CN111504777A - Method for reading elastic modulus of non-uniform material - Google Patents
Method for reading elastic modulus of non-uniform material Download PDFInfo
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- CN111504777A CN111504777A CN202010481939.XA CN202010481939A CN111504777A CN 111504777 A CN111504777 A CN 111504777A CN 202010481939 A CN202010481939 A CN 202010481939A CN 111504777 A CN111504777 A CN 111504777A
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N3/00—Investigating strength properties of solid materials by application of mechanical stress
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Abstract
The invention discloses a method for reading the elastic modulus of a non-uniform material, which comprises the following steps: in a full stress-strain curve, sequentially selecting 100 different point values from left to right, wherein the interval between the point values is controlled by axial strain; performing one-time least square fitting on the selected 100 point values, and recording the slope; after continuously selecting the 101 st point value, carrying out one-time least square fitting on continuous 100 point values which are calculated from the 2 nd point value and contain the 101 th point value, and recording the slope of the continuous 100 point values; and by analogy, continuing to perform fitting according to the method, and recording the slope, wherein the maximum value of the slope of the straight line is the elastic modulus of the material. The method has the advantages that the elastic modulus of the non-uniform material is obtained by utilizing the maximum tangent modulus, so that subjective errors caused by manual selection of straight line segments are avoided, and the result is more objective and accurate; the method is simple and feasible to read on the basis of the original stress-strain.
Description
Technical Field
The invention relates to the technical field of elastic modulus calculation, in particular to a method for reading the elastic modulus of a non-uniform material.
Background
The elastic modulus is an important parameter for measuring the physical and mechanical properties of the material, and the elastic modulus refers to the ratio of the positive stress sigma to the elastic positive strain of a test piece under uniaxial stress.
For elastic materials, the stress-strain relationship is a linear relationship, and the slope of a straight line is the elastic modulus of the material, but for non-uniform materials, the stress-strain relationship is a curve, and when the elastic modulus is obtained, the slope of the straight line of the curve before the peak is generally taken as the elastic modulus of the material.
However, there is no uniform standard for how to define the straight line segments therein and the start and stop points of the straight line segments, and the straight line segments selected by different people or the same person at different times are different, which inevitably causes different elastic moduli of reading, and has a large subjective error, which greatly affects the result.
Disclosure of Invention
The invention discloses a method for reading the elastic modulus of a non-uniform material, which aims to solve the technical problem of subjective error in the elastic modulus calculation process.
The invention designs a method for reading the elastic modulus of the non-uniform material, which can objectively and accurately read the elastic modulus of the non-uniform material and avoid human subjective factors.
In order to achieve the purpose, the invention adopts the following technical scheme:
a method for reading the elastic modulus of a non-uniform material specifically comprises the following steps:
step one, a filter containing 100 points is adopted, 100 different point values are sequentially selected from left to right in a full stress-strain curve, and the interval between the point values is controlled by axial strain;
step two, performing one-time least square fitting on the selected 100 point values, and recording the slope;
after continuously selecting the 101 st point value, performing one-time least square fitting on continuous 100 point values which are calculated from the 2 nd point value and contain the 101 th point value, and recording the slope of the continuous 100 point values;
after continuously selecting the 102 th point value, continuously performing one-time least square fitting on continuous 100 point values which are calculated from the 3 rd point value and contain the 102 th point value, and recording the slope;
and step five, by analogy, continuing fitting according to the method of the step three or the method of the step four, and recording the slope, wherein the maximum value of the slope is the elastic modulus of the material.
Further, in the first step, the selection method of 100 point values includes: starting from the 1 st point value of the stress-strain curve, when the axial strain threshold is exceeded, adding a new point value in the calculation; and continuously selecting different new point values by adopting the same method, wherein the slopes of the selected 100 point values are determined by a least square fitting method.
Further, the interval between the point values is controlled by the axial strain, and the axial strain threshold is 0.01%, i.e. every 0.01% increase in axial strain, a new point value is added.
Further, in the stage of the curve before the peak, the slope of the least square method fitting straight line is increased and then reduced, and when the curve approaches to the straight line section, the slope of the least square method fitting straight line section reaches the maximum.
The method has the advantages that the elastic modulus of the non-uniform material is obtained by utilizing the maximum tangent modulus, so that subjective errors caused by manual selection of straight line segments are avoided, and the result is more objective and accurate; the method is simple and feasible to read on the basis of the original stress-strain.
Drawings
FIG. 1 is a schematic diagram of the full stress-strain curve of the present invention.
Detailed Description
The technical solutions of the present invention will be described clearly and completely with reference to the accompanying drawings, and it should be understood that the described embodiments are some, but not all embodiments of the present invention. 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.
A method for reading the elastic modulus of a non-uniform material specifically comprises the following steps:
(1) in the full stress-strain curve as shown in fig. 1, 100 different point values are sequentially selected from left to right by using a filter comprising 100 points, and the interval between the point values is controlled by the axial strain.
