JP5149894B2 - Simulation method, simulation program, and simulation apparatus for ultrasonic bonding between metals - Google Patents

Description

  The present invention relates to a method for simulating ultrasonic bonding between metals, a simulation program, and a simulation apparatus.

When joining the same kind or different kinds of metals, there is a technique for melting and joining the metal surfaces by increasing the temperature such as welding.
On the other hand, there is also a technique (ultrasonic bonding technique) in which the same or different metals are bonded to each other by causing a metal-to-metal bond by applying a load that vibrates at high speed to the bonding portion between the metals. The present invention belongs to the latter.

  Normally known physical property values of metals are measured by pulling metals at a speed of several m / sec. Therefore, as in the case of ultrasonic caulking, which is one of the ultrasonic bonding techniques, the physical property values in the case where different kinds of metals are bonded to each other by causing the ball to collide with the portion to be bonded at several tens of kHz (such as this) Such physical properties are referred to as “high-speed strain rate-dependent physical properties”). For this reason, there is a problem that it is impossible to simulate the joining strength (also referred to as “loosening torque” or “caulking torque”) and the deformation amount (warpage amount) of the metal to be joined.

  Advantages of using ultrasonic caulking include that the bonding strength between metals is large and that the amount of deformation (warpage) of the metal is small compared to normal ball caulking. However, for example, in the current simulation, there is a problem that the normal ball caulking can obtain a larger bonding strength than the ultrasonic caulking, and the actually measured phenomenon cannot be reproduced by the simulation. Note that “normal ball caulking” is a technique in which a ball collides (deforms) only once with a metal-joined portion.

Although different from the technique related to ultrasonic bonding, Patent Document 1 discloses a technique for evaluating the reliability (strength) of a solder joint.
WO 2006/100741 “Electronic Package Evaluation Device, Electronic Package Optimization Device, and Computer-Readable Recording Medium Recording Electronic Package Evaluation Program”

  An object of the present invention is to provide a simulation method, a simulation program, and a simulation apparatus for ultrasonic bonding between metals capable of simulating bonding strength with high accuracy in ultrasonic bonding between metals. And

  The simulation method for ultrasonic bonding according to the first aspect of the present invention is an ultrasonic bonding simulation method for executing a simulation for ultrasonic bonding of a first metal and a second metal. In this method, a stress calculating step for calculating stress at each point in the first and second metal elements at each time, and a joint node for calculating the number of nodes entering the other metal by displacement based on the stress. In the case where there is a node entering the other metal in the score calculation step, the friction coefficient between the first and second metals in the high-speed strain rate region is associated with the number of nodes entering the other metal. Based on the virtual friction coefficient storage unit that stores the virtual friction coefficient, the virtual friction coefficient for obtaining the friction coefficient between the first and second metals in the high-speed strain rate region corresponding to the number of nodes entering the other metal An acquisition step.

  Here, when a high-speed vibration is applied as a load to the joint between the metals, and a certain range of one metal (first metal) enters the other metal (second metal), The coefficient of friction between the first and second metals is acquired according to the number of nodes included in a certain range of one metal. Therefore, the joining strength such as the loosening torque proportional to the friction coefficient can be simulated with high accuracy.

  The simulation method for ultrasonic bonding according to the second aspect of the present invention is an ultrasonic bonding simulation method for executing a simulation for ultrasonic bonding of a first metal and a second metal. In this method, a stress calculating step for calculating stress at each point in the first and second metal elements at each time, and a joint node for calculating the number of nodes entering the other metal by displacement based on the stress. In the score calculation step and the surface of the element including the node entering the other metal, the sum of the absolute values of the stresses of the nodes entering the other metal in the surface is added to the other metal in the surface. A contact pressure average value calculating step of calculating a contact pressure average value by dividing by the number of entering nodes;

  Here, when high-speed vibration is applied as a load to the joint between the metals, and one metal (first metal) locally enters the other metal (second metal), The contact pressure average value is calculated by averaging only the nodes having a large stress value included in the local range of one metal. Therefore, it is possible to simulate the bonding strength such as the loosening torque proportional to the contact pressure average value with high accuracy.

  ADVANTAGE OF THE INVENTION According to this invention, when joining metals mutually ultrasonically, it becomes possible to simulate joining strength with high precision.

