A method for measuring and calculating the interlaminar shear strength of heterogeneous multilayer composite plates
By constructing the formula for normal stress and shear stress calculation of composite plates, the problem of inaccurate measurement of shear strength between heterogeneous multi-layer composite plates is solved, and the accurate analysis of the mechanical properties of composite plates is achieved.
Patent Information
- Application Number
- CN202210557058.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2022-05-19
- Publication Date
- 2025-04-11
- Estimated Expiration
- 2042-05-19
AI Technical Summary
It is difficult to accurately measure the interlayer shear strength of heterogeneous multilayer composite panels, especially when the mechanical properties of different materials are different and the thickness of each layer is different.
Based on the pure bending theory, a formula for calculating the normal stress during pure bending of three rectangular cross-section composite plates composed of different elastic modulus and different thicknesses was constructed, and a method for calculating shear stress at any position in the neutral surface position and thickness direction of the composite plate was derived, and the interlayer shear strength of n-layer rectangular cross-section composite plates was then calculated.
Through this method, the shear stress distribution and interlayer shear strength of heterogeneous multi-layer rectangular cross-section composite plates can be accurately calculated, breaking through the limitations of the existing method and providing more accurate mechanical properties analysis.
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Figure CN114839082B_ABST
Abstract
Description
Technical Field
[0001] The invention relates to the technical field of measurement and calculation of shear strength between layers of composite plates, and in particular to a method for measuring and calculating shear strength between layers of heterogeneous multi-layer composite plates. Background Art
[0002] Composite materials are materials with new properties that are composed of two or more materials of different properties using physical or chemical methods on a macroscopic scale. They have a series of advantages such as high specific strength and specific stiffness, high temperature resistance, and designable strength. They are widely used in aerospace, construction, transportation, machinery and other fields, and the strength of specimens made of composite materials has also become a hot topic of concern.
[0003] For composite materials with laminated structure, when adjacent layers have relative displacement, stress will be generated inside the specimen to prevent such change, and the existence of interlaminar stress will cause interlaminar damage of composite materials, so composite materials have poor interlaminar damage strength, especially interlaminar shear strength. Since composite materials often cause interlaminar damage during use, which in turn leads to the destruction of the entire specimen, it is an important task to improve the interlaminar shear strength of composite specimens and accurately test their shear strength.
[0004] Factors that affect the interlaminar shear strength of composite plates include surface treatment, composite temperature, composite process, etc. Many scholars have used various methods to improve the interlaminar shear strength of composite plates. Tw A, Qiang SA et al. deposited silicon carbide nanowires on carbon fibers by electrophoretic deposition, and then used chemical vapor deposition to in-situ graft graphene to prepare carbon fiber reinforced epoxy resin composites. The interlaminar shear strength of the composite was tested by a three-point bending test. Due to the improved interface between carbon fiber and epoxy resin, the interlaminar shear strength of the material was significantly improved. R Ding et al. grafted Ti2C modified by 3-aminopropyltriethoxysilane onto the surface of carbon fibers to improve the interface properties of continuous carbon fiber reinforced epoxy resin composites, and tested the interlaminar shear strength of the composite by a three-point bending test. The shear strength was significantly improved. Qiu B, Sun T et al. introduced carboxymethyl cellulose (CMC) and graphene oxide (GO) into the surface of carbon fibers through hydrogen bonds to make carbon fiber reinforced epoxy resin composites. The interlaminar shear strength of the composite was tested by a short beam shear method. The results showed that CMC and GO can significantly improve the interlaminar shear strength of the composite. At present, there are many studies on how to improve the interlaminar shear strength of composite material specimens, but there are few studies on the accurate test and calculation methods of the interlaminar shear strength of composite materials, which is very unfavorable for accurately exploring the mechanical properties of composite materials.
[0005] At present, the main methods for testing the interlaminar shear strength of composite materials are: ① three-point bending method (short beam shear method); ② four-point bending method; ③ asymmetric four-point bending method. Since the four-point bending method has a high requirement on the specimen length and the structure of the loading head is complex, the three-point bending method with a simple test is more commonly used. Madhavi P et al. studied the interlaminar shear strength of glass fiber fabric and carbon fiber fabric composites and tested their interlaminar shear strength using a short beam shear test; Pahr DH et al. studied the interlaminar shear strength of the same material using a short beam shear method and a double lap shear method. The results showed that the results obtained by the two test methods were significantly different. Finite element analysis proved that the standardized interlaminar shear strength evaluation procedure was more or less effective for the short beam shear method test. However, whether it is the three-point bending method, the four-point bending method, or the asymmetric four-point bending method, they are only applicable to the calculation of interlaminar shear strength of single-layer plates or isotropic plates (a single-layer plate is defined as a laminate composed of one or several layers of the same material and the same main direction). When the test specimen is not a single-layer board or an isotropic board, the obtained shear strength will be significantly different from the actual shear strength of the material. This is because according to the latest standards JC / T773-2010 and ASTM D2344, the formulas used to test shear strength are Among them, F is the maximum load, b is the width of the specimen, and H is the thickness of the specimen. This formula does not take into account the change in the elastic modulus of multi-layer plates, so it is only applicable to single-layer plates or isotropic plates with the neutral plane at the geometric center of the thickness.