The selection method of 100 point values comprises the following steps:
starting from the first point value of the stress-strain curve (denoted by number 1), when the distance exceeds the axial strain threshold, a new point value is added in the calculation, denoted by number 2, that is to say: when the interval exceeds the axial strain threshold value by 0.01 percent, adding a new point value No. 2;
and by analogy, continuously selecting subsequent different point values, and respectively marking the selected 100 point values as No. 1, No. 2, No. 3, No. 4, No. 5, No. 6, No. 7, No. 8 and No. 9. . . . . . 98, 99 and 100, the slopes of the 100 point values are all determined by a least squares fitting method.
(2) And performing one least square fitting on 100 point values selected by the method, namely fitting the point values including No. 1, No. 2, No. 3 and No. 4. . . . . . . The first fit was made to 100 point values, including numbers 99 and 100, and the slope was recorded.
(3) And after continuously selecting No. 101 by adopting the same method, performing least square fitting on continuous 100 point values which are calculated from the No. 2 point value and contain the No. 101 point value, namely No. 2, No. 3, No. 4 and No. 5. . . . . . . The 99, 100 and 101 point values were fitted and their slopes recorded.
(4) After the No. 102 point value is continuously selected by adopting the same method, the least square method fitting is carried out on continuous 100 point values which are calculated from the No. 3 point value and contain the No. 102 point value, namely, the point values comprise No. 3, No. 4 and No. 5. . . . . . . Point values No. 99, 100, 101 and 102 were fitted and their slopes recorded.
(5) And (4) continuing to perform fitting according to the method in the step (3) or (4) after a new point value appears subsequently, and recording the slope, wherein the maximum value of the slope is the elastic modulus of the material.
In particular, in the process of the selection method of 100 point values, the interval between the point values is controlled by the axial strain, the axial strain threshold value is 0.01%, namely, a new point value is added every time the axial strain is increased by 0.01%.
In particular, in the stage of the curve before the peak, the slope of the least square method fitting straight line is increased and then reduced, and when the curve approaches to the straight line section, the slope of the least square method fitting straight line section reaches the maximum.
In particular, the maximum value of the slope of the least squares fit straight line is the elastic modulus of the material.
According to the invention, the elastic modulus of the non-uniform material is obtained by utilizing the maximum tangent modulus, so that subjective errors caused by manual selection of straight line segments are avoided, and the result is more objective and accurate; the method is simple and feasible to read on the basis of the original stress-strain.
It is to be understood that the above description is not intended to limit the present invention, and the present invention is not limited to the above examples, and those skilled in the art may make modifications, alterations, additions or substitutions within the spirit and scope of the present invention.
Claims (4)
1. A method for reading the elastic modulus of a non-uniform material is characterized by comprising the following steps:
step one, a filter containing 100 points is adopted, 100 different point values are sequentially selected from left to right in a full stress-strain curve, and the interval between the point values is controlled by axial strain;
step two, performing one-time least square fitting on the selected 100 point values, and recording the slope;
after continuously selecting the 101 st point value, performing one-time least square fitting on continuous 100 point values which are calculated from the 2 nd point value and contain the 101 th point value, and recording the slope of the continuous 100 point values;
after continuously selecting the 102 th point value, continuously performing one-time least square fitting on continuous 100 point values which are calculated from the 3 rd point value and contain the 102 th point value, and recording the slope;
and step five, by analogy, continuing fitting according to the method of the step three or the method of the step four, and recording the slope, wherein the maximum value of the slope is the elastic modulus of the material.
2. The method for reading the elastic modulus of the inhomogeneous material as claimed in claim 1, wherein in the first step, the 100 points are selected by: starting from the 1 st point value of the stress-strain curve, when the axial strain threshold is exceeded, adding a new point value in the calculation; the same method continues with the selection of different new point values, the slopes of the selected 100 point values being determined by a least squares fit method.
3. A method for reading the elastic modulus of a non-uniform material as claimed in claim 2, wherein the interval between the point values is controlled by the axial strain, and the threshold value of the axial strain is 0.01%, i.e. every 0.01% increase of the axial strain, a new point value is added.
4. A method as claimed in claim 3, wherein during the pre-peak period, the slope of the least squares fit line increases and then decreases, and when the line approaches the straight line, the slope of the least squares fit line reaches the maximum.
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Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112014217A (en) * | 2020-09-08 | 2020-12-01 | 湖南省力宇燃气动力有限公司 | Elastomer stiffness determination method |
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| CN101303283A (en) * | 2008-04-11 | 2008-11-12 | 北京联合大学 | Double-elastic modulus method when material load-deformation curve initial straight line segment is short |
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2020
- 2020-05-29 CN CN202010481939.XA patent/CN111504777A/en active Pending
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| JP2006015866A (en) * | 2004-07-01 | 2006-01-19 | Yokohama Rubber Co Ltd:The | Simulation method of heterogeneous material |
| CN101303283A (en) * | 2008-04-11 | 2008-11-12 | 北京联合大学 | Double-elastic modulus method when material load-deformation curve initial straight line segment is short |
| CN102359910A (en) * | 2011-07-27 | 2012-02-22 | 绍兴文理学院 | Determination method for critical plastic yield-point and initial elastic modulus of soil stress-strain curve |
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| CN112014217A (en) * | 2020-09-08 | 2020-12-01 | 湖南省力宇燃气动力有限公司 | Elastomer stiffness determination method |
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