CN105136573B - A kind of static Young's modulus measurement method - Google Patents
A kind of static Young's modulus measurement method Download PDFInfo
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- CN105136573B CN105136573B CN201510539837.8A CN201510539837A CN105136573B CN 105136573 B CN105136573 B CN 105136573B CN 201510539837 A CN201510539837 A CN 201510539837A CN 105136573 B CN105136573 B CN 105136573B
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Abstract
The present invention relates to a kind of static Young's modulus measurement methods, belong to Young's modulus static measurement field.The present invention derives the Young's modulus static measurement formula based on finite element according to the theory relation in finite element theory between load, displacement, stiffness matrix.The present invention is measured without using special equipment and test specimen, only need to can be tested Young's modulus by common displacement measurement instrument, can be effectively reduced testing cost；The present invention is based on finite element theories, have wide applicability, can measure the Young's modulus under material actual condition, foundation is provided for structure optimization；Labyrinth test specimen can be measured, be applicable to the live Young's modulus test of arbitrary engineering structure, foundation is provided for selection；Based on finite element theory, measurement error meets the requirement of practical engineering application.
Description
Technical field
The present invention relates to a kind of static Young's modulus measurement methods, belong to Young's modulus static measurement field.
Background technology
Young's modulus is the important object for characterizing solid material deformation and resisting deformability with internal force relationship, description solid material
Reason amount, one of important parameter when it is mechanical component selection in engineering, therefore the Young's modulus measurement of material have important
Meaning.
The test of country's Young's modulus mainly uses static state method to test at present, predominantly static stretch method and beam deflection
Two kinds of method is mostly at present to improve measurement accuracy, such as Hall displacement using high-precision measuring apparatus to the improvement of both methods
Measuring appliance, laser interferometer, capacitance sensor etc., but there is still a need for dedicated test test specimen and special displacement test equipment, tests
Cost is higher.Both methods restricted application simultaneously, is not suitable for high temperature and fragile material, and test is constantly accompanied by relaxation mistake
Journey cannot truly reflect the variation of material internal structure.Measurement result has large error apart from actual value, influences in engineering
The selection and optimization of mechanical component.
Invention content
The object of the present invention is to provide a kind of static Young's modulus measurement methods, can realize through common displacement measurement
Instrument can test Young's modulus, to solve high, the unsuitable high-temperature brittleness testing of materials of current material Young's modulus measurement cost,
The problem of cannot really reflecting material internal structure variation.
The present invention is realized by following technical scheme：A kind of static Young's modulus measurement method, carries according in finite element theory
Theory relation between lotus, displacement, stiffness matrix derives the Young's modulus static measurement formula based on finite element；First, it is assumed that
Test specimen 1,2 is that structure, trellis-type and mesh generation, boundary condition, load are identical, material isotropic, only Young mould
Two different test specimens are measured, the Young's modulus of wherein test specimen 1 is unknown, can not calculate displacement, therefore test specimen 1 is tested by static displacement
Obtain displacement；Then, it is identical with static experiment that environmental parameter is arranged in test specimen 2 in finite element software, establish with it is static
Consistent finite element model is tested, and assumes Young's modulusValue, carry out finite element solving, find and measurement point corresponding points
Displacement.It will、、It brings intoObtain the Young's modulus of test specimen 1。
Obtain the calculation formula of Young's modulusThe specific method is as follows：
First, it is assumed that test specimen 1,2 is that structure, trellis-type and mesh generation, boundary condition, load are identical, material
Two different test specimens of isotropic, only Young's modulus, according to finite element theory, the relationship of load and displacement：
（1）
In formula：For load；
For global stiffness matrix；
For displacement.
Can obtain test specimen 1,2 load and displacement relationship：
（2）
In formula：For the global stiffness matrix of test specimen 1；
For the global stiffness matrix of test specimen 2；
For the displacement of test specimen 1；
For the displacement of test specimen 2.
