essence of the invention. Additionally, it should be noted that the attached drawings are intended only to facilitate an understanding of the concept of the present invention and should not be interpreted as limiting the concept of the invention.

[0033] Hereinafter, preferred embodiments according to the present invention will be described in detail with reference to the attached drawings. Identical or similar components are given the same reference number regardless of the drawing symbols, and redundant descriptions thereof will be omitted.

[0034] FIG. 2 is a diagram illustrating a method for visualizing a forging process using a deformation process map and CSI according to an embodiment of the present invention. The following steps can be implemented by a computer system equipped with a microprocessor and memory capable of executing a structural analysis program and can be stored on a known recording medium.

[0035] Referring to FIG. 2, the method for visualizing a forging process using a deformation process map and CSI according to an embodiment of the present invention is a method for visualizing a forging process, comprising the step (S100) of first performing finite element analysis on a material to generate a geometric material model including mesh elements of a three-dimensional shape, wherein one or more parameters for a metal material to be manufactured through a forging process are input into a computer that performs finite element analysis to generate a material model in the form of a three-dimensional mesh for the material.

[0036] Next, in the step (S110) of generating a deformation process map by performing a hot forging process on the material, the state of the material being deformed during the progress of the hot forging process is received through a predetermined sensor installed in the forging device, and by reflecting it in the material model generated in step S100, the current state of the material according to the degree of process progress can be visually checked.

[0037] Here, hot forging is a metal forming process that processes a material into a predetermined shape. Generally, during hot forging, the material is heated to 75% of its melting temperature, and as the stress and energy required for plastic deformation decrease as it approaches the melting temperature, the production rate can be increased.

[0038] Next, in the step (S120) of calculating power distribution efficiency (η) and CSI according to the location of the material model by applying one or more parameters defined in the deformation process map using one or more subroutines, the power distribution efficiency and CSI are calculated through a subroutine based on a pre-prepared computer program using data such as stress and strain of the material being processed. Here, the subroutine is code written through a structural analysis program such as ABAQUS based on the Fortran language, and can calculate the power distribution efficiency (η) and CSI by receiving multiple parameters regarding stress and strain of the material detected by a sensor as the forging process progresses.

[0039] And, as a step (S130) of mapping and displaying power distribution efficiency (η) and CSI at local locations in the material model, by matching the result value calculated in step S120 to each location on the 3D material model according to finite element analysis, a deformation process map for each location in the material model can be displayed.

[0040] The deformation process map disclosed in the embodiments of the present invention represents the influence of temperature and strain rate during high-temperature forming in a map form, and includes a safe region with excellent workability and an instable region with poor workability; in particular, it can represent the high-temperature workability of a metal alloy by combining information regarding the power distribution efficiency and flow instability of the microstructure during high-temperature deformation.

[0041] However, for process parameter optimization, it is important to identify undesirable regions of unstable flow. Furthermore, since temperature and strain during hot working can vary by location, an evaluation of local crack-prone areas is required. In particular, for large or complex forged products, temperature and strain can vary significantly depending on the location.

[0042] In particular, while safe operation can be predicted through such deformation process maps, it can be said that there is a high possibility of localized cracking caused by the process.

[0043] Therefore, when analyzing flow instability in conventionally constructed deformation process maps, most prior studies on crack formation have been conducted in conjunction with plastic instability maps; however, there is a limitation in that they cannot indicate the local locations of cracks that may occur during the hot working process.

[0044] In contrast to this, according to the forging process visualization method of the present invention, a three-dimensional material model of a material is implemented through finite element analysis, and a deformation process map for each location of the material model is provided, thereby making it possible to identify areas on the material where there is a possibility of local crack occurrence.

[0045] Hereinafter, one or more subroutines for implementing a forging process visualization method using a deformation process map and CSI according to an embodiment of the present invention, and a method for calculating power distribution efficiency (η) and CSI using the same will be described in detail.

[0046] FIG. 3 is a diagram showing a method for calculating power distribution efficiency (η) and CSI included in a method for visualizing a forging process using a deformation process map and CSI according to an embodiment of the present invention.

[0047] Referring to FIG. 3, according to an embodiment of the present invention, a method for calculating the derived power distribution efficiency (η) and CSI through finite element analysis can be applied to a material model implemented with a 3D mesh derived by finite element analysis through first to third subroutines (100, 200, 300) written in a predetermined programming language.

