KR100911629B1 - Method of prediction of Deformation Behavior and Interfacial Friction under Hot Working Conditions using Inverse Analysis - Google Patents

Abstract

The present invention provides a method for predicting deformation behavior of a material under hot forming conditions, comprising: a first step of obtaining experimental data through compression experiments according to different compression speeds; A second step of determining an objective function value determined by the load set through FEM simulation according to the experimental conditions in the first step and the assumption of the unknown coefficient of the flow stress function and the load of the experimental data in the first step; The second step is to determine the unknown coefficient of the flow stress function by repeating the second step until the objective function value of the second step satisfies the convergence condition. By performing the simulation, it is possible to determine the flow stress of the material and the friction between the tool and the material at the same time, so that the deformation behavior of the unknown material can be easily predicted, so that the parts industry or the material development can be used.

Molding condition, deformation behavior, prediction method, reverse engineering

Description

Method of prediction of Deformation Behavior and Interfacial Friction under Hot Working Conditions using Inverse Analysis}

1 is a flowchart showing a method for predicting deformation behavior of a material under molding conditions according to the present invention;

2 is a table showing the chemical composition of Nb-V steel and low carbon steel and high carbon steel,

Figure 3 (a) is a graph showing the experimental load of the Nb-V steel specimens at each compression rate at 900 ^° C,

Figure 3 (b) is a graph showing the test load of the Nb-V steel specimen at each compression rate at 950 ^° C,

Figure 4 (a) is a graph showing the experimental load of the low carbon steel specimens according to each compression rate,

Figure 4 (b) is a graph showing the experimental load of the high carbon steel specimens according to each compression rate,

Figure 5 (a) is a graph comparing the load through the FEM simulation using the experimental stress and the flow stress determined through reverse engineering for the Nb-V steel specimen at a compression rate of 0.40mm / sec, 900 ^o C ,

Figure 5 (b) is a graph comparing the load through the FEM simulation using the experimental stress and the flow stress determined through reverse engineering for the Nb-V steel specimen at a compression rate of 0.40mm / sec, 950 ^o C ,

Figure 6 (a) is a graph comparing the load through the FEM simulation using the experimental stress and the flow stress determined through reverse engineering for the low carbon steel specimen at a compression rate of 0.80mm / sec, 1000 ^o C,

FIG. 6 (b) is a graph comparing loads obtained by experiments with FEM simulations using flow stress determined through reverse engineering for high carbon steel specimens at a compression rate of 0.80 mm / sec and 1000 ^° C.

7 is a table showing the value of the undefined coefficient of the flow stress function of the Nb-V steel specimen obtained by reverse engineering,

8 (a) is a graph comparing the stress-strain curves predicted through reverse engineering with the stress-strain curves experimentally determined according to strain rates in Nb-V steel specimens at 900 ^° C.

8 (b) is a graph comparing the stress-strain curves predicted through reverse engineering with the stress-strain curves experimentally determined according to the strain rate in the Nb-V steel specimen at 950 ^° C.

Figure 9 (a) is a graph comparing the stress-strain curve predicted through the reverse engineering and the stress-strain curve according to the strain rate in the low carbon steel specimen at 1000 ^o C,

Figure 9 (b) is a graph comparing the stress-strain curve predicted through the reverse engineering and the stress-strain curve by the experiment according to the strain rate in the high carbon steel specimen at 1000 ^o C,

10 is a table showing the values of the shear friction factor according to each specimen obtained by reverse engineering,

11 is a comparison of the barreling shape through FEM simulation based on the experimental barreling shape and the friction factor predicted through reverse engineering for Nb-V steel specimens at 900 ^o C and the compression speed V of 0.40mm / sec. One Graph,

12 is a comparison of the barreling shape through FEM simulation based on the experimental barreling shape and the friction factor predicted through reverse engineering for Nb-V steel specimens at 950 ^° C and compression rate V of 0.40mm / sec. One Graph,

FIG. 13 is a graph comparing the barreling shape through FEM simulation based on the barreling shape according to the experiment and the friction factor predicted through reverse engineering for the low carbon steel specimen at 1000 ^o C and the compression rate V at 0.80 mm / sec. ,