Test specimen 1,2 load are identical, by formula（2）Global stiffness matrix and the relationship of displacement in test specimen 1,2, which can be obtained, is：
（3）
Then, according in finite element theory, the stiffness matrix and Young's modulus of isotropic material are linear i.e.：
（4）
In formula：For global stiffness matrix；
For Young's modulus；
For the global stiffness matrix of unit Young's modulus.
By formula（4）The global stiffness matrix of test specimen 1,2 is represented by：
（5）
In formula：For the Young's modulus of test specimen 1；
For the Young's modulus of test specimen 2；
For the global stiffness matrix of the unit Young's modulus of test specimen 1；
For the global stiffness matrix of the unit Young's modulus of test specimen 2.
By formula（5）Bring formula into（3）It can obtain：
（6）
Due to test specimen 1,2 structures, trellis-type and mesh generation, boundary condition all same, according to finite element theory
The global stiffness matrix of unit Young's modulus is identical, i.e.,：
（7）
By formula（7）Bring formula into（6）It can obtain：
（8）
Motion vectorLinear correlation, it is according to linear algebra theory, then vectorialIn corresponding element it is same
Sample meets linear relationship, i.e.,：
（9）
In formula：For on test specimen 1iThe displacement of point；
For on test specimen 2iThe displacement of point.
It obtains、With the Young's modulus of test specimen 2, the Young's modulus of test specimen 1 can be obtained。
The invention has the advantages that：
1, it is measured without using special equipment and test specimen, only need to can test poplar by common displacement measurement instrument
Family name's modulus can effectively reduce testing cost；
2, the present invention is based on finite element theories, have wide applicability, can measure the Young mould under material actual condition
Amount, foundation is provided for structure optimization；
3, labyrinth test specimen can be measured, is applicable to the live Young's modulus test of arbitrary engineering structure,
Foundation is provided for selection；
4, it is based on finite element theory, measurement error meets the requirement of practical engineering application.
Description of the drawings
Fig. 1 is the implementation method schematic diagram of the present invention.
Specific implementation mode
With reference to the accompanying drawings and examples, the invention will be further described, but present disclosure be not limited to it is described
Range.
Embodiment 1：As shown in Figure 1, a kind of static Young's modulus measurement method, according to load in finite element theory, displacement,
Theory relation between stiffness matrix derives the Young's modulus static measurement formula based on finite element；First, it is assumed that test specimen 1,2
Identical for structure, trellis-type and mesh generation, boundary condition, load, material isotropic, only Young's modulus are different
Two test specimens, the Young's modulus of wherein test specimen 1 is unknown, can not calculate displacement, therefore test specimen 1 is tested by static displacement and obtains displacement
Amount；Then, it is identical with static experiment that environmental parameter is arranged in test specimen 2 in finite element software, establishes consistent with static experiment
Finite element model, and assume Young's modulusValue, carry out finite element solving, find the displacement with measurement point corresponding points.It will、、It brings intoObtain the Young's modulus of test specimen 1。
Obtain the calculation formula of Young's modulusThe specific method is as follows：
First, it is assumed that test specimen 1,2 is that structure, trellis-type and mesh generation, boundary condition, load are identical, material
Two different test specimens of isotropic, only Young's modulus, according to finite element theory, the relationship of load and displacement：
（1）
In formula：For load；
For global stiffness matrix；
For displacement.
Can obtain test specimen 1,2 load and displacement relationship：
（2）
In formula：For the global stiffness matrix of test specimen 1；
For the global stiffness matrix of test specimen 2；
For the displacement of test specimen 1；
For the displacement of test specimen 2.
Test specimen 1,2 load are identical, by formula（2）Global stiffness matrix and the relationship of displacement in test specimen 1,2, which can be obtained, is：
（3）
Then, according in finite element theory, the stiffness matrix and Young's modulus of isotropic material are linear i.e.：
（4）
In formula：For global stiffness matrix；
For Young's modulus；
For the global stiffness matrix of unit Young's modulus.
By formula（4）The global stiffness matrix of test specimen 1,2 is represented by：
（5）
In formula：For the Young's modulus of test specimen 1；
For the Young's modulus of test specimen 2；
For the global stiffness matrix of the unit Young's modulus of test specimen 1；
For the global stiffness matrix of the unit Young's modulus of test specimen 2.