[0048] The above first subroutine (100) calculates the stress change rate (Δσ) of the material model according to the progress of the hot forging process, and the second subroutine (200) calculates the rate of change of strain for the material model ( The third subroutine (300) calculates the strain sensitivity (m) based on the data calculated from the first and second subroutines (100, 200), and calculates the power distribution efficiency (η) and CSI according to the strain sensitivity (m).

[0049] To explain the method for calculating power distribution efficiency (η) and CSI using this, first, according to the execution of the first subroutine (100), one or more parameters related to the stress (σ) currently occurring in the material are loaded from the sensor of the hot forging equipment (110), and the current stress (σ) is calculated using the parameters. Von mises Calculate ) (120). At this time, the stress can be calculated as Von mises stress.

[0050] Additionally, in accordance with the execution of the second subroutine (200), one or more parameters related to the rate of strain according to the deformation of the current material are loaded from the sensor of the hot forging equipment (210), and the current equivalent plastic strain rate ( Calculates ) (220).

[0051] And, in accordance with the execution of the third subroutine (300), the stress (σ) calculated in the aforementioned procedure Von-mises ) and plastic strain rate ( The sensitivity (m) is calculated using ) (310).

[0052] In detail, the third subroutine (300) can calculate the strain rate sensitivity (m) from the deformation process map, which is a key factor determining the dynamic behavior of the material, and through this, can calculate the efficiency of dissipation, i.e., the power dissipation efficiency (η).

[0053] The strain sensitivity (m) described above can be expressed as shown in Equation 1 below.

[0054]

[0056] It can be calculated as follows. Here, 'UVARM1' and 'UVARM2' refer to the output values ​​of the first and second subroutines (100, 200), respectively.

[0057] Next, the third subroutine (300) can calculate the power distribution efficiency (η) using the strain sensitivity (m) (320). First, the power distribution efficiency (η) is defined by the following mathematical formula 2.

[0058]

[0060] Additionally, according to an embodiment of the present invention, the third subroutine (300) can calculate a crack susceptibility index (CSI), which is a new hot working analysis index based on Ziegler parameters.

[0061] The aforementioned CSI represents the plastic instability phenomenon developed by Ziegler in terms of sensitivity (m) and power dispersion efficiency (η) used in hot processes.

[0062] In detail, instability criteria can be established under various different assumptions, and a general method is to apply the stability concept of Ziegler's plasticity to the dissipation function of the material model, and the Ziegler parameter (ξ) is defined by the following mathematical equation 3.

[0063]

[0065] According to the plastic instability theory, R is Same as ( ), D is a dissipative function that represents the structural behavior of the material, and can be expressed as shown in Equation 4 below.

[0066]

[0068] And, the function related to metallurgical stability is given by J, and since J is determined by dissipation through the metal process, if J is substituted into D in Equation 4, the Ziegler instability criterion can be expressed as Equation 5 below.

[0069]

[0071] In addition, the above mathematical formula 5 can be expanded as shown in the following mathematical formula 6.

[0072]

[0074] In addition, the Ziegler parameter can be expressed by the following mathematical formula 7.

[0075]

[0077] And, since the stress (Von Mises Stress, σ) is always greater than 0, dividing both sides of the equation by the stress yields the following mathematical equation 8.

[0078]

[0080] According to the above mathematical formula 8, the crack sensitivity index (CSI) can be defined as shown in the following mathematical formula 9.

[0081]

[0083] The third subroutine (300) can calculate the CSI value according to the above mathematical formula 9 (320).

[0084] Next, the third subroutine (300) stores a parameter regarding the power distribution efficiency (η) in the variable UVAR3 (330). At this time, the system can output the η value on the screen.

[0085] And, if the process continues according to the progress status of the forging process, the first subroutine (100) is stress (σ von-mises Previous time (t) for ) calculation k-1 Stress (σ) at )old ) is stored in variable UVAR1 (140), and the second subroutine (200) is strain rate ( Previous time (t) for ) calculation k-1 Strain rate at ) ) can be saved in UVAR2.

[0086] Then, the system sequentially repeats steps from step 110, which loads parameters regarding the current stress to be input into the material model, to step 330, which stores the calculated strain rate, according to a preset interval until the end of the forging process (340).