FIG. 14 is a graph comparing the barreling shape through FEM simulation based on the barreling shape according to the experiment and the friction factor predicted through reverse engineering for the high carbon steel specimen at 1000 ^° C. and the compression rate V at 0.80mm / sec. ,

FIG. 15 (a) shows the stress-strain curve at each temperature and strain rate and the stress-strain curve predicted by Taheri and the stress measured in the experiment by the flow stress function in the low carbon steel predicted by reverse engineering. A graph comparing the strain curves,

 FIG. 15 (b) shows the stress-strain curve at each temperature and strain rate and the stress-strain curve predicted by Taheri and the stress measured in the experiment by the flow stress function in the high carbon steel predicted by reverse engineering. Graph comparing strain curves

(A) is a graph showing the measured value and the Taheri value and the value predicted by reverse engineering by experiment of dynamic recrystallization at 1000 ^° C., strain rate 0.5 / sec of low carbon steel,

FIG. 16 (b) is a graph showing the measured values, the Taheri values, and the values predicted by reverse engineering by experiments of dynamic recrystallization at 1000 ^° C. and strain rate 0.5 / sec of high carbon steel.

The present invention relates to a method for predicting the deformation behavior of a material under hot forming conditions, and more particularly to a method for predicting the deformation behavior of a material under hot forming conditions and surface friction between a tool and the material by using reverse engineering. .

In the prior art, a model representing the relationship between stress and strain has been proposed to approximate the actual experimental data, and various methods have been proposed for expressing flow characteristics at high temperatures, with particular emphasis on microscopic aspects.

R. Colas, High temperature deformation of low carbon steels, Mater . Forum 1990; 14: In 253, the flow stress is expressed by dynamic recovery before the critical deformation, dynamic recrystallization afterwards, and the flow stress is divided into two cases.

Also, recently, S. Serajzadeh and AK Taheri, Prediction of flow stress at hot working condition, Mech, Research Com . 30 (2003) pp.87-93. Modeled the flow stress of steel in the austenite range by applying the Bergstrom dislocation theory with the Avrami-type equation considering the effect of temperature changes, and added the effect of strain rate. In other words, in order to express the flow stress of steel in the Austenite range as temperature, strain rate, and strain, the flow stress to represent dynamic recovery and dynamic recrystallization by measuring the size of initial austenite crystals obtained from numerous experiments from a microscopic perspective Expressed. The model presented is a good representation of the flow and microstructural properties of the material during hot deformation.

However, according to the prior art, in the method of expressing the flow stress, the two cases should be expressed separately by the dynamic recovery before the critical deformation and afterwards by the dynamic recrystallization, and also in the model proposed by Taheri, Since the models of the flow stress are determined microscopically through numerous experiments, there are many problems in that it takes a lot of cost and energy to predict the flow stress of the unknown material for application to the actual metal forming process.

The present invention has been made to solve the above problems of the prior art, and through the compression experiment in the hot forming conditions of the material using reverse engineering, it is possible to predict the flow stress of the material and the friction conditions between the material and the tool at the same time It is an object of the present invention to provide a method of predicting the deformation behavior of a material under hot forming conditions that can express all the deformation ranges of the material from a macroscopic point of view.

In order to solve the above problems, a method of predicting deformation behavior of a material under molding conditions according to the present invention is performed in a conventional information processing apparatus, and includes a first input of experimental data through compression experiments according to different compression speeds. Step S10; The second step (S20) determines the objective function value determined by the load set through the FEM simulation according to the experimental conditions in the first step and the assumption of the unknown coefficient of the flow stress function and the load of the experimental data in the first step (S20). ); And a third step (S30) of determining the unknown coefficient of the flow stress function by repeating the second step until the objective function value of the second step satisfies the convergence condition.

In addition, the flow stress function in the second step is

,로 이루어지며,

Consisting of,

인 것을 특징으로 한다.here

It is characterized by that.

In addition, the objective function in the second step is

인 것을 특징으로 한다.

It is characterized by that.

In addition, the convergence condition in the second step is

및

인 것을 특징으로 한다.

And

It is characterized by that.