It is the figure which showed two metal used as a simulation object, the ball | bowl collided periodically with those junction parts, and the horn which periodically plucks the ball | bowl. It is sectional drawing (the 1) which showed the junction part of an arm and a baseplate in detail. It is sectional drawing (the 2) which showed the junction part of an arm and a baseplate in detail. It is a block diagram which shows the structure of the ultrasonic bonding simulation apparatus between the metals which concern on one Embodiment of this invention. It is the figure which showed the stress-strain curve. It is a perspective view which shows an example of the element set on the metal. It is sectional drawing which shows an example of a joining area | region. It is a figure which shows an example of the node which entered in the other element. It is a figure which shows the data structure of the virtual friction coefficient data of FIG. It is a flowchart of the calculation process of the stress which arises in each point of each element of a baseplate. It is a figure which shows an example of a simulation result. It is a figure which shows the example of a storage medium.

Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings.
In the following, a technique for crimping (deforming) a metal using ultrasonic waves will be described. However, the present invention uses other techniques (such as wire bonding) for joining the same or different metals using ultrasonic waves. ) Is also applicable.

FIG. 1 is a diagram illustrating two metals to be simulated, a ball that is periodically collided with a joint portion thereof, and a horn that periodically pricks the ball.
In the example shown in FIG. 1, an arm (aluminum) and a base plate (stainless steel) are joined using an ultrasonic joining technique.

The horn 1 picks up the ball 2 at a predetermined frequency (usually several tens of kHz). The inner diameter of the boss part (hole part) of the arm is larger than the ball diameter, and the arm 3 does not contact the ball 2.
2 and 3 are cross-sectional views showing the joint portion between the arm and the base plate in more detail.

  As shown in FIG. 2, the protrusion of the base plate 4 repeatedly collides with the ball 2 picked up by the horn 1, so that a certain area of the protrusion of the base plate 4 enters the arm 3 as shown in FIG. Two metals, that is, the base plate 4 and the arm 3 are joined. At this time, an intermetallic compound (in this example, an alloy of aluminum and stainless steel) is generated. One of the reasons why the joining of metals by ultrasonic caulking has a larger joining strength than the joining of metals by ordinary ball caulking is that this intermetallic compound is generated in the caulking process. Is called.

FIG. 4 is a block diagram illustrating a configuration of an ultrasonic welding simulation apparatus between metals according to an embodiment of the present invention.
As illustrated in FIG. 4, the ultrasonic bonding simulation apparatus 10 includes a simulation execution unit 21 that inputs input data 11 and executes a simulation.

  The input data 11 includes physical property data 12, virtual friction coefficient data 13, condition data 14, shape data (model data) 15, joint region data 16, and determination data 17.

  In the present embodiment, since the base plate (stainless steel) 4 is periodically periodically swung by the balls 2, the displacement of the base plate 4 becomes a problem. For this reason, the physical property data 12 holds the relationship between stress and strain (stress-strain curve) in the base plate 4, that is, stainless steel.

FIG. 5 is a diagram showing a stress-strain curve.
The curve in FIG. 5 shows the relationship between stress and strain when a rigid body such as a metal is pulled at a certain speed. In the figure, the yield point is a critical point. For example, if the strain is equal to or less than the value of the yield point, the rigid body can return to its original shape. Usually, the curve to the yield point is a straight line with a certain gradient. The slope of this straight line is known as the Young's modulus. The curve portion after the yield point is called the SS curve.

  It is said that the actual measurement after the yield point can be performed up to a pulling speed of about 10 m / sec. Therefore, when it is desired to use a physical property value for a higher pulling speed in the simulation, it is necessary to estimate the value by some method.

When the ratio of the dynamic yield strength σ _d and the static yield strength σ _S (σ _d / σ _S ) is determined from the strain rate ε in the region of high tensile speed, the following Cooper-Symonds Is used.
σ _d / σ _S ) = 1 + (ε / D) ^{1 / P}
Here, D and P are known constants depending on the type of metal.

Actually, since the phenomenon is simulated when the base plate 4 is held on the ball 2 at several tens of kHz, it should not be related to the above-described argument of the pulling speed. However, the following points have been pointed out by experts in this field, and this simulation is also executed based on the pointed-out contents.
-The stress-strain curve of normal ball caulking is close to the stress-strain curve when the tensile speed is 0.5 m / sec.
-The stress-strain curve when the metal is bent by applying a frequency of 10 kHz or 20 kHz to the ball is close to the stress-strain curve when the tensile speed is 5 m / sec.
The stress-strain curve when the ball is given a frequency of 40 kHz and the metal is bent is close to the stress-strain curve when the tensile speed is 20 m / sec.

