KR20230055484A - Apparatus and method for predicting physical properties of multilayer films - Google Patents

Abstract

The present invention relates to a physical property predicting device of multilayer films and a method thereof. According to the present invention, a configuration of the method can predict physical properties of all stacks and has an effect of predicting stress and a strain of each layer when an external force occurs, wherein the external force includes homogenized stiffness of all the stacks of multilayer films as well as expansion stress in consideration of a temperature change and a humidity change which are environment factors in the multilayer films obtained by stacking at least two films for an isotropic material of which physical properties in a machine direction and a transverse direction are the same.

Description

Apparatus and method for predicting physical properties of multilayer films}

The present invention relates to an apparatus and method for predicting physical properties of a multilayer film.

Polymer film refers to a non-fibrous flat plastic molding with a thickness of 0.25 mm or less. It is lightweight, has good barrier properties, has excellent transparency, and is relatively inexpensive. It is used in almost all fields.

Synthetic polymers such as polyethylene (PE), polypropylene (PP), polyvinyl chloride (PVC), and polyethylene terephthalate (PET) are processed into polymer films and widely used at home and abroad. Currently, numerous synthetic polymers are used alone or blended. It is used as a material for polymer films.

In particular, in the case of polyethylene (PE), depending on the density, copolymerization, and branching type, low-density polyethylene (LDPE), medium-density polyethylene (MDPE), high-density polyethylene (HDPE), linear low-density polyethylene (LLDPE), and metallocene linear low-density polyethylene (mLLDPE) ) and so on.

The low-density polyethylene (LDPE) is polyethylene with a low crystallinity of 0.910 to 0.925 g/cm ³ , and after successful synthesis by ICI in 1933, attention was paid to its excellent electrical properties, and it was used as an insulating material for military radars, and then used as an insulating material for various packaging materials. It is one of the general-purpose resins whose uses have been expanded to Its main uses include general packaging, agriculture, shrink film, and paper coating. In particular, it has long chain branches and has excellent melt strength, making it suitable for coating applications.

The medium-density polyethylene is polyethylene having a density of 0.926 to 0.940 g/cm ³ , and is polymerized at about 500 atm and 115 to 120° C. using benzoyl peroxide as an initiator. There is also a method of mixing high-density and low-density polyethylene.

The high-density polyethylene (HDPE) is polyethylene having a density of 0.941 to 0.965 g/cm ³ and low branching and high crystallinity, and has excellent hardness, mechanical strength, and heat resistance, but has slightly poor processability. Industrial production methods include a low-pressure method using an alkylaluminum-titanium halide as a catalyst (Ziegler method) and a medium-pressure method using a silica-alumina-chromia catalyst (Philips method).

The linear low-density polyethylene (LLPDE) is a resin prepared by copolymerizing ethylene and an alpha olefin at low pressure using a polymerization catalyst, and has a narrow molecular weight distribution, short-chain branches of a constant length, and no long-chain branches. Compared to low-density polyethylene (LDPE), it has excellent tensile strength, impact resistance and fracture resistance. Linear low-density polyethylene film has high breaking strength, elongation, tear strength, and drop impact strength along with the characteristics of general polyethylene, so it is increasingly used in stretch films and overlap films, where conventional low-density polyethylene or high-density polyethylene are difficult to apply. are doing

The metallocene linear low-density polyethylene (mLLDPE) is an ethylene copolymer polymerized under a metallocene catalyst and is widely used in packaging or film production because of its high tensile strength and easy extrusion. Polyethylene made by metallocene catalytic polymerization has a higher molecular weight than polyethylene made by Ziegler-Natta polymerization, making it impenetrable to bullets. If this new polyethylene is made into a bulletproof vest, it is stronger than Kevlar.

Multilayer film is a composite film in which different types of films are laminated for the purpose of multifunctionalization of the film. For example, a film combining the excellent mechanical properties of polyethylene (PE) and the printing aesthetics of cellophane, nylon and vinyl alcohol-ethylene Various multilayer films by combinations of copolymers and the like are used as packaging materials.

In the case of developing such a multilayer film as a material, it is necessary to predict physical properties such as elastic modulus, shear modulus, and Poisson's ratio of the entire laminate.

When the elastic modulus is "E", the shear modulus is "G", and the Poisson's ratio is "υ", the relationship between them is as follows: .

[Formula a]

A material has properties in which transverse strain (deformation in the direction perpendicular to the load) and longitudinal strain (deformation in the load direction) are mutually proportional within the elastic range, and the ratio of these two deformations is a constant value by the material within the elastic limit. and this ratio is called Poisson's ratio.

In addition, the elastic modulus indicates the degree of strain that occurs when an elastic material receives stress, and the elastic modulus is referred to as "E" and stress ) is "σ" and the strain is "ε", the relationship between them is as shown in the following equation b.

[Formula b]

On the other hand, since multilayer film materials exhibit anisotropy in the machine direction (MD) and transverse direction (TD) in the manufacturing process, homogenized rigidity of the entire laminate of multilayer films is required for material robust design. In addition, it is necessary to predict the stress and strain of each layer when an external force is generated.

The stress-strain curve is mainly used to indicate various mechanical properties such as proportional limit, elastic limit, yield point, ultimate strength (strength), and elongation of a material. It is usually obtained through tests such as uniaxial tension and compression with a material testing machine. When performing a tensile test, a specimen of most materials is pulled at a constant speed and the amount of deformation is increased to measure the stress, from which a load deformation curve can be obtained. From this load-strain curve, a stress-strain curve unrelated to the size of the specimen is obtained and the result of the tensile test is shown. In general, the stress-strain curve is expressed as nominal stress and nominal elongation.

In the region of elastic deformation, since there is no actual movement of the material, the material returns to its original state when the applied force is released. However, after the yield point, the material cannot withstand the pulling force, so the movement of the material occurs. This part is called the plastic deformation region, and even if the applied force is released, the material does not return to its original state.

Another meaning of the stress-strain curve is that part of the force applied to the material is absorbed by the material in the form of material movement. That is, a part of the applied force is used for plastic deformation, and the force used here is not recovered unlike the force used for elastic deformation. Therefore, in the case of ductile materials, even if a force is applied to the material beyond the yield strength, a part of the force is absorbed by the plastic deformation of the material and the material elongates, and in the case of brittle materials, since plastic deformation hardly occurs, All of them are used for destruction as they are, and when a force greater than the yield strength is applied, destruction occurs instantaneously.

In the case of a plane stress state such as a lamina, the stress-strain relationship is expressed using a stiffness matrix as follows.

A technique for measuring the relationship between stress and strain is disclosed in Korean Patent Laid-open Publication No. 10-2009-0112369 (published on October 28, 2009) in "Stress-Strain Rate in Microstructures". Relationship measurement method" has been disclosed.

