JP7571664B2 - Method, program, and device for predicting crack growth in plastic processing - Google Patents

Description

The present invention relates to a prediction method, program, and device for predicting the growth of cracks that occur in a workpiece during a plastic processing process. Note that plastic processing includes hot processing such as forging and rolling.

Nowadays, plastic processing is being carried out on workpiece materials in a variety of fields. There is a demand for analysis of cracks and consideration of countermeasures for cracks in workpiece materials used in this plastic processing. For example, super heat-resistant alloys used in aircraft engines and power generation gas turbines have the property of becoming embrittled at low temperatures, and their workability is highly dependent on temperature. For this reason, in the hot processing process of super heat-resistant alloys, there is a risk that cracks will occur during processing if the mold shape and processing conditions are not appropriate, which will increase the amount of correction work required for the processed product and cause defects. Therefore, in order to shorten product delivery times and stabilize quality, it is necessary to predict the location and size of cracks at the design stage and consider countermeasures to suppress cracks in advance.

Conventionally, a commonly known method for predicting cracks is to calculate an index for evaluating destruction using the finite element method and compare it with a threshold value to predict the location of crack occurrence. Regarding prediction of crack growth, Patent Document 1 discloses a method for determining the stress state under a specified load condition in a state where no crack has occurred, and then, in a state where a virtual crack exists that connects the end position and tip position of the crack with a straight line, determining a stress intensity factor that reflects the stress state in a state where no crack exists, and determining the direction of crack growth.

JP 2008-216184 A

Patent Document 1 describes a method for predicting crack propagation, but does not describe how to handle cracks when the material in the vicinity of the crack undergoes plastic deformation, so it is not possible to track changes in the direction of the crack due to plastic deformation. As a result, it is not possible to grasp the stress components acting on the crack, and the method cannot be applied in situations where the crack propagates along with the plastic deformation of the workpiece material.

As described above, Patent Document 1 was unable to predict the growth of cracks accompanying plastic deformation of the workpiece with high accuracy and in a short period of time.

The objective of the present invention is to make it possible to predict the location of crack initiation and its progression with high accuracy and in a short time, taking into account the state of plastic deformation of the workpiece when plastic processing is performed.

In order to achieve the above object of the present invention, the present invention provides a crack growth prediction method for predicting the growth of a crack that occurs in a workpiece during plastic processing, the method comprising the steps of:
Determining the occurrence of cracks in the workpiece;
Identifying a crack occurrence position where the crack has occurred;
After the plastic processing simulation:
Identifying a crack initiation step in the plastic processing simulation in which a crack occurs at the identified crack initiation position;
Identifying an initial crack initiation normal vector indicating a normal direction of the crack at the crack initiation step and the crack initiation position;
predicting the growth of the crack by identifying a crack normal vector in a simulation step after the crack generation step based on the initial crack generation normal vector;
This is a method for predicting crack growth.

The present invention also includes a crack growth prediction device that executes the crack growth prediction method, and a crack growth prediction program itself, which is a computer program that causes a computer to execute the crack growth prediction method, or a storage medium that stores the program.

The present invention makes it possible to predict the progression of defects during plastic processing more easily, i.e., with less calculation required and with high accuracy.

1 is a diagram showing the configuration of a crack growth prediction device according to one embodiment of the present invention; 1 is a flowchart showing an overall flow of a crack growth prediction method according to one embodiment of the present invention. 4 is a flowchart showing details of step S1 of the crack growth prediction method in one embodiment of the present invention. FIG. 4 is a diagram showing processing condition information used in one embodiment of the present invention. FIG. 13 is a diagram showing the relationship between a breakdown value and a simulation step when one embodiment of the present invention is applied. FIG. 13 is a diagram showing the arrangement of vectors that crack a crack surface when one embodiment of the present invention is applied. FIG. 2 is a diagram for explaining a process of rolling a ring with a cylindrical main roll and a cylindrical mandrel to which one embodiment of the present invention is applied. FIG. 13 is a diagram showing fracture values and crack growth evaluation values to which one embodiment of the present invention is applied. FIG. 13 is a diagram showing the normal direction identified in the crack generation step in step S4 of one embodiment of the present invention. FIG. 13 shows the normal directions identified in the simulation step following the crack initiation step in step S5 of one embodiment of the present invention. FIG. 11 illustrates the normal directions identified in the next simulation step of FIG. 10 in step S5 of one embodiment of the present invention.

