System and method for reverse strength design of multilayer materials

Abstract

This relates to a system and method for reverse designing the strength of multilayer materials, which allows for reverse design of multilayer materials without manufacturing test pieces of the multilayer material, and more specifically, it is possible to derive the required physical properties of the undetermined layer (p) to achieve the target strength of the multilayer material.

Description

[Technical Field]

[0001] This application claims the benefit of priority based on Korean Patent Application No. 10-2023-0085447, dated July 3, 2023, and all contents disclosed in the documents of said Korean patent application are incorporated herein by reference.

[0002] The present invention relates to a system and method that allows for reverse engineering the strength of multilayer materials, particularly multilayer films. [Background technology]

[0003] Polymer films are non-fiber type flat plastic moldings with a thickness of 0.25 mm or less. They are lightweight, have good barrier properties, are highly transparent, and are relatively inexpensive, so they are used in almost all fields, including packaging materials, household goods, electronic devices, automobiles, and aircraft.

[0004] Synthetic polymers such as polyethylene (PE), polypropylene (PP), polyvinyl chloride (PVC), and polyethylene terephthalate (PET) are processed into polymer films and are widely used both domestically and internationally. Currently, many synthetic polymers are used alone or blended as polymer film materials.

[0005] However, there is a limit to how a single film can meet the complex physical properties required. To overcome this limitation, we are developing multilayer materials with a structure in which two or more films are laminated.

[0006] In the development process of a multilayer material, the physical properties, particularly strength, of the multilayer material cannot be calculated by simply combining the physical properties of the individual films. Conventionally, to evaluate the physical properties, particularly strength, of a multilayer material, multilayer material specimens were manufactured for each combination and the manufactured specimens were evaluated. This method of manufacturing multilayer material specimens not only takes time to manufacture, but also has limitations in that it is difficult to evaluate both the types and physical properties of various films.

[0007] Therefore, there is a need for a method that can predict the physical properties, especially the strength, of a multilayer material without directly manufacturing the multilayer material. In particular, there is a strong need for a system and method with a new concept that can suggest design directions for some layers in order to realize the target physical properties of the multilayer material. Summary of the Invention [Problem to be solved by the invention]

[0008] As described above, an object of the present invention is to provide a system and method that can suggest design directions for some layers to achieve a target strength of a multilayer material in a simulation step. [Means for solving the problem]

[0009] To achieve the above object, the present invention provides a system for reverse engineering the strength of a multilayer material. Specifically, the system for reverse engineering the strength of a multilayer material according to the present invention is a system for reverse engineering the strength of a multilayer material in which n layers, including an undetermined layer p, are stacked.

[0010] In one embodiment, the strength reverse design system for the multilayer material calculates the principal stress direction strength value [F] of each layer k except for the undetermined layer p. k and the target strength value of the multilayer material [

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[0011] Specifically, the control unit calculates the strength value [F] of each layer k in the principal stress direction. k and the strength value in the principal stress direction of the arbitrarily applied undetermined layer p [F] pThe calculated strength value of the multilayer material [

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[0012] In one specific embodiment, the input value input to the input unit is, for each layer k except for the undetermined layer p, the elastic modulus E k , Poisson's ratio υ k , shear modulus G k , thickness Z k , and stacking angle θ k and a total thickness h of the multilayer material.

[0013] In one specific embodiment, the control unit calculates the stress of each layer k, p by multiplying the stacking angle θ of each layer k, p by the stress of each layer k, p. k、p Applying the principal direction stress [σ] of each layer k, p k、p Strength in the principal stress direction of each layer k, p [F] k、p The strength discrimination parameter [f] that determines the strength of the multilayer material k、p The principal direction stress [σ] of each layer k and p k、p and the intensity discrimination parameter [f] k、p The safety factor S for each layer k and p is calculated by combining k、p Then, the calculated safety factor S for each floor k and p is calculated. k、p Calculated strength value of multilayer material from [

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[0014] Specifically, the control unit calculates the force / N and moment / M of the multilayer material from the total thickness h of the multilayer material. The deformation rate ε of the intermediate surface is calculated using the force / N and moment / M of the multilayer material and the inverse matrices [a], [b], [c], and [d] of the stiffness matrix [A], [B], and [D] of the multilayer material. 0 and the curvature K. The deformation rate ε of the mid-surface 0 , curvature K, and thickness Z of each layer k, p k、p By utilizing the information, the deformation rate ε of each layer k and p k、p Then, the deformation rate ε of each layer k and p is calculated. k、p x、y and the stiffness matrix [Q] of each layer k, p k、p Using the stress σ of each layer k, p k、p Calculate.

[0015] In one embodiment, the safety factor S of each layer k, p k、p Calculated strength value of multilayer material from [

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[0016] In a specific embodiment, the calculated strength value of the multilayer material [

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[0017] In another specific embodiment, the calculated strength value of the multilayer material [

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[0018] For example, the calculated strength value of a multi-layer material [

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[0019] The present invention also provides a method for reverse designing the strength of a multilayer material. The present invention is a method for reverse designing the strength of a multilayer material in which n layers including an undetermined layer p are stacked.

[0020] In one embodiment, the method for reverse designing the strength of a multilayer material according to the present invention includes: for each layer k except for an undetermined layer p, calculating the principal stress direction strength value [F] of each layer k; kand the target strength value of the multilayer material [

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[0021] In one embodiment, in the step of inputting the input values, the input values ​​are, for each layer k except for the undetermined layer p, the elastic modulus E of each layer k. k , Poisson's ratio υ k , shear modulus G k , thickness Z k , and stacking angle θ k and a total thickness h of the multilayer material.