[0087] Hereinafter, the technical concept of the present invention will be explained in detail through an example in a hot process applying a forging process visualization method using a deformation process map according to an embodiment of the present invention.

[0088] FIG. 4 is a diagram illustrating a finite element analysis model provided by a forging process visualization method using a deformation process map according to an embodiment of the present invention, and a screen showing stress and CSI values.

[0089] Referring to FIG. 4, according to the method for visualizing a forging process using a deformation process map according to an embodiment of the present invention, a material model with a three-dimensional mesh shape can be realized through finite element analysis of the material during the forging process, and the distribution of temperature and stress on the material model can be displayed through a color image (a).

[0090] In addition, the material model of the finite element analysis can display the distribution of power distribution efficiency (η) and CSI values ​​for specific locations according to user operation (b).

[0091] FIG. 5 is a diagram comparing a conventional deformation process map and a map of CSI values ​​according to an embodiment of the present invention.

[0092] Referring to FIG. 5, the conventional deformation process map (a) reflects the plastic instability map calculated through the above mathematical formula 5, represented by black hatching. The contour line values ​​represent the power distribution efficiency (η). According to the example deformation process map, a peak efficiency of 0.47 is shown at approximately 1050 ℃, indicating that the hot working process is under good conditions.

[0093] In addition, according to the CSI map (b) obtained using the CSI value expressed in the above mathematical formula 9, it can be seen that the boundary between them is similar to the result derived from the CSI value based on the Ziegler plastic instability map. In particular, the CSI boundary is similar to the Ziegler plastic instability boundary when the CSI value reaches 0.85, and thus it can be determined that the boundary where cracks may occur in the material has a CSI value of 0.85.

[0094] FIG. 6 is a diagram illustrating a screen in which a subroutine is applied to a finite element analysis model according to an embodiment of the present invention.

[0095] Referring to FIG. 6, a screen illustrating the application of the subroutine of the present invention to an FE simulation is shown, at 900 ℃ and 1 s -1 Under the condition, the change in the CSI and η values ​​for each element with respect to the reduction value is shown. Since 0 < m < 1, the value ranges for CSI and η in the above Equation 9 are 0.5 < CSI < 1 and 0 < η < 1, respectively. Also, ①, ②, ③, and ④ indicated on the image refer to the four notches installed in the material during the process, respectively.

[0096] As shown in FIGS. 6(a) to (c), when R ≤ 30%, the CSI and η values ​​are in the range of 0.6 to 0.7 under good forming conditions. And when R = 48%, as shown in FIG. 7(d), the CSI value at position ④ increases to 0.87, which indicates plastic instability.

[0097] In addition, as shown in Figures 6(e) and (f), plastic instability occurs at notch ③ when R ≥ 56%. The values ​​of η and CSI change with decreasing values; while the value of η decreases as R increases, the value of CSI increases and indicates plastic instability as it approaches 1.

[0098] FIG. 7 is a diagram comparing a map of conventional Ziegler parameters and CSI values ​​according to an embodiment of the present invention.

[0099] Referring to Fig. 7, the CSI and ξ values ​​at notches ③ and ④ are shown based on the decrease value. When R = 48%, the CSI and ξ values ​​are 0.87 and -19.4, respectively. Since a negative ξ value indicates plastic instability, the CSI value is 0.87, which can be seen as a result similar to the boundary of the Ziegler instability map as shown in Fig. 6 above.

[0100] However, the Ziegler parameter (ξ) value becomes unstable between + and - around the zero boundary, even though R is in the range of 20% to 40%. The ξ value is calculated on a logarithmic scale in the form of a differential equation and is as shown in Equation 3 above. This phenomenon occurs when using subroutines, as calculations are performed using small increments due to the nature of finite element analysis.

[0101] As shown in Figure 7, when R = 48%, the ξ value of notch ④ decreased sharply to -19.4, and when R = 56%, the ξ value of notch 3 decreased to -52, and the Ziegler parameter value showed instability between + and - around the zero boundary, even though R is in the range of 20% to 40%. On the other hand, the CSI value has stable values ​​in the range of 0.56 to 0.65 when R < 40%, but a difference occurs after R > 48%.