  Accordingly, the stress-strain curve corresponding to the pulling speed is set in the physical property data 12 depending on the frequency of the ultrasonic wave designated in the condition data 14 (returning to the description of FIG. 4). .

The condition data 14 designates an ultrasonic wave application condition and a friction coefficient.
The ultrasonic wave application condition specifies how fast the horn 1 is vibrated and the ball is picked up. By designating the items of frequency, amplitude, and feed rate (of the horn), the ultrasonic application conditions can be designated.

  In this embodiment, since the ball 2 and the arm 3 are not in direct contact, the friction coefficient of the ball 2 and the base plate 4 and the friction coefficient of the arm 3 and the base plate 4 are specified. The friction coefficient between the ball 2 and the base plate 4 is a fixed value through simulation. However, since the arm 3 and the base plate 4 are joined with the passage of time, the friction coefficient between the ball 2 and the base plate 4 changes. Here, an initial value (for example, 0.1) of the friction coefficient between the arm 3 and the base plate 4 is given.

  The shape data (model data) 15 is data indicating the shapes of two types of metals to be simulated. This data includes an element set on each metal and each point (node, element center) on the element.

FIG. 6 is a perspective view showing an example of an element set on a metal.
The element shown in FIG. 6 is a cube, and has an element center, a node located at each vertex of the cube, and a node located at the midpoint of each side of the cube.

  The joint area data 16 in FIG. 4 is data defining base plate elements that are likely to contact the arm elements (base plate elements that are likely to be joined to the arm elements). For example, in FIG. 7, the surface of the element included in the shaded area is defined as such a region. That is, among the elements shown in FIG. 6, a surface that is positioned so as to face the arm element is defined as a joining region.

  In the determination data 17, a threshold value of the bonding strength (loosening torque, caulking torque) and the deformation amount (warpage amount) is designated. For example, if the bonding strength is smaller than the bonding strength threshold or if the deformation amount is larger than the deformation amount threshold, it is assumed that the condition or shape is inappropriate, and the simulation is restarted by changing the condition or shape. .

  As shown in FIG. 6, the elements on the arm side and the base plate side, which were initially in the shape of a cube, are also deformed by the action of stress as the calculation proceeds, for example, a base plate that faces the elements of the arm. In this plane, as shown in FIG. 8, at a certain time, the node of the plane of the base plate may enter the element of the arm.

Such a point is counted as a node entering the other element in the present embodiment. For example, in FIG. 8, the point P is counted as a node entering the other element.
As shown in FIG. 9, the virtual friction coefficient data 13 in FIG. 4 is data in which the number of nodes entering the other element is associated with the friction coefficients (in the high-speed strain rate region) of the arm 3 and the base plate 4. It is.

Here, the “high-speed strain speed region” means a case where a ball that vibrates at a high frequency (several tens of kHz) acts as a load on a joint portion between metals.
In FIG. 9, the friction coefficient (in the high-speed strain rate region) of the arm 3 and the base plate 4 is shown with respect to the range of the number of nodes entering the other element. As the number of nodes entering the other element increases, the value of this friction coefficient also increases.

  The simulation execution unit 21 in FIG. 4 is realized by a calculation program using, for example, a finite element method. And it is the execution base which makes the stress calculation part 22, the displacement calculation part 23, the joint node number calculation part 24, the virtual friction coefficient acquisition part 25, and the contact pressure average value calculation part 26 execute as many times as necessary.

  The stress calculation unit 22 calculates the stress at each point in each element of the arm 3 and the base plate 4 at each time. The displacement calculation unit 23 calculates the displacement of the elements of the arm 3 and the base plate 4 corresponding to the stress value calculated by the stress calculation unit 22 based on the physical property data 12 that stores the relationship between stress and strain. The joint node number calculation unit 24 calculates the number of nodes of the elements of the base plate 4 that have entered the elements of the arm 3 based on the calculated displacement.

  The virtual friction coefficient acquisition unit 25, when there is a node of the element of the base plate 4 that has entered the element of the arm 3, based on the virtual friction coefficient data 13, the node of the element of the base plate 4 that has entered the element of the arm 3 The coefficient of friction between the arm 3 and the base plate 4 in the high-speed strain rate region corresponding to the number of.

  The contact pressure average value calculation unit 26, when there is a node of the element of the base plate 4 that has entered the element of the arm 3, includes a node of the element of the base plate 4 that has entered the element of the arm 3 , The contact pressure average value is calculated by dividing the sum of the absolute values of the stresses of the nodes entering the element of the arm 3 in the plane by the number of nodes entering the element of the arm 3 in the plane.