[0022] In a specific embodiment, the strength value of the multilayer material [

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[0023] Specifically, the step of calculating the stress of each layer k, p includes the steps of calculating the force / N and moment / M of the multilayer material from the total thickness h of the multilayer material, and calculating the deformation rate ε of the intermediate surface using the inverse matrices [a], [b], [c], and [d] of the force / N and moment / M of the multilayer material and the stiffness matrix [A], [B], and [D] of the multilayer material. 0 and the step of calculating the curvature K, and the deformation rate ε of the intermediate surface 0 , curvature K, and thickness Z of each layer k, p k、p By utilizing the information, the deformation rate ε of each layer k and p k、p and the step of calculating the deformation rate ε k、p x、y and the stiffness matrix [Q] of each layer k, p k、p Using the stress σ of each layer k, p k、p and calculating:

[0024] In one embodiment, the safety factor S of each layer k, p k、p Calculated strength value of multilayer material from [

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[0025] In a specific example, the calculated strength value of the multilayer material [

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[0026] In another specific example, the calculated strength value of the multilayer material [

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[0027] The system and method for reverse design of strength of a multilayer material according to the present invention enables reverse design of a multilayer material without manufacturing a multilayer material specimen. Specifically, the present invention can derive the required physical properties of an undetermined layer p to achieve a target strength of the multilayer material. [Brief explanation of the drawings]

[0028] [Figure 1] 1 is a configuration diagram of a multilayer material property prediction system according to a first embodiment of the present invention. [Figure 2] 1 is a flowchart of a method for reverse designing strength of a multilayer material according to an embodiment of the present invention. [Figure 3] 1 is a flowchart of a method for reverse designing strength of a multilayer material according to an embodiment of the present invention. [Figure 4] 1 is a flowchart of a method for reverse designing strength of a multilayer material according to an embodiment of the present invention. [Figure 5] FIG. 1 is a schematic diagram showing the orientation of a multilayer material. DETAILED DESCRIPTION OF THE INVENTION

[0029] The present invention provides a system for reverse engineering the strength of a multilayer material in which n layers (n is an integer of 2 or more) are stacked.

[0030] In one embodiment, the strength reverse design system for a multilayer material according to the present invention calculates the principal stress direction strength value [F] of each layer k except for the undetermined layer p. k and the target strength value of the multilayer material [

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[0031] Specifically, the control unit calculates the strength value [F] of each layer k in the principal stress direction. k and the strength value in the principal stress direction of the arbitrarily applied undetermined layer p [F] p The calculated strength value of the multilayer material [

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[0032] In the present invention, the unspecified layer p is a general term for a layer whose physical properties or characteristics are not specified, and may be one or more layers contained in a multilayer material. In one example, the present invention includes a case where all the multilayer material has unspecified layers p. When all the multilayer material has unspecified layers p, the strength value [F] in the principal stress direction of each layer k excluding the unspecified layer p is k is not entered.

[0033] In the present invention, the term "multilayer material" includes a laminate of two or more materials, such as a laminate of two or more planar materials. The planar material may be a plastic molded product or a film, and may be a fibrous material as well as a non-fibrous material.

[0034] In the present invention, the strength value in the principal stress direction of the undetermined layer p [F]p is applied as an arbitrary value, and the calculated strength value of the multilayer material [

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[0035] The strength reverse design system for multilayer materials according to the present invention is able to calculate the target strength value [

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[0036] For more specific descriptions of the present invention, please refer to Korean Patent Applications Nos. 2022-0086176, 2022-0086160, and 2022-0071405. All contents disclosed in the documents of these patent applications are incorporated herein by reference.

[0037] In one embodiment, the input value input to the input unit is the strength value [F] of each layer k in the principal stress direction. k Specifically, the input value input to the input section is the elastic modulus E of each layer k, excluding the undetermined layer p. k , Poisson's ratio υ k , shear modulus G k , thickness Z k , and stacking angle θ k and a total thickness h of the multilayer material.

[0038] In one embodiment, when the multilayer material includes one or more layers k that are not undetermined layers p, k and p are each independently an integer between 1 and n, and the sum of k and p satisfies n.

[0039] In another embodiment, the multilayer material may have all undetermined layers p. In this case, the input value input to the input unit is replaced with information about the undetermined layer p. Specifically, the input value input to the input unit is, for each layer p that is an undetermined layer p, the elastic modulus E of each layer p. p , Poisson's ratio υ p , shear modulus G p , thickness Z p and stacking angle θ p and the total thickness h of the multilayer material. The input value for the undetermined layer p may be any value. Alternatively, if some of the input values ​​for the undetermined layer p are known, the known value may be input, and other values ​​may be any value. As another example, the input value input to the input section may be a principal stress direction strength value [F] of the undetermined layer p that is arbitrarily applied.p It could be.

[0040] Using the above input values, the control unit calculates the stress of each layer k, p, and then calculates the calculated strength value of the multilayer material [

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[0041] Specifically, the control unit calculates the stress of each layer k, p. The calculated stress of each layer k, p is multiplied by the stacking angle θ of each layer k, p. k、p Applying the principal direction stress [σ] of each layer k, p k、p Then, the strength in the principal stress direction of each layer k and p [F] k、p The strength discrimination parameter [f] that determines the strength of the multilayer material k、p The principal direction stress [σ] of each layer k and p is k、p and the intensity discrimination parameter [f] k、p The safety factor S for each layer k and p is calculated by combining k、p The calculated safety factor S for each floor k and p is k、p Calculated strength value of multilayer material from [

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[0042] In one embodiment, the control unit can calculate the stress of each layer k, p by the following process. For example, the control unit calculates the force / N and moment / M of the multilayer material from the total thickness h of the multilayer material. The control unit calculates the deformation rate ε of the intermediate surface using the calculated force / N and moment / M of the multilayer material and the inverse matrices [a], [b], [c], and [d] of the stiffness matrix [A], [B], and [D] of the multilayer material. 0 and the curvature K. The calculated deformation rate ε of the intermediate surface 0 , curvature K, and thickness Z of each layer k, p k、p By utilizing the information, the deformation rate ε of each layer k and p k、pThen, the deformation rate ε of each layer k and p is calculated. k、p x、y and the stiffness matrix [Q] of each layer k, p k、p Using the stress σ of each layer k, p k、p Calculate.