For reference, in "Method for Measuring Stress-Strain Relationship in Microstructures" of Korean Patent Laid-open Publication No. 10-2009-0112369 (published on October 28, 2009),

A first step of experimentally measuring the load and displacement of the microstructure;

a second step of assuming an initial value of stress-strain using the measured load and displacement;

A third step of calculating load and displacement by performing finite element analysis based on the assumed initial value of stress-strain;

A fourth step of comparing the load and displacement calculated through the finite element analysis with the experimentally measured load and displacement and revising the stress-strain relationship using the following formula when a preset error range is exceeded;

A fifth step of calculating load and displacement by performing finite element analysis based on the revised stress-strain relationship,

The load and displacement calculated in the fifth step are compared with the experimentally measured load and displacement, and if they exceed a predetermined error range, the fourth and fifth steps are repeated, and if they are within the error range, the final A stress-strain relationship measuring method in a microstructure is disclosed, characterized in that the revised stress-strain relationship is set as the unique stress-strain relationship of the microstructure.

However, the technology disclosed in Publication No. 10-2009-0112369 above is applicable to microstructures, and is not suitable for application to the development of multilayer film materials as in the present invention. .

In order to design robust materials in the process of developing multi-layer film materials, not only the homogenized stiffness of the entire laminate, but also the stress and strain of each layer when external forces including expansion stress in consideration of temperature and humidity changes, which are environmental factors, are generated. The development of such a predictive device is required as a technical task by requiring prediction of the .

Publication of Patent Publication No. 10-2009-0112369

An object of the present invention is to solve the technical problem as described above, in the case of developing a multilayer film in which two or more films are laminated for an isotropic material having the same physical properties in the machine direction and the transverse direction, each layer Utilization can be increased by converting into the elastic modulus and Poisson's ratio using a combination of 1 modulus, shear modulus, elastic modulus, Poisson's ratio and bulk modulus, and the elastic modulus of the entire laminate, shear modulus modulus), Poisson's ratio, etc., and can predict not only the homogenized stiffness of the entire stack of multilayer films, but also the environmental factors such as temperature change and humidity change. It is an object of the present invention to provide an apparatus and method for predicting physical properties of a multilayer film capable of predicting stress and strain.

As a means for achieving the above object,

In one embodiment, the present invention provides (a) at least one physical property of the lame first modulus, shear modulus, elastic modulus, Poisson's ratio, and bulk modulus of elasticity for each layer, and (b) in the x direction of the multilayer film. an input unit for inputting at least one physical property of the angle in the machine direction of each layer, the thickness of each layer, the thermal expansion coefficient, the moisture expansion coefficient, the temperature change value, and the humidity change value of each layer; a control unit connected to the input unit and including a property calculation unit of the multilayer film, which is an entire laminate, and a strain and stress calculation unit for each layer; a display connected to the controller; And it provides an apparatus for predicting physical properties of a multilayer film comprising a storage unit connected to the control unit.

In one specific example, the apparatus for predicting physical properties of the multilayer film predicts physical properties of a multilayer film in which two or more films are laminated, targeting an isotropic material having the same physical properties in the machine direction and the transverse direction.

In another specific example, the controller sets the stiffness matrix of the multilayer film, which is the entire laminate, using the physical properties input to the input unit, and calculates the physical properties of the multilayer film, which is the entire laminate, using the set inverse matrix value.

In one embodiment, the apparatus for predicting physical properties of a multilayer film according to the present invention,

For each layer, the combination of the first lamé modulus and the shear modulus, the elastic modulus, Poisson's ratio, and the bulk modulus, and the angle in the machine direction of each layer relative to the x-direction of the multilayer film, the thickness of each layer, the thermal expansion coefficient of each layer, and the moisture an input unit for inputting an expansion coefficient, a temperature change value, and a humidity change value;

A control unit connected to the input unit and including a property calculation unit of the multilayer film, which is the entire laminate, and a strain and stress calculation unit for each film layer, a display connected to the control unit, and a storage unit connected to the control unit,

The control unit,

In the multilayer film in which two or more films are laminated for an isotropic material having the same physical properties in the machine direction and the transverse direction,

For each layer, a combination of the first lame modulus (λ ^k ), shear modulus (G ^k ), elastic modulus (E ^k ), Poisson's ratio (υ ^k ), and bulk modulus of elasticity (K ^k ) is input, and the combination is elastic. Modulus (E ^k ) and Poisson's ratio (υ ^k ) are converted into the modulus of elasticity (E ^k ), Poisson's ratio (υ ^k ), and shear modulus (G ^k ) to determine the stiffness of each layer in the machine direction and transverse direction The matrix is calculated, the lamination angle of each layer in the machine direction is input, the lamination angle of the multilayer film is reflected in the derived stiffness matrix, the stiffness matrix of the multilayer film, which is the entire laminate, is reset, and the thickness information of each layer is received. The stiffness matrix of the multilayer film, which is the entire laminate, is calculated using the reset stiffness matrix value, the inverse matrix for the stiffness matrix of the multilayer film, which is the entire laminate, is set, and the total thickness of the multilayer film, which is the entire laminate, and the set inverse matrix value Calculate the elastic modulus, shear modulus, and Poisson's ratio of the multilayer film, which is the entire laminate, using

In another embodiment, the control unit inputs the thermal expansion coefficient, moisture expansion coefficient, temperature change value, and humidity change value of each layer, and the thermal expansion coefficient, moisture expansion coefficient, temperature change value, and humidity change of each layer. Using the value, the free lamina hydrothermal strain due to the moisture expansion of each layer is calculated for each layer in the principal direction, and the lamination angle of each layer is calculated based on the free lamina hydrothermal strain. The hydrothermal strain transformation of the multilayer film is calculated by reflecting , and the hydrothermal strain transformation of the multilayer film, the rigid matrix of the multilayer film, and the hydrothermal force generated in the multilayer film based on the thickness of each layer ( Hygrothermal force and hydrothermal moments are calculated, external forces are added to the hydrothermal forces and hydrothermal moments to configure total forces and total moments, and the total forces and total moments and multi-layer The thermal expansion coefficient and the water expansion coefficient of the multilayer film are obtained using the compliance matrix for the stiffness matrix of the film, and the intermediate force and total moment are obtained using the compliance matrix for the stiffness matrix of the multilayer film. The strain and curvatures of a midplane are calculated, and the stress of each layer is calculated using the strain of each layer and the stiffness matrix of the multilayer film.