Hereinafter, an embodiment of the present invention will be described with reference to the drawings. In this embodiment, a process in a simulation of plastic processing of a workpiece (plastic processing simulation) will be described. Here, a crack in this embodiment refers to a defect that progresses over time, such as a crack, a split, a tear, a fracture, or a breakage. Furthermore, progress refers to a state in a crack that changes over time, regardless of whether it is expressed as "progress" or "advancement," and may include the amount of progress or direction of progress, which indicates the size or length, as well as the shape.
<System Configuration>
First, FIG. 1 shows the configuration of a crack growth prediction device 100 for predicting crack growth in this embodiment. The crack growth prediction device 100 can be realized by a so-called computer. For this reason, the crack growth prediction device 100 has a processing unit 1100 that can be realized by an arithmetic device such as a CPU. The processing unit 1100 executes various calculations according to a plastic processing simulation program 1210 stored in a memory 1200. The contents of this will be described later. In addition, the plastic processing simulation program 1210 can be distributed via a network (not shown) or stored in the crack growth prediction device 100 via a storage medium that stores the program. Note that, as an example, the plastic processing simulation program 1210 is a set of a solver program and a postprocessor program. However, the plastic processing simulation program 1210 may be another program, and may be a set of other programs such as a preprocessor program. In addition, since the plastic processing simulation program is used in this embodiment for the purpose of predicting the growth of a crack, it may be called a crack growth prediction program.

The crack progression prediction device 100 also has an output unit 1300 that provides information to the user. This can be realized by a display monitor or the like. The crack progression prediction device 100 also has an input unit 1400 that accepts operations from the user. This can be realized by a pointing device such as a keyboard or a mouse. Here, the output unit 1300 and the input unit 1400 may be realized by a terminal device in a separate housing from the crack progression prediction device 100. In this case, the terminal device can be realized by a tablet, smartphone, or other device in addition to a PC.

The crack growth prediction device 100 further includes a storage device for storing various information. The storage device stores workpiece material characteristic information 1001, processing condition information 1002, and simulation result information 1003. The contents of these will be described later. Note that the storage device may be realized by a file system in a separate housing from the crack growth prediction device 100.

In the present embodiment, the crack growth prediction device 100 is described as a computer that executes processing according to software. However, the entire software or a part of the software may be realized by hardware such as a dedicated circuit or an FPGA (Field Programmable Gate Array).
<Crack growth prediction method>
Fig. 2 is a flowchart showing the overall process of the crack growth prediction method of this embodiment for predicting crack growth. The crack growth prediction method will be described below with reference to Fig. 2. Note that, in this case, the subject of each process is described as a processing unit 1100, but this is the process according to the plastic processing simulation program 1210 as described above.

In the following, first, an overview of the entire flowchart in FIG. 2 will be described, and then each step will be described in detail. In step S1, the processing unit 1100 starts a plastic processing simulation that reproduces a specified processing method. To this end, the processing unit 1100 accepts a simulation instruction input by a user via the input unit 1400. Then, the processing unit 1100 calculates the fracture value of the processed material included in the simulation instruction.

Next, in step S2, the processing unit 1100 identifies as candidate positions material points (positions) where the fracture value calculated in step S1 exceeds a preset threshold value in the final step of the plastic processing simulation. The processing unit 1100 then determines, from among these, the candidate position selected by the user via the input unit 1400 from among the identified candidate positions, as the crack occurrence position. Note that the processing unit 1100 may identify one candidate position and determine this as the crack occurrence position.

Next, in step S3, the processing unit 1100 identifies the simulation step in which the fracture value exceeds the threshold value for the first time at the crack occurrence position determined in step S2 as the crack occurrence step.

Next, in step S4, the processing unit 1100 identifies the normal direction in which the crack occurred in the crack occurrence step at the crack occurrence position. This normal direction is the normal direction to the crack surface, and can be realized by identifying the crack normal vector (same below).

Next, in step S5, the processing unit 1100 identifies the normal direction of the crack in each simulation step after the crack occurrence step. In other words, the processing unit 1100 identifies the normal direction of the crack in each simulation step after the simulation step in which the fracture value exceeds the threshold value for the first time. This makes it possible to predict cracks in the workpiece.