[0006] In recent years, with the vigorous development of composite materials, the application of multi-material system composite plates has become increasingly widespread, such as metal and fiber reinforced composite composites, carbon / glass hybrid plates, etc. For such heterogeneous multilayer composite plates, due to the different mechanical properties of different materials and the different thicknesses of each layer of material, the neutral plane of the composite plate is no longer the geometric center of thickness, and the shear strength obtained by the existing test method without considering the change of modulus is also inaccurate. Therefore, it will be of great theoretical significance and application value to establish a scientific method for accurately calculating the interlayer shear strength of heterogeneous multilayer composite plates and break through the limitations of existing methods. Summary of the invention
[0007] In view of the technical problem that the existing method for measuring the interlaminar shear strength of composite materials is only applicable to single-layer composite plates or isotropic plates, and the neutral plane is at the geometric center of the thickness, the present invention proposes a method for measuring and calculating the interlaminar shear strength of heterogeneous multi-layer composite plates, which measures the shear strength more accurately.
[0008] In order to achieve the above-mentioned purpose, the technical scheme of the present invention is implemented as follows: a method for measuring and calculating the interlaminar shear strength of a heterogeneous multilayer composite plate, characterized in that the steps are as follows: starting from the pure bending theory, a normal stress calculation formula for a rectangular cross-section composite plate composed of three layers of plates with different elastic moduli and different thicknesses during pure bending is constructed; a method for calculating the shear stress at the neutral plane position and any position in the thickness direction of the composite plate is established based on the normal stress calculation formula; and a general calculation formula for the normal stress, neutral plane position and interlaminar shear stress distribution of an n-layer rectangular cross-section composite plate during pure bending is derived.
[0009] The calculation method of normal stress in pure bending of three-layer rectangular cross-section composite plates with elastic modulus and thicknesses E1, h1, E2, h2 and E3, h3 is:
[0010] With the symmetry axis of cross section A as the y-axis and the neutral axis as the z-axis, a spatial rectangular coordinate system is established. e is the external moment applied to the three-layer composite plate; the two sections with a distance of dx before deformation are e Under the action of the action, the two plates rotate around their respective neutral axes. Although the cross section runs through three layers of composite plates with different moduli, it remains flat after deformation. At this time, the strain at the position y away from the neutral plane is Where ρ is the radius of curvature of the neutral surface, then the stress here is E i is the elastic modulus of the composite plate;
[0011] For any micro internal force σdA on cross section A, which is composed of a parallel force system perpendicular to the cross section, since the internal force on cross section A is balanced with the external force on the left side of cross section A, the force system is reduced to a couple moment M z , that is, the bending moment:
[0012]
[0013] Among them, A1 is the area of the cross section A in the first layer, A2 is the area of the cross section A in the second layer, and A3 is the area of the cross section A in the third layer; E1 is the modulus of the first layer, E2 is the modulus of the second layer, and E3 is the modulus of the third layer; The bending moment is:
[0014]
[0015] Then, the stress in the first layer is That is, the normal stress of this layer during pure bending is:
[0016]
[0017] Similarly, the normal stress of the second layer in pure bending is:
[0018]
[0019] Normal stress in pure bending of the third layer:
[0020]
[0021] The calculation method of the neutral plane position of the composite plate is: when the modulus and thickness of each layer of the three-layer composite plate are given, the distance h0 from the neutral plane to the bottom is:
[0022]
[0023] Among them, h1 is the thickness of the first layer of plate, h2 is the thickness of the second layer of plate, and h3 is the thickness of the third layer of plate.
[0024] The calculation method of the shear stress at any position in the thickness direction of the three-layer rectangular cross-section composite plate is:
[0025] When a three-layer rectangular cross-section beam is bent by a transverse force, there is not only normal stress but also shear stress on the cross section. If the span of the beam is much larger than the height of the cross section, the normal stress during pure bending can still be used to calculate the normal stress during transverse bending.
[0026] Take a plane prr'p' with a distance y from the neutral plane and parallel to the neutral plane. Assume that the plane prr'p' is located on the first layer, F s is the shear force on section A and coincides with the y-axis. A section prnn1 is cut out from the composite plate. Then the section rnn'r' acts on the normal stress caused by the bending moment M, and the section pn1n1'p' acts on the normal stress caused by the bending moment M+dM. The resultant force on the section rnn'r' is:
[0027]
[0028]
[0029] in, A0 is the area of the cross section rnn'r', A 12 is the area of the first layer of section A below the horizontal line rr';
[0030] Similarly, the resultant force of the cross section pn1n1'p' is:
[0031]
[0032] In the top face prr 'p':
[0033] dF s =τbdx;
[0034] Where τ represents the shear stress of the horizontal line rr', and the force dF s , Satisfies the equilibrium equation:
[0035] Therefore, the shear stress when the plane prr'p' is located in the first layer can be obtained:
[0036] Similarly, the shear stress when the plane prr'p' is located in the second layer can be obtained:
[0037] in, A 22 is the area of the second layer of section A below the horizontal line rr';
[0038] If the plane prr'p' is located on the third layer, the shear stress is:
[0039] in, A 32 is the area of the third layer of section A below the horizontal line rr';
[0040] When the short beam shear method is used to test the shear strength, the loading head is located at the mid-span of the beam. At this time, on the cross section A: F is the load; Then we have:
[0041] ①In the first layer: -(h1+h2+h3-h0)≤y<-(h2+h3-h0), the shear stress is:
[0042]
[0043] ②In the second layer: -(h2+h3-h0)≤y<h0-h3, the shear stress is:
[0044]
[0045] ③ In the third layer: h0-h3≤y≤h0, the shear stress is:
[0046]
[0047] For an n-layer rectangular cross-section composite plate with a width of b, the modulus of the i-th layer is assumed to be E i , thickness is h i , the distance between the neutral plane and the bottom is h0, and the normal stress of the i-th layer in pure bending can be inferred: Distance of neutral plane from bottom: And the interlaminar shear stress of this layer:
[0048]
[0049] Where M is the bending moment, Ai2 represents the area of the i-th layer of cross section A under the horizontal line rr', A k represents the area of the kth layer of the cross section A, F s is the cross-sectional internal force, h k is the height of the kth layer.
