CN111563894A - Method and system for measuring bending stiffness of continuous fiber reinforced material - Google Patents
Method and system for measuring bending stiffness of continuous fiber reinforced material Download PDFInfo
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Abstract
The invention relates to a method and a system for measuring bending stiffness of a continuous fiber reinforced material. The method comprises the following steps: acquiring a bending deformation image of a continuous fiber reinforced material sample; extracting a central line of a bending deformation shape by adopting an image processing method according to the bending deformation image; fitting the central line of the bending deformation shape by adopting a uniform quadruplicate B-spline curve to obtain a fairing fitting curve; determining curvature and bending moment according to the fairing fitting curve; and determining the bending rigidity of the continuous fiber reinforced material sample according to the curvature and the bending moment. The method can accurately measure the bending stiffness of the continuous fiber reinforced material.
Description
Technical Field
The invention relates to the field of bending stiffness measurement, in particular to a method and a system for measuring bending stiffness of a continuous fiber reinforced material.
Background
Composite materials have found widespread use in the aerospace and automotive industries in recent years due to their superior properties of low density, high stiffness and high strength. The composite material consists of a matrix and a reinforcement, and the rigidity of the reinforcement is far greater than that of the matrix, so that the rigidity and the strength are provided for the composite material.
In structural engineering applications, continuous fiber materials have excellent mechanical properties and good formability and are often used as reinforcement materials for composite materials. Resin Transfer Molding (RTM) molding is currently the predominant molding manufacturing method for continuous fiber resin-based composites. In RTM, the first stage is the formation of dry fiber reinforcement to make a preform, and after formation the orientation and distribution of the fibers in the preform has a significant effect on the resin infusion in the second stage (mainly affecting resin permeability), and the orientation of the reinforcing fibers plays a crucial role in the mechanical properties of the final material. Therefore, numerical simulation of the forming process is essential, which can accurately predict the deformation of the fiber reinforcement, optimize the forming process conditions, avoid defects, and improve efficiency. For accurate modeling, an accurate knowledge of the mechanical behavior of the fiber-reinforced material is required. The fiber reinforcement material undergoes mainly stretching, in-plane shearing and bending deformation in the forming. Currently, most of the traditional simulation models only consider the stretching and in-plane shear deformation of fiber reinforced body materials, and adopt the film deformation theory to neglect the bending rigidity of the materials. One of the main reasons for this problem is the lack of an accurate measurement of the flexural stiffness of the material that characterizes the fiber reinforcement.
Disclosure of Invention
The invention aims to provide a method and a system for measuring the bending stiffness of a continuous fiber reinforced material, which can accurately measure the bending stiffness of the continuous fiber reinforced material.
In order to achieve the purpose, the invention provides the following scheme:
a method of measuring bending stiffness of a continuous fiber reinforced material, comprising:
acquiring a bending deformation image of a continuous fiber reinforced material sample;
extracting a central line of a bending deformation shape by adopting an image processing method according to the bending deformation image;
fitting the central line of the bending deformation shape by adopting a uniform quadruplicate B-spline curve to obtain a fairing fitting curve;
determining curvature and bending moment according to the fairing fitting curve;
and determining the bending rigidity of the continuous fiber reinforced material sample according to the curvature and the bending moment.
Optionally, the acquiring a bending deformation image of the continuous fiber reinforced material sample specifically includes:
and acquiring a bending deformation image of the continuous fiber reinforced material sample by using a CCD (charge coupled device) camera.
Optionally, the extracting a central line of the bending deformation shape according to the bending deformation image by using an image processing method specifically includes:
smoothing, enhancing contrast, thresholding and smoothing the shape of the curved image to obtain a processed image;
and performing skeletonization on the processed image by adopting a thinning method, and extracting a central line of the bending deformation shape.
Optionally, fitting the central line of the bending deformation shape by using a uniform quartic B-spline curve to obtain a fairing fitting curve, specifically including:
fitting the central line of the bending deformation shape by adopting a piecewise curve function to obtain a first fairing fitting curve;
and optimizing the first fairing fitted curve by adopting a method combining energy functional minimization and least square error to obtain a second fairing fitted curve.