[0043] In another embodiment, the control unit calculates the safety factor S of each layer k, p by the following process: k、p Calculated strength value of multilayer material from [

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[0044] In one embodiment, the calculated strength value of the multilayer material [

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[0045] For example, the calculated strength value of a multi-layer material [

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[0046] As another example, the calculated strength value of a multilayer material [

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[0047] The present invention also provides a method for reverse engineering the strength of a multilayer material in which n layers including an undetermined layer p are laminated.

[0048] In one embodiment, the method for reverse engineering strength design of a multilayer material according to the present invention includes: For each layer k except for the undetermined layer p, the strength value in the principal stress direction of each layer k [F] k and the target strength value of the multilayer material [

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[0049] Here, n is an integer of 2 or more, p is an integer between 1 and n, and the sum of k and p is n.

[0050] In one example, the present invention includes a case where all the multilayer material has an undetermined layer p. When all the multilayer material has an undetermined layer p, the strength value [F] in the principal stress direction of each layer k excluding the undetermined layer p k is not entered.

[0051] In a specific example, in the step of inputting the input values, the input values ​​are, for each layer k except for the undetermined layer p, the elastic modulus E of each layer k k , Poisson's ratio υ k , shear modulus G k , thickness Z k , and stacking angle θ k and a total thickness h of the multilayer material.

[0052] In another embodiment, the multilayer material may have all undetermined layers p. In this case, the input value input to the input unit is the elastic modulus E of each layer p for each undetermined layer p. p , Poisson's ratio υ p , shear modulus G p , thickness Z p and stacking angle θ p and the total thickness h of the multilayer material. The input value for the undetermined layer p may be any value. Alternatively, if some of the input values ​​for the undetermined layer p are known, the known value may be input, and other values ​​may be any value. As another example, the input value input to the input section may be a principal stress direction strength value [F] of the undetermined layer p that is arbitrarily applied. p It could be.

[0053] In one embodiment, the strength value of the multilayer material [

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[0054] In a specific example, the step of calculating the stress of each layer k, p is as follows: Calculating the force / N and moment / M of the multilayer material from the total thickness h of the multilayer material; The deformation ratio ε of the intermediate surface is calculated using the inverse matrices [a], [b], [c], and [d] of the multilayer material's force / N and moment / M and the stiffness matrix [A], [B], and [D] of the multilayer material. 0 and calculating the curvature K; Deformation ratio ε of the intermediate surface 0 , curvature K and thickness Z of each layer k, p k、p By utilizing the information, the deformation rate ε of each layer k and p k、p and calculating Deformation rate ε of each layer k, p k、p x、y and the stiffness matrix [Q] of each layer k, p k、p Using the stress σ of each layer k, p k、p and calculating:

[0055] In another specific example, the safety factor S of each layer k, p k、p Calculated strength value of multilayer material from [

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[0056] In one embodiment, the calculated strength value of the multilayer material [

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[0057] In another embodiment, the calculated strength value of the multilayer material [

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[0058] Conversely, the calculated strength value of the multilayer material [

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[0059] For example, the strength of a multilayer material can be calculated as follows.

[0060] Elastic modulus E of each layer k, p k、p , Poisson's ratio υ k、p , shear modulus G k、p , thickness Z k、p , stacking angle θ k、p and a step (step a) of inputting at least one of the total thickness h of the multilayer material and calculating the stress of each layer k, p; The calculated stress of each layer k and p is applied to the stacking angle θ of each layer k and p. k、p Applying the principal direction stress [σ] of each layer k, p k、p (step b) converting Strength in the principal stress direction [F] of each layer k, p entered separately k、p The strength discrimination parameter [f] that determines the strength of the multilayer material k、p (step c) configuring the Principal direction stress [σ] of each layer k, p k、p and the intensity discrimination parameter [f] k、p Step d: Calculating the safety factor for each layer k and p by combining the above. and a step (d) of extracting the minimum value of the calculated safety factors for each layer k, p and defining it as the strength value of the multilayer material.

[0061] As an example, the process for predicting the strength of a multi-layer material in the present invention is as follows.

[0062] The input information is the elastic modulus E in the machine direction (MD) 1 and transverse direction (TD) 2 of each layer k, p. k、p 1、2 , Poisson's ratio υ in the machine direction 1 and transverse direction 2 of each layer k, p k、p 1、2 , the shear modulus G in the machine direction 1 and transverse axis 2 of each layer k, p K、P1、2 , the angle θ of each layer's machine direction 1 relative to the x direction of the multilayer material k、p , the thickness Z of each layer k, p k、p , and the total thickness h of the multilayer material.

[0063] First, using the input information, the stress σ of each layer k and p is calculated. k、p x、y Then, the calculated stress σ of each layer k and p is calculated. k、p x、y The stacking angle θ of each layer k and p k、p Applying the principal direction stress [σ] of each layer k, p k、p 1、2 Also, the strength in the principal stress direction of the undetermined layer p [F] p is applied arbitrarily.

[0064] Strength in the principal stress direction of each layer k, p [F] k、p 1、2 The strength discrimination parameter [f] that determines the strength of the multilayer material k、p 1、2 Here, the strength in the principal stress direction of each layer k and p [F] k、p 1、2 is the strength in the principal stress direction of the undetermined layer p [F] p 1、2 The explanation will be given assuming that the principal direction stress [σ] of each layer k and p is included. k、p 1、2 and the intensity discrimination parameter [f] k、p 1、2 The safety factor S for each layer k and p is calculated by combining k、p f For example, the safety factor S of each of the above stories k and p is calculated. k、p f To calculate this, the Tsai-Wu criterion can be applied, or the maximum stress criterion, the maximum strain criterion, or the Tsai-Hill criterion can be appropriately applied.