Further, the first step of determining the difference between the barreling shape determined by the FEM simulation according to the experimental conditions and the flow stress function and the assumed friction factor in the first step and the barreling shape extracted by the first step experiment. Step 4 (S40); And a fifth step S50 of determining the friction factor by repeating the fourth step until the difference in the area of the barrel shape determined in the fourth step satisfies the convergence condition. The test load in the above is a simulation result based on the flow stress of the test specimen used in the literature.

Hereinafter, the present invention is a method of determining a desired coefficient by minimizing the difference between a value determined from an experiment and a finite element analysis result, that is, a method of predicting deformation behavior of a material under hot forming conditions using reverse engineering techniques. With reference to the accompanying drawings will be described in detail a preferred embodiment of the present invention.

1 is a flowchart showing a method for predicting deformation behavior of a material under molding conditions according to a preferred embodiment of the present invention.

In the method for predicting deformation behavior of a material under molding conditions according to the present invention, as shown in FIG. 1, first, each ring specimen collects data through compression experiments according to different compression speeds (S10).

Low niobium-low vanadium steel, low carbon steel and high carbon steel were used as the material for the specimens.

Figure 2 shows a table showing the chemical composition of Nb-V steel and low carbon steel and high carbon steel, Figure 2 shows the chemical composition of each specimen used in the compression test, the outer diameter of this chemical composition 25mm x inner diameter 22.5mm x Ring specimens having a specification of 15 mm in height were used.

In this test, hot isothermal test conditions and no lubrication conditions were applied. In this experiment, Nb-V steels were tested to have three different compression rates at isothermal at 900 ^o C and 950 ^o C, and low carbon and high carbon steel at isothermal at 1000 ^o C.

Figure 3 (a) is a graph showing the load according to the test of the Nb-V steel specimens at each compression rate at 900 ^° C, Figure 3 (b) is Nb according to each compression rate at 950 ^° C -Graph showing the test load of the V-steel specimens, Figure 4 (a) is a graph showing the test load of the low carbon steel specimens according to each compression rate, Figure 4 (b) is a compression rate for each This is a graph showing the load by the experiment of high carbon steel specimens.

As shown in Figures 3 (a) and 3 (b), Nb-V steels were tested at lower rates of 0.09, 0.40, 2.50 mm / sec of the upper mold at isothermal temperatures of 900 ^o C and 950 ^o C. , The faster the compression rate of the upper mold, the lower the temperature.

And the experimental results according to the descending speed of 0.15, 0.80, 2.00mm / sec of the upper mold at 1000 ^o C of low carbon steel and high carbon steel is as shown in Figure 4 (a) and 4 (b).

However, the barreling geometry as experimental data uses results obtained from FEM simulations that apply flow stress values obtained by experiments in the literature, assuming appropriate friction factors.

After collecting the experimental data, as shown in the flow chart of FIG. 1, the conditions such as the compression speed and temperature are input, and the FEM simulation is performed assuming an initial unknown coefficient in the flow stress function (S20a).

The flow stress function (σ _f ) used here is defined as Equation 1 by combining the Arrhenius-type equation with the Zener-Hollomon variable combined with the dependence of the flow stress temperature and strain rate.

Here, each variable is as follows.

는 유효 변형률,

는 유효변형률 속도, Z'는 보완된 Zener-Hollomon 변수, T 는 절대온도, R은 기체상수, n, m, k, p, a ₀ - a ₇ 는 미정계수들이다. 상기 미정계수는 k, p는 유동응력이 변형률 속도에 더욱 민감하게 반응하도록 하기 위해 설정된 미정계수이고, 상기 n, m은 각각 변형률, 변형률 속도에 더욱 민감하도록 하기 위해서 설정된 미정계수이다. here

Is the effective strain,

Is the effective strain rate, Z 'is the complementary Zener-Hollomon variable, T is the absolute temperature, R is the gas constant, and n , m, k, p, a ₀ - a ₇ are the unknowns. K and p are unknown coefficients set to make the flow stress more sensitive to strain rate, and n and m are unknown coefficients set to be more sensitive to strain and strain rate, respectively.

Therefore, Equation 1 expressing the flow stress function including the above unknown coefficient is sensitive to softening phenomenon, strain rate, and molding temperature by dynamic recrystallization or dynamic recovery phenomenon in hot.