[0050] For a three-layer rectangular cross-section composite plate with a width of b, assuming that the thickness of the composite plate is h, the elastic modulus of the first and second layers of the composite plate is E, and the elastic modulus of the third layer is nE, the distance from the neutral plane to the bottom is obtained When E1>3E3+E2, the neutral plane is located at the first layer; when E1≤3E3+E2 and E3≤3E1+E2, the neutral plane is located at the second layer; when E3>3E1+E2, the neutral plane is located at the third layer.
[0051] When the elastic modulus of the three-layer plate is the same, the rectangular cross-section composite plate degenerates into a single-layer composite plate or an isotropic laminate. At this time, the interlaminar shear stress is parabolically symmetrically distributed in the thickness direction, and the shear stress reaches the maximum at the geometric center of the thickness. The maximum interlaminar shear stress is proportional to the average shear stress. The ratio of the interlaminar shear stress to the average shear stress, that is, the maximum relative interlaminar shear stress, is 1.5, where H is the total thickness of the composite plate and b is the width; when the elastic modulus of the third layer gradually increases in the direction of being greater than the elastic modulus of the first and second layers, the neutral plane and the neutral axis gradually move toward the third layer. At this time, the composite plate is anisotropic, and the ratio of the interlaminar shear stress to the average shear stress, that is, the relative interlaminar shear stress, changes significantly faster in the third layer than in the first and second layers, and the maximum relative interlaminar shear stress is always located on the neutral axis.
[0052] For a three-layer rectangular cross-section composite plate with the same thickness of each layer and certain elastic modulus of the first and second layers, as the elastic modulus of the third layer gradually increases, its maximum relative interlaminar shear stress shows a trend of first decreasing and then increasing; for a three-layer rectangular cross-section composite plate with the same thickness and different elastic moduli, when the maximum modulus plate is composited on the second layer, the maximum relative interlaminar shear stress of the composite plate reaches the maximum; when the minimum modulus plate is composited on the second layer, the maximum relative interlaminar shear stress of the composite plate reaches the minimum.
[0053] When the upper and lower layers of a three-layer composite plate are made of the same composite material and the middle layer is a glue layer, the maximum interlaminar shear stress decreases with the increase of the thickness of the glue layer; the thinner the glue layer, the more the composite plate tends to be a single-layer composite plate, and the calculated shear strength difference becomes smaller and smaller; and as the thickness of the glue layer increases, the calculated shear strength difference gradually increases.
[0054] Beneficial effects of the present invention: Combined with the maximum load and interlaminar failure position measured by the three-point bending test, the method of the present invention can accurately calculate the shear stress distribution and interlaminar shear strength of heterogeneous multilayer rectangular cross-section composite plates. The present invention establishes a scientific method for accurately calculating the interlaminar shear strength of heterogeneous multilayer composite plates, breaks through the limitations of existing interlaminar shear strength testing methods, and fills the gap in this field.
[0055] For heterogeneous composite plates with composite materials, adhesive layers and steel plates in the upper, middle and lower layers respectively, the interlaminar shear stress calculated by the existing method is still parabola-symmetrically distributed, and the shear stress reaches the maximum at the geometric center of the composite plate thickness, and does not reflect the influence of modulus change on shear stress distribution. The interlaminar shear strength calculated based on the maximum load is much higher than the true value. The present invention establishes the relationship between interlaminar shear stress distribution and plate modulus change. The calculated interlaminar shear stress changes significantly in the steel layer with the largest modulus, while the change in the adhesive layer with the smallest modulus is relatively unobvious, and the obtained interlaminar shear strength is close to the true value. BRIEF DESCRIPTION OF THE DRAWINGS
[0056] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.
[0057] Figure 1 It is a schematic diagram of the process of the present invention.
[0058] Figure 2 Schematic diagram of the structure of the three-layer rectangular cross-section composite plate of the present invention during pure bending, wherein (a) is a stereoscopic diagram and (b) is a cross-sectional diagram along xoy.
[0059] Figure 3 This is the cross-sectional view of the neutral plane of the three-layer rectangular cross-section composite plate at the first layer.
[0060] Figure 4 Schematic diagram of the force analysis of the three-layer rectangular cross-section composite plate of the present invention, wherein (a) is the force condition of the cross section A of the composite plate, and (b) is the force condition of the prnn1 part of the composite plate.
[0061] Figure 5 Schematic diagram of the structure of an n-layer rectangular cross-section composite plate.
[0062] Figure 6 This is a curve of the ratio of interlaminar shear stress to average shear stress in the thickness direction of a three-layer rectangular cross-section composite plate with the same thickness of each layer when E1=E2=E and E3=nE.
[0063] Figure 7It is the ratio curve of maximum shear stress to average shear stress of three-layer rectangular cross-section composite plate with the same thickness of each layer when E1=E, E2=tE, E3=nE.
[0064] Figure 8 When the thickness of the upper and lower layers of the board is the same and there is a glue layer in the middle, the interlaminar shear stress distribution under different glue layer thicknesses.
[0065] Fig. 9 Schematic diagram of the three-point bending test of heterogeneous multilayer rectangular cross-section composite plates.
[0066] Fig.10 For a "glass fiber PP+glue+glass fiber PP" composite board, the interlaminar shear strength calculated by the present invention is compared with that calculated by the prior art method.
[0067] Fig.11 For a "glass fiber PP+glue+glass fiber PP" composite board, the interlaminar shear stress distribution calculated by the present invention is compared with that calculated by the existing method.
[0068] Fig.12 For a "glass fiber PP+glue+steel" heterogeneous composite board, the interlaminar shear strength calculation method of the present invention is compared with the existing method.
[0069] Fig.13 For a "glass fiber PP+glue+steel" heterogeneous composite board, the interlaminar shear stress distribution is calculated and compared between the present invention and the existing method. DETAILED DESCRIPTION
[0070] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.
[0071] like Figure 1 As shown, a method for measuring and calculating the interlaminar shear strength of heterogeneous multilayer composite plates is provided. For heterogeneous multilayer composite plates, starting from the pure bending theory, a calculation formula for the normal stress of a rectangular cross-section composite plate composed of three layers of plates with different elastic moduli and different thicknesses during pure bending is constructed; a calculation method for the shear stress at the neutral plane position and any position in the thickness direction of the composite plate is established based on the normal stress calculation formula; and a general calculation formula for the normal stress, neutral plane position and interlaminar shear stress distribution of an n-layer rectangular cross-section composite plate during pure bending is derived. For a three-layer rectangular cross-section composite plate, the interlaminar shear strength of the sample is calculated using the existing method and the present invention respectively, in combination with the maximum load and interlaminar failure position measured by the three-point bending test, and the two sets of data are compared and specifically analyzed.
[0072] For a three-layer rectangular cross-section composite plate with elastic modulus and thickness E1, h1, E2, h2, E3, h3 respectively, it is assumed that only a pair of equal and opposite force couples act on the longitudinal symmetry plane of the composite plate to make the composite plate pure bending. With the symmetry axis of cross section A as the y-axis and the neutral axis as the z-axis, a spatial rectangular coordinate system is established, such as Figure 2 As shown in (a), M e is the external moment of force applied to the composite plate. The two sections with a distance of dx before deformation have a moment of force M e Under the action of rotation around their respective neutral axes, although the cross section runs through three layers of composite plates with different moduli, it still remains flat after deformation, such as Figure 2 (b). At this time, the strain at a position y away from the neutral surface Where ρ is the radius of curvature of the neutral surface, then the stress here is E i is the elastic modulus of the plate at that location.
[0073] For any micro internal force σdA on the cross section A, which is composed of a spatial parallel force system perpendicular to the cross section, the parallel force system can be simplified into three internal force components: the axial force F parallel to the x-axis N =∫ A σdA; moment M of the couple about the y axis y =∫ A zσdA; moment M about the z axis z =∫ A ydA. Since the internal force on cross section A is balanced with the external force on the left side of cross section A, the equilibrium equation shows that F N =∫ A σdA=0,couple moment M y =∫ A zσdA=0. Therefore, the internal force system on the cross section A can be reduced to a couple moment M z , that is, the bending moment:
[0074] Among them, A1 is the area of the cross section A in the first layer, A2 is the area of the cross section A in the second layer, and A3 is the area of the cross section A in the third layer; E1 is the modulus of the first layer, E2 is the modulus of the second layer, and E3 is the modulus of the third layer. The bending moment is:
[0075]
[0076] Then, the stress in the first layer is That is, the normal stress of this layer during pure bending is:
[0077]
[0078] Similarly, the normal stress of the second layer in pure bending is:
[0079]
[0080] Normal stress in pure bending of the third layer:
[0081]
[0082] When the modulus and thickness of each layer constituting the three-layer rectangular cross-section composite plate change, the position of the neutral plane also changes accordingly. Based on the situation where the neutral plane is located in different layers, the distance h0 from the neutral plane to the bottom is calculated to obtain the specific position of the neutral plane.
[0083] Assume that the neutral surface is located at the first layer, such as Figure 3 As shown in Figure 2, the distribution law of normal stress in pure bending of the composite plate shows that:
[0084]
[0085] Substituting formulas (2), (3) and (4) into formula (5), we can obtain:
[0086]
[0087]
[0088] Among them, A 01 is the area of the first layer of cross section A above the neutral axis, A 10 is the area of the first layer of cross section A below the neutral axis, h1 is the thickness of the first layer, h2 is the thickness of the second layer, and h3 is the thickness of the third layer.
[0089] For the case where the neutral plane is located on the second and third layers, the distance h0 from the neutral plane to the bottom is calculated according to the above method, and the results are:
[0090] In summary, when the modulus and thickness of each layer of the three-layer rectangular cross-section composite plate are given, the position of the neutral plane can also be obtained, specifically the distance from the neutral plane to the bottom:
[0091]
[0092] When a three-layer rectangular cross-section beam is subjected to lateral bending, there is not only normal stress but also shear stress on the cross section A. When the ratio of the beam span to the cross-section height is greater than 5, the normal stress result calculated by pure bending theory is slightly lower, but the error does not exceed 1%, which meets the accuracy requirements in engineering. Therefore, formulas (2), (3) and (4) can still be used to calculate the normal stress during lateral bending.