A continuous fiber reinforced material bending stiffness measurement system comprising:
the image acquisition module is used for acquiring a bending deformation image of the continuous fiber reinforced material sample;
the image processing module is used for extracting a central line of the bending deformation shape according to the bending deformation image by adopting an image processing method;
the curve fitting module is used for fitting the central line of the bending deformation shape by adopting a uniform quartic B-spline curve to obtain a fairing fitting curve;
the curvature/bending moment determining module is used for determining curvature and bending moment according to the fairing fitting curve;
and the bending rigidity determining module is used for determining the bending rigidity of the continuous fiber reinforced material sample according to the curvature and the bending moment.
Optionally, the image obtaining module specifically includes:
and the image acquisition unit is used for acquiring the bending deformation image of the continuous fiber reinforced material sample by adopting a CCD (charge coupled device) camera.
Optionally, the image processing module specifically includes:
the image processing unit is used for carrying out smoothing, contrast enhancement, thresholding and shape smoothing on the curved image to obtain a processed image;
and the central line extraction unit is used for performing skeletonization on the processed image by adopting a thinning method and extracting the central line of the bending deformation shape.
Optionally, the curve fitting module specifically includes:
the fitting unit is used for fitting the central line of the bending deformation shape by adopting a piecewise curve function to obtain a first fairing fitting curve;
and the optimization unit is used for optimizing the first fairing fit curve by adopting a method combining energy functional minimization and least square error to obtain a second fairing fit curve.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects:
compared with the existing bending test method, the bending test method is simple to operate and set, allows the measurement of large enough bending deformation, obtains a wide bending moment-curvature relation, can accurately measure the bending rigidity of the continuous fiber reinforced material, and can be applied to the measurement of the bending rigidity of other materials. Based on the quartic uniform B-spline curve, selecting proper function segmentation quantity, overcoming the defect that a single polynomial curve function is limited by fitting precision and is easy to cause oscillation, and obtaining a smoother curve; in addition, the energy functional minimization and the least square error minimization are combined, the curve fitting error and the curve energy function are considered, the defect that unnecessary swinging is easily caused by a least square curve fitting method is overcome, a more reasonable curve is obtained, and the bending rigidity measurement accuracy is improved.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without inventive exercise.
FIG. 1 is a schematic diagram of a bending stiffness measurement method of the present invention;
FIG. 2 is a schematic view of a bending test apparatus according to the present invention;
FIG. 3 is a flow chart of a method for measuring bending stiffness of a continuous fiber reinforced material according to the present invention;
FIG. 4 is a schematic view of the curved shape smoothing process of the present invention;
FIG. 5 is a skeletonization and midline plot of the present invention;
FIG. 6 is a graph showing the effect of the number of uniform four B spline line segments on the curvature map fitting error and the smoothness;
FIG. 7 is an experimental plot of the present invention;
FIG. 8 is a structural diagram of a system for measuring bending stiffness of a continuous fiber reinforced material according to the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention aims to provide a method and a system for measuring the bending stiffness of a continuous fiber reinforced material, which can accurately measure the bending stiffness of the continuous fiber reinforced material.
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.
Recent studies have shown that bending stiffness is closely related to the shape and morphology of wrinkles, and therefore, to accurately predict defects that may occur during the forming process of wrinkles and the like, bending deformation must be considered in numerical simulation. Since relative slippage between fibers is very likely to occur, the bending stiffness of the continuous fiber reinforcement is not directly related to the in-plane tensile modulus, which is much less than that of a classical continuous material structure, and therefore the value thereof needs to be measured by an experimental method. Therefore, the invention provides a method for measuring the bending stiffness of a continuous fiber reinforced material, which adopts a cantilever beam clamping mode to carry out a bending test, utilizes a CCD (charge coupled device) camera to shoot a bending deformation shape image, calculates the bending deformation shape curvature of the fiber reinforced material based on an improved uniform B-spline curve theory, and further calculates the bending stiffness of the material; the method for measuring the bending stiffness of the continuous fiber reinforced material can also be applied to other material bending stiffness test methods.