Subsequently, the objective function value is determined using the load obtained by the experiment (S10) and the load obtained through the FEM simulation (S20a). (S20b)

Here, the objective function is set as in Equation 2.

와

는 주어진 ｉ에서의 실험에 의한 측정값 및 예측된 하중을 각각 나타낸다. X ₁ , x ₂ ,... x _k is a rheological variable, n is the total number of measured data points, and the subscript i is the number of measured values. And

Wow

Represents the experimentally measured values and the predicted loads at given i, respectively.

Therefore, x ₁ , x ₂ ,... x _k is n , m, k, p, a ₀ -a ₇

Corresponds to

In the experiment (S10), Nb-V steel was experimented at three different compression rates, respectively, at an isothermal temperature of 900 ^° C. and 950 ^° C. Therefore, Equation 2 may be expressed by Equation 3.

In addition, since the low carbon steel and the high carbon steel were experimented to have three different compression rates at an isothermal temperature of 1000 ^° C., Equation 2 may be expressed by Equation 4.

Next, if the objective function value is determined by inputting the experimental load and the FEM simulation load into the equations (3) and (4), the target function value is repeated until the target convergence condition is satisfied (S30a). ).

Here, as a method of minimizing the objective functions of Equations 3 and 4, the BFGS (Broyden-Fletcher-Goldfarb-Shanno) and the golden splitting search (Golden-section) are used to directly update the Hessian matrix. Gradient methods, including search, are considered. And the convergence condition of the present invention is set by the equation (5) and (6).

Where s is the number of repetitions and ε ₁ and ε ₂ are both specific tolerances of 0.0001. Of course, the smaller the convergence condition in Equation 5, the more accurate the result can be obtained, but it was determined to be 0.0001 in consideration of the simulation calculation time.

Equation (6) is a convergence condition that does not satisfy the convergence condition so that the undetermined coefficient is set again and the undetermined coefficient can be determined when the amount of change every time the calculation is repeated becomes small.

As described above, when the objective function value set by the test load and the FEM simulation load satisfies Equations 5 and 6, the 12 undefined coefficients are determined to determine the flow stress function (S30b).

FIG. 5 (a) compares the loads through FEM simulation based on experimental loads and flow stresses determined by reverse engineering for Nb-V steel specimens at a compression rate of 0.40 mm / sec and 900 ^° C. One graph, FIG. 5 (b) shows the FEM simulation based on the experimental stress and the flow stress determined by reverse engineering for Nb-V steel specimens with compression speed of 0.40mm / sec and 950 ^° C. Figure 6 (a) shows a FEM simulation based on experimental stresses and flow stresses determined by reverse engineering for low carbon steel specimens at a compression rate of 0.80 mm / sec and 1000 ^o C. Fig. 6 (b) shows the FEM based on the experimental stress and the flow stress determined by reverse engineering for high carbon steel specimens with a compression rate of 0.80 mm / sec and 1000 ^o C. Graph comparing the load through the simulation, Figure 7 is due to reverse engineering This table shows the value of the unknown coefficient of the flow stress function of the solved Nb-V steel specimen.

As shown in the graphs of FIGS. 5A and 5B, 900 at the compression rate V = 0.40 mm / sec of the upper mold of Nb-V steel, respectively. ^o C and 950 ^o Loads are simulated based on load data (square points) measured at C and flow stresses predicted by reverse engineering. That is, from the first simulation value indicated by the dashed line, the first simulation represented by the dashed line, and finally after 17 iterations, the optimized value represented by the solid line is obtained, which is almost identical to the measured value. Could represent a value.

Likewise, FIGS. 6 (a) and 6 (b) show the measured load data and the predicted load at V = 0.80 mm / sec at 1000 ^° C. of the low and high carbon steel specimens.

In general, if the optimization technique is repeated within 15 times to satisfy convergence conditions in other steel grades, it may be almost identical to the actual experimental load data as shown in FIGS. 5 and 6.

Based on this, the flow stress function of the Nb-V steel specimen, that is, the unknown coefficient of Equation (1), is calculated as shown in FIG. 7 and the flow stress function of the Nb-V steel is determined.