[0093] Take the plane prr'p' with a distance y from the neutral plane and parallel to the neutral plane. Assume that the plane prr'p' is located in the first layer, such as Figure 4 As shown in (a), F s is the shear force on cross section A and coincides with the y-axis. A portion prnn1 is cut out from the composite plate. The force is as follows: Figure 4 (b) As shown in Figure 2, the normal stress caused by the bending moment M acts on the cross section rnn'r', and the normal stress caused by the bending moment M+dM acts on the cross section pn1n1'p'. The resultant force on the cross section rnn'r' is:
[0094]
[0095]
[0096] in, A0 is the area of the cross section rnn'r', A 12 It is the area of the first layer of section A located under the horizontal line rr'.
[0097] Similarly, the resultant force of the cross section pn1n1'p' is:
[0098]
[0099] In the top face prr 'p':
[0100] dF s =τbdx (9)
[0101] Where τ represents the shear stress of the horizontal line rr', and the force dF s , Satisfies the equilibrium equation:
[0102]
[0103] Substituting formulas (7), (8) and (9) into formula (10), we can obtain the shear stress:
[0104] Similarly, if the plane prr'p' is located on the second layer, the shear stress is:
[0105] in, A 22 It is the area of the second layer of cross section A located under the horizontal line rr'.
[0106] If the plane prr'p' is located on the third layer, the shear stress is:
[0107] in, A 32 It is the area of the third layer of section A located under the horizontal line rr'.
[0108] When the short beam shear method is used to test the shear strength, that is, the three-point bending test, the loading head is located at the mid-span of the beam. At this time, on the cross section A: F is the load. Then we have:
[0109] ①In the first layer: -(h1+h2+h3-h0)≤y<-(h2+h3-h0), the shear stress is:
[0110]
[0111] ②In the second layer: -(h2+h3-h0)≤y<h0-h3, the shear stress is:
[0112]
[0113] ③ In the third layer: h0-h3≤y≤h0, the shear stress is:
[0114]
[0115] For an n-layer rectangular cross-section composite plate with a width of b, such as Figure 5 As shown, assuming that the modulus of the i-th layer of plate is E i , thickness is h i , the distance between the neutral plane and the bottom is h0. Similarly, the normal stress of the i-th layer in pure bending can be deduced Distance from neutral plane to bottom And the interlaminar shear stress of this layer:
[0116]
[0117] Where M is the bending moment, A i2 represents the area of the i-th layer of cross section A under the horizontal line rr', A k represents the area of the kth layer of the cross section A, F s is the shear force on cross section A.
[0118] For a three-layer rectangular cross-section composite plate with a width of b and a thickness of h for each layer, assuming that the elastic modulus of the first and second layers is E and the elastic modulus of the third layer is nE, the interlaminar shear stress and the average shear stress at any position in the thickness direction can be calculated by the above method of the present invention. The ratio of is the relative interlaminar shear stress, H is the total thickness of the composite plate, such as Figure 6 As shown. Since the thickness of each layer is the same, formula (6) shows that: the distance from the neutral plane to the bottom When E1>3E3+E2, the neutral plane is located at the first layer; when E1≤3E3+E2 and E3≤3E1+E2, the neutral plane is located at the second layer; when E3>3E1+E2, the neutral plane is located at the third layer.
[0119] Depend on Figure 6 It can be seen that when the modulus of the three layers of plate materials are the same, the composite plate degenerates into a single-layer composite plate or an isotropic laminate. At this time, the interlaminar shear stress is parabolically symmetrically distributed in the thickness direction, and the shear stress reaches the maximum at the geometric center of the thickness of the composite plate. The ratio of the maximum shear stress to the average shear stress (maximum relative interlaminar shear stress) is 1.5. In this case, the calculation method of the present invention is consistent with the existing method. When the elastic modulus of the third layer gradually increases in the direction greater than the modulus of the first and second layers, the neutral plane and the neutral axis gradually move toward the third layer. At this time, the composite plate is anisotropic, and the relative interlaminar shear stress in the third layer changes significantly faster than the first and second layers, and the maximum relative interlaminar shear stress is always located on the neutral axis.
[0120] In order to further explore the variation law of the maximum shear stress at the neutral axis of the cross section, the present invention calculates the maximum relative interlaminar shear stress when the thickness of each layer is h, the elastic modulus E1=E, E2=tE, E3=nE (n ranges from 0.01 to 100), as shown in Figure 7 As shown. Figure 7 It can be found that: ① When the modulus of the first and second layers are the same (t = 1), with the increase of the modulus of the third layer, the maximum relative interlaminar shear stress first decreases and then increases, reaching the minimum at n = 1.60, which is 1.49; ② When t takes the values of 10, 50 and 100 respectively, the maximum relative shear stress still decreases first and then increases with the increase of the mature n. From this, the following rule can be inferred: For a three-layer rectangular cross-section composite plate with a certain modulus of the first and second layers, as the modulus of the third layer gradually increases, its maximum relative interlaminar shear stress first decreases and then increases.
[0121] Further comprehensive analysis can be deduced that: for three-layer rectangular cross-section composite plates with the same thickness and different moduli, when the plate with the largest elastic modulus is composited on the second layer, the maximum relative interlaminar shear stress of the composite plate reaches the maximum; when the plate with the smallest modulus is composited on the second layer, the maximum relative interlaminar shear stress of the composite plate reaches the minimum. For n-layer rectangular cross-section composite plates with different plate thickness and elastic modulus, the shear stress distribution in the cross-section thickness direction can also be calculated according to the above formula of the present invention.