  FIG. 10 is a flowchart of a process for calculating the stress generated at each point of each element of the base plate 4. Based on the calculated stress, the bonding strength (loosening torque) and the deformation amount (warpage amount) of the base plate 4 are also calculated. This process is executed by the ultrasonic bonding simulation apparatus 10 of FIG.

In FIG. 10, in step S <b> 1, the stress calculation unit 22 calculates the stress (vector amount) at each point in each element of the arm 3 and the base plate 4 at the current time.
In step S <b> 2, based on the calculated stress (vector amount), the displacement calculation unit 23 calculates the displacement (vector amount) of each point of the element. Further, the deformation amount calculation unit 27 calculates the warp amount (scalar amount) of the base plate based on the calculated displacement (vector amount).

  In step S <b> 3, the number of nodes of the element of the base plate 4 that has entered the element of the arm 3 is calculated by the joint node number calculation unit 24 based on the calculated displacement (vector amount), and the number of nodes is “ It is determined whether it is greater than "0".

  If it is determined in step S3 that the number of nodes of the element of the base plate 4 that has entered the element of the arm 3 is greater than “0”, in step S4, the virtual friction coefficient acquisition unit 25 uses the virtual friction coefficient data 13 as a basis. The friction coefficient between the arm 3 and the base plate 4 in the high-speed strain rate region corresponding to the number of nodes of the element of the base plate 4 that has entered the element of the arm 3 is acquired.

  In step S5, the contact pressure average value calculation unit 26 enters the element of the arm 3 in the plane of the element of the base plate 4 including the node of the element of the base plate 4 that has entered the element of the arm 3. The contact pressure average value is calculated by dividing the sum of the absolute values of the stresses at the respective nodes by the number of nodes that have entered the elements of the arm 3 in the plane. Note that either of steps S4 and S5 may be executed first.

In step S6, the simulation execution unit 21 determines whether or not the calculation is finished.
If it is determined in step S6 that the calculation is not completed, the process returns to step S1, and the stress (vector quantity) at the next time is calculated using the stress value (vector quantity) at the current time.

  When it is determined in step S6 that the calculation has been completed, in step S7, the loosening torque calculating unit 28 calculates a loosening torque indicating the joint strength between the arm 3 and the base plate 4.

  In addition, the process which outputs the comparison result compared with each threshold value hold | maintained in the determination data 17 can also be added after this step S7.

Next, the loose torque calculation process executed in step S7 of FIG. 10 will be described in more detail.
The contact force is obtained from the following equation (1).
Contact force = contact area x 2 x (total contact force / number of contact surfaces) (1)
Then, the loosening torque is obtained from the following equation (2).
Loosening torque = Contact force x Virtual friction coefficient x Caulking radius (2)
Here, the number of contact surfaces is the number of surfaces of the elements of the base plate 4 that are in contact with the arm 3, and the contact area is the proportion of the surface of the elements of the base plate 4 that is in contact with the arms 3 that is actually The total amount of contact force is the sum of contact forces of all surfaces of the elements of the base plate 4 that are in contact with the arm 3, and the caulking radius is the radius of the boss portion.

For example, for the following data, the contact force and the loosening torque are calculated as follows.
Contact area: 0.831
Number of contact surfaces: 204
Total contact force: 12393
Virtual coefficient of friction: 0.1
Caulking radius: 1.14
Contact force = 100.97 (N)
Loosening torque = 11.51 (N · mm)
FIG. 11 is a diagram illustrating an example of a simulation result.

In FIG. 11, the loosening torque, the Bp (base plate) warpage amount, and the like when the virtual friction coefficient values are “0.1”, “0.2”, and “0.3” are obtained.
The average contact pressure is obtained by dividing the total contact force by the number of contact surfaces (total contact force / number of contact surfaces).

  As shown in FIG. 11, even if the value of the virtual friction coefficient is increased, the contact force calculated as a calculation result by the above equation (1) is substantially constant. However, since the loosening torque is proportional to the virtual friction coefficient as shown in the above equation (2), increasing the value of the virtual friction coefficient increases the value of the loosening torque. Since the virtual friction coefficient increases, the base plate becomes difficult to move, so the amount of Bp warpage is slightly reduced. In addition, when the expressions (1) and (2) are referred to together, it can be said that the loosening torque is proportional to the contact pressure average.