[0065] The calculated safety factor S for each layer k and p k、pf The minimum value (S k、p f ) min The strength value of the multilayer material [

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[0066] The calculated safety factor S for each layer k and p k、p f The minimum value (S k、p f ) min The strength value of the multilayer material [

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[0067] In the first method, the steps from the step a) of calculating the stress of each layer k, p to the step d) of calculating the safety factor of each layer k, p are repeated once, and the calculated safety factor S k、p f The minimum value (S k、p f ) min The strength value of the multilayer material [

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[0068] In the second method, the steps from the step a) of calculating the stress of each layer k, p to the step d) of calculating the safety factor of each layer k, p are repeated n times, and the value calculated in the i-th cycle is reflected in the input value to perform the i+1-th cycle. The strength when all n layers that make up the multilayer material are broken is calculated as the strength value of the multilayer material [

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[0069] In the third method, the steps of calculating the stress of each layer k, p (step a) through calculating the safety factor of each layer k, p (step d) are repeated, and the value calculated in the i-th cycle is reflected as an input value to perform the i+1-th cycle. If the strength of the multilayer material defined by comparing the value calculated in the i-th cycle with the value calculated in the i+1-th cycle does not increase any further, the value calculated in the i-th cycle is defined as the strength of the multilayer material. Here, i is an integer between 1 and n-1, and n is the number of layers k, p that make up the multilayer material. For each cycle, the calculated safety factor S of each layer k, p is calculated. k、p f The minimum value (S k、p f ) min The strength value of the multilayer material in the cycle is calculated as follows:

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[0070] In another embodiment, the calculated safety factor S of each layer k, p k、p f The minimum value (S k、p f ) min The strength value of the multilayer material [

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[0071] Strength value of multilayer material [

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[0072] Conversely, if the value defined as the strength value of the multi-layer material [Number] i x、y does not meet the preset ULF (Ultimate Laminate Failure) criterion, the elastic modulus of the broken layer determined in that cycle will be adjusted and recalculated. As a specific example, a coefficient r will be applied to adjust the elastic modulus of the broken layer. For example, when r = 0, it is assumed that the broken layer in that cycle loses its stress sharing ability in that direction in the next loading cycle. When 0 < r < 1, it is assumed that the broken layer in that cycle partially loses its stress sharing ability in the next loading cycle. At the same time, the strength of the broken layer is changed to infinity and adjusted so that no breakage occurs in the same layer in the next loading cycle.

[0073] In another embodiment, when one or more of the elastic modulus E k、p , Poisson's ratio υ k、p , shear modulus G k、p , thickness Z k、p , stacking angle θ k、p , and the total thickness h of the multi-layer material of each layer k, p are input, the step (step a) of calculating the stress of each layer k, p can be performed as follows.

[0074] First, the information input includes the elastic modulus E in the machine direction (MD) 1 and the transverse direction (TD) 2 of each layer k, p k、p 1、2 , the Poisson's ratio υ in the machine direction 1 and the transverse direction 2 of each layer k, p k、p 1、2 , the shear modulus G in the machine direction 1 and the transverse direction 2 of each layer k, p K、P ​1、2 , the angle θ of each layer's machine direction 1 relative to the x direction of the multilayer material k、p , the thickness Z of each layer k, p k、p , and the total thickness h of the multilayer material.

[0075] The above elastic modulus E k、p 1、2 , Poisson's ratio υ k、p 1、2 , Shear modulus G k、p 1、2 The stiffness matrix [Q] of each layer k and p in the machine direction 1 and transverse direction 2 is calculated using k、p 1、2 Calculate the stiffness matrix [Q] of each layer k and p in the machine direction 1 and transverse axis 2. k、p 1、2 Inverse matrix (compliance matrix) [S] k、p 1、2 Set the above stiffness matrix [Q] k、p 1、2 The stacking angle θ of each layer k and p k、p Reflecting the stiffness matrix [Q] of each layer k, p k、p x、y and set the thickness Z of each layer k and p. k、p The stiffness matrix of the multi-layer material [A] is calculated using the information transmitted and the re-set stiffness matrix value. x、y , [B] x、y , [D] x、y Then, calculate the stiffness matrix [A] of the multilayer material. x、y , [B] x、y , [D] x、y Inverse matrix (compliance matrix) for [a] x、y , [b] x、y , [c] x、y , [d] x、y Set.

[0076] Next, the mid-plane strain and curvature are calculated using the inverse matrix for any force / F and moment / M, and the calculated mid-plane strain and curvature are used to calculate the thickness Z of each layer k and p. k、p The information is used to calculate the strain of each layer k and p.

[0077] Specifically, any force / F and moment / M are assumed to be virtual external forces, and can be defined using the total thickness value to virtually apply a unit normal stress to a multilayer material.

[0078] The above force / N and moment / M and the stiffness matrix of the multi-layer material [A] x、y , [B] x、y , [D] x、y Inverse matrix (compliance matrix) for [a] x、y , [b] x、y , [c] x、y , [d] x、y Using the midplane strain ε 0 x、y and curvatures k, p x、y、s is calculated, and the intermediate surface deformation rate ε 0 x、y and curvatures k, p x、y、s and the thickness Z of each layer k and p k、p By utilizing the information, the deformation rate (strain) ε of each layer k and p k、p x、y Calculate the deformation rate (strain) of each layer k, p and the stiffness matrix [Q] of each layer k, p. k、p x、y Using the stress σ of each layer k, p k、p x、y Then, the calculated stress σ of each layer k and p is calculated. k、p x、y The stacking angle θ of each layer k and p k、p Applying the principal direction stress [σ] of each layer k, pk、p 1、2 Convert to.