8 (a) is a graph comparing the stress-strain curve predicted by reverse engineering with the stress-strain curve experimentally determined according to the strain rate in the Nb-V steel specimen at 900 ^° C., FIG. 8 (b) ) Is a graph comparing the stress-strain curve experimentally predicted by the reverse engineering with the strain-strain curve predicted by reverse engineering for the Nb-V steel specimen at 950 ^° C. FIG. 9 (a) is 1000 ^° C. Is a graph comparing the stress-strain curves and the predicted stress-strain curves according to the strain rate for the low carbon steel specimens in Fig. 9 (b) is an experiment according to the strain rate for the high carbon steel specimen at 1000 ^o C It is a graph comparing the stress-strain curve and the predicted stress-strain curve by.

When the flow stress curves are expressed by inputting strain rates 0.005, 0.05, 0.5, and 5 into the flow stress function of the Nb-V steel having the friction coefficient determined in the second step as described above, FIGS. As shown in FIG.

 Similarly, in FIGS. 9A and 9B, the flow stress functions assumed by reverse engineering of low carbon and high carbon steels in which strain rates of 0.01, 0.5, 1.0, and 1.5 are input to the stress function are measured. You can see that it almost matches the data value.

Furthermore, the present invention further comprises the step (S40a) of performing the FEM simulation through the experimental conditions and the determined flow stress function and the assumed friction factor.

Here, in the case of metal processing, when the large plastic deformation occurs between the material and the tool, the shear friction model that the friction is constant during the process is more appropriate than the Coulomb friction model. Since it is used, it is determined by equation (7).

과 같다. 여기서 σ _f 는 재료의 유동응력이다.Where τ _i is the shear strength of the contact surface and k is the shear yield stress of the soft material of the two contacts. When the shear strain energy yielding condition is reached, k is

Is the same as Where σ _f is the flow stress of the material.

10 is a table showing the values of the shear friction factor for each specimen predicted by reverse engineering.

The barrel reel shape of the specimen measured by the experiment in the first step is extracted and discretized using digital image processing (Sobel edge detect algorithm). The coordinates of the outer barrel shape obtained by the application of the edge detect algorithm are drawn by a composite 3 ^rd B-spline curve created by interpolation of point data.

Then, the difference between the area surrounded by the outer barrel ring shape through the experiment and the B-spline curve of the outer barrel ring shape calculated through FEM simulation is obtained (S40b).

Furthermore, by minimizing the difference between the areas of the two curves (S50a), the shear friction factor m _f is determined (S50b), and the shear friction factor through this experiment is shown in the table shown in FIG.

And, as shown in Figure 10, it can be seen that the shear friction factor is determined slightly differently depending on the compression rate. This illustrates the importance of reverse engineering according to the present invention in the light of the fact that reverse engineering is proposed on the basis of data from experiments.

11 is 900 ^o C, the compression velocity V is 0.40mm / sec in the Nb-V steel in a sample compared to the barrel ring shape predicted by the barrel and ring-shaped reverse engineering according to the experimental graph, FIG. 12 950 ^o C , A graph comparing the predicted barrel ring shape with the predicted barrel ring shape for Nb-V steel specimens at a compression speed of 0.40 mm / sec. FIG. 13 is 1000 ^o C and a compression speed of V is 0.80 mm / sec. A graph comparing the barrel ring shape according to the experiment and the predicted barrel ring shape in the low carbon steel specimen, FIG. 14 shows the barrel ring shape according to the experiment in the high carbon steel specimen at 1000 ^° C. and the compression speed V of 0.80 mm / sec. A graph comparing the predicted barreling shape.

11 to 14, it can be seen that the measured barrel ring shape and the predicted barrel ring shape at four points A, B, C, and D of the ring specimen are in close agreement with each other.

These results are predictable through minimizing the closed area by fitting the measured and calculated shapes to the B-spline curve.

In addition, the predicted inner and outer geometries of other steel grades are close to the measured geometries. These results indicate that the ring compression test indicates the presence of high friction during high temperature deformation and the greatest sensitivity to the shape of the specimen due to load and friction.

Therefore, the present invention can determine the load and friction at the same time through the reverse engineering technique through the compression experiment from the macroscopic perspective, it is a very suitable method to establish the friction model, and simultaneously establish the friction model and the rheological model have.