  In the above description, the arm and the base plate as shown in FIG. 1 are taken as an example. In the case of the arm and the base plate, as shown in FIG. 2, the base plate is gently attached to the arm to form a gentle protrusion. In such a case, the node does not enter the other element locally, and the calculation result of the contact pressure average value of the present embodiment described above and the conventional calculation method of the contact pressure average value have a large calculation result. Does not make a difference.

  However, there may be a case where a protruding portion having a large degree of protrusion is formed from the beginning in the joint portion between the metals. In such a case, the node locally enters the other element, and the calculation method of the contact pressure average value of the present embodiment described above can increase the calculation result compared to the conventional calculation method of the contact pressure average value.

  That is, according to the calculation method of the contact pressure average value of the present embodiment, since the stress is averaged only for the nodes that have locally entered the other element, only the nodes having a large stress value are averaged. Thus, the average value of the contact pressure can be increased.

  Therefore, even in the case where a protruding part with a large degree of protrusion is formed at the joint part between the metals, the joining strength is increased by locally entering one metal into the other metal by ultrasonic joining. Can be simulated.

FIG. 12 is a diagram illustrating an example of a storage medium.
The simulation process of ultrasonic bonding between metals in the present invention can be realized by the information processing apparatus 41. The program and data for the processing of the present invention can be loaded from the storage device 45 of the information processing device 41 to the memory of the information processing device 41 and executed, or loaded from the portable storage medium 43 to the memory of the information processing device 41. It is also possible to execute it by loading it into the memory of the information processing device 41 from the external storage device 42 via the network 46.

Claims (8)