[0079] The present invention will be described in more detail below with reference to the drawings and examples, but the scope of the present invention is not limited thereto.

[0080] (First embodiment) FIG. 1 is a configuration diagram of a strength reverse design system for a multilayer material according to a first embodiment of the present invention.

[0081] As shown in FIG. 1, the strength reverse design system for a multilayer material according to the first embodiment of the present invention includes an input unit 10 for inputting input values, a control unit 20 connected to the input unit 10, a display 30 connected to the control unit 20, and a storage unit 40 connected to the control unit 20.

[0082] The input values ​​input to the input unit 10 are the strength values ​​in the principal stress direction [F] of each layer k except for the undetermined layer p. k and the target strength value of the multilayer material [

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[0083] In some cases, the input values ​​may further include additional input values, such as the elastic modulus E of each layer k in the machine direction (MD, hereinafter set to "1" and meaning the main direction) and transverse direction (TD, hereinafter set to "2"), k 1、2 , Poisson's ratio υ in the machine direction 1 and transverse direction 2 of each layer k k 1、2 , the shear modulus G in the machine direction 1 and transverse axis 2 of each layer k k 1、2 , the angle θ of each layer's machine direction 1 relative to the x direction of the multilayer material k, the thickness Z of each layer k k The additional input values ​​also include the total thickness h of the multi-layer material.

[0084] The control unit 20 may include, for example, a multilayer material property calculation unit 21 and an individual layer deformation rate and stress calculation unit 22. The control unit 20 calculates the principal stress direction strength value [F] of each layer k. k and the strength value in the principal stress direction of the arbitrarily applied undetermined layer p [F] p The calculated strength value of the multilayer material [

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[0085] In the present invention, the term "multilayer materials" refers to a laminate having a structure in which two or more materials are laminated. For example, the multilayer materials may refer to a multilayer film of a polymer or the like, or a composite material of different materials such as FRP (fiber reinforced plastics) and an aluminum pouch. For example, the multilayer materials may refer to a multilayer film.

[0086] (Second embodiment) FIG. 2 is a flowchart of a method for reverse designing strength of a multilayer material according to one embodiment of the present invention.

[0087] Specifically, Figure 2 shows the process of calculating the stress for each layer in a multilayer material in which two or more materials are laminated.

[0088] Elastic modulus E of each layer k in the machine direction 1 and transverse direction 2 k 1、2 , Poisson's ratio υ in the machine direction 1 and transverse direction 2 of each layer k k 1、2 , the shear modulus G in the machine direction 1 and transverse axis 2 of each layer k k1、2 , the angle θ of each layer's machine direction 1 relative to the x direction of the multilayer material k , the thickness Z of each layer k k is input (S11).

[0089] The above elastic modulus E k 1、2 , Poisson's ratio υ k 1、2 , Shear modulus G k 1、2 Using the above, the stiffness matrix [Q] of each layer k in the machine direction 1 and transverse direction 2 is calculated. k 1、2 is calculated as in the following equation (1) (S12).

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[0091] (For isotropic materials, G = E / 2(1 + υ).)

[0092] The stiffness matrix [Q] of each layer k in the machine direction 1 and transverse direction 2 calculated in this way k 1、2 Inverse matrix (compliance matrix) [S] k 1、2 is set (S13).

[0093] The stiffness matrix [Q] derived above k 1、2 The stacking angle θ of each layer k k Reflecting this, the stiffness matrix [Q] for each layer k k x、y is reset as shown in the following equation (2) (S14).

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[0095] The stiffness matrix of the entire laminated multilayer material [A] is calculated using the stiffness matrix value reset by transmitting the thickness information of each layer k. x、y , [B] x、y , [D] x、y is calculated as in the following equation (3) (S15).

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[0097] The stiffness matrix [A] of the multilayer material, which is the entire laminate, calculated in this way x、y , [B] x、y , [D] x、y Inverse matrix (compliance matrix) for [a] x、y , [b) x、y , [c] x、y , [d] x、y is set as shown in the following equation (4) (S16).

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[0099] In the present invention, in order to virtually apply a unit normal stress to the entire multilayer material, it can be defined as the following equation (5) or equation (6) using the total thickness (S17): where equation (5) is applied when calculating the strength of the multilayer material in the x direction, and equation (6) is applied when calculating the strength of the multilayer material in the y direction.

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[0101]

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[0102] Input total force / N and total moment / M and stiffness matrix of the multilayer material that is the total laminate [A] x、y , [B] x、y , [D] x、y Inverse matrix (compliance matrix) for [a] x、y , [b] x、y , [c] x、y , [d] x、y Using the strain of the midplane, ε 0 x、y and curvatures k, p x、y、s is calculated as in the following equation (7) (S18).

[0103]

number

[0104] The deformation ratio ε of the intermediate surface 0 x、y and curvature k x、y、s and the thickness Z of each layer k input through the input section. k By utilizing the information, the deformation rate (strain) ε of each layer k k x、y is calculated as in the following equation (8) (S19).

[0105]

number

[0106] The deformation rate (strain) of each layer k and the stiffness matrix [Q] of each layer k k x、y Using the stress σ of each layer k, k x、y is calculated as in the following equation (9) (S20).

[0107]

number

[0108] The second embodiment illustrates a process of calculating stress for each layer k using input values ​​for each layer k except for the undetermined layer p. The second embodiment can be applied to the undetermined layer p in the same manner. As one example, the input values ​​for the undetermined layer p can be arbitrarily applied. As another example, if some of the input values ​​for the undetermined layer p are recognized, the recognized values ​​can be input, and arbitrary values ​​can be input for the other input values.