Then, in step S6, the processing unit 1100 calculates an evaluation value of crack growth for the workpiece using the processing results up to step S6. This evaluation value is a parameter that indicates the degree of crack growth, and is correlated with the depth of crack growth. The calculation of the evaluation value in step S6 may be omitted. This completes the explanation of the entire crack growth prediction method. Below, the details of each step in the crack growth prediction method will be explained. The details of each step will be explained in the following order. First, the details of step S1 will be explained using FIG. 3. Next, the details of steps S2 to S6 will be explained.
<<Step S1: Breakdown value calculation process>>
In step S1, the processing unit 1100 calculates a fracture value in the workpiece according to the flowchart showing the details of step S1 of the crack growth prediction method in this embodiment shown in Fig. 3. This fracture value is an evaluation index for crack generation. Therefore, by using this fracture value, it is possible to determine whether or not a crack will occur.

First, in step S1001, the processing unit 1100 reads the pre-machining shape of the workpiece and the die shape included in the simulation instructions from the workpiece characteristic information 1001. For example, if the processing is rolling, the roll shape is read as the die shape. Thus, in this step, the processing unit 1100 reads information indicating the processing characteristics of the workpiece.

Next, in step S1002, the processing unit 1100 reads the stress-strain curve and thermal properties of the workpiece from the workpiece characteristic information 1001. For example, the thermal properties may be the density, thermal conductivity, emissivity, etc. of the workpiece. Thus, in this step, the processing unit 1100 reads information indicating the characteristics of the workpiece itself. Furthermore, the workpiece characteristic information 1001 includes information indicating the processing characteristics of the workpiece and information indicating the characteristics of the workpiece itself.

Next, in step S1003, the processing unit 1100 reads a crack growth prediction model from the workpiece material characteristic information 1001. This crack growth prediction model information includes a calculation formula for the fracture value C, which is an index for evaluating the occurrence of a crack, a threshold value C0, which is a threshold value for the index used to determine the occurrence of a crack, and a calculation formula for crack growth.

Next, in step S1004, the processing unit 1100 reads the processing conditions for the workpiece from the processing condition information 1002. This processing condition information 1002 is shown in FIG. 4. As shown in FIG. 4, the processing conditions can include the heating temperature of the workpiece, the time from when the workpiece is removed from the heating furnace to when it is placed in the processing machine, the reduction speed during processing, and the reduction amount. Also, if the processing is rolling, the number of rotations of the rolls can be used. Note that in this embodiment, at least one of these can be used as the processing condition.

Next, in step S1005, the processing unit 1100 divides the shape of the workpiece and the shape of the die read in step S1001 into elements of the finite element method.

Next, in step S1006, the processing unit 1100 divides the processing time into multiple time segments, i.e., into each simulation step in the plastic processing simulation.

Next, in step S1007, the processing unit 1100 calculates state information for each simulation step i divided in step S1006 by the finite element method (more specifically, state information of elements in the finite element method obtained in the plastic processing simulation) based on the information read in steps S1001 to 1005. As state information, for example, the maximum principal stress σ_max, the von Mises equivalent stress σ_eff, the equivalent plastic strain ε, and the stress component σ are calculated. Note that examples of the stress component σ include σ_xx, σ_yy, σ_zz, σ_xy, σ_yz, and σ_xz. The processing unit 1100 then stores the resulting state information in the storage device or memory 1200.

Next, in step S1008, the processing unit 1100 calculates the destruction value C(i) in each simulation step i divided in step S1006. For this purpose, the processing unit 1100 applies the state information of each simulation step i to the crack growth prediction model read in step S1003 to perform the calculation. The processing unit 1100 also calculates this destruction value C(i) for each element in the finite element method. Then, the processing unit 1100 records the calculated destruction value C(i) in the memory 1200. This ends the processing of step S1.
<<Step S2: Determining Crack Occurrence Position>>
In step S2, the processing unit 1100 identifies the destruction value C(n) of each element in the final simulation step of the plastic processing simulation from each destruction value C(i) calculated in step S1. Then, the processing unit 1100 compares the destruction value C(n) with a threshold value C0 previously set in the storage device. As a result, a position showing a destruction value C(n) equal to or greater than the threshold value C0 is identified as a candidate position. Then, the output unit 1300 outputs this candidate position and the corresponding destruction value C(n). In response to this output, the processing unit 1100 determines one or more candidate positions designated by the user via the input unit 1400 as crack occurrence positions. As described above, the processing unit 1100 may automatically determine the crack occurrence position.