FIG. 15 (a) shows the stress-strain curves at the respective temperatures and strain rates and the stress-strain curves predicted by Taheri and the stress measured by the experiments by the flow stress function in the low carbon steel predicted by reverse engineering. Fig. 15 (b) shows the stress-strain curve at each temperature and strain rate and the stress-strain predicted by Taheri as a function of flow stress in high carbon steel predicted by reverse engineering. This is a graph comparing the stress-strain curve measured by the curve and the experiment.

The validity of the present invention is confirmed by comparison with the stress-strain curves presented by Taheri, as shown in FIGS. 15A and 15B according to respective temperatures and strain rates. It can be seen that the flow stress function predicted by the engineering is similar to the Taheri model presented previously.

FIG. 16 (a) is a graph showing the experimental measured value and the Taheri value and the predicted value by reverse engineering of the dynamic recrystallization process at 1000 ^° C. and the strain rate 0.5 / sec of the low carbon steel, and FIG. 16 (b) is the high carbon steel It is a graph showing the measured values of the dynamic recrystallization process and the Taheri values and the predicted values by reverse engineering at 1000 ^o C and strain rate 0.5 / sec.

 In addition, the expression of the metal flow by dynamic recovery and recrystallization is also shown to be similar to the model and the actual measurement presented by Taheri, as shown in Figs. 16 (a) and 16 (b).

This indicates that the flow stress function obtained by reverse engineering through compression experiments on the macro side effectively expresses the micro side.

In the method of predicting the deformation behavior of the material under the hot forming conditions of the present invention configured as described above, by performing FEM simulation by ring compression experiment and reverse engineering using the same, the flow stress and friction are simultaneously determined, such as glass. The flow stress at high temperature of materials without any data can be determined only by the load test data, and it can be applied not only to ring specimens but also to various types of specimens or compression tests, so that the deformation behavior of materials can be easily predicted and used in the parts industry or material development. There is an advantage that can be.

In addition, since the new flow stress function can be applied to the dynamic recrystallization process as well as the flow model during molding, there is an advantage that it is possible to predict the dynamic recovery and the recrystallization motion without the microstructural approach.

In addition, since the flow stress function considers the temperature and the strain rate together, there is an advantage of predicting the accurate flow stress.

In addition, the flow stress and friction conditions can be predicted only through compression experiments, thereby reducing energy and cost, as well as expressing all deformation ranges of the material in one equation, and the temperature, strain rate, and strain rate due to undefined coefficients. It can be supplemented to make it more sensitive to, so from a macro perspective, the dynamic recovery and recrystallization movement can be predicted.

Claims (7)

In the method of predicting deformation behavior for a material under hot forming conditions performed in a conventional information processing apparatus, A first step of receiving experimental data corresponding to a plurality of experimental conditions for the material; The objective determined by the load set by the finite element method ('FEM') simulation according to the experimental conditions in the first stage and the assumption of the undefined coefficient of the flow stress function, and the load of the experimental data in the first stage. Determining a function value; A third step of determining the unknown coefficient of the flow stress function by repeating the second step until the objective function value of the second step satisfies the convergence condition; Wherein, the experimental data is a result of performing a compression experiment on the material in accordance with the experimental conditions in advance, wherein the experimental conditions, the prediction method of the deformation behavior, characterized in that the compression speed. The method of claim 1, The flow stress function in the second step is

, Where each variable

Prediction method of deformation behavior, characterized in that. The method of claim 1, wherein the objective function in the second step is

Prediction method of deformation behavior, characterized in that. The method of claim 1, wherein the convergence condition in the third step is

And

Prediction method of deformation behavior, characterized in that. The method of claim 1, wherein the prediction method is A fourth step of determining the difference between the barreling shape determined by FEM simulation according to the experimental conditions and the flow stress function and the assumed friction factor in the first step and the barreling shape extracted from the experimental data of the first step. ; And A fifth step of determining the friction factor by repeating the fourth step until the difference in the area of the barrel shape determined in the fourth step satisfies a convergence condition; Method for predicting the deformation behavior further comprises. The method of claim 5, wherein the friction factor is a shear friction factor. delete

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