[0102] Fig. 7(c) shows 900 ℃, 1 s in FE simulation using a subroutine. -1and, the changes in CSI and ξ values ​​at R = 48% are shown. Under extreme plastic instability, the CSI value increases to 0.87 at notch ④ at R = 48%. Similarly, ξ shows a negative value of -19.4. However, while the CSI value remains stable at 0.68 at notch 3, the Ziegler parameter shows -1.63, which is the instability boundary, as shown in Fig. 7(c).

[0103] Based on the above results, it can be seen that in the simulation by finite element analysis as shown in Figures 6 and 7, the CSI value has the advantages of the η value, which represents workability during forming, and the ξ value, which represents plastic instability.

[0104] Accordingly, the forging process visualization method using a deformation process map according to an embodiment of the present invention can be used as a suitable indicator for determining plastic instability when local cracks occur at specific locations in a product having a complex shape during hot working.

[0105] Although many details are described in detail in the above description, this should be interpreted as an example of a preferred embodiment rather than as a limitation to the scope of the invention. Accordingly, the invention should not be determined by the described embodiment, but by the claims and equivalents thereof. Explanation of the symbols

[0106] 100, 110, 120, 140 : 1st subroutine 200, 210, 220, 240 : 2nd subroutine 300, 310, 320, 330, 340 : 3rd Subroutine

Claims

Claim 1 A visualization method for a forging process using a deformation process map, comprising: a step of generating a geometric material model including mesh elements of a three-dimensional shape by performing finite element analysis on a material to be hot forged; a step of calculating a power distribution efficiency (η) and CSI according to location by connecting one or more process parameters occurring during the progress of the hot forging process on the material to the material model using one or more subroutines; and a step of mapping and displaying the power distribution efficiency (η) and CSI calculated according to the local location of the material to the material model. Claim 2 In claim 1, the subroutine comprises: a first subroutine for calculating the rate of change of stress (Δσ) of the material model according to the progress of the hot forging process; and the rate of change of strain for the material model ( A method for visualizing a forging process using a deformation process map, comprising: a second subroutine for calculating ); and a third subroutine for calculating strain sensitivity (m) based on data calculated from the first and second subroutines, and calculating power distribution efficiency (η) and CSI according to the strain sensitivity (m). Claim 3 In claim 2, the step of calculating the power distribution efficiency (η) and CSI according to position by connecting one or more process parameters occurring during the progress of the hot forging process for the material to the material model using the one or more subroutines comprises the current time (t) at which the first subroutine is input to the material model. k A step of loading parameters regarding stress at ); the first subroutine according to the parameters at the current time (t k ) or, previous time (t k-1 From ) to current time(t k Stress (σ) in the material model up to ) von-mises A step of calculating ); a step in which the second subroutine loads a parameter regarding the current strain rate of the material model; and a step in which the second subroutine calculates the current time (t) according to the parameter k ) or, previous time (t k-1 From ) to current time(t k Strain rate of the material model up to ) A step of calculating ); the third subroutine calculates the stress (σ von-mises ) and strain rate( A step of calculating sensitivity (m) using ); a step in which the third subroutine calculates the power distribution efficiency (η) and CSI using the sensitivity (m); a step in which the third subroutine stores parameters regarding the power distribution efficiency (η); and, depending on the progress state of the forging process, the first subroutine calculates stress (σ von-mises Previous time (t) for ) calculation k-1 Stress (σ) at ) old ) stores, and the second subroutine is the strain rate ( Previous time (t) for ) calculation k-1 Strain rate at ) A method for visualizing a forging process using a deformation process map, comprising: a step of storing ); and a step of sequentially repeating, according to a preset interval, from the step of loading parameters regarding current stress to be input into the material model until the end of the forging process to the step of storing the calculated strain rate. Claim 4 In claim 3, the above stress (σ von-mises ) is a forging process visualization method using a deformation process map, which is calculated as Von mises stress. Claim 5 In claim 4, the strain sensitivity (m) is given by the following mathematical formula, A method for visualizing a forging process using a deformation process map, calculated as follows (wherein 'UVARM1' and 'UVARM2' are the output values ​​of the first and second subroutines, respectively) Claim 6 In claim 1 or claim 5, the power distribution efficiency (η) is given by the following mathematical formula, A forging process visualization method using a deformation process map, calculated as follows. Claim 7 In claim 1, the above CSI is the following mathematical formula, A forging process visualization method using a deformation process map, calculated as follows. Claim 8 A method for visualizing a forging process using a deformation process map, wherein the subroutine is implemented in ABAQUS.

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