As a result, it is desirable for the processing unit 1100 to record the determined crack occurrence position in the memory 1200. Note that the crack occurrence position in this embodiment refers to the element itself of the finite element method where a crack occurs, that is, the element shows a destruction value C(n) equal to or greater than the threshold value C0, a position within the element, or a contact point on the boundary surface between elements.
<<S3: Crack Generation Step Identification Step>>
In step S3, the processing unit 1100 proceeds with the plastic processing simulation, and obtains the relationship between the fracture value C(i) at the crack occurrence position determined in step S2 and each simulation step i divided in step S1006. As a result, the processing unit 1100 obtains the relationship between the fracture value and the simulation step shown in FIG.

Then, the processing unit 1100 identifies the simulation step i where the fracture value C(i) at the crack occurrence position first becomes equal to or greater than the threshold value C0. In other words, the processing unit 1100 identifies the simulation step i that satisfies the relationship between (Equation 1) and (Equation 2). Note that the fracture value C(i) has the property of monotonically increasing with the passage of time, that is, with the progress of the simulation steps.

<<S4: Step of Specifying Normal Direction of Crack in Crack Generation Step>>
Next, step S4 will be described with reference to FIG. 9. FIG. 9 is a diagram showing the normal direction identified in the crack generation step in step S4. In FIG. 9, (a) is a schematic representation of the workpiece as a cube, which is composed of elements (shown in FIG. 9(a) as regions separated by solid lines separating the cubes; the same applies hereinafter). In FIG. 9(a), there are 5×5=25 elements exposed to the front of the page. Among these, the section A is used as an example, that is, (b) is used to explain the identification of the normal direction in the crack generation step.

First, in step S4, the processing unit 1100 uses state information about the crack occurrence position in the simulation step in which the fracture value C(i) becomes equal to or greater than the threshold value C0 for the first time at the crack occurrence position determined in step S2 to identify the crack normal vector N0 in that step. In this embodiment, the crack normal vector N0 is identified by taking as an example a case in which a crack occurs perpendicular to the maximum principal stress direction. The crack normal vector N0 is also referred to as the crack occurrence normal vector.

In the example shown in FIG. 9(b), simulation step i=10 is the crack occurrence step. Also, it is assumed that the crack occurrence position determined in step S2 is located at the upper center of cross section A. Furthermore, tension (stress), which is the cause of crack occurrence, is applied to cross section A. Therefore, at the crack occurrence position, maximum principal stress according to tension occurs in opposing directions. Note that the coordinate axes in FIG. 9(b) are as shown. Using state information regarding the crack including this maximum stress, the processing unit 1100 identifies the crack normal vector N0 in the crack occurrence step shown in FIG. 9(b).

Then, the processing unit 1100 records the crack normal vector N0 in the memory 1200. Note that, although an example is shown here that assumes that the crack occurs perpendicular to the maximum principal stress direction, if there is another method for determining the crack initiation normal direction of the crack surface in the crack initiation step, that method may be used. In this way, the processing unit 1100 can identify the normal direction of the crack in the crack initiation step.

Then, the processing unit 1100 can identify the crack in-plane vector U0 and the crack in-plane vector V0 that define the crack normal vector N0 from the crack normal vector N0. Here, in this embodiment, the identification of these crack in-plane vector U0 and crack in-plane vector V0 is performed in step S5. Note that in FIG. 9(b), the crack in-plane vector U0 is oriented perpendicular to the drawing.

In addition, in this embodiment, the crack in-plane vector V0 is a vector whose end point is another adjacent element as shown in the figure. However, it is not limited to another element, and may be within the same element as the starting point.

In the examples of Figures 9 to 11, for the sake of simplicity, the crack in-plane vector U0 is perpendicular to the paper surface of the drawing, and is not shown in Figures 10 and 11. Various methods for identifying the crack in-plane vector U0 and the crack in-plane vector V0 can be assumed, and one example will be described in the detailed description of step S5.
<<S5: Calculation process of the normal direction of the crack after the crack generation step>>
In step S5, the normal direction of the crack after the crack occurrence at the crack occurrence position is obtained. First, the processing unit 1100 identifies a crack in-plane vector U0 and a crack in-plane vector V0 that are perpendicular to the crack normal vector N0 identified in step S4 and have different directions from each other. For this purpose, an example is shown in Figure 6. Here, the starting points of the vectors U0 and V0 are at the crack occurrence position, so the crack surface can be defined by the starting points and end points of the crack in-plane vector U0 and the crack in-plane vector V0.