[0122] In engineering practice, two plates of the same size are usually glued together to form a three-layer composite plate of "plate + glue + plate". At this time, the thickness of the glue layer is also an important factor affecting the interlaminar shear strength of the composite plate. Here, for the two cases of E1 = 100GPa, E2 = 3GPa, E3 = 100GPa and E1 = 100GPa, E2 = 3GPa, E3 = 200GPa, the method of the present invention calculates and analyzes the influence of the thickness of the glue layer on the interlaminar shear stress, as shown in the following figure: Figure 8 shown.
[0123] Depend on Figure 8 It can be seen that when the load F = 1kN, in the above two cases, the maximum interlaminar shear stress of the composite plate decreases with the increase of the thickness of the adhesive layer. The useful inspiration of this conclusion is that in engineering applications, the thickness of the adhesive layer can be appropriately increased to reduce the maximum interlaminar shear stress of the composite plate, and then the interlaminar damage can be avoided as much as possible under the condition of constant adhesive layer strength.
[0124] Experimental study on the measurement and calculation of interlaminar shear strength of heterogeneous multilayer composite plates:
[0125] 1.Main raw materials and equipment: 3M TM Scotch-Weld TM Composite material bonding polyurethane adhesive DP6310NS; 2mm thick glass fiber reinforced PP plate; 2mm thick DP590 steel plate; electronic universal testing machine.
[0126] 2. Tensile test
[0127] The glass fiber reinforced PP board was cut into strips of 15 mm*180 mm, and the tensile modulus was measured by an electronic universal testing machine: E=9.835 GPa.
[0128] 3. Three-point bending test
[0129] The standard size of the three-point bending test specimen is: (1) thickness H ≥ 2 mm; (2) the recommended length is: l = 10H, (3) the recommended width is: b = 5H. The schematic diagram of the three-point bending test is as follows Fig. 9 As shown, the fillet radius of the loading head is: r1 = 5mm ± 0.2mm; the fillet radius of the support is: r2 = 2mm ± 0.2mm; the span is: L = 5H ± 0.3mm, H is the average thickness of a group of specimens.
[0130] The glass fiber PP board and steel board were surface treated respectively, and then bonded with polyurethane adhesive DP6310NS to form "glass fiber PP + glue + glass fiber PP" composite board and "glass fiber PP + glue + steel" heterogeneous composite board. After curing at room temperature for 48 hours, the thickness of the composite board was measured respectively, and the test specimens were cut according to the above-mentioned size standards. Finally, a three-point bending test was carried out using a universal testing machine, with no less than 5 tests for each specimen, and the maximum load at the time of interlayer failure of the two composite boards was measured and recorded.
[0131] 4. Comparison of calculated interlaminar shear strength between the present invention and the existing method
[0132] Comparison of the interlaminar shear strength calculation results of the "glass fiber PP + glue + glass fiber PP" composite board, as shown in Table 1 and Fig.10 As shown. The experimental results show that: with the increase of the thickness of the adhesive layer, the maximum load at the time of interlayer destruction gradually increases, but the interlayer shear strength calculated by the present invention remains basically unchanged. In the combined test, the composite plates all cracked at the interface between the adhesive and the glass fiber PP plate. Because the interface shear strength is certain, the reliability of the calculation results of the present invention can be proved. By comparing the calculation results of the present invention with those of the existing method, it can be found that: when the adhesive layer is thin, the calculation results of the two are very close. When the thickness of the adhesive layer increases to 1.43mm, the results of the existing method are significantly greater than the results of the present invention. This is because, when the adhesive layer is thinner, the composite plate tends to be a single-layer composite plate, and the existing method is suitable for calculating the interlayer shear strength of a single-layer composite plate; however, when the thickness of the adhesive layer increases and the composite plate tends to be anisotropic, the existing method cannot consider the changes in the modulus of each layer of the composite plate, and is still calculated as a single-layer composite plate. Therefore, the calculation results are significantly deviated from the true value.
[0133] To further illustrate the limitations of existing methods, Fig.11 The calculation results of the shear stress in the thickness direction of the sample section under the maximum load are given. It can be found that with the increase of the thickness of the adhesive layer, the difference between the maximum interlaminar shear stress (i.e., interlaminar shear strength) calculated by the existing method and the present invention gradually increases.
[0134] Table 1 Comparison of calculation results of interlaminar shear strength of "glass fiber PP + glue + glass fiber PP" composite board
[0135]
[0136] The test and calculation results of the "glass fiber PP + glue + steel" heterogeneous composite board are shown in Table 2 and Fig.12As shown. When the composite plate is subjected to a three-point bending test, its failure position is still the interface between the glue and the glass fiber PP plate. Therefore, the true interlaminar shear strength of the composite plate must be consistent with that of "glass fiber PP + glue + glass fiber PP". Although the maximum loads at the time of failure of the two are different, the accurate measurement and calculation method will definitely give consistent results. By comparing Table 2 and Table 1, it can be found that the interlaminar shear strengths of the two composite plates calculated by the present invention are basically the same, that is, about 6.5Mpa, while the interlaminar strength of the "glass fiber PP + glue + steel" heterogeneous composite plate calculated by the existing method does exceed 10MPa, which is significantly different from the true value. This is because the "glass fiber PP + glue + steel" heterogeneous composite plate is completely anisotropic, and the existing method cannot take into account the changes in the modulus of each layer, so the calculation results deviate significantly from the true value.