In addition, the present invention provides a method for predicting physical properties of a multilayer film. In one embodiment, the method for predicting physical properties of a multilayer film according to the present invention is a multilayer film in which two or more films are laminated for an isotropic material having the same physical properties in the machine direction and the transverse direction,

(a) physical properties of one or more of the lame first modulus, shear modulus, elastic modulus, Poisson's ratio, and bulk modulus of elasticity for each layer, and (b) the angle in the machine direction of each layer with respect to the x-direction of the multilayer film, each layer inputting any one or more physical properties of a thickness, a thermal expansion coefficient of each layer, a moisture expansion coefficient, a temperature change value, and a humidity change value;

Calculating a rigid matrix of the multilayer film, which is an entire laminate, using input physical property values; and

Calculating at least one of the elastic modulus, shear modulus, and Poisson's ratio of the multilayer film, which is the entire laminate, from the rigid matrix of the multilayer film.

In a specific example, calculating the rigid matrix of the multilayer film,

Calculating a stiffness matrix of each layer in the machine direction and the transverse direction using the input physical property values;

Resetting the stiffness matrix of the multilayer film, which is the entire laminate, by receiving the lamination angle of each layer in the machine direction and reflecting the lamination angle of the multilayer film on the derived stiffness matrix; and

A step of receiving thickness information of each layer and calculating a stiffness matrix of the multilayer film, which is an entire laminate, using a reset stiffness matrix value.

In another specific example, the step of calculating any one or more of the elastic modulus, shear modulus, and Poisson's ratio of the multilayer film, which is the entire laminate, from the rigid matrix of the multilayer film,

Setting an inverse matrix for the rigid matrix of the multilayer film, which is the entire laminate; and

Calculating at least one of the elastic modulus, shear modulus, and Poisson's ratio of the multilayer film, which is the entire laminate, using the total thickness of the multilayer film and the set inverse matrix value.

In one embodiment, the method for predicting physical properties of a multilayer film according to the present invention,

A first step of inputting a combination of a first lame coefficient (λ ^k ), a shear modulus (G ^k ), an elastic modulus (E ^k ), a Poisson's ratio (υ ^k ), and a bulk modulus of elasticity (K ^k ) for each layer;

A second step of converting the combination into a modulus of elasticity (E ^k ) and a Poisson's ratio (υ ^k );

A third step of calculating stiffness matrices in the machine direction and transverse direction of each layer using the elastic modulus (E ^k ), Poisson's ratio (υ ^k ), and shear modulus (G ^k );

A fourth step of resetting the stiffness matrix of the multilayer film, which is the entire laminate, by receiving the lamination angle of each layer in the machine direction and reflecting the lamination angle of the multilayer film on the derived stiffness matrix;

A fifth step of receiving thickness information of each layer and calculating a stiffness matrix of the multilayer film, which is an entire laminate, using a reset stiffness matrix value;

A sixth step of setting an inverse matrix for the rigid matrix of the multilayer film, which is the entire laminate; and

A seventh step of calculating the elastic modulus, shear modulus, and Poisson's ratio of the multilayer film, which is the entire laminate, using the total thickness of the multilayer film, which is the entire laminate, and the set inverse matrix value.

In a specific embodiment, the method of the present invention, in the second step, the combination (λ ^k , When G ^k ), it is preferable to convert the elastic modulus (E ^k ) and Poisson's ratio (υ ^k ) using the following equation (1).

(1)

(One)

In a specific embodiment, the method of the present invention, in the second step, the combination (λ ^k , When G ^k ), it is preferable to convert the elastic modulus (E ^k ) and Poisson's ratio (υ ^k ) using the following equation (2).

(2)

(2)

In a specific embodiment, the method of the present invention, in the second step, the combination (λ ^k , When G ^k ), it is preferable to convert the elastic modulus (E ^k ) and Poisson's ratio (υ ^k ) using the following equation (3).

(3)

(3)

In a specific embodiment, the method of the present invention, in the second step, the combination (λ ^k , When K ^k ), it is preferable to convert the elastic modulus (E ^k ) and Poisson's ratio (υ ^k ) using the following equation (4).

(4)

(4)

In a specific embodiment, the method of the present invention, in the second step, the combination (G ^k , E ^k ), it is preferable to convert the elastic modulus (E ^k ) and Poisson's ratio (υ ^k ) using the following equation (5).

(5)

(5)

In a specific embodiment, the method of the present invention, in the second step, the combination (G ^k , υ ^k ), it is preferable to convert the elastic modulus (E ^k ) and Poisson's ratio (υ ^k ) using the following equation (6).

(6)

(6)

In a specific embodiment, the method of the present invention, in the second step, the combination (G ^k , When K ^k ), it is preferable to convert the elastic modulus (E ^k ) and Poisson's ratio (υ ^k ) using the following equation (7).

(7)

(7)

In a specific embodiment, the method of the present invention, in the second step, the combination (K ^k , E ^k ), it is preferable to convert the elastic modulus (E ^k ) and Poisson's ratio (υ ^k ) using the following equation (8).

(8)

(8)

In a specific embodiment, the method of the present invention, in the second step, the combination (K ^k , υ ^k ), it is preferable to convert the elastic modulus (E ^k ) and Poisson's ratio (υ ^k ) using the following equation (9).

(9)

(9)

In a specific embodiment, the method of the present invention, in the third step, using the elastic modulus (E ^k _1,2 ), Poisson's ratio (υ ^k _1,2 ), and the shear modulus (G ^k _1,2 ), each It is preferable to calculate the stiffness matrix ([Q] ^k _1,2 ) of the layer (k) in the machine direction (1) and the transverse direction (2) according to the following equation (10).

(10)

(10)

(For isotropic materials, G = E / 2(1+υ))

In a specific embodiment, in the method of the present invention, in the fourth step, each layer (k) is formed by reflecting the stacking angle (θk) of each layer (k) on the derived rigid matrix ([Q] ^k _1,2 ). It is preferable to reset the stiffness matrix ([Q] ^k x,y) of Equation (11) below.

(11)

(11)

In a specific embodiment, the method of the present invention, in the fifth step, receives the thickness information of each layer (k) and resets the stiffness mattress value to use the entire laminated multilayer material rigid mattress ([A]x, It is preferable to calculate y, [B]x,y, [D]x,y) as the following equation (12).

(12)

(12)

In a specific embodiment, in the method of the present invention, in the sixth step, the multi-layer rigid mattress ([A]x,y, [B]x,y, [D]x,y), which is the entire laminate, is calculated. It is preferable to set the compliance matrix ([a]x,y, [b]x,y, [c]x,y,[d]x,y) as shown in Equation (13).