Here, a method for identifying these crack in-plane vectors U0 and V0 will be described. The processing unit 1100 determines the crack in-plane vector U0 and V0 so as to satisfy the relationship in (Equation 3), so that they can be used as vectors that define the crack surface because they are perpendicular to the crack normal vector N0 and are not in the same direction (including not being in the opposite direction by 180 degrees). In other words, the crack normal vector N0 can be defined as the cross product of the crack in-plane vector U0 and the crack in-plane vector V0.

In addition, the crack in-plane vector U0 and the crack in-plane vector V0 must satisfy the following (Equation 4) and (Equation 5).

Here, although there are an infinite number of solutions for (Equation 4) and (Equation 5), the processing unit 1100 can identify a solution that uniquely indicates the crack in-plane vector U0 and the crack in-plane vector V0 by establishing rules for how to determine the crack in-plane vector U0 and the crack in-plane vector V0. In this embodiment, the processing unit 1100 sets the rules shown in the following (Equation 6) to (Equation 8).

Note that N0x, N0y, and N0z are the x, y, and z components of the crack normal vector N0, and U0x, U0y, and U0z are the x, y, and z components of the crack in-plane vector U0. Here, using equations 6 to 8, the processing unit 1100 calculates the x, y, and z components of the crack in-plane vector U0.

Then, the processing unit 1100 uses the crack normal vector N0 as the rotation axis and repeatedly rotates the vector U0 by the angle θ to obtain a vector that is perpendicular to the crack normal vector N0 and does not have the same direction as the vector U0. In this way, the processing unit 1100 can obtain candidates for the crack in-plane vector U0 and the crack in-plane vector V0. Note that the angle θ can be set as an input condition, and can be input via the input unit 1400 and recorded in the memory 1200 when, for example, the crack growth prediction model is loaded in step S1003. In addition, when determining the crack in-plane vector U0 and the crack in-plane vector V0, other examples may be used as long as they satisfy the relationship shown in (Equation 3).

Furthermore, the end points of the crack in-plane vector U0 and the crack in-plane vector V0 define the crack surface at each simulation step from the crack generation step to the final step of the plastic processing simulation. For this reason, it is necessary to set positions inside the workpiece as the end points. Therefore, the processing unit 1100 determines whether the candidate end points of the crack in-plane vector U0 and the crack in-plane vector V0 are points inside the workpiece. Then, the processing unit 1100 selects two candidate positions within the workpiece from among the candidate end points. In other words, the processing unit 1100 identifies one end point each for the crack in-plane vector U0 and the crack in-plane vector V0.

Furthermore, the processing unit 1100 may select the candidate end points by, for example, selecting the candidate end points closest to the start point in order of shortest distance.

The direction of the crack normal vector N0 depends on the magnitude of the crack in-plane vector U0 and the in-plane vector V0, so it is preferable for the processing unit 1100 to set these to a predetermined magnitude that has been set in advance. In other words, the processing unit 1100 takes the magnitudes du and dv of the crack in-plane vector U0 and the crack in-plane vector V0 as input conditions. The processing unit 1100 then calculates the crack in-plane vector U0 and the crack in-plane vector V0, which are recorded in advance in the memory 1200, so that they are the same magnitude as the input conditions du and dv. In the following explanation, each vector and position in the crack generation step may be referred to with the word "initial" added. For example, they may be referred to as the initial crack in-plane vectors U0 and V0, and the initial crack normal vector N0.

Next, the processing unit 1100 identifies the crack in-plane vector U(i) and the crack in-plane vector V(i) in each simulation step from the crack generation step to the final step of the plastic processing simulation. This identification is performed by identifying the positions after displacement of the end points of the initial crack in-plane vectors U0 and V0 in each simulation step, and calculating the crack in-plane vector whose end point is the position after the displacement. The displacement of the end point position is obtained by utilizing the fact that in plastic processing simulation using the finite element method, the deformation and displacement of each element are calculated for each simulation step.