FIG. 1 is a schematic diagram of a bending stiffness measurement method of the present invention. Firstly, shooting a bending deformation shape image of a sample by a high-resolution CCD camera (2048 multiplied by 2048 pixels), then extracting a central line of the bending deformation shape by adopting an image processing technology, finally fitting a bending curve function based on an optimized uniform B-spline curve, calculating curvature and corresponding bending moment along the central line by using the fitting curve, and obtaining the slope of the bending moment-curvature curve as the bending rigidity of the sample.
FIG. 2 is a schematic view of a bending test apparatus according to the present invention. The cross section of the sample was painted white with some dry white powder (to increase contrast with the background (black) and facilitate taking the midline in later image processing), the sample was clamped and deformed in cantilever fashion using a metal holder, a CCD camera (for taking a picture of the sample deformation) was connected to the acquisition software, and the image acquired by the acquisition software was transferred to the image processing software ImageJ for image processing. In image processing, the scale is placed in the same plane as the sample front edge and the scale is used to calculate the scaling factor (pixels/mm).
FIG. 3 is a flow chart of a method for measuring bending stiffness of a continuous fiber reinforced material according to the present invention. As shown in fig. 3, a method for measuring bending stiffness of a continuous fiber reinforced material includes:
step 101: the method for acquiring the bending deformation image of the continuous fiber reinforced material sample specifically comprises the following steps:
and acquiring a bending deformation image of the continuous fiber reinforced material sample by using a CCD (charge coupled device) camera.
A high-resolution CCD camera (2048 x 2048 pixels) is used for shooting a static image of the bending deflection shape of the sample, and the shot image is transmitted to acquisition software for processing.
Step 102: extracting a central line of a bending deformation shape by adopting an image processing method according to the bending deformation image, and specifically comprising the following steps of:
and carrying out smoothing, contrast enhancement, thresholding and shape smoothing on the bending deformation image to obtain a processed image. For the above four processes, the specific operations are as follows: 1) selecting a Gaussian blur filter to carry out smoothing processing on the bending deformation image, and reducing the noise level in the image; 2) contrast enhancement optimizes signal-to-noise ratio and normalizes the signal for processing and visualization; 3) performing thresholding to separate (also referred to as dividing) pixels having luminance values within a desired range from pixels not within the desired range and to separate the bending deflection shape of the sample from other parts; 4) the shape smoothing process is performed to make the curved shape smoother. FIG. 4 is a schematic diagram of the smoothing process for curved shapes according to the present invention, wherein a is the shape of noise and b is the shape of noise after smoothing.
And performing skeletonization on the processed image by adopting a thinning method, and extracting a central line of the bending deformation shape. Extracting a central line of the bending deflection shape of the test piece by using a skeletonization method defined by a thinning method in ImageJ, and specifically operating the following steps: using the scaling factor, physical cartesian coordinates of points on the skeleton are generated, and the curve represented by these discrete points is the centerline (deflection curve) of the bending deformation shape, with the results shown in fig. 5, which is the skeletonization and centerline plot of the present invention.
Step 103: adopting uniform four-time B-spline curve to fit the central line of the bending deformation shape to obtain a fairing fitting curve, which specifically comprises the following steps:
and step 1031, fitting the central line of the bending deformation shape by adopting a piecewise curve function to obtain a first fairing fitting curve.