[0109] (Third embodiment) 3 is a flowchart of a method for inverse strength design of a multilayer material according to an embodiment of the present invention. The input values ​​and the principal stress direction strength value [F] of an undetermined layer p are arbitrarily applied. p The calculated strength value of the multilayer material [

number

[0110] Referring to FIG. 3, the calculated stress σ of each layer k and p k、p x、y The stress in the x and y directions of each layer is calculated by the layer angle θ k、p Using this information, the stress [σ] in the MD and TD directions (principal directions) of each layer k and p k、p 1、2 Here, the following formula (10) is used (S21).

[0111]

number

[0112] In addition, the strength in the principal stress direction of each layer k, excluding the undetermined layer p, [F] k 1、2 is inputted as follows, for example (S22):

[0113] Unidirectional tensile strength of each layer k: F k 1t , One-way compressive strength: F k 1c

[0114] Bidirectional tensile strength of each layer k: F k 2t , Two-way compressive strength: F k 2c

[0115] Six-direction tensile strength of each layer k: F k 6、 1-2 direction biaxial tensile strength: F k 12

[0116] Here, for the undetermined layer p, the strength value in the principal stress direction of the undetermined layer p [F] is arbitrarily applied. p 1、2 Enter.

[0117] Here, the directions of each layer k and p are as shown in Figure 5. Referring to Figure 5, the horizontal direction of the multilayer material is set as the 1 direction or x direction, the vertical direction is set as the 2 direction or y direction, and the diagonal direction is set as the 6 direction or s direction.

[0118] Using the input intensities of each layer k and p, a parameter for determining the strength of the entire multilayer material is constructed as shown in the following equation (11) (S23). The following equation (11) is an example of applying the Tsai-Wu criterion.

[0119]

number

[0120] Here, if the experimental value of biaxial tensile strength cannot be used, it can be assumed as in the following equation (12).

[0121]

number

[0122] Principal direction stress in layers k and p [σ] k、p 1、2and the intensity discrimination parameter [f] k、p 1、2 Utilizing the safety factor S for each layer k and p k、p f For example, when the Sai-U discriminant method is applied, the safety factor can be calculated as shown in the following formula (13).

[0123]

number

[0124] By solving the quadratic equation in equation (12), the safety factor S for each story k and p is obtained. k、p f Two solutions are obtained for the positive value S k、p fa is the tensile strength, negative value S k、p fr represents the compressive strength. Comparing the safety factors of each layer k and p, the layer k and p that show the smallest safety factor i can be defined as the fracture layer (S25).

[0125] In this case, the safety factor of the fracture layer is the strength value at the loading cycle i [

number

[0126]

number

[0127] Furthermore, in the previous step S17, when a unit normal stress is applied using equation (6), the y-direction strength of the multilayer material is derived using equation (15).

[0128]

number

[0129] If the result of the loading cycle meets the preset ULF (Ultimate Laminate Failure) criteria (S27), a defined strength value [

number

number

[0130] If the ULF criteria are not met, steps S29 and S30 are performed and the entire algorithm cycle is reapplied.

[0131] Here, the ULF standard can be applied by selecting one of the following examples 1 to 3 (S27).

[0132] (Example 1) During the loading cycle (i=1), when any one of the layers constituting the multilayer material reaches fracture, that strength is selected as the final strength of the multilayer material.

[0133] (Example 2) After n loading cycles, when all layers (n pieces) that make up the multilayer material have broken, the strength is selected as the final strength of the multilayer material.

[0134] (Example 3) When comparing the results of the i-th loading cycle with the results of the (i+1)-th loading cycle, if the intensity does not increase, the intensity selected in the i-th loading cycle is selected as the final intensity.

[0135] Strength values ​​of multilayer materials defined in S26 [ [Numerals] i x、y If it does not meet the ULF standard, the elastic modulus of the fracture layer determined in cycle i will be adjusted and recalculated (S29). In this case, the coefficient r will be applied to adjust the elastic modulus of the fracture layer. For example, when r = 0, it is assumed that the stress sharing ability of the fracture layer in the cycle in the relevant direction is lost in the next loading cycle, and when 0 < r < 1, it is assumed that the stress sharing ability of the fracture layer in the cycle is partially lost in the next loading cycle.

[0136] (Fourth Embodiment) FIG. 4 is a flowchart of a strength inverse design method for a multilayer material according to another embodiment of the present invention.

[0137] Calculated strength value of the multilayer material [Numerals] u 1、2 Once it is calculated, it will be determined whether it is within the error range of the preset target strength value of the multilayer material [Numerals] t 1、2 (S30).

[0138] Calculated strength value of the multilayer material [Numerals] u 1、2 If the calculated strength value of the multilayer material is [Numerals] t 1、2 outside the error range of the target strength value of the multilayer material, then the calculated strength value of the multilayer material​​​​​

number

number

[0139] Calculated strength value of multilayer material [

number

number

number

[0140] Conversely, the calculated strength value of the multilayer material [

number

number

number

number

[0141] Calculated strength value of the multilayer material [

number

number

number

number

[0142] (Fifth embodiment) In another embodiment of the present invention, if the input value to be input to the input unit is not readily available, it can be derived through a conversion process using other physical property values.

[0143] In one embodiment, the elastic modulus E of each layer k k and Poisson's ratio υ of each layer k k In the process of inputting, the first Lamé coefficient λ k , shear modulus G k and bulk modulus K k For example, the elastic modulus E can be calculated using the following formulas 1 to 9. k and Poisson's ratio υ k It is possible to convert it into

[0144] The available combinations are k , G k When this is the case, the following formula 1 is used.

[0145]

number

[0146] The available combinations are k , E k When this is the case, the following formula 2 is used.