Then, the processing unit 1100 uses these to identify the normal vector N(i) of the crack surface for each simulation step using (Equation 9) and records it in the memory 1200.

Here, a specific example of identifying the crack in-plane vector U(i) and the crack in-plane vector V(i) will be described with reference to Figures 10 and 11. Figure 10 shows the normal direction identified in the simulation step (i = 11) following the crack generation step in step S5.

In the simulation step (i=11), the cross section A is deformed by tension. The processing unit 1100 then identifies the crack in-plane vector U (i=11) and the crack in-plane vector V (i=11) in accordance with the deformation of the cross section A. In other words, the cross section A is crushed in the vertical direction on the drawing from FIG. 9 to FIG. 10. Therefore, the processing unit 1100 identifies the crack in-plane vector V whose end point is a position displaced by the deformation amount of the crack in-plane vector V0. The processing unit 1100 identifies the end point of the crack in-plane vector U (i=11) as the same as the end point of the crack in-plane vector U0, since the crack in-plane vector U0 is in a direction that is not affected by tension.

In this way, in step S5, the processing unit 1100 identifies the end point of the crack in-plane vector according to the cause of the crack, such as tension, and uses this to identify the crack surface or crack normal vector N(i). Note that this identification of the crack surface or crack normal vector N(i) is merely an example and is not limited to this.

Then, the processing unit 1100 applies the crack in-plane vector V (i = 11) and the crack in-plane vector U (i = 11) to equation 9 to identify the crack normal vector N (i = 11). In this way, the processing unit 1100 can identify the crack propagation direction. This crack normal vector N (i = 11) is in the direction shown in Figure 10.

Furthermore, the processing unit 1100 calculates the amount of crack growth using (Equation 10) and (Equation 11).

As a result, the processing unit 1100 can predict that the crack has progressed to the crack advancement tip, which indicates the tip of the crack advancement direction, by the amount of progress shown by D (i = 11) in Figure 10.

Note that (Equation 10) and (Equation 11) are merely examples, and other formulas and other conditions may be used.

Then, the above process is executed at each simulation step. FIG. 11 is a diagram showing the normal direction identified at the simulation step next to FIG. 10. In FIG. 11, cross section A is further crushed than the cross section shown in FIG. 10 due to tension. Therefore, in response to this deformation, the processing unit 1100 identifies the crack in-plane vector V(i=12) that is more horizontal (parallel) on the figure than the crack in-plane vector V(i=11). As a result, the processing unit 1100 identifies the normal vector N(i=12) that is more downward on the figure than the normal vector N(i=11). In addition, the processing unit 1100 identifies the crack advance destination in simulation step i=12 as the position advanced from i=11 as shown in the figure.

Thus, in this embodiment, in steps S4 and S5, the processing unit 1100 executes the following processes.
(1) In the crack initiation step, identify the normal vector N0 from the state information.
(2) From this normal vector N0, identify the crack in-plane vector U0 and the crack in-plane vector V0.
(3) The crack in-plane vector U(i) and the crack in-plane vector V(i) in the next simulation step are determined from the crack in-plane vector U0 and the crack in-plane vector V0, taking into account deformation and displacement due to factors such as tension.
(4) Next, identify the normal vector N(i) from the crack in-plane vector U(i) and the crack in-plane vector V(i) at each simulation step.
(5) (3) and (4) are repeated and executed for each simulation step, thereby continuously and propagatingly identifying the normal vectors of each simulation step. As described above, the processing unit 1100 calculates the crack normal vectors in each simulation step from the crack generation step to the final step of the plastic processing simulation using the start and end points of the crack in-plane vector U0 and the crack in-plane vector V0. Then, the processing unit 1100 records this in the memory 1200. Note that the processing unit 1100 may calculate the start points of the crack in-plane vector Ui and the crack in-plane vector Vi in each simulation step, or may reuse the start points of the crack in-plane vector U0 and the crack in-plane vector V0. Furthermore, in this embodiment, the end points of the crack in-plane vector U0 and the crack in-plane vector V0 are set to be in different elements from the start points, but they may be in the same element.

In addition, in step S4, the processing unit 1100 can also identify the local deformation and rotation of the workpiece in the vicinity of the crack initiation position, for example, by the deformation gradient tensor or displacement gradient tensor of continuum mechanics. This allows the processing unit 1100 to identify the normal direction of the crack after the crack initiation step, that is, the crack normal vector N(i), in step S5.