A single polynomial curve function usually requires a very high order to have a good fitting accuracy and is prone to cause oscillations, whereas through experimental observations it was found that the bending deflection curve of a continuous fiber reinforcement usually consists of a plurality of curved shapes, so a piecewise curve function is used. For a given curve, its curvature is plotted against the arc length, resulting in a curvature map of the curve. The curve has good smoothness if there are no or few slope discontinuities in the curvature map. Selection of the number of segments for a uniform quartic B-spline: too few segments are used to represent the characteristics of the curve represented by these sample points, and too many segments are used to make the fitted curve follow the noise and have many unwanted fluctuations. Increasing the number of segments can reduce the fitting error between the sample data point and the fitting curve, but the smoothness of the curvature graph on the fitting curve becomes poor, and both the fitting precision and the curvature smoothness should be considered, so as to achieve a better fitting effect solution. In the invention, curve fitting is respectively carried out for one, three and four sections to respectively obtain the results shown in fig. 6, and in the process, when the curvature diagram begins to fluctuate, although the tolerance requirement cannot be met, the increase of the number of the sections is stopped, and finally the sections are selected to be divided into three sections. FIG. 6 is a graph showing the effect of the number of uniform quadruplicate B spline segments on curvature map fitting error and smoothness, according to the present invention, wherein FIGS. 6(a), (B) and (c) show the results obtained when one, three and four segments of fitting are used, respectively (left of the graph: sample data points and fitting curves; right of the graph: corresponding curvature distribution diagram): (a) the fitting error is 5.71 when one-section fitting is adopted; (b) when three-section fitting is adopted, the fitting error is 3.31; (c) the fitting error is 3.1 when four-segment fitting is used).
Step 1032: and optimizing the first fairing fitted curve by adopting a method combining energy functional minimization and least square error to obtain a second fairing fitted curve.
The energy functional minimization is combined with the least square error method, the defect of the least square curve fitting method is overcome, and the energy functional is used as the fairing term, so that the curve and the curved surface are smoother. And a fitting target function form is adopted, and curve fitting errors and a curve energy function are considered.
Step 104: and determining the curvature and the bending moment according to the fairing fitting curve.
The calculation process of the curvature and the bending moment in the invention is as follows:
the uniform quartic B-spline curve is a piecewise polynomial curve composed of multiple segments, each segment is a quartic B-spline function, and m segments are respectively numbered as 1, 2i-1And DiAre the start and end of the ith segment. The position vector of the point p on the ith segment is:
wherein X and Y are global Cartesian coordinates, u(i)Is the local parameter value of the point p along the i-th segment, B, varying from 0 to 1i+k-1Is a control point, Mk,4Is the basis function of a quartic B-spline curve:
from the local function of the p-point in equation (1), a global functional form is derived that represents the p-point location vector:
where m is the number of bus segments of the uniform quartic B-spline curve and t is the global parameter value for point p that varies from 0 to 1 along the uniform quartic B-spline curve.
Local parameter value u(i)The relationship to the global parameter value t is as follows:
u(i)＝mt-[mt](4)
[ mt ] represents the maximum integer not exceeding the product of m and t, i is the line segment number where the point p is located, and can be obtained according to the global parameter value:
i＝[mt]+1 (5)
Nh,4(t) global basis functions called uniform quartic B-spline curves:
combining the minimization of the energy functional with the minimization of the least square error, and considering the curve fitting error and the curve energy function to obtain the target function as follows:
where n is the total number of sample points, wjα, τ being a weighting factor, C (t) being a position vector of the global parameter value t on the uniform quartic B-spline curve, C ' (t), C ' (t) and C ' (t) representing the first, second and third derivatives of C (t) with respect to the global parameter t, respectively;
is a sampling point PjWherein chord length methods are used to calculate their values;
is a vector that stores c (t) control points; p ═ P0P1… Pn]TIs a vector of stored sample points, A is an (n +1) × (m +4) matrix of scalars, and W is a stored weighting factor WjAn (n +1) × (n +1) matrix:
n, N 'and N' are the first, second and third derivatives of N, respectively, with respect to the global parameter t; n is a vector containing a uniform quartic B-spline global basis function, N ═ N0，4(t)···Nm+3，4(t)]T(ii) a Because of the similarity with the mechanical properties of the material, K ═ jeep ═ jt(αN′(N′)T+βN″(N″)T+τN″′(N″′)T) dt is called the system stiffness matrix; item(s)
Referred to as the error term of the fit,
called the fairing term, which acts to smoothly fit the curve.