[0137] To further illustrate that the existing methods are not suitable for the calculation of heterogeneous composite plates, Fig.13 The calculation results of shear stress in the thickness direction of the sample section under the maximum load are given. It can be found that the interlaminar shear stress calculated by the existing method is still parabola-symmetrically distributed, and the shear stress reaches the maximum at the geometric center of the composite plate thickness, and does not reflect the influence of modulus change on shear stress distribution. Therefore, the interlaminar shear strength calculated based on the maximum load is much higher than the true value. The present invention establishes the relationship between interlaminar shear stress distribution and plate modulus change. The calculated interlaminar shear stress changes significantly in the steel layer with the largest modulus, while the change in the glue layer with the smallest modulus is relatively insignificant, and the obtained interlaminar shear strength is close to the true value.
[0138] Table 2 Comparison of calculation results of interlaminar shear strength of “glass fiber PP+rubber+steel” heterogeneous composite panels
[0139]
[0140] It can be seen from the above embodiments that:
[0141] (1) The position of the neutral plane of the composite plate and the interlaminar shear stress are related to the elastic modulus and thickness of the constituent materials. The shear stress reaches its maximum at the neutral axis. The interlaminar shear stress changes rapidly in the high modulus interlaminar region and does not change significantly in the minimum modulus layer.
[0142] (2) For a three-layer rectangular cross-section composite plate with the same thickness of each layer and a certain modulus of the first and second layers, as the modulus of the third layer gradually increases, its maximum relative interlaminar shear stress shows a trend of first decreasing and then increasing.
[0143] (3) For three-layer rectangular cross-section composite plates with the same thickness and different elastic moduli, when the maximum modulus plate is composited on the second layer, the maximum relative interlaminar shear stress of the composite plate reaches the maximum; when the minimum modulus plate is composited on the second layer, the maximum relative interlaminar shear stress of the composite plate reaches the minimum.
[0144] (4) For the "glass fiber PP + glue + glass fiber PP" composite board, the thinner the glue layer, the more the composite board tends to be a single-layer composite board, and the existing method is also applicable to the calculation of the interlayer shear strength of this type of composite board; when the thickness of the glue layer increases and the composite board tends to be anisotropic, the existing method cannot consider the change of the elastic modulus of each layer of the composite board and still calculates it as a single-layer composite board. Therefore, the calculation result obviously deviates from the true value, while the present invention can still give a more accurate result.
[0145] (5) For the "glass fiber PP + glue + steel" heterogeneous composite board, the interlaminar shear stress calculated by the existing method is still parabola-symmetrically distributed, and the shear stress reaches the maximum at the geometric center of the composite board thickness, which does not reflect the effect of modulus change on shear stress distribution. The calculated interlaminar shear strength is much higher than the true value. However, the present invention establishes the relationship between interlaminar shear stress distribution and plate modulus change. The calculated interlaminar shear stress changes significantly in the steel layer with the largest modulus, while the change in the glue layer with the smallest modulus is relatively insignificant, and the obtained interlaminar shear strength is close to the true value.
[0146] The above embodiments illustrate that: for heterogeneous multi-layer composite panels, the shear strength calculated by the method of the present invention is more accurate than that calculated by the existing methods.
[0147] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims
1. A method for measuring and calculating the interlaminar shear strength of a heterogeneous multilayer composite plate, characterized in that: The steps are as follows: starting from the pure bending theory, a calculation formula for the normal stress of a rectangular cross-section composite plate composed of three layers of plates with different elastic moduli and different thicknesses during pure bending is constructed; a calculation method for the shear stress at the neutral plane position and any position in the thickness direction of the composite plate is established based on the normal stress calculation formula; a general calculation formula for the normal stress, neutral plane position and interlayer shear stress distribution of an n-layer rectangular cross-section composite plate during pure bending is derived; For an n-layer rectangular cross-section composite plate with a width of b, the modulus of the i-th layer is assumed to be E i , thickness is h i , the distance between the neutral plane and the bottom is h0, and the normal stress of the i-th layer in pure bending can be inferred: Distance of neutral plane from bottom: And the interlaminar shear stress of this layer: Where M is the bending moment, A i2 represents the area of the i-th layer of cross section A under the horizontal line rr', A k represents the area of the kth layer of the cross section A, F s is the cross-sectional internal force, h k is the height of the kth layer, y represents the distance from the neutral surface, E k represents the modulus of the kth layer of the plate, h m Represents the height of the mth layer, m=k+1, k+2...n.
2. The method for measuring and calculating the interlaminar shear strength of a heterogeneous multilayer composite plate according to claim 1, characterized in that: The calculation method of normal stress in pure bending of three-layer rectangular cross-section composite plates with elastic modulus and thicknesses E1, h1, E2, h2 and E3, h3 is: With the symmetry axis of cross section A as the y-axis and the neutral axis as the z-axis, a spatial rectangular coordinate system is established. e is the external moment applied to the three-layer composite plate; the two sections with a distance of dx before deformation are e Under the action of the action, the two plates rotate around their respective neutral axes. Although the cross section runs through three layers of composite plates with different moduli, it remains flat after deformation. At this time, the strain at the position y away from the neutral plane is Where ρ is the radius of curvature of the neutral surface, then the stress here is E i is the elastic modulus of the composite plate; For any micro internal force σdA on cross section A, which is composed of a parallel force system perpendicular to the cross section, since the internal force on cross section A is balanced with the external force on the left side of cross section A, the force system is reduced to a couple moment M z , that is, the bending moment: Among them, A1 is the area of the cross section A in the first layer, A2 is the area of the cross section A in the second layer, and A3 is the area of the cross section A in the third layer; E1 is the modulus of the first layer, E2 is the modulus of the second layer, and E3 is the modulus of the third layer; The bending moment is: Then, the stress in the first layer is That is, the normal stress of this layer during pure bending is: Similarly, the normal stress of the second layer in pure bending is: Normal stress in pure bending of the third layer:
3. The method for measuring and calculating the interlaminar shear strength of a heterogeneous multilayer composite plate according to claim 2, characterized in that: The calculation method of the neutral plane position of the composite plate is: when the modulus and thickness of each layer of the three-layer composite plate are given, the distance h0 from the neutral plane to the bottom is: Among them, h1 is the thickness of the first layer of plate, h2 is the thickness of the second layer of plate, and h3 is the thickness of the third layer of plate.