(13)

(13)

In a specific embodiment, the method of the present invention, in the seventh step, the total thickness (h) of the multilayer material, which is the entire laminate, and the set inverse matrix ([a]x,y, [b]x,y, [c] Using the x,y,[d]x,y) values, the elastic modulus (/Ex,y), Poisson's ratio (/υx,y), and shear modulus (/Gx,y) of the multilayer material, which is the entire laminate, are It is preferable to calculate as in Formula (14).

(14)

(14)

In another embodiment, the method of the present invention,

An eighth step of inputting the thermal expansion coefficient, moisture expansion coefficient, temperature change value, and humidity change value of each layer;

Calculate the free lamina hydrothermal strain by the moisture expansion of each layer in the main direction of each layer using the thermal expansion coefficient, moisture expansion coefficient, temperature change value, and humidity change value of each layer. Ninth calculation steps,

A tenth step of calculating a hydrothermal strain transformation of the multilayer film by reflecting the stacking angle of each layer in the free lamina hydrothermal strain;

An eleventh step of calculating hydrothermal force and hydrothermal moments generated in the multilayer film based on the hydrothermal strain deformation of the multilayer film, the stiffness matrix of the multilayer film, and the thickness of each layer;

A twelfth step of constructing total forces and total moments by adding an external force to the hydrothermal forces and hydrothermal moments;

A 13th step of obtaining the thermal expansion coefficient and the moisture expansion coefficient of the multilayer film using the total force and total moment and a compliance matrix for the stiffness matrix of the multilayer film;

A 14th step of calculating strain and curvatures of a midplane using the total force and total moment and a compliance matrix for the stiffness matrix of the multilayer film;

A fifteenth step of calculating the stress of each layer (k) using the strain of each layer and the stiffness matrix of the multilayer film is further included.

In a specific embodiment, in the method of the present invention, the ninth step is the pre-lamina hydrothermal strain due to the moisture expansion of each layer (k) for each circumferential direction of each layer (k) using the following equation (15) ( It is preferable to calculate free lamina hydrothermal strain) (e ^k _1,2 ).

(15)

(15)

In a specific embodiment, in the method of the present invention, it is preferable that the tenth step calculates the hydrothermal strain transformation (e ^k _x,y,s ) of the multilayer film using the following equation (16) .

(16)

(16)

In a specific embodiment, in the method of the present invention, the eleventh step is the hydrothermal force (N ^HT _x,y,s ) and hydrothermal moment (hygrothermal force) generated in the multilayer film using the following equation (17) moments) (M ^HT _x,y,s ) is desirable.

(17)

(17)

In a specific embodiment, in the method of the present invention, it is preferable that the twelfth step calculates total forces (/N) and total moments (/M) using the following equation (18) do.

(18)

(18)

In a specific embodiment, in the method of the present invention, in the thirteenth step, the strain (∈ _x,y ) and curvatures (k _{x, y,s} ) is preferably calculated.

(19)

(19)

In a specific embodiment, in the method of the present invention, it is preferable that the 14th step calculates the strain (ε _x,y ) of each layer (k) using the following equation (20).

(20)

(20)

In a specific embodiment, in the method of the present invention, it is preferable that the 15th step calculates the stress (σ _x,y ) of each layer (k) using the following equation (21).

(21)

(21)

In the present invention, when developing a multilayer film in which two or more films are laminated targeting an isotropic material having the same physical properties in the machine direction and the transverse direction, the first lamé modulus, the shear modulus, the elastic modulus, the Poisson's ratio, and the volume of each layer Utilization can be increased by converting the elastic modulus and Poisson's ratio using a combination of elastic moduli, and physical properties such as elastic modulus, shear modulus, and Poisson's ratio of the entire laminate can be improved. It is possible to predict not only the homogenized stiffness of the entire laminate of multilayer films, but also the stress and strain of each layer when an external force occurs, including the expansion stress in consideration of temperature change and humidity change, which are environmental factors. have an effect that can

1 is a block diagram of an apparatus for predicting physical properties of a multilayer film according to a first embodiment of the present invention.
2 is a flowchart of a method for predicting physical properties of a multilayer film according to a second embodiment of the present invention.
3 is a flowchart of a method for predicting physical properties of a multilayer film according to a third embodiment of the present invention.

Hereinafter, preferred embodiments of the present invention will be described in detail with reference to the accompanying drawings in order to explain the present invention in detail to the extent that those skilled in the art can easily practice the present invention. Other objects, features, and operational advantages, including the object, operation, and effect of the present invention, will become clearer from the description of the preferred embodiment.

For reference, the embodiments disclosed herein are only presented by selecting the most preferred embodiments to help those skilled in the art to understand among various possible examples, and the technical idea of the present invention is not necessarily limited or limited only by the presented embodiments. Instead, various changes, additions, and modifications including equivalents or substitutes are possible within the scope of the technical spirit of the present invention.

In addition, the expression of terms or words used in the specification and claims of the present application are defined based on the principle that the inventor can appropriately define the concept of terms in order to best explain his or her invention. , It should not be construed as limited to ordinary or dictionary meanings, but should be interpreted as meanings and concepts consistent with the technical spirit of the present invention. As an example, a singular expression includes a plurality of expressions unless the context clearly indicates otherwise, and an expression related to a direction is set based on a position shown on the drawing for convenience of explanation, and is “connected” or “connected”. The expression "to be" includes not only a direct connection or connection, but also a connection or connection through another component in the middle. In addition, the expression "~ unit" includes a unit realized using hardware, a unit realized using software, a unit realized using both hardware and software, and the like, and one unit includes one or more pieces of hardware or software. , or two or more units may be realized using one piece of hardware or software.

1st embodiment

1 is a block diagram of an apparatus for predicting physical properties of a multilayer film according to a first embodiment of the present invention.

As shown in FIG. 1, the configuration of the apparatus for predicting physical properties of a multilayer film according to the first embodiment of the present invention allows the user to determine the first lame coefficient (λ ^k ), shear modulus (G ^k ) and elasticity for each layer. The combination of the modulus (E ^k ), Poisson's ratio (υ ^k ), and bulk modulus (K ^k ), each layer machine direction (Machine Direction, MD, hereinafter set to '1' for the x-direction of the multilayer film) and the main direction mean) angle (θ _k ), thickness of each layer (k) (Z _k ), thermal expansion coefficient (α ^k _1,2 ) of each layer (k), moisture expansion coefficient (β ^k _1,2 ), temperature An input unit 10 for inputting a change value (ΔT) and a humidity change value (ΔC), and a physical property calculator 21 connected to the input unit 10 and calculating the physical properties of the multilayer film, which is the entire laminate, and the strain of each film layer and a control unit 20 including a stress calculator 22, a display 30 connected to the control unit 20, and a storage unit 40 connected to the control unit 20.

In the present invention, a multilayer material means a laminate having a structure in which two or more materials are laminated, and may mean a multilayer film such as a polymer, and FRP (fiber reinforced plastics) and aluminum It may mean a composite material between heterogeneous materials such as a pouch. For example, the multi-layer material may mean a multi-layer film.

Meanwhile, the input unit 10 is for the user to input actual physical property values, but is not necessarily limited thereto. For example, the input unit 10 may access a database DB in which information to be input to the input unit 10 is stored.

In addition, in the Poisson's ratio (υ ^k _1,2 ) in the machine direction (1) and the transverse direction (2) of each layer (k), υ _1,2 is when force is applied to the material in the machine direction (1) ( loading), means the Poisson's ratio related to deformation in the transverse direction (TD, hereinafter set as '2'), and υ _2,1 is when the material is loaded in the transverse direction (2), It means the Poisson's ratio related to the deformation in direction (1). Meanwhile, when the material is an isotropic material, υ _1,2 = υ _2,1 = υ.

Meanwhile, the angle θk may mean a counterclockwise angle of each layer with respect to the x direction of the multilayer material.

In addition, the thickness (Zk) of each layer (k) may mean coordinate information from the center of the thickness of the entire laminate in a multi-layer material.

The display 30 includes a name input field, a thickness input field, an angle input field for each layer, a machine direction (MD) elastic modulus input field for each layer, a transverse direction (TD) elastic modulus input field, a Poisson's ratio input field, a thermal expansion coefficient input field, and a width of the sample. An input screen on which a vertical length input box, an X-axis tensile force input box, a Y-axis tensile force input box, a shear force input box, and a temperature change input box are arranged may be provided.

The display 30 may provide an output screen on which the x-direction elastic modulus, the y-direction elastic modulus, Poisson's ratio, shear modulus, bulk modulus, and thermal expansion coefficient are arranged.

Second Embodiment

2 is a flowchart of a method for predicting physical properties of a multilayer film according to a second embodiment of the present invention.

As shown in FIG. 2, the method for predicting physical properties of a multilayer film according to the second embodiment of the present invention,

In the multilayer film in which two or more films are laminated for an isotropic material having the same physical properties in the machine direction and the transverse direction,

Inputting a combination of the first lame coefficient (λ ^k ), the shear modulus (G ^k ), the elastic modulus (E ^k ), the Poisson's ratio (υ ^k ), and the bulk modulus (K ^k ) of each layer (S11); ,

Converting the combination into a modulus of elasticity (E ^k ) and a Poisson's ratio (υ ^k ) (S12);

Using the elastic modulus (E ^k ), Poisson's ratio (υ ^k ), and shear modulus (G ^k ), the stiffness matrix in the machine direction (1) and transverse direction (2) of each layer (k) ([ Q] ^k _1,2 ) is calculated as the following equation (10) (S13);

(10)

(10)

(For isotropic materials, G = E / 2(1+υ))

The compliance matrix ([S] k _1,2 ) for the stiffness matrix ([Q] ^k _1,2 ) in the machine direction (1) and the transverse direction (2) of each layer ⁽ k) thus calculated Setting step (S14),

Step S15 of receiving the stacking angle θk of each layer k in the machine direction 1 (S15);

The stiffness matrix ([Q] ^k _x,y ) of the multilayer film, which is the entire laminate, is calculated by reflecting the lamination angle (θ _k ) of the multilayer film in the derived stiffness matrix ([Q] ^k _1,2 ) by the following equation (11) ) and the step of setting (S14),

(11)

(11)

Step (S17) of receiving the thickness (Zk) of each layer (k);

The stiffness mattress ([A] _x,y , [B] x, _{y ,} [D] _{x,y )} of the multilayer film, which is the entire laminate, is determined by using the stiffness mattress value reset after receiving the thickness information of each layer (k). A step (S18) of calculating as in the following equation (12);

(12)

(12)

The compliance matrix ([a] _{x , y} , _[ b] _x,y , [c] _x,y , [d] _x,y ) as in the following equation (13) (S19),

(13)

(13)

A step (S20) of calculating and inputting the total thickness (h) of the multilayer material, which is the entire laminated body;

Using the total thickness (h) of the multilayer film, which is the entire laminate, and the values of the inverse matrix ([a] _x,y , [b] _x,y , [c] _x,y , [d] _{x,y )} A step (S21) of calculating the elastic modulus (/E _x,y ), shear modulus (/G _x,y ), and Poisson's ratio (/υ _x,y ) of the chain multilayer film according to the following equation (14) It is done by

(14)

(14)

)간의 관계식(G = E / 2(1+υ))을 이용하여, 제어부(20)에 의해 탄성 계수(E^k) 및 포아송비(υ^k)로부터 전단계수(G^k)를 산출한다.In the step (S11) of inputting a combination of the lame first modulus (λk), shear modulus (Gk), elastic modulus (Ek), Poisson's ratio (υ ^k ), and bulk modulus (Kk), the elastic modulus of the isotropic material (E) and shear modulus (G) and Poisson's ratio (

The shear modulus (G ^k ) is calculated from the elastic modulus (E ^k ) and Poisson's ratio (υ ^k ) by the control unit 20 using the relational expression (G = E / 2 (1 + υ)) between.

3rd embodiment

3 is a flowchart of a method for predicting physical properties of a multilayer film according to a third embodiment of the present invention.

As shown in FIG. 3, the method for predicting physical properties of a multilayer film according to the third embodiment of the present invention,

In the multilayer film in which two or more films are laminated for an isotropic material having the same physical properties in the machine direction and the transverse direction,

Inputting the thermal expansion coefficient (α ^k _1,2 ), moisture expansion coefficient (β ^k _1,2 ), temperature change value (ΔT), and humidity change value (ΔC) of each layer (k) (S31); ,

Using the thermal expansion coefficient (α ^k _1,2 ), moisture expansion coefficient (β ^k _1,2 ), temperature change value (ΔT), and humidity change value (ΔC) of each layer (k) input as described above, each Calculating the free lamina hydrothermal strain (e ^k _1,2 ) due to the water expansion of each layer (k) in each principal direction of the layer (k) as in the following equation (15) (S32 )and,

(15)

(15)

Step S33 of receiving the stacking angle θk of each layer k in the machine direction 1 (S33);

By reflecting the lamination angle (θk) of each layer (k) in the calculated free lamina hydrothermal strain, the hydrothermal strain transformation (e ^k _x,y,s ) as in the following equation (16) (S34);

(16)

(16)

Inputting the stiffness matrix ([Q] ^k _x,y ) of the multilayer film, which is the entire laminate calculated in the second embodiment (S35);

Step S36 of inputting the thickness Zk of each layer k;

The hydrothermal strain strain (e ^k _x,y,s ) of the multilayer film, which is the entire laminate, and the rigid matrix ([Q] ^k _x,y ) of the multilayer film, which is the entire laminate calculated in the second embodiment, and each layer Based on the thickness (Z _k ) of (k), the hydrothermal force (N ^HT _x,y,s ) and hydrothermal moments (M ^HT _x,y,s ) generated in the multilayer film, which is the entire laminate ) as in the following equation (17) (S37);

(17)

(17)

_Total ^{forces (} _/ N) and total moments (/M) as in the following equation (18) (S38);

(18)

(18)

_The compliance matrix ₍ [a] _{x , y} , [b] _x,y , [c] _x,y , [d] _x,y ) input (S39);

The inverse matrix of the total force (/N) and total moment (/M) and the stiffness matrix ([A] _x,y , [B] _x,y , [C] _x,y ) of the multilayer film, which is the entire laminate ( compliance matrix) ([a] _x,y , [b] _x,y , [c] _x,y ,[d] _x,y ) to calculate the strain (∈ _x,y) of the midplane ) and curvatures (k _{x, y, s} ) as in the following equation (19) (S40);

(19)

(19)

Each layer (k) utilizes the strain (∈ _x,y ) and curvature (k _x,y,s ) of the intermediate plane and the thickness (Z _k ) information of each layer (k) input through the input unit 10. A step (S41) of calculating the strain (ε _{x, y} ) of ) as in the following equation (20);

(20)

(20)

Inputting the stiffness matrix ([Q] ^k _x,y ) of the multilayer film, which is the entire laminate calculated in the second embodiment (S42);

Stress of each layer (k) using the strain of each layer (k) and the stiffness matrix ([Q] ^k _x,y ) of the multilayer film, which is the entire laminate calculated in the second embodiment (σ _{x, y} ) is calculated as in Equation (21) below (S43).

(21)

(21)

The operation of the apparatus and method for predicting physical properties of a multilayer film according to embodiments of the present invention according to the above configuration is as follows.

In order to predict the physical properties of the multi-layer material, the user uses the input unit 10 while viewing the input screen displayed on the display 30 to determine the first lamé coefficient (λ ^k ), shear modulus (G ^k ), and elastic modulus (E ^k ). Enter the combination of Poisson's ratio (υ ^k ) and bulk modulus (K ^k ) (S11).

As the above combination (λ ^k , G ^k ), (λ ^k , E ^k ), (λ ^k ,υ ^k ), (λ ^k , K ^k ), (G ^k , E ^k ),(G ^k , υ ^k ), (G ^k , K ^k ), (K ^k , E ^k ), (K ^k , υ ^k ).

The physical property calculation unit 21 of the multilayer film, which is the entire laminated body of the control unit 20, converts the combination into the elastic modulus (E ^k ) and Poisson's ratio (υ ^k ) using the following Equations 1 to 9 ( S12).

If the combination is (λ ^k , When G ^k ), according to Equation 1 below.

If the combination is (λ ^k , When E ^k ), according to Equation 2 below.

If the combination is (λ ^k , When υ ^k ), according to Equation 3 below.

If the combination is (λ ^k , When K ^k ), according to Equation 4 below.

If the combination is (G ^k , When E ^k ), according to Equation 5 below.

If the combination is (G ^k , When υ ^k ), according to Equation 6 below.

If the combination is (G ^k , When K ^k ), according to Equation 7 below.

If the combination is (K ^k , When E ^k ), according to Equation 8 below.

If the combination is (K ^k , When υ ^k ), according to Equation 9 below.

Next, the physical property calculation unit 21 of the multilayer film, which is the entire laminate of the control unit 20, calculates the elastic modulus (E ^k _1,2 ), Poisson's ratio (υ ^k _1,2 ), and shear modulus (G ^k _1,2 ), the stiffness matrix ([Q] ^k _1,2 ) of each layer (k) in the machine direction (1) and the transverse direction (2) is calculated as in Equation 10 (S12) .

(Use the relation G = E / 2(1+υ) for isotropic materials).

Subsequently, the physical property calculation unit 21 of the multilayer film, which is the entire laminate of the control unit 20, calculates the stiffness matrix ([Q] ^k _{1, 2} ) is obtained as an inverse matrix ([S] ^k _1,2 ) and set as a compliance matrix (S13). This is for converting a stiffness matrix, which is a singular matrix, into an invertible matrix in which an inverse matrix exists.

Next, the physical property calculation unit 21 of the multilayer film, which is the entire stack of the control unit 20, reflects the stacking angle (θ _k ) of the multilayer film to the derived rigid matrix ([Q] ^k _1,2 ), and the entire stacking The stiffness matrix ([Q] ^k _x,y ) of the chain multilayer film is reset as shown in Equation 11 below (S14).

Subsequently, the physical property calculator 21 of the multilayer film, which is the entire laminate of the controller 20, receives the thickness information of each layer (k) and uses the reset stiffness matrix value to determine the stiffness of the multilayer film ([A ] _x,y , [B] _x,y , [D] _x,y ) is calculated as in Equation 12 below (S15).

Next, the physical property calculator 21 of the multilayer film, which is the entire laminate of the control unit 20, calculates the stiffness matrix of the multilayer film, which is the entire laminate ([A] _x,y , [B] _x,y , [C] _x The compliance matrix ([a] _{x, y} , [b] _{x, y} , [c] _{x, y} , [d] _{x, y} ) for , y is set as in Equation ₁₃ below ( S16).

Subsequently, the physical property calculator 21 of the multilayer film, which is the entire laminate of the control unit 20, calculates the total thickness (h) of the multilayer film, which is the entire laminate, from the thickness information of each layer (k), and then calculates the inverse matrix ([a ] _x,y , [b] _x,y , [c] _x,y ,[d] _x,y ) using the values of the elastic modulus (/E _x,y ) and shear modulus (/ G _x,y ) and Poisson's ratio (/υ _x,y ) are calculated as in Equation 14 below (S17).

Next, the user uses the input unit 10 while viewing an input screen (not shown) displayed on the display 30 to determine the thermal expansion coefficient (α ^k _1,2 ) and moisture expansion coefficient (β ^k ₁ ) of each layer (k). _,2 ), the temperature change value (ΔT), and the humidity change value (ΔC) are input (S21), and each film layer strain and stress calculation unit 22 of the control unit 20 reads them.

^k _1,2), 온도 변화값(

T), 습도 변화값(

C)을 이용하여 각 층(k)의 주방향별로 각 층(k)의 수분 팽창에 의한 프리 라미나 열수 변형률(free lamina hydrothermal strain)(e^k _1,2)을 다음의 수학식 15와 같이 산출한다(S22).Subsequently, the strain and stress calculation unit 22 of each film layer of the control unit 20 inputs the thermal expansion coefficient (α ^k _1,2 ) of each layer (k), the moisture expansion coefficient (

^k _1,2 ), temperature change value (

T), humidity change value (

C), the free lamina hydrothermal strain (e ^k _1,2 ) due to the moisture expansion of each layer (k) in each principal direction of each layer (k) is calculated as in Equation 15 below It is calculated (S22).

Next, the strain and stress calculation unit 22 of each film layer of the control unit 20 reflects the lamination angle of each layer (k) to the calculated free lamina hydrothermal strain to obtain a multilayer film, which is an entire laminate. The hydrothermal strain transformation (e ^k _{x, y, s} ) of is calculated as in Equation 16 below (S23).

Subsequently, the strain and stress calculation unit 22 of each film layer of the control unit 20 calculates the hydrothermal strain strain (e ^k _x,y,s ) of the multilayer film, which is the entire laminate, and the entire laminate, which is the entire laminate calculated in the second embodiment. Based on the stiffness matrix of the multilayer film ([Q] ^k _x,y ) and the thickness of each layer (Z _k ), the hydrothermal force (N ^HT _x,y,s ) and The hydrothermal moments (M ^HT _x,y,s ) are calculated as in Equation 17 below (S24).

Next, the strain and stress calculation unit 22 of each film layer of the control unit 20 calculates the mechanical load (N ^HT _x,y,s ) and the hydrothermal moment (M ^HT _x,y,s ) By adding external forces (N, M), which are mechanical loading, total forces (/N) and total moments (/M) are configured as in Equation 18 below (S25).

Subsequently, the strain and stress calculation unit 22 of each film layer of the control unit 20 calculates the total force (/N) and total moment (/M) and the stiffness matrix of the multilayer film, which is the entire laminate calculated in the second embodiment. The compliance matrix for ([A] _x,y , [B] _x,y , [C] _x,y )([a] _x,y , [b] _x,y , [c] _x,y , [d] _{x, y} ) to calculate the strain (∈ _{x, y} ) and curvatures (k _{x, y, s} ) of the midplane as shown in Equation 19 below (S26).

Next, the strain and stress calculation unit 22 of each film layer of the control unit 20 inputs the strain (∈ _x,y ) and curvature (k _x,y,s ) of the intermediate plane through the input unit 10. Using the received thickness (Z _k ) information of each layer (k), the strain (ε _x,y ) of each layer (k) is calculated as in Equation 20 below (S27).

Subsequently, the strain and stress calculation unit 22 of each film layer of the controller 20 calculates the strain of each layer (k) and the stiffness matrix of the multilayer film ([Q ] ^k _x,y ), the stress (σ _x,y ) of each layer (k) is calculated as in Equation 21 below (S28).

The controller 20 stores the thus calculated strain (ε _x,y ) and stress (σ _x,y ) of each layer (k) in the storage unit 40 and displays the display 30 at the same time. output through

10: input unit
20: control unit
21: physical property calculation unit of the multilayer film, which is the entire laminate
22: Strain and stress calculation unit for each film layer
30: display
40: storage unit

Claims (15)

(a) physical properties of one or more of the lame first modulus, shear modulus, elastic modulus, Poisson's ratio, and bulk modulus of elasticity for each layer, and (b) the angle in the machine direction of each layer with respect to the x-direction of the multilayer film, each layer an input unit for inputting any one or more physical properties of a thickness, a thermal expansion coefficient of each layer, a moisture expansion coefficient, a temperature change value, and a humidity change value;
a control unit connected to the input unit and including a property calculation unit of the multilayer film, which is an entire laminate, and a strain and stress calculation unit for each layer;
a display connected to the controller; and
Device for predicting physical properties of a multilayer film comprising a storage unit connected to the control unit.
According to claim 1,
The device for predicting physical properties of the multilayer film,
A device for predicting physical properties of a multilayer film, characterized in that for predicting the physical properties of a multilayer film in which two or more films are laminated targeting an isotropic material having the same physical properties in the machine direction and the transverse direction.
According to claim 1,
The control unit,
Using the physical properties input in the input unit, the stiffness matrix of the multilayer film, which is the entire laminate, is set,
An apparatus for predicting physical properties of a multilayer film, characterized in that for calculating the physical properties of the multilayer film, which is an entire laminate, using the set inverse matrix value.
According to claim 1,
For each layer, the combination of the first lamé modulus and the shear modulus, the elastic modulus, Poisson's ratio, and the bulk modulus, and the angle in the machine direction of each layer relative to the x-direction of the multilayer film, the thickness of each layer, the thermal expansion coefficient of each layer, and the moisture an input unit for inputting an expansion coefficient, a temperature change value, and a humidity change value;
A control unit connected to the input unit and including a property calculation unit of the multilayer film, which is the entire laminate, and a strain and stress calculation unit for each film layer, a display connected to the control unit, and a storage unit connected to the control unit,
The control unit,
In the multilayer film in which two or more films are laminated for an isotropic material having the same physical properties in the machine direction and the transverse direction,
For each layer, a combination of the first lame modulus (λ ^k ), shear modulus (G ^k ), elastic modulus (E ^k ), Poisson's ratio (υ ^k ), and bulk modulus of elasticity (K ^k ) is input, and the combination is elastic. Modulus (E ^k ) and Poisson's ratio (υ ^k ) are converted into the modulus of elasticity (E ^k ), Poisson's ratio (υ ^k ), and shear modulus (G ^k ) to determine the stiffness of each layer in the machine direction and transverse direction The matrix is calculated, the lamination angle of each layer in the machine direction is input, the lamination angle of the multilayer film is reflected in the derived stiffness matrix, the stiffness matrix of the multilayer film, which is the entire laminate, is reset, and the thickness information of each layer is received. The stiffness matrix of the multilayer film, which is the entire laminate, is calculated using the reset stiffness matrix value, the inverse matrix for the stiffness matrix of the multilayer film, which is the entire laminate, is set, and the total thickness of the multilayer film, which is the entire laminate, and the set inverse matrix value An apparatus for predicting physical properties of a multilayer film, characterized in that the elastic modulus, shear modulus, and Poisson's ratio of the multilayer film, which is the entire laminate, are calculated by using.
According to claim 4,
The control unit inputs the thermal expansion coefficient, moisture expansion coefficient, temperature change value, and humidity change value of each layer, and uses the thermal expansion coefficient, moisture expansion coefficient, temperature change value, and humidity change value of each layer to determine the main characteristics of each layer. The pre-lamina hydrothermal strain due to the water expansion of each layer is calculated for each direction, the lamination angle of each layer is reflected in the pre-lamina hydrothermal strain, the hydrothermal strain strain of the multilayer film is calculated, and the hydrothermal strain strain of the multilayer film is calculated. And, calculating the hydrothermal force and hydrothermal moment generated in the multilayer film based on the rigid mattress of the multilayer film and the thickness of each layer, and adding an external force to the hydrothermal force and hydrothermal moment to configure the total force and total moment, The thermal expansion coefficient and the water expansion coefficient of the multilayer film are obtained using the total force and total moment and the inverse matrix for the stiffness matrix of the multilayer film, and using the total force and total moment and the inverse matrix for the stiffness matrix of the multilayer film An apparatus for predicting physical properties of a multilayer film, characterized in that the strain and curvature of the intermediate plane are calculated, and the stress of each layer is calculated using the strain of each layer and the stiffness matrix of the multilayer film.
In the multilayer film in which two or more films are laminated for an isotropic material having the same physical properties in the machine direction and the transverse direction,
(a) physical properties of one or more of the lame first modulus, shear modulus, elastic modulus, Poisson's ratio, and bulk modulus of elasticity for each layer, and (b) the angle in the machine direction of each layer with respect to the x-direction of the multilayer film, each layer inputting any one or more physical properties of a thickness, a thermal expansion coefficient of each layer, a moisture expansion coefficient, a temperature change value, and a humidity change value;
Calculating a rigid matrix of the multilayer film, which is an entire laminate, using input physical property values; and
A method for predicting physical properties of a multilayer film comprising calculating at least one of an elastic modulus, shear modulus, and Poisson's ratio of a multilayer film, which is an entire laminate, from a stiffness matrix of the multilayer film.
According to claim 6,
Calculating the rigid mattress of the multilayer film,
Calculating a stiffness matrix of each layer in the machine direction and the transverse direction using the input physical property values;
Resetting the stiffness matrix of the multilayer film, which is the entire laminate, by receiving the lamination angle of each layer in the machine direction and reflecting the lamination angle of the multilayer film on the derived stiffness matrix; and
A method of predicting physical properties of a multilayer film comprising the step of receiving thickness information of each layer and calculating a stiffness matrix of the multilayer film, which is an entire laminate, using a reset stiffness matrix value.
According to claim 6,
Calculating at least one of the elastic modulus, shear modulus, and Poisson's ratio of the multilayer film, which is the entire laminate, from the rigid matrix of the multilayer film,
Setting an inverse matrix for the rigid matrix of the multilayer film, which is the entire laminate; and
A method of predicting physical properties of a multilayer film comprising calculating at least one of an elastic modulus, a shear modulus, and a Poisson's ratio of the multilayer film, which is an entire laminate, using the total thickness of the multilayer film and the set inverse matrix value.
According to claim 6,
A first step of inputting a combination of a first lame coefficient (λ ^k ), a shear modulus (G ^k ), an elastic modulus (E ^k ), a Poisson's ratio (υ ^k ), and a bulk modulus of elasticity (K ^k ) for each layer;
A second step of converting the combination into a modulus of elasticity (E ^k ) and a Poisson's ratio (υ ^k );
A third step of calculating stiffness matrices in the machine direction and transverse direction of each layer using the elastic modulus (E ^k ), Poisson's ratio (υ ^k ), and shear modulus (G ^k );
A fourth step of resetting the stiffness matrix of the multilayer film, which is the entire laminate, by receiving the lamination angle of each layer in the machine direction and reflecting the lamination angle of the multilayer film on the derived stiffness matrix;
A fifth step of receiving thickness information of each layer and calculating a stiffness matrix of the multilayer film, which is an entire laminate, using a reset stiffness matrix value;
A sixth step of setting an inverse matrix for the rigid matrix of the multilayer film, which is the entire laminated body; and
A method for predicting physical properties of a multilayer film comprising a seventh step of calculating the elastic modulus, shear modulus, and Poisson's ratio of the multilayer film, which is the entire laminate, using the total thickness of the multilayer film, which is the entire laminate, and the set inverse matrix value.
According to claim 9,
^In _the third step _{, the} machine ^direction (1) ^and A method for predicting physical properties of a multilayer film that calculates the stiffness matrix ([Q] ^k _1,2 ) in the transverse direction (2) as in Equation (10):

(10)
In the equation, for an isotropic material, G = E / 2 (1 + υ).
According to claim 9,
In the fourth step, the stiffness matrix ([Q] ^k x,y of each layer (k) is reflected by the stacking angle (θk) of each layer (k) in the derived stiffness matrix ([Q] ^k _1,2 ). ) Method for predicting physical properties of a multilayer film that resets as in Equation (11):

(11).
According to claim 9,
In the fifth step, the stiffness mattress of the multi-layer material ([A]x,y, [B]x,y, [D A method for predicting physical properties of a multilayer film in which ]x,y) is calculated as in Equation (12):

(12).
According to claim 9,
In the sixth step, the inverse matrix ([a]x,y, [ b] x, y, [c] x, y, [d] x, y) as the following formula (13) Method of predicting physical properties of a multilayer film:

(13).
According to claim 9,
In the seventh step, the total thickness (h) of the multilayer material, which is the entire laminate, and the set inverse matrix ([a]x,y, [b]x,y, [c]x,y,[d]x,y) The multilayer film that calculates the elastic modulus (/Ex,y), Poisson's ratio (/υx,y), and shear modulus (/Gx,y) of the multilayer material, which is the entire laminate, using the values Property prediction method:

(14).
According to claim 9,
An eighth step of inputting a thermal expansion coefficient, a moisture expansion coefficient, a temperature change value, and a humidity change value of each layer;
A ninth step of calculating pre-laminar hydrothermal strain by the moisture expansion of each layer for each circumferential direction of each layer using the thermal expansion coefficient, moisture expansion coefficient, temperature change value, and humidity change value of each layer;
A tenth step of calculating the hydrothermal strain of the multilayer film by reflecting the stacking angle of each layer in the pre-lamina hydrothermal strain;
An eleventh step of calculating hydrothermal force and hydrothermal moment generated in the multilayer film based on the hydrothermal strain of the multilayer film, the stiffness matrix of the multilayer film, and the thickness of each layer;
a twelfth step of constructing total force and total moment by adding an external force to the hydrothermal force and hydrothermal moment;
A thirteenth step of obtaining a coefficient of thermal expansion and a coefficient of moisture expansion of the multilayer film using the total force and total moment and an inverse matrix of the stiffness matrix of the multilayer film;
A 14th step of calculating the strain and curvature of the intermediate plane using the total force and total moment and an inverse matrix for the rigid matrix of the multilayer film; and
The method of predicting physical properties of the multilayer film further comprising a fifteenth step of calculating the stress of each layer using the strain of each layer and the stiffness matrix of the multilayer film.

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