To implement the objective function solution, some boundary constraints are introduced. The fitted curve is required to pass through the first sampling point (the first sampling point is the pinch point of the bending deformation curve), the second derivative of the fitted curve of the last sampling point is zero (the last sampling point is the free end of the bending deformation curve), and the corresponding mathematical constraints are as follows:
the objective function under the boundary conditions is:
r matrix satisfies
D＝[C(0) C″(1)]TWhere Ψ is the Lagrangian multiplier vector, ψ ═ ψ1ψ2]TThe other terms have the same meaning, and the minimum is obtained
The following equation is obtained:
solving equation (15) yields equation (16)
The curvature of any point C (t) on the uniform quartic B-spline curve can be calculated by using the formula (16);
calculating the bending moment of any point A on the flexibility curve under the action of gravity by a formula (17);
wherein s is the abscissa of the curve of the point A; q is the weight per unit length of the sample (N/mm);
a unit vector that is the direction of gravity; l is the total length of the deflection curve; u is the Frey's inner coordinate of point B moving from A to F along the curve; du is the differential of u.
Step 105: and determining the bending rigidity of the continuous fiber reinforced material sample according to the curvature and the bending moment.
And calculating a bending moment-curvature curve according to the curvature and the bending moment, wherein the bending moment-curvature curve is the bending rigidity curve of the material. (Note: bending moment in bending moment-curvature curve means bending moment per unit width of material, which is equal to M/d, d is width of material sample in bending test.)
Continuous fiber reinforced composite materials such as Hexcel G1151 and 2.5D interlayer angle interlocking Interlock are selected to verify the measurement method, and experimental results prove that the bending stiffness measurement method is simple and convenient to use and effective in calculation results, and the calculation results are shown in figure 7. Fig. 7 is a graph of experimental bending according to the present invention, where a is a curvature graph using Hexcel G1151, b is a curvature-bending moment graph using Hexcel G1151, c is a curvature graph using 2.5D inter-layer angle Interlock, and D is a curvature-bending moment graph using 2.5D inter-layer angle Interlock, and it should be noted that bending may occur during bending, but when bending is small, the influence on the test result may be ignored.
The invention provides a method for measuring bending stiffness of a continuous fiber reinforced material, which is used for the research of determining the bending stiffness of the continuous fiber reinforced material by an experimental method; the method has the main technical idea that the bending deformation geometric characteristics of the test piece are obtained through an image processing technology, a fairing bending deformation central line curve is obtained through fitting based on an improved uniform four-time B-spline curve fitting method, the bending deformation curvature and the bending moment of the continuous fiber reinforced material can be accurately measured and calculated through combination of experimental calculation, and further the bending rigidity of the fiber reinforced material is obtained.
FIG. 8 is a structural diagram of a system for measuring bending stiffness of a continuous fiber reinforced material according to the present invention. As shown in fig. 8, a continuous fiber reinforced material bending stiffness measurement system includes:
the image acquisition module 201 is used for acquiring a bending deformation image of the continuous fiber reinforced material sample.
And the image processing module 202 is configured to extract a central line of the curved deformation shape according to the curved deformation image by using an image processing method.
And the curve fitting module 203 is used for fitting the central line of the bending deformation shape by adopting a uniform quartic B-spline curve to obtain a fairing fitting curve.
And a curvature/bending moment determining module 204, configured to determine a curvature and a bending moment according to the fairing fit curve.
And the bending rigidity determining module 205 is used for determining the bending rigidity of the continuous fiber reinforced material sample according to the curvature and the bending moment.
The image obtaining module 201 specifically includes:
and the image acquisition unit is used for acquiring the bending deformation image of the continuous fiber reinforced material sample by adopting a CCD (charge coupled device) camera.
The image processing module 202 specifically includes:
and the image processing unit is used for carrying out smoothing, contrast enhancement, thresholding and shape smoothing on the curved image to obtain a processed image.
And the central line extraction unit is used for performing skeletonization on the processed image by adopting a thinning method and extracting the central line of the bending deformation shape.
The curve fitting module 203 specifically includes:
and the fitting unit is used for fitting the central line of the bending deformation shape by adopting a piecewise curve function to obtain a first fairing fitting curve.
And the optimization unit is used for optimizing the first fairing fit curve by adopting a method combining energy functional minimization and least square error to obtain a second fairing fit curve.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. For the system disclosed by the embodiment, the description is relatively simple because the system corresponds to the method disclosed by the embodiment, and the relevant points can be referred to the method part for description.
The principles and embodiments of the present invention have been described herein using specific examples, which are provided only to help understand the method and the core concept of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In view of the above, the present disclosure should not be construed as limiting the invention.
Claims (8)
1. A method for measuring bending stiffness of a continuous fiber reinforced material is characterized by comprising the following steps:
acquiring a bending deformation image of a continuous fiber reinforced material sample;
extracting a central line of a bending deformation shape by adopting an image processing method according to the bending deformation image;
fitting the central line of the bending deformation shape by adopting a uniform quadruplicate B-spline curve to obtain a fairing fitting curve;
determining curvature and bending moment according to the fairing fitting curve;
and determining the bending rigidity of the continuous fiber reinforced material sample according to the curvature and the bending moment.
2. The method for measuring bending stiffness of continuous fiber reinforced material according to claim 1, wherein the acquiring of the bending deformation image of the continuous fiber reinforced material sample specifically comprises:
and acquiring a bending deformation image of the continuous fiber reinforced material sample by using a CCD (charge coupled device) camera.
3. The method for measuring bending stiffness of continuous fiber reinforced material according to claim 1, wherein the extracting a central line of a bending deformation shape by using an image processing method according to the bending deformation image specifically comprises:
smoothing, enhancing contrast, thresholding and smoothing the shape of the curved image to obtain a processed image;
and performing skeletonization on the processed image by adopting a thinning method, and extracting a central line of the bending deformation shape.
4. The method for measuring bending stiffness of continuous fiber reinforced material according to claim 1, wherein the fitting of the midline of the bending deformation shape by using a uniform quartic B-spline curve to obtain a fairing fitting curve specifically comprises:
fitting the central line of the bending deformation shape by adopting a piecewise curve function to obtain a first fairing fitting curve;
and optimizing the first fairing fitted curve by adopting a method combining energy functional minimization and least square error to obtain a second fairing fitted curve.
5. A continuous fiber reinforced material bending stiffness measurement system, comprising:
the image acquisition module is used for acquiring a bending deformation image of the continuous fiber reinforced material sample;
the image processing module is used for extracting a central line of the bending deformation shape according to the bending deformation image by adopting an image processing method;
the curve fitting module is used for fitting the central line of the bending deformation shape by adopting a uniform quartic B-spline curve to obtain a fairing fitting curve;
the curvature/bending moment determining module is used for determining curvature and bending moment according to the fairing fitting curve;
and the bending rigidity determining module is used for determining the bending rigidity of the continuous fiber reinforced material sample according to the curvature and the bending moment.
6. The system for measuring bending stiffness of continuous fiber reinforced material according to claim 5, wherein the image acquisition module specifically comprises:
and the image acquisition unit is used for acquiring the bending deformation image of the continuous fiber reinforced material sample by adopting a CCD (charge coupled device) camera.
7. The system for measuring bending stiffness of continuous fiber reinforced material according to claim 5, wherein the image processing module specifically comprises:
the image processing unit is used for carrying out smoothing, contrast enhancement, thresholding and shape smoothing on the curved image to obtain a processed image;
and the central line extraction unit is used for performing skeletonization on the processed image by adopting a thinning method and extracting the central line of the bending deformation shape.
8. The system for measuring bending stiffness of continuous fiber reinforced material according to claim 5, wherein the curve fitting module specifically comprises:
the fitting unit is used for fitting the central line of the bending deformation shape by adopting a piecewise curve function to obtain a first fairing fitting curve;
and the optimization unit is used for optimizing the first fairing fit curve by adopting a method combining energy functional minimization and least square error to obtain a second fairing fit curve.
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| 李军成著: "《形状可调的参数曲线曲面造型方法研究》", 31 May 2018, 成都：西南交通大学出版社 * |
| 王蕾: "基于图像技术的织物折皱回复性能研究", 《中国博士学位论文全文数据库 工程科技I辑》 * |
| 马立彬等编著: "《卫星导航定位与北斗系统应用 深化北斗应用 促进产业发展 2018版》", 31 August 2018, 北京：测绘出版社 * |
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