By formula（5）Bring formula into（3）It can obtain：
（6）
Due to test specimen 1,2 structures, trellis-type and mesh generation, boundary condition all same, according to finite element theory
The global stiffness matrix of unit Young's modulus is identical, i.e.,：
（7）
By formula（7）Bring formula into（6）It can obtain：
（8）
Motion vectorLinear correlation, it is according to linear algebra theory, then vectorialIn corresponding element it is same
Sample meets linear relationship, i.e.,：
（9）
In formula：For on test specimen 1iThe displacement of point；
For on test specimen 2iThe displacement of point.
It obtains、With the Young's modulus of test specimen 2, the Young's modulus of test specimen 1 can be obtained。
Claims (1)
1. a kind of static Young's modulus measurement method, it is characterised in that：According to load, displacement, stiffness matrix in finite element theory
Between theory relation, derive the Young's modulus static measurement formula based on finite element；First, it is assumed that test specimen 1,2 is structure, net
Lattice type and mesh generation, boundary condition, load are identical, two different test specimens of material isotropic, only Young's modulus,
The Young's modulus of wherein test specimen 1 is unknown, can not calculate displacement, therefore test specimen 1 is tested by static displacement and obtains displacement；So
Afterwards, test specimen 2 is arranged that environmental parameter is identical with static experiment in finite element software, establishes the finite element consistent with static experiment
Model, and assume Young's modulusValue, carry out finite element solving, find the displacement with measurement point corresponding points；
It will、、It brings intoObtain the Young's modulus of test specimen 1；
Obtain the calculation formula of Young's modulusThe specific method is as follows：
First, it is assumed that test specimen 1,2 is that structure, trellis-type and mesh generation, boundary condition, load are identical, material is every
Two different test specimens of the same sex, only Young's modulus, according to finite element theory, the relationship of load and displacement：
（1）
In formula：For load；
For global stiffness matrix；
For displacement；
Can obtain test specimen 1,2 load and displacement relationship：
（2）
In formula：For the global stiffness matrix of test specimen 1；
For the global stiffness matrix of test specimen 2；
For the displacement of test specimen 1；
For the displacement of test specimen 2；
Test specimen 1,2 load are identical, by formula（2）Global stiffness matrix and the relationship of displacement in test specimen 1,2, which can be obtained, is：
（3）
Then, according in finite element theory, the stiffness matrix and Young's modulus of isotropic material are linear i.e.：
（4）
In formula：For global stiffness matrix；
For Young's modulus；
For the global stiffness matrix of unit Young's modulus；
By formula（4）The global stiffness matrix of test specimen 1,2 is represented by：
（5）
In formula：For the Young's modulus of test specimen 1；
For the Young's modulus of test specimen 2；
For the global stiffness matrix of the unit Young's modulus of test specimen 1；
For the global stiffness matrix of the unit Young's modulus of test specimen 2；
By formula（5）Bring formula into（3）It can obtain：
（6）
Due to test specimen 1,2 structures, trellis-type and mesh generation, boundary condition all same, according to finite element theory unit
The global stiffness matrix of Young's modulus is identical, i.e.,：
（7）
By formula（7）Bring formula into（6）It can obtain：
（8）
Motion vectorLinear correlation, it is according to linear algebra theory, then vectorialIn corresponding element it is equally full
Sufficient linear relationship, i.e.,：
（9）
In formula：For on test specimen 1iThe displacement of point；
For on test specimen 2iThe displacement of point；
It obtains、With the Young's modulus of test specimen 2, the Young's modulus of test specimen 1 can be obtained。
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| CN112347672A (en) * | 2020-10-29 | 2021-02-09 | 东风汽车股份有限公司 | Method for measuring Young modulus of plastic part |
| CN113239519B (en) * | 2021-04-14 | 2022-03-01 | 上海医钛科技有限公司 | Construction method of Young modulus prediction model of additive manufacturing lattice material based on small slenderness |
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