4. The method for measuring and calculating the interlaminar shear strength of a heterogeneous multi-layer composite plate according to claim 3 is characterized in that: The calculation method of the shear stress at any position in the thickness direction of the three-layer rectangular cross-section composite plate is: When a three-layer rectangular cross-section beam is bent by a transverse force, there is not only normal stress but also shear stress on the cross section. If the span of the beam is much larger than the height of the cross section, the normal stress during pure bending can still be used to calculate the normal stress during transverse bending. Take a plane prr'p' with a distance y from the neutral plane and parallel to the neutral plane. Assume that the plane prr'p' is located on the first layer, F s is the shear force on section A and coincides with the y-axis. A section prnn1 is cut out from the composite plate. Then the section rnn'r' acts on the normal stress caused by the bending moment M, and the section pn1n1'p' acts on the normal stress caused by the bending moment M+dM. The resultant force on the section rnn'r' is: in, A0 is the area of the cross section rnn'r', A 12 is the area of the first layer of section A below the horizontal line rr'; Similarly, the resultant force of the cross section pn1n1'p' is: In the top face prr 'p': dF s =τbdx; Where τ represents the shear stress of the horizontal line rr', and the force dF s , Satisfies the equilibrium equation: Therefore, the shear stress when the plane prr'p' is located in the first layer can be obtained: Similarly, the shear stress when the plane prr'p' is located in the second layer can be obtained: in, A 22 is the area of the second layer of section A below the horizontal line rr'; If the plane prr'p' is located on the third layer, the shear stress is: in, A 32 is the area of the third layer of section A below the horizontal line rr'; When the short beam shear method is used to test the shear strength, the loading head is located at the mid-span of the beam. At this time, on the cross section A: F is the load; Then we have: ①In the first layer: -(h1+h2+h3-h0)≤y<-(h2+h3-h0), the shear stress is: ②In the second layer: -(h2+h3-h0)≤y<h0-h3, the shear stress is: ③ In the third layer: h0-h3≤y≤h0, the shear stress is:
5. The method for measuring and calculating the interlaminar shear strength of a heterogeneous multi-layer composite plate according to claim 1, characterized in that: For a three-layer rectangular cross-section composite plate with a width of b, assuming that the thickness of the composite plate is h, the elastic modulus of the first and second layers of the composite plate is E, and the elastic modulus of the third layer is nE, the distance from the neutral plane to the bottom is obtained When E1>3E3+E2, the neutral plane is located at the first layer; when E1≤3E3+E2 and E3≤3E1+E2, the neutral plane is located at the second layer; when E3>3E1+E2, the neutral plane is located at the third layer.
6. The method for measuring and calculating the interlaminar shear strength of a heterogeneous multi-layer composite plate according to claim 1, characterized in that: When the elastic modulus of the three-layer plate is the same, the rectangular cross-section composite plate degenerates into a single-layer composite plate or an isotropic laminate. At this time, the interlaminar shear stress is parabolically symmetrically distributed in the thickness direction, and the shear stress reaches the maximum at the geometric center of the thickness. The maximum interlaminar shear stress is proportional to the average shear stress. The ratio of the interlaminar shear stress to the average shear stress, that is, the maximum relative interlaminar shear stress, is 1.5, where H is the total thickness of the composite plate and b is the width; when the elastic modulus of the third layer gradually increases in the direction of being greater than the elastic modulus of the first and second layers, the neutral plane and the neutral axis gradually move toward the third layer. At this time, the composite plate is anisotropic, and the ratio of the interlaminar shear stress to the average shear stress, that is, the relative interlaminar shear stress, changes significantly faster in the third layer than in the first and second layers, and the maximum relative interlaminar shear stress is always located on the neutral axis.
7. A method for measuring and calculating the interlaminar shear strength of a heterogeneous multi-layer composite plate according to claim 6, characterized in that: For a three-layer rectangular cross-section composite plate with the same thickness of each layer and certain elastic modulus of the first and second layers, as the elastic modulus of the third layer gradually increases, its maximum relative interlaminar shear stress shows a trend of first decreasing and then increasing; for a three-layer rectangular cross-section composite plate with the same thickness and different elastic moduli, when the maximum modulus plate is composited on the second layer, the maximum relative interlaminar shear stress of the composite plate reaches the maximum; when the minimum modulus plate is composited on the second layer, the maximum relative interlaminar shear stress of the composite plate reaches the minimum.
8. A method for measuring and calculating the interlaminar shear strength of a heterogeneous multi-layer composite plate according to claim 1 or 7, characterized in that: When the upper and lower layers of a three-layer composite plate are made of the same composite material and the middle layer is a glue layer, the maximum interlaminar shear stress decreases with the increase of the thickness of the glue layer; the thinner the glue layer, the more the composite plate tends to be a single-layer composite plate, and the calculated shear strength difference becomes smaller and smaller; and as the thickness of the glue layer increases, the calculated shear strength difference gradually increases.