[0147]

number

[0148] The available combinations are k , υ k When this is the case, it is determined by the following formula 3.

[0149]

number

[0150] The available combinations are k, K. k When this is the case, it is determined by the following formula 4.

[0151]

number

[0152] Available combinations are G k , E k When this is the case, it is determined by the following formula 5.

[0153]

number

[0154] Available combinations are G k , υ k When this is the case, it is determined by the following formula 6.

[0155]

number

[0156] Available combinations are G k , K. k When this is the case, it is determined by the following formula 7.

[0157]

number

[0158] Available combinations are K k , E k When this is the case, it is determined by the following formula 8.

[0159]

number

[0160] Available combinations are K k , υ k When this is the case, it is determined by the following formula 9.

[0161]

number

[0162] The above formulas 1 to 9 are examples, and two or more formulas can be combined as needed. [Explanation of symbols]

[0163] 10: Input section 20: Control unit 21: Multilayer material property calculation section 22: Deformation rate and stress calculation section for each layer 30: Display 40: Preservation Department 100: Multi-layer material

Claims

1. In a system for reverse engineering the strength of a multilayer material in which n layers including an undetermined layer (p) are laminated, For each layer (k) except for the undetermined layer (p), the strength value in the principal stress direction of each layer (k) ([F] ｋ ) and the target strength value of the multilayer material ([ [Equation 1] ] ｔ an input unit to which an input value including a control unit that calculates the strength of the multilayer material by applying the input value input to the input unit; a display coupled to the control unit; a storage unit coupled to the control unit, The control unit Strength value in the principal stress direction of each layer (k) ([F] ｋ ) and the principal stress direction strength value ([F]) of the arbitrarily applied undetermined layer (p) ｐ ) to calculate the strength value of the multilayer material ([ [Equation 2] ] ｕ ) is derived, Calculated strength value of multilayer material ([ [Equation 3] ] ｕ ) is the preset target strength value of the multilayer material ([ [Equation 4] ] ｔ ) and determine whether it is within the error range of A strength inverse design system for a multilayer material, wherein n is an integer of 2 or more, p is an integer between 1 and n, and the sum of k and p is n.

2. The input value input to the input unit is For each layer (k) except for the undetermined layer (p), the elastic modulus (E ｋ ), Poisson's ratio (υ ｋ ), shear modulus (G ｋ ), thickness (Z ｋ ), and stacking angle (θ ｋ ) and one or more of the following: The total thickness (h) of the multilayer material; The strength reverse design system for a multilayer material according to claim 1, further comprising any one or more of the following:

3. The control unit Calculate the stress in each layer (k, p), The stress of each layer (k, p) is related to the stacking angle (θ ｋ、ｐ ) to calculate the principal direction stress ([σ] ｋ、ｐ ) and Strength of each layer (k, p) in the principal stress direction ([F] ｋ、ｐ ) is used as a strength discrimination parameter ([f] ｋ、ｐ ) and The principal direction stress ([σ]) of each layer (k, p) ｋ、ｐ ) and intensity discrimination parameter ([f] ｋ、ｐ ) and calculate the safety factor (S ｋ、ｐ ) is calculated, The calculated safety factor (S ｋ、ｐ ) to calculate the strength value of the multilayer material ([ [Equation 5] ] ｕ The strength reverse design system for a multilayer material according to claim 1, wherein the strength reverse design system derives a

4. The control unit Calculate the force ( / N) and moment ( / M) of the multilayer material from the total thickness (h) of the multilayer material; The deformation rate (ε) of the intermediate surface is calculated using the inverse matrix ([a], [b], [c], [d]) of the multilayer material's force ( / N) and moment ( / M) and the stiffness matrix ([A], [B], [D]) of the multilayer material. ０ ) and curvature (K), The deformation ratio of the intermediate surface (ε ０ ), curvature (K), and thickness of each layer (k, p) (Z ｋ、ｐ ) information, the deformation rate (ε ｋ、ｐ ) is calculated, The deformation rate (ε ｋ、ｐ ｘ、ｙ ) and the stiffness matrix ([Q] ｋ、ｐ ) to calculate the stress (σ ｋ、ｐ 4. The strength reverse design system for a multilayer material according to claim 3, wherein the strength reverse design system calculates the strength of the multilayer material.

5. The safety factor (S ｋ、ｐ ) to calculate the strength value of the multilayer material ([ [Equation 6] ] ｕ ) is derived as follows: The minimum value of the calculated safety factor for each layer (k, p) ((S ｋ、ｐ ) min) is extracted, The extracted minimum value ((S ｋ、ｐ ) min) meets the pre-set ULF standard, it is considered as the calculated strength value ([ [Equation 7] ] ｕ 4. The strength reverse design system for a multilayer material according to claim 3, wherein the strength reverse design system for a multilayer material is defined as follows:

6. Calculated strength value of multilayer material ([ [Equation 8] ] ｕ ) is the target strength value of the multilayer material ([ [Equation 9] ] ｔ ) in determining whether it is within the error range of Calculated strength value of multilayer material ([ [Equation 10] ] ｕ ) is the target strength value of the multilayer material ([ [0011] ] ｔ ) is within the error range, the principal stress direction strength value ([F] ｐ 2. The strength reverse design system for a multilayer material according to claim 1, wherein the strength reverse design system presents the following as an appropriate value:

7. Calculated strength value of multilayer material ([ [0012] ] ｕ ) is the target strength value of the multilayer material ([ [0013] ] ｔ ) in determining whether it is within the error range of Calculated strength value of multilayer material ([ [0014] ] ｕ ) is the target strength value of the multilayer material ([ [Equation 15] ] ｔ ) If the error is outside the range of Calculated strength value of multilayer material ([ [0016] ] ｕ ) is the target strength value of the multilayer material ([ [Equation 17] ] ｔ ), the strength value in the principal stress direction of the undetermined layer (p) ([F] ｐ ) and the calculated strength value of the multilayer material ([ [Equation 18] ] ｕ ) and recalculate Calculated strength value of multilayer material ([ [Equation 19] ] ｕ ) is the target strength value of the multilayer material ([ [Equation 20] ] ｔ ), the strength value in the principal stress direction of the undetermined layer (p) ([F] ｐ ) and the calculated strength value of the multilayer material ([ [0000] ] ｕ The strength reverse design system for a multilayer material according to claim 1, wherein the strength reverse design system recalculates the strength of the multilayer material.