For example, the deformation gradient tensor when the shape of the workpiece in simulation step i=1 is set as the reference configuration and the shape of the workpiece in simulation step i=2 is set as the current configuration is denoted as F, and the tensor obtained by transposing the deformation gradient tensor and taking the inverse matrix is denoted as F^(-T). In this case, the crack normal vector N(i=2) at i=2 can be expressed by applying F^(-T) to the crack normal vector N(i=1) at i=1. Specifically, the processing unit 1100 identifies the normal vector N(i=2) using the history of the following fracture condition equation (Equation 12).

In this embodiment, the time-related parameters are defined in the simulation step (i), but time or instant (t) may also be used.
<<S6: Calculation process of evaluation value of crack growth>>
In step S6, the processing unit 1100 obtains a unit normal vector from the normal vector N(i) of the crack at each simulation step up to the final step of the plastic processing simulation at the crack occurrence position. Then, the processing unit 1100 calculates a stress vector acting on the crack surface from the stress components σ_xx, σ_yy, σ_zz, σ_xy, σ_yz, σ_xz at the crack occurrence position and the unit normal vector. Then, the processing unit 1100 calculates an evaluation value of the crack growth using the calculation formula of the crack growth read in step S1003. It is preferable that the processing unit 1100 records the evaluation value in the memory 1200. Then, it is preferable that the processing unit 1100 records the results of each process (step) including the evaluation value as simulation result information 1003. Furthermore, it is preferable that the output unit 1300 outputs the simulation result information 1003.
<Verification example>
This embodiment is applicable to ring rolling. Among them, an example of application of this embodiment to a Ni-based alloy, which is relatively prone to cracks in a hot ring rolling process, will be described.

After heating a rectangular workpiece 1 made of a Ni-based alloy to 900°C, the occurrence of cracks was judged by a plastic processing simulation of the process of rolling a ring with a cylindrical main roll 2 and a cylindrical mandrel 3 shown in Figure 7. The dimensions of the workpiece 1 are inner diameter: 450 mm, outer diameter: 600 mm, and height: 500 mm.

Here, the following (Equation 13) to (Equation 18) are used as the calculation formula for the destruction value C and the calculation formula for the crack growth, respectively. Note that here, the threshold value C0 is equal to 1, and if the destruction value C exceeds 1, it is determined that a crack has occurred. Furthermore, this determination can be performed by the processing unit 1100 of the crack growth prediction device 100 of this embodiment.

where Cc is the temperature-dependent characteristic threshold.

Here, σ_c is the normal stress component acting on the crack surface.

In the final step of the simulation, point P1 on the inner corner of the upper end face of the ring was selected from the points where the fracture value C exceeded the threshold value C0, and crack growth was evaluated at P1. Figure 8 shows the history of fracture value C and crack growth evaluation value at P1. It was confirmed that the crack growth evaluation value could be calculated after the time when the fracture value exceeded the threshold value, and that crack growth could be easily predicted without modifying the finite element model.

The present invention is not limited to the above-described embodiment, but includes various modified examples. For example, the above-described embodiment has been described in detail to explain the present invention in an easy-to-understand manner, and is not necessarily limited to having all of the configurations described. In addition, it is possible to replace a part of a certain configuration of this embodiment with a different configuration. It is also possible to add other configurations to the configuration of this embodiment. In other words, it is possible to add, delete, or replace other configurations with respect to part of the configuration of this embodiment.

According to one embodiment of the present invention, the crack normal direction at the time of crack occurrence is identified and the coordinates of the vector defining the crack surface at that time are recorded, so that the normal direction of the crack surface after crack occurrence can be tracked and crack progression can be evaluated.

