CN109100220B - Test method for obtaining uniaxial stress-strain relation of structural element - Google Patents

Test method for obtaining uniaxial stress-strain relation of structural element Download PDF

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CN109100220B
CN109100220B CN201810752469.9A CN201810752469A CN109100220B CN 109100220 B CN109100220 B CN 109100220B CN 201810752469 A CN201810752469 A CN 201810752469A CN 109100220 B CN109100220 B CN 109100220B
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CN109100220A (en
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蔡力勋
陈辉
包陈
刘晓坤
张志杰
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Chengdu Weili Tesi Technology Co ltd
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N3/00Investigating strength properties of solid materials by application of mechanical stress
    • G01N3/08Investigating strength properties of solid materials by application of mechanical stress by applying steady tensile or compressive forces
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N3/00Investigating strength properties of solid materials by application of mechanical stress
    • G01N3/20Investigating strength properties of solid materials by application of mechanical stress by applying steady bending forces
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2203/00Investigating strength properties of solid materials by application of mechanical stress
    • G01N2203/0001Type of application of the stress
    • G01N2203/0003Steady
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2203/00Investigating strength properties of solid materials by application of mechanical stress
    • G01N2203/0014Type of force applied
    • G01N2203/0016Tensile or compressive
    • G01N2203/0017Tensile
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2203/00Investigating strength properties of solid materials by application of mechanical stress
    • G01N2203/0014Type of force applied
    • G01N2203/0016Tensile or compressive
    • G01N2203/0019Compressive
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2203/00Investigating strength properties of solid materials by application of mechanical stress
    • G01N2203/0014Type of force applied
    • G01N2203/0023Bending
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2203/00Investigating strength properties of solid materials by application of mechanical stress
    • G01N2203/0058Kind of property studied
    • G01N2203/0069Fatigue, creep, strain-stress relations or elastic constants
    • G01N2203/0075Strain-stress relations or elastic constants
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2203/00Investigating strength properties of solid materials by application of mechanical stress
    • G01N2203/02Details not specific for a particular testing method
    • G01N2203/025Geometry of the test
    • G01N2203/0252Monoaxial, i.e. the forces being applied along a single axis of the specimen

Abstract

The invention relates to the field of mechanical tests, aims to solve the problems of narrow application range and large application limitation of a test method in the prior art, and provides a test method for obtaining a uniaxial stress-strain relation of a structural element, which comprises the following steps: 1) applying a monotonic load test to the object structural element and obtaining a load P-displacement h curve of the object structural element; 2) solving the area W enclosed by the P-h curves under different displacements h, namely the deformation energy W, and obtaining a deformation energy W-displacement h curve; 3) and performing linear fitting and other substitution calculation on the W-h curve under a lnh-lnW log-log coordinate system to finally obtain the uniaxial stress-strain relation of the measured material. The invention has the advantages that on one hand, the applicable objects are enlarged; on the other hand, the method unifies the analysis method for obtaining the uniaxial stress-strain relation of the measured material through different object component load-displacement curves, the same theoretical model and analysis steps are adopted, and the theoretical model is simpler than the prior art.

Description

Test method for obtaining uniaxial stress-strