JP4179095B2 - Interlaminar stress calculation method in laminated materials - Google Patents

Description

  The present invention relates to a method for obtaining an interlayer stress by numerical analysis when a bending stress is applied to a laminated material including a composite material.

  Numerical analysis using a finite-element method (FEM) is widely used as a stress analysis method for mechanical products and building structural materials. FEM divides an object into finite elements having relatively simple characteristics and models them, and analyzes the performance, behavior, and the like of the entire system (see, for example, Patent Document 1).

In recent years, laminated materials containing composite materials such as FRP (fiber reinforced plastics) formed by filling glass fibers or carbon fibers have been used as structural materials for aircraft, ships, automobiles, and the like. The technique described in Patent Document 1 performs modeling by replacing a laminated material with a uniform material having equivalent characteristics, thereby reducing the number of FEM elements in such a laminated material and speeding up computation. .
JP 2002-082998 A (paragraphs 0013 to 0042, FIGS. 1 to 6)

  Such composite materials and laminate materials are resistant to stress along the plane direction of the laminate surface, but when stress is applied in the laminate direction, the material is peeled off even at a relatively low stress, and has a characteristic of being easily broken. . In order to verify the possibility of this peeling, it is necessary to determine the stress in the stacking direction.

  Since such stress cannot be obtained by the calculation in the modeling as described above, conventionally, there has been no choice but to create and analyze a solid (solid) model in which the object is also divided in the stacking direction. In the calculation using such a solid model, the number of elements increases by a factor of the number of divisions in the stacking direction, which increases the amount of computation and consumes a large amount of computer resources, thus increasing the number of man-hours.

  Therefore, an object of the present invention is to provide an interlaminar stress calculation method in a laminated material that can be analyzed with a simple model and a small amount of calculation and computer resources.

  In order to solve the above problems, an interlayer stress calculation method in a laminated material according to the present invention is to create a shell model in which the laminated material is modeled by a number of flat plate elements, and numerically analyze the shell model by a finite element method. Then, the stress distribution along the surface direction of both surfaces of each flat plate element is calculated, the curvature radii in the two principal stress directions on the plane are obtained for each flat plate element, and the direction of the direction corresponding to the calculated curvature radius is calculated. The interlayer stress corresponding to the stress in the direction is calculated from the stress values on both surfaces, and the sum of the interlayer stress in the two directions is taken as the solution of the maximum interlayer stress in the flat plate element.

  Here, each modeled flat element is actually a part of a curved plate. In the present invention, assuming that the main stress is distributed along the surface of the curved plate, that is, the curved surface, the stress in the stacking direction is obtained from the stress balance relationship.

Here, the interlayer stress (tensile stress) σmax corresponding to the stress in a predetermined direction is the surface of the curvature center side as the surface, the stress values on the front and back surfaces are σ _table , σ _back , and the calculated radius of curvature is R, When the plate thickness is represented by t,
σmax = t / 8 / R × (σ _table− σ _back )
Is calculated by

When the thickness is non-uniform (including the case where the thickness is non-uniform due to in-plane stress), the stress σz in the thickness direction corresponding to the stress in the predetermined direction is the surface of the curvature center side as the surface. The stress value in each stress direction is the σ _{M table} , the σ _{m table} , the stress value in the respective stress direction on the back surface is the σ _{M back} , the σ _{m back} surface, and the curvature radius in the respective stress direction is the _{RM table} , R _{m. When the} curvature radii in the stress directions of the _front and back surfaces are expressed as RM _back , R _{m back} , and plate thickness as t,
σz = t / 8 × (σ M _Table / R _{M Table} - [sigma] _{M Back} / R _{M back} + sigma _{m Table} / R _{m Table} - [sigma] _{m Back} / R _{m back)}
Is calculated by

  When the laminated material is an anisotropic laminated plate obtained by laminating a plate that propagates stress only in one direction of the plane with different stress propagation directions, by comparing the direction of the principal stress between adjacent elements, It is preferable to obtain a differential value of the interlaminar shear stress resulting from each stress and multiply this by the thickness per layer to obtain the interlaminar shear stress. Alternatively, by comparing the principal stress between adjacent elements, a differential value of the interlaminar shear stress caused by each stress of the principal stress may be obtained, and this may be multiplied by the thickness per layer to obtain the interlaminar shear stress. . Further, the in-plane stress may be obtained from the main stress and the hook law in each layer, and the interlaminar shear stress may be obtained from the balance between the calculation result and the force in each layer.

  In an anisotropic laminated board in which such a laminated material is laminated with different stress propagation directions such as a plate (such as FRP having a uniform fiber direction) that propagates stress only in one direction of the flat plate, the stress propagation direction is The layer matching the stress direction (for example, in the case of FRP, the layer whose fiber direction matches the stress direction) bears the propagation of the stress component. As a result, since the direction in which the stress is applied is different for each layer, a shear stress is generated. The present invention obtains an approximate value of the shear stress by modeling the generation of the shear stress.

  According to the present invention, since the elements are not divided in the thickness direction (stacking direction) by using the shell model that models the composite material as a flat plate element, the number of elements is less than a fraction of that of the solid model. Can be easily reduced, making modeling easier, and reducing the amount of computation and computer resources.

  Further, even in the anisotropic laminated plate, it is possible to grasp the approximate value of the shear stress generated between the layers without dividing the element according to each laminated material. With this approximate value, it is also possible to predict a dangerous location where breakage or peeling occurs.

  DESCRIPTION OF EXEMPLARY EMBODIMENTS Hereinafter, preferred embodiments of the invention will be described in detail with reference to the accompanying drawings. In order to facilitate the understanding of the description, the same reference numerals are given to the same components in the drawings as much as possible, and duplicate descriptions are omitted.

  FIG. 1 is a block diagram showing a numerical analysis technique including an interlayer stress calculation method according to the present invention. In this numerical analysis, the interlaminar stress when a laminated plate is bent is analyzed using FEM. This numerical analysis is performed on various computers, but each means shown below may be configured as a single program or as software including a program group including a plurality of programs. Also good. Furthermore, each unit may operate on a different computer, or each unit may be configured by a plurality of software programs that operate on different computers. In this case, the program includes not only a program having an input / output function itself but also a so-called macro, script, etc. that operates on a specific program.

  First, the FEM model generation unit 20 generates bulk data representing the shape of the target unit (a target plate is represented by a shell model), and a load applied to the plate and plate constraint data. Bulk data may be generated by directly inputting data of each node, but node data may be generated by setting the number of divisions based on shape data such as CAD data. Alternatively, input data may be generated by setting the shape, the number of divisions, and the like using a GUI (Graphical User Interface).

  The FEM analysis means 30 calculates the in-plane stress acting in the plane direction for each element based on the known bulk data and load / constraint conditions based on the known FEM analysis technique. The obtained in-plane stress data is sent to the interlayer stress analysis means 40 together with the bulk data generated by the FEM model generation means 20. The interlaminar stress analysis means 40 includes a shape analysis means 41 for performing a model shape analysis method according to the present invention using bulk data, a stress analysis means 42 for analyzing in-plane stress, and a model shape and in-plane stress. It comprises stress calculation means 43 for obtaining interlayer stress by the interlayer stress calculation method according to the invention.

  Hereinafter, some examples of the interlayer stress calculation method executed by the interlayer stress calculation means will be described in detail.

  FIG. 2 is a schematic view showing a laminated material to be analyzed in this example. The laminated material 1 shown in FIGS. 2 (a) and 2 (b) has a laminated structure composed of multiple layers of members 10 to 12, and is a curved plate protruding and curving upward in the drawing. is there. Hereinafter, the surface on the side close to the center of curvature of the curved plate is referred to as the front surface, and the surface on the far side is referred to as the back surface (the lower surface in the figure is the front surface and the upper surface is the back surface). As shown in FIG. 2A, the laminated material 1 is stressed in the direction in which the curved plate is extended (returned to the flat plate), that is, in the direction in which the curvature decreases, or on the contrary, as shown in FIG. Let us consider a case where the curved plate is further bent, that is, a stress is applied in a direction in which the curvature is further increased. When the curved plate is extended, a tensile stress is generated on the front surface and a compressive stress is generated on the back surface, whereby a tensile stress is applied between the layers. When the bent plate is further bent, a compressive stress is generated on the front surface and a tensile stress is generated on the back surface, thereby generating a compressive stress (indicated by a broken line in the figure) between the layers. In such a laminate 1, the layers are bonded to each other with an adhesive or the like. Usually, such an adhesive is strong against stress in the direction along the layer, but weak against force in the lamination direction. The adhesive breaks due to the tensile stress, and delamination occurs. Further, when FRP or the like is used instead of the laminated material 1, the stress in the direction along the fiber direction such as glass fiber or carbon fiber mixed in the plastic is strengthened, but the direction perpendicular to the fiber direction is increased. It is not strengthened against stress. In particular, in the case of a plate-like member, the fiber direction is arranged in the plane direction of the plate, so that it is weak against the above-described tensile stress.

  In the present embodiment, the tensile stress generated between the layers in the laminated material and the composite material is obtained by numerical analysis. A flowchart of this numerical analysis is shown in FIG. First, in step S1, the laminated material 1 is modeled by a shell model shown in FIG. The shell model is a model in which an object is divided by a finite number of planes (shell elements). Each shell element is, for example, a quadrilateral with no thickness surrounded by four nodes (nodes), and the plate thickness, material, and the like are expressed as parameters of each shell element. At this time, the laminated material 1 is modeled on the assumption that it is a homogeneous member in the thickness direction.

  In step S2, stress analysis by the finite element method (FEM) is performed with this shell model. Specifically, a difference in stress (hereinafter referred to as differential stress) in a direction along the planes of both surfaces (front surface and back surface) of each shell element is obtained. The differential stress has stress components in two directions, a first principal stress and a second principal stress (see FIG. 4).

  Next, interlayer stress is obtained for each shell element. First, in step S3, an initial value is set for the shell element number. In subsequent step S4, the radius of curvature of the shell element along the first principal stress direction in the target shell element is obtained. Referring to the shell element Ai shown in FIG. 4 as an example, a cross section of the shell model cut along the first principal stress direction in the shell element Ai is as shown in FIG. The shell elements adjacent to Ai in this direction are denoted by Aj and Ak, the line segments along the cross-sectional direction of each shell element are denoted by Li, Lj and Lk, and the centers thereof are denoted by Oi, Oj and Ok. At this time, the vertical line of Li passing through Oi is Ti, and the vertical lines of Lj and Lk passing through Oj and Ok are similarly Tj and Tk, respectively. If the intersection of Ti and Tj is Cj, and the intersection of Ti and Tk is Ck, the radius of curvature R can be expressed as the average value of the distance between Cj-Oi and the distance between Ck-Oi. In step S5, the radius of curvature of the shell element along the second principal stress direction in the target shell element is obtained by the same method.

  In step S6, an interlayer stress resulting from the first principal stress is obtained from the obtained curvature radius and the first principal stress values of both surfaces of the shell element Ai. As shown in FIG. 6, the first principal stress direction is taken as the Y-axis direction, the direction from the flat plate center Oi to the center of curvature is taken as the X-axis, and Oi is taken as the origin O.

  The stress tensor at the origin O is

によって表される。原点ＯからＹ軸方向にｙだけ移動した位置における応力テンソルは、主応力がその大きさを維持しながら、その働く角度が円弧に沿って変化すると仮定すると、

Represented by Assuming that the stress tensor at a position moved by y in the Y-axis direction from the origin O assumes that the working angle changes along the arc while maintaining the magnitude of the principal stress.

によって表される。ここで、テンソルの座標変換において、角度θが微少量であるからｓｉｎθ＝θ、ｃｏｓθ＝１と近似するとともに、２次の項を無視すると、（２）式におけるτは、

Represented by Here, in the coordinate conversion of the tensor, since the angle θ is very small, it is approximated as sin θ = θ, cos θ = 1, and ignoring the second order term, τ in the equation (2) is

で表せる。また、応力の釣り合い方程式から、

It can be expressed as From the stress balance equation,

が成り立つ。（３）（４）式より、

Holds. (3) From equation (4)

が成立する。ここで、平板が図７に示される状態にあるとすると、

Is established. Here, if the flat plate is in the state shown in FIG.

が成り立つ。（５）（６）式より

Holds. (5) From equation (6)

となり、これを積分すると、

And integrating this,

となる。物体の表面では面に垂直な応力成分は０となるから、ｘ＝±ｔ／２でσ_xx＝０となる。したがって、（８）式は、

It becomes. Since the stress component perpendicular to the surface is 0 on the surface of the object, σ _xx = 0 when x = ± t / 2. Therefore, equation (8) is

と書き直せる。（９）式より引っ張り応力の最大値σmaxは

Can be rewritten. From equation (9), the maximum value of tensile stress σmax is

で表せる。ここで、両表面の応力σ_表、σ_裏とσ₀の関係は、

It can be expressed as Here, the stress σ _{table on} both surfaces, the relationship between σ _back and σ ₀ is

となるから、（１０）式は、

Therefore, equation (10) becomes

で表せる。σ_表−σ_裏がＦＥＭで求めた差応力値に相当するから、両者から層間の最大引っ張り応力σmaxを求めることができる。ステップＳ７では、同様の手法により、第２の主応力に対応する層間の最大引っ張り応力を求める。ステップＳ８では、ステップＳ６とＳ７で求めた層間の最大引っ張り応力を合算することで層間の最大引っ張り応力値を算出する。そして、ステップＳ９で全シェル要素についての算出が終了したか否かを判定し、未了と判定した場合には、対象シェル要素を次のシェル要素に変更して（ステップＳ１０）ステップＳ４へ戻り、ステップＳ４〜Ｓ８の処理を繰り返す。全シェル要素の計算が終了したと判定したら、処理を終了する。これにより全シェル要素について層間の最大引っ張り応力を算出することができる。

It can be expressed as Since the σ _front- sigma _back corresponds to the differential stress value obtained by FEM, the maximum tensile stress σmax between the layers can be obtained from both. In step S7, the maximum tensile stress between layers corresponding to the second principal stress is obtained by the same method. In step S8, the maximum tensile stress value between layers is calculated by adding the maximum tensile stress values obtained in steps S6 and S7. In step S9, it is determined whether or not calculation for all shell elements has been completed. If it is determined that calculation has not been completed, the target shell element is changed to the next shell element (step S10), and the process returns to step S4. , Steps S4 to S8 are repeated. If it is determined that all shell elements have been calculated, the process ends. Thereby, the maximum tensile stress between layers can be calculated for all shell elements.

  In such a stress analysis, it is usually sufficient to obtain the maximum interlayer stress in order to determine whether or not peeling occurs. However, when the solid model is used, a correct interlayer stress distribution cannot be calculated unless a sufficient number of divisions is taken in the layer direction. On the other hand, in the interlayer stress calculation method according to the first embodiment, a simple model (shell model) can be used to approximately obtain the maximum interlayer stress without obtaining the stress distribution in the layer direction. Analysis with resources is possible.

  In this embodiment, the interlayer tension at the stress concentration portion is calculated. FIG. 8 shows a cross-sectional image of the compressive stress concentration site. By applying a compressive force F to the laminated plate 5 (consisting of the members 50 to 55), the stress concentration portion swells due to the Poisson's ratio, and a tensile stress σ in the plate thickness direction is generated based on the same principle as the nut split.

  With reference to the flowchart of FIG. 9, the analysis method of Example 2 is demonstrated. First, the thickness t ′ after deformation on each element and node is calculated from the output data of the FEM analysis (step S11). The plate thickness after deformation is as follows, where the original plate thickness is t, the Poisson's ratio is ν, and the elastic modulus is E.

により表される。

It is represented by

Next, a vector P in the direction perpendicular to the surface is obtained from the node data (step S12). Then, the curvature of the surface of each node is calculated (step S13). This can be obtained by obtaining the curvature at the node assuming that the surface is the position where each node coordinate is shifted in the vector P direction by half the plate thickness t ′ after deformation. Similarly, the curvature of the back surface of each node is calculated (step S14). This can be obtained by calculating the curvature at the node, assuming that the position where each node coordinate is shifted by half the plate thickness t ′ after deformation in the direction opposite to the vector P is the back surface. By taking the average by using the curvature of the obtained node, determining the curvature of the element (curvature R _{M table} and the back surface of curvature R _{M back} surface) (step S15).

  Finally, an interlayer stress value is calculated using the calculated curvature and the principal stress calculated by FEM (step S16). Specifically, the tensile stress value between layers is calculated by the following equation.

これは、実施例１の（１２）式の曲率を表と裏で分割した形になる。また、この層間引張応力によっても板厚が変化することになるので、ステップＳ１１〜１６を繰り返せば、層間引張応力による変形を加味した応力計算を行うことができる。

This is a form obtained by dividing the curvature of the expression (12) of Example 1 into the front and the back. Further, since the plate thickness also changes due to the interlayer tensile stress, if steps S11 to S16 are repeated, the stress calculation taking into account the deformation due to the interlayer tensile stress can be performed.

In this embodiment, the shear stress generated by the anisotropy of each layer is calculated. Since members such as CFRP (anisotropic members) basically propagate only the stress component along the fiber direction, the deformation direction of each layer differs when a load is applied. May occur. For example, consider a case where a boomerang-shaped plate 6 as shown in FIG. 10 is pulled. Here, if the tensile direction is 0 °, the applied tensile stress flows along the shape of the plate in the vicinity of the inner corner at the center of the plate 6, so that an induced stress σ ^{90 in the} 90 ° direction is generated. This and the flow of tensile stress σ ⁰ should be connected to each other.

  However, when the plate 6 is configured by laminating such anisotropic members, as shown in FIG. 11, the stress in the 90 ° direction is handled only by the layer 63 whose fiber direction runs along the 90 ° direction, Only the layer 60 whose fiber direction runs along this 0 ° direction is responsible for the stress in the 0 ° direction. As a result, a shear stress τ is generated between the layers 60 and 63.

For simplification, as shown in FIG. 12, in the case of a quasi-isotropic laminate in which the layers running along the directions of 0 °, −45 °, + 45 °, and 90 ° are laminated in this order, as shown in FIG. think of. FIG. 13 shows a flowchart of the calculation process. First, the in-plane stress σ _ij ^h of the h layer is calculated based on the hook rule and Kirchhoff's assumption in each layer (step S21).

  Specifically, the in-plane strain of each layer is the same as the average value of the in-plane strain (Kirchhoff's assumption), and if the average value follows the hook law of the average stress averaged over each layer, Equation (15) is It holds.

左辺は、各層の歪みを、右辺の第１項はＥが弾性率、Ｇが剪断弾性率であり、第２項は面内応力の平均値（既知）を表す。左辺は既知であるから、右辺、つまり、各層の歪みが求まる。さらに、各層におけるフック則から次の（１６）〜（１８）式が成り立つ。

The left side represents the strain of each layer, the first term on the right side represents E as the elastic modulus, G as the shear elastic modulus, and the second term represents the average value (known) of the in-plane stress. Since the left side is known, the right side, that is, the distortion of each layer is obtained. Further, the following equations (16) to (18) are established from the hook rule in each layer.

これにより、各層の面内応力を求めることができる。

Thereby, the in-plane stress of each layer can be obtained.

Next, the shear stress τ _jz ^h is obtained from the equation of force balance in each layer (step S22). This balance equation can be expressed by equation (19).

この釣り合いの方程式は偏微分方程式であるが、実際には、差分法によって解析的に解を求める。図１２には、こうして求めたτｘｚとτｙｚの例を示す。この手法では、層ごとに剪断応力値を求めることができるが、計算はその分複雑になる。

This balance equation is a partial differential equation, but in practice, a solution is obtained analytically by the difference method. FIG. 12 shows examples of τxz and τyz obtained in this way. In this method, the shear stress value can be obtained for each layer, but the calculation is complicated accordingly.

  In the fourth embodiment and the fifth embodiment described later, the calculation of the third embodiment is simplified. One of the purposes of analyzing the interlaminar stress is to grasp the risk of delamination. In this case, it is only necessary to obtain an approximate value corresponding to the maximum value of the interlayer stress. Example 4 and Example 5 are methods for calculating this approximate value.

  Interlaminar shear stress occurs mainly between two layers where the fibers are parallel to the principal stress. Therefore, let us focus only on these layers and assume the following. (1) The lamination is quasi-isotropic, and there are two layers in which the fibers are almost parallel to the main stress in any direction. (2) All layers have the same thickness. (3) The elastic modulus in the direction perpendicular to the fibers of each layer is sufficiently smaller than the elastic modulus in the fiber direction.

  Details of the processing of the fourth embodiment will be described with reference to FIG. First, based on the FEM analysis result, a coordinate system Mm (see FIG. 15) is obtained in which the target point of the target element is the origin and the main stress direction of the target point is the axial direction (step S31). Next, the barycentric positions of the target element and the peripheral elements are obtained and converted to this Mm coordinate system (step S33). Then, the curvatures (∂θ / ∂M and ∂θ / ∂m) of the main stress line are obtained (step S35). This corresponds to a differential value of the main stress direction obtained by comparing the direction of the main stress line in the Mm coordinate system between adjacent elements. Based on this curvature, an approximate value of the interlayer stress is obtained (step S37).

  In order to obtain an approximate value, if the flow of the induced stress flows across the layers, the stress between the layers is obtained by integrating the magnitude of the induced stress in the thickness direction. That is, the following formula is established.

こうして求めたτ_mzとτ_Mzのベクトル和の大きさ、つまり、（τ_mz ²＋τ_Mz ²）^0.5を剪断応力の概略値とする。これにより簡略化した演算で概略値を求めることができる。

The magnitude of the vector sum of τ _mz and τ _Mz thus obtained, that is, (τ _mz ² + τ _Mz ² ) ^0.5 is taken as the approximate value of the shear stress. Thereby, an approximate value can be obtained by a simplified calculation.

  This example uses the same assumptions as in Example 4, but the approximate value of the interlaminar shear stress is obtained from the differential value of the in-plane shear stress. The contents of the processing will be described with reference to FIG.

The processes in steps S31 and S33 are the same as those in the fourth embodiment shown in FIG. Next, the stress of the peripheral element is converted into the Mm coordinate system (step S34). Then, a differential value of the in-plane shear stress in the Mm coordinate system is obtained (step S36). This is because the in-plane shear stress in the Mm coordinate system can be expressed as cos θ sin θ (σ _M −σ _m ). The differential value is obtained by comparing between adjacent elements. Τ _mz and τ _Mz are obtained by multiplying the obtained differential value by the layer thickness, and the approximate value of the shear stress is obtained by obtaining the magnitude of the vector sum (step S38). In this method, the approximate value can be obtained by a simplified calculation as in the fourth embodiment.

The result of actual interlayer stress calculation using some of the embodiments described above will be briefly described. First, the analysis when a load is applied in the direction in which the bent plate is extended will be described. FIG. 17 shows the analysis model, and the unit of length is millimeter. The applied load is 350 kgf (about 3430 N). FIG. 18 shows the analysis result of Example 1. The interlayer stress of the curved portion was 2.1 kgf / mm ² (20.6 MPa), and the bending stress was 160 kgf / mm ² (1570 MPa).

  19 to 21 are analysis of interlayer tension due to stress concentration. FIG. 19 shows an analysis model in which an in-plane load is applied to a boomerang-shaped plate. The magnitude of the load is 141 kgf (about 1380 N). FIG. 20 is a diagram simulating a mechanism for generating a pull between layers. When the size of the stress concentration portion is a, the generated interlayer stress is given by the following equation.

図２１に実施例２による演算結果を示す。図中（ｂ）は、(ａ）の内側角部分の拡大図である。層間引っ張り応力の最大値は０．０１１ｋｇｆ／ｍｍ²（０．１１ＭＰａ）であった。ａ＝３ｍｍとすると、式（２１）から得られる層間引っ張り応力は０．０３ｋｇｆ／ｍｍ²（０．２９ＭＰａ）であり、オーダー的には一致している。

FIG. 21 shows the calculation result according to the second embodiment. In the figure, (b) is an enlarged view of the inner corner portion of (a). The maximum value of the interlayer tensile stress was 0.011 kgf / mm ² (0.11 MPa). When a = 3 mm, the interlayer tensile stress obtained from the equation (21) is 0.03 kgf / mm ² (0.29 MPa), which is in order.

22 to 25 show analyzes when a load is applied to the bolt fastening portion. FIG. 22 shows an analysis model, and the calculation was performed assuming that the bolt load is 500 kgf (about 4900 N) and the load is perpendicular to the hole surface as shown in FIG. FIG. 24 shows an analysis result according to the fourth embodiment, and FIG. 25 shows an analysis result according to the fifth embodiment. Both show good agreement, and the maximum value is about 10 kgf / mm ² / mm (about 98 MPa / mm). The value of the interlaminar shear stress is obtained by multiplying the thickness per laminated ply. When the thickness is 0.1 mm, it becomes 1 kgf / mm ² (about 9.8 MPa).

It is a block diagram which shows the method of numerical analysis including the interlayer stress calculation method which concerns on this invention. It is the schematic which shows the laminated material (curved board) which analyzes in Example 1, The case where (a) extends a curved board and the case where (b) further bends a curved board are shown. 3 is a flowchart of analysis of Example 1. FIG. 3 is a diagram illustrating a shell model in the first embodiment. It is a figure which shows the cross section of the shell element in FIG. It is a figure explaining how to obtain | require the interlayer stress of Example 1. FIG. It is another figure explaining how to obtain the interlayer stress of Example 1. It is a figure which shows the cross-sectional image of the compressive-stress concentration site | part which Example 2 analyzes. 10 is a flowchart of analysis in Example 2. It is a figure explaining the stress at the time of pulling a boomerang shape board. It is a figure explaining the force which acts on an anisotropic laminated board. FIG. 6 is a diagram for explaining a pseudo-isotropic laminate that is a premise of Example 3. 10 is a flowchart of calculation processing according to the third embodiment. 10 is a flowchart of calculation processing according to the fourth embodiment. It is a figure explaining the relationship between coordinate system Mm and the principal stress direction. 10 is a flowchart of calculation processing according to the fifth embodiment. 2 is an analysis model according to Example 1. FIG. It is the analysis result of FIG. 4 is an analysis model according to Example 2. It is the figure which simulated the tension generating mechanism between layers. It is an analysis result of FIG. 4 is an analysis model according to Examples 4 and 5. It is a figure which shows the simulation of the load to the bolt hole of FIG. It is an analysis result of Drawing 22 by Example 4. It is an analysis result of FIG. 22 by Example 5. FIG.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1, 5, 6 ... Laminated material (curved board), 10-12, 50-55, 60-63 ... member, 20 ... FEM model production | generation means, 30 ... Analysis means, 40 ... Interlaminar stress analysis means, 41 ... Shape Analysis means 42 ... Stress analysis means 43 ... Stress calculation means A ... Shell element L ... Line segment along the cross-sectional direction, O ... Center of the line segment, T ... Perpendicular line, C ... Intersection of perpendicular lines.

Claims (6)

A method for calculating an interlaminar stress in a laminating material by calculating a stress generated between layers when bending stress is applied to the laminating material,
Creating a shell model in which the laminated material is modeled by a number of flat plate elements;
By numerically analyzing the shell model by the finite element method, the stress distribution along the surface direction of both surfaces in each flat plate element is calculated,
For each plate element, find the radius of curvature in the two principal stress directions on the plane,
Calculate the interlayer stress corresponding to the stress in the direction from the stress value on both surfaces in the direction corresponding to the calculated radius of curvature,
A method for calculating an interlayer stress in a laminated material, wherein a sum of interlayer stresses in two directions is a solution of a maximum interlayer stress in the flat plate element. The interlaminar stress σmax corresponding to the stress in the direction is the surface of the curvature center side as the surface, the stress values in the direction of the _front and back surfaces are σ _table , σ _back , the calculated curvature radius is R, and the plate thickness is t In terms of
σmax = t / 8 / R × (σ _table− σ _back )
The interlayer stress calculation method in the laminated material according to claim 1, which is calculated by: The stress σz in the thickness direction corresponding to the stress in the direction is the stress in the stress direction of each of the σ _{M table} , σ _{m table} , and back surface, with the surface on the curvature center side as the surface. Values are σ _{M back} , σ _{m back} , surface radii of curvature in the stress direction on the RM _table , R _{m table} , and radii of curvature on the back in the stress direction on the RM _back , R _{m back} , plate thickness t In terms of
σz = t / 8 × (σ M _Table / R _{M Table} - [sigma] _{M Back} / R _{M back} + sigma _{m Table} / R _{m Table} - [sigma] _{m Back} / R _{m back)}
The interlayer stress calculation method in the laminated material according to claim 1, which is calculated by:   The laminated material is an anisotropic laminated plate obtained by laminating plates in which stress propagates only in one direction on a plane with different stress propagation directions, and the direction of the principal stress is compared between adjacent elements. 2. A method for calculating an interlaminar stress according to claim 1, wherein a differential value of the interlaminar shear stress due to each stress is obtained, and an approximate value of the interlaminar shear stress is obtained by multiplying the differential value by the thickness per layer.   The laminated material is an anisotropic laminated plate obtained by laminating a plate in which stress propagates only in one direction on a plane with different stress propagation directions, and by comparing the principal stress between adjacent elements, 2. A method for calculating an interlaminar stress according to claim 1, wherein a differential value of the interlaminar shear stress resulting from each of the main stresses is obtained, and an approximate value of the interlaminar shear stress is obtained by multiplying the differential value by the thickness per layer. The laminated material is an anisotropic laminated plate obtained by laminating plates in which stress propagates only in one direction on a plane with different stress propagation directions, and the in-plane stress is obtained from the main stress and the hook law in each layer. 2. An interlayer stress calculation method according to claim 1, wherein the interlayer shear stress is obtained from the balance between the calculation result and the force in each layer.

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