1 Workpiece, 2 Main roll, 3 Mandrel, 100 Crack growth prediction device, 1100 Processing unit, 1200 Memory, 1210 Plastic processing simulation program, 1300 Output unit, 1400 Input unit, 1001 Workpiece characteristic information, 1002 Processing condition information, 1003 Simulation result information

Claims (13)

A method for predicting the progress of a crack that occurs in a workpiece during plastic processing, comprising:
Simulation of the plastic processing for the above-mentioned plastic processing:
Determining the occurrence of cracks in the workpiece;
Identifying a crack occurrence position where the crack has occurred;
After the plastic processing simulation:
Identifying a crack initiation step in the plastic processing simulation in which a crack occurs at the identified crack initiation position;
Identifying an initial crack initiation normal vector indicating a normal direction of the crack at the crack initiation step and the crack initiation position;
predicting the growth of the crack by identifying a crack normal vector in a simulation step after the crack generation step based on the initial crack generation normal vector;
Crack growth prediction method. The crack growth prediction method according to claim 1,
The crack initiation step is identified based on a history of a fracture condition formula.
Crack growth prediction method. The crack growth prediction method according to claim 1,
With respect to the crack generating step:
Identifying the initial crack initiation normal vector using state information on the crack initiation position obtained by the plastic processing simulation;
Identifying multiple in-plane vectors of the initial crack that satisfy all of the following requirements:
is perpendicular to the crack initiation normal vector,
The crack initiation position is the starting point, and the end point is within the workpiece,
Each is in a different direction,
Crack growth prediction method. The crack growth prediction method according to claim 3,
For each simulation step after the crack initiation step:
Identifying a position after displacement of an end point of the initial crack in-plane vector in the simulation step;
Identifying a crack in-plane vector whose end point is the position after the displacement;
Identifying a crack normal vector based on the crack in-plane vector;
A prediction of the growth of the crack is performed based on the crack normal vector.
Crack growth prediction method. The crack growth prediction method according to claim 3,
In the plastic processing simulation, the workpiece is divided into a plurality of elements using a wire element method;
A method for predicting crack growth during plastic processing, wherein the end points and start points of the multiple initial crack in-plane vectors are within the same element. The crack growth prediction method according to claim 3,
A method for predicting crack propagation during plastic processing, in which a pre-specified crack in-plane vector is repeatedly rotated a predetermined angle around the crack initiation normal vector as a rotation axis, thereby identifying the multiple candidate positions. A crack growth prediction program that causes a computer to execute the crack growth prediction method according to any one of claims 1 to 6. A crack growth prediction device having a processing unit and a memory storing a plastic processing simulation program, which predicts the growth of a crack that occurs in a workpiece during plastic processing, comprising:
The processing unit executes the plastic working simulation program to:
Simulation of the plastic processing for the above-mentioned plastic processing:
Determining the occurrence of cracks in the workpiece;
Identifying a crack occurrence position where the crack has occurred;
After the plastic processing simulation:
Identifying a crack occurrence step in the plastic processing simulation in which a crack occurs at the identified crack occurrence position;
Identifying an initial crack initiation normal vector indicating a normal direction of the crack at the crack initiation step and the crack initiation position;
predicting the growth of the crack by identifying a crack normal vector in a simulation step after the crack generation step based on the initial crack generation normal vector;
Crack growth prediction device. 9. The crack growth prediction device according to claim 8,
The processing unit identifies the crack occurrence step based on a history of a fracture condition equation.
Crack growth prediction device. 9. The crack growth prediction device according to claim 8,
The processing unit, in relation to the crack generating step,
Identifying the initial crack initiation normal vector using state information on the crack initiation position obtained by the plastic processing simulation;
Identifying multiple in-plane vectors of the initial crack that satisfy all of the following requirements:
is perpendicular to the crack initiation normal vector,
The crack initiation position is the starting point, and the end point is within the workpiece,
Each is in a different direction,
Crack growth prediction device. The crack growth prediction device according to claim 10,
The processing unit, for each simulation step after the crack initiation step,
Identifying a position after displacement of an end point of the initial crack in-plane vector in the simulation step;
Identifying a crack in-plane vector whose end point is the position after the displacement;
Identifying a crack normal vector based on the crack in-plane vector;
A prediction of the growth of the crack is performed based on the crack normal vector.
Crack growth prediction device. The crack growth prediction device according to claim 10,
The processing unit includes:
In the plastic processing simulation, the workpiece is divided into a plurality of elements using a wire element method;
A crack propagation prediction device in plastic processing, wherein the end point and start point of the multiple initial crack in-plane vectors are within the same element. The crack growth prediction device according to claim 10,
The processing unit includes:
A crack propagation prediction device for plastic processing that identifies the multiple candidate positions by repeatedly rotating a pre-specified crack in-plane vector by a predetermined angle around the crack initiation normal vector as a rotation axis.

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