In the ultrasonic bonding simulation method for executing simulation for ultrasonic bonding of the first metal and the second metal,
A stress calculating step of calculating stress at each point in the first and second metal elements at each time;
A joining node number calculating step of calculating the number of nodes of the first metal that has entered the second metal by displacement based on stress;
When there is a node of the first metal that has entered the second metal, the ball that vibrates at high speed acts as a load on the joint between the first metal and the second metal . Based on a virtual friction coefficient storage unit that stores the friction coefficient between 1 and the second metal in association with the number of nodes of the first metal that has entered the second metal, a virtual friction coefficient acquisition step corresponding to the number of the first metal of the node, and acquires the previous SL friction coefficient between the first and the second metal which has entered,
Sum of absolute values of stresses of the nodes of the first metal that have entered the second metal in the plane of the element including the node of the first metal that has entered the second metal. A contact pressure average value calculating step of calculating a contact pressure average value by dividing by the number of nodes of the first metal that has entered the second metal in the plane;
And a step of calculating a loosening torque based on the acquired friction coefficient and the calculated average value of contact pressure . In the ultrasonic bonding simulation method for executing simulation for ultrasonic bonding of the first metal and the second metal,
A stress calculating step of calculating stress at each point in the first and second metal elements at each time;
A joining node number calculating step of calculating the number of nodes of the first metal that has entered the second metal by displacement based on stress;
Sum of absolute values of stresses of the nodes of the first metal that have entered the second metal in the plane of the element including the node of the first metal that has entered the second metal. A contact pressure average value calculating step of calculating a contact pressure average value by dividing by the number of nodes of the first metal that has entered the second metal in the plane;
When there is a node of the first metal that has entered the second metal, the ball that vibrates at high speed acts as a load on the joint between the first metal and the second metal. Based on a virtual friction coefficient storage unit that stores the friction coefficient between 1 and the second metal in association with the number of nodes of the first metal that has entered the second metal, A virtual friction coefficient obtaining step for obtaining a friction coefficient between the first metal and the second metal corresponding to the number of nodes of the first metal that have entered;
A step of calculating a loosening torque based on the calculated contact pressure average value and the acquired friction coefficient, and an ultrasonic bonding simulation method comprising: Based on the physical property data storage unit that stores the relationship between stress and strain in the first and second metals, the first and second corresponding to the stress value calculated by the stress calculation unit. A displacement calculating step of calculating a displacement of the metal element;
2. The ultrasonic bonding simulation method according to claim 1, wherein, in the step of calculating the number of joint nodes, the number of nodes of the first metal that has entered the second metal is calculated based on the calculated displacement. . In an ultrasonic bonding simulation program for causing a computer to execute a simulation for ultrasonic bonding of a first metal and a second metal,
A stress calculating step of calculating stress at each point in the first and second metal elements at each time;
A joining node number calculating step of calculating the number of nodes of the first metal that has entered the second metal by displacement based on stress;
When there is a node of the first metal that has entered the second metal, the ball that vibrates at high speed acts as a load on the joint between the first metal and the second metal . The second coefficient of friction between the first metal and the second metal is stored in association with the number of nodes of the first metal that has entered the second metal. It corresponds to the number of nodes of the first metal that enters the metal, and prior Symbol virtual friction coefficient acquisition step of acquiring the coefficient of friction between the first and the second metal,
Sum of absolute values of stresses of the nodes of the first metal that have entered the second metal in the plane of the element including the node of the first metal that has entered the second metal. A contact pressure average value calculating step of calculating a contact pressure average value by dividing by the number of nodes of the first metal that has entered the second metal in the plane;
An ultrasonic welding simulation program that causes the computer to execute a step of calculating a loosening torque based on the acquired friction coefficient and the calculated average value of contact pressure . In an ultrasonic bonding simulation program for causing a computer to execute a simulation for ultrasonic bonding of a first metal and a second metal,
A stress calculating step of calculating stress at each point in the first and second metal elements at each time;
A joining node number calculating step of calculating the number of nodes of the first metal that has entered the second metal by displacement based on stress;
Sum of absolute values of stresses of the nodes of the first metal that have entered the second metal in the plane of the element including the node of the first metal that has entered the second metal. A contact pressure average value calculating step of calculating a contact pressure average value by dividing by the number of nodes of the first metal that has entered the second metal in the plane;
When there is a node of the first metal that has entered the second metal, the ball that vibrates at high speed acts as a load on the joint between the first metal and the second metal. The second coefficient of friction between the first metal and the second metal is stored in association with the number of nodes of the first metal that has entered the second metal. A virtual friction coefficient obtaining step for obtaining a friction coefficient between the first metal and the second metal corresponding to the number of nodes of the first metal that have entered the metal;
An ultrasonic joining simulation program that causes the computer to execute a step of calculating a loosening torque based on the calculated contact pressure average value and the acquired friction coefficient . The ultrasonic bonding simulation program stores the stress value calculated by the stress calculation unit based on a second storage unit of the computer that stores a relationship between stress and strain in the first and second metals. A displacement calculating step of calculating a displacement of the first and second metal elements corresponding to
5. The ultrasonic joining simulation according to claim 4, wherein, in the joining node number calculating step, the number of nodes of the first metal that has entered the second metal is calculated based on the calculated displacement. program. In the ultrasonic bonding simulation apparatus for executing a simulation for ultrasonic bonding of the first metal and the second metal,
An application condition of ultrasonic waves applied to the metal, and an analysis condition data storage unit that stores an initial value of a friction coefficient between the first and second metals;
A model data storage unit for storing model data indicating the shapes of the first and second metals, and data relating to elements defined on the model;
Among the defined elements, a contact area definition information storage unit that stores information that defines a surface that is likely to come into contact with the second metal;
A friction coefficient between the first metal and the second metal when a ball that vibrates at a high speed acts as a load on a joint between the first metal and the second metal is included in the surface that is likely to contact. Among the nodes, a virtual friction coefficient storage unit that stores the number of nodes of the first metal that has entered the second metal in association with the number of nodes;
A stress calculator that calculates stress at each point in the first and second metal elements at each time;
A joint node number calculation unit for calculating the number of nodes of the first metal that has entered the second metal by displacement based on stress;
Corresponding to the number of nodes of the first metal that have entered the second metal based on the virtual friction coefficient storage section when there are nodes of the first metal that have entered the second metal. to a virtual friction coefficient acquisition unit that acquires the previous SL friction coefficient between the first and the second metal,
Sum of absolute values of stresses of the nodes of the first metal that have entered the second metal in the plane of the element including the node of the first metal that has entered the second metal A contact pressure average value calculating unit that calculates a contact pressure average value by dividing the first metal by the number of nodes of the first metal that has entered the second metal in the plane;
An ultrasonic bonding simulation apparatus comprising: a bonding strength calculating unit that calculates a loosening torque based on the acquired friction coefficient and the calculated average contact pressure value . A physical property data storage unit for storing a relationship between stress and strain in the first and second metals;
A displacement calculator that calculates the displacement of the first and second metal elements corresponding to the stress value calculated by the stress calculator based on the physical property data storage unit;
The ultrasonic joining simulation apparatus according to claim 7, wherein the joining node number calculating unit calculates the number of nodes of the first metal that has entered the second metal based on the calculated displacement. .

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