8. A method for reverse engineering the strength of a multilayer material in which n layers including an undetermined layer (p) are laminated, comprising: For each layer (k) except for the undetermined layer (p), the strength value in the principal stress direction of each layer (k) ([F] ｋ ) and the target strength value of the multilayer material ([ [Equation 22] ] ｔ ) is input; For the input value entered in the input section and the undetermined layer (p), the principal stress direction strength value ([F] ｐ ) to calculate the strength value of the multilayer material ([ [Equation 23] ] ｕ ) and Calculated strength value of the multilayer material ([ [0000] ] ｕ ) is the preset target strength value of the multilayer material ([ [Equation 25] ] ｔ and determining whether the error is within the error range of A method for inverse strength design of a multilayer material, wherein n is an integer of 2 or more, p is an integer between 1 and n, and the sum of k and p is n.

9. In the step of inputting the input value, The input value is For each layer (k) except for the undetermined layer (p), the elastic modulus (E ｋ ), Poisson's ratio (υ ｋ ), shear modulus (G ｋ ), thickness (Z ｋ ), and stacking angle (θ ｋ ) and one or more of the following: The total thickness (h) of the multilayer material; The method for reverse designing strength of a multilayer material according to claim 8, further comprising any one or more of the following:

10. The strength value of the multilayer material ([ [Equation 26] ] ｕ ) is calculated by Calculating the stress in each layer (k, p); The stress of each layer (k, p) is related to the stacking angle (θ ｋ、ｐ ) to calculate the principal direction stress ([σ] ｋ、ｐ ), Strength of each layer (k, p) in the principal stress direction ([F] ｋ、ｐ ) is used as a strength discrimination parameter ([f] ｋ、ｐ ) The principal direction stress ([σ]) of each layer (k, p) ｋ、ｐ ) and intensity discrimination parameter ([f] ｋ、ｐ ) and calculate the safety factor (S ｋ、ｐ ) The calculated safety factor (S ｋ、ｐ ) to calculate the strength value of the multilayer material ([ [0000] ] ｕ 9. The method for reverse strength design of a multilayer material according to claim 8, further comprising the step of:

11. The step of calculating the stress in each layer (k, p) is Calculating the force ( / N) and moment ( / M) of the multilayer material from the total thickness (h) of the multilayer material; The deformation rate (ε) of the intermediate surface is calculated using the inverse matrix ([a], [b], [c], [d]) of the multilayer material's force ( / N) and moment ( / M) and the stiffness matrix ([A], [B], [D]) of the multilayer material. ０ ) and curvature (K); The deformation ratio of the intermediate surface (ε ０ ), curvature (K), and thickness of each layer (k, p) (Z ｋ、ｐ ) information, the deformation rate (ε ｋ、ｐ ) and The deformation rate (ε ｋ、ｐ ｘ、ｙ ) and the stiffness matrix ([Q] ｋ、ｐ ) to calculate the stress (σ ｋ、ｐ 11. The method for reverse strength design of a multilayer material according to claim 10, further comprising the step of:

12. The safety factor (S ｋ、ｐ ) to calculate the strength value of the multilayer material ([ [0000] ] ｕ ) is derived by The calculated safety factor (S ｋ、ｐ ) the smallest value ((S ｋ、ｐ ) min); The extracted minimum value ((S ｋ、ｐ ) min) meets the pre-set ULF standard, it is considered as the calculated strength value ([ [0000] ] ｕ 11. The method for reverse strength design of a multilayer material according to claim 10, further comprising:

13. Calculated strength value of the multilayer material ([ [Equation 30] ] ｕ ) is the preset target strength value of the multilayer material ([ [Equation 31] ] ｔ The step of determining whether the error is within the error range of Calculated strength value of multilayer material ([ [Equation 32] ] ｕ ) is the target strength value of the multilayer material ([ [Equation 33] ] ｔ ) is within the error range, the strength value in the principal stress direction of the undetermined layer (p) ([F] ｐ 9. The strength reverse design method for a multilayer material according to claim 8, wherein the strength reverse design method presents the following as an appropriate value:

14. Calculated strength value of the multilayer material ([ [Equation 34] ] ｕ ) is the preset target strength value of the multilayer material ([ [Equation 35] ] ｔ The step of determining whether the error is within the error range of Calculated strength value of multilayer material ([ [Equation 36] ] ｕ ) is the target strength value of the multilayer material ([ [Equation 37] ] ｔ ) If the error is outside the range of Calculated strength value of multilayer material ([ [Number 38] ] ｕ ) is the target strength value of the multilayer material ([ [0.39] ] ｔ ), the strength value in the principal stress direction of the undetermined layer ([F] ｐ ) and the calculated strength value of the multilayer material ([ [Equation 40] ] ｕ ) and recalculate Calculated strength value of multilayer material ([ [Equation 41] ] ｕ ) is the target strength value of the multilayer material ([ [0.001] ] ｔ ), the strength value in the principal stress direction of the undetermined layer ([F] ｐ ) and the calculated strength value of the multilayer material ([ [Equation 43] ] ｕ 9. The method for reverse designing strength of a multilayer material according to claim 8, wherein the strength of the multilayer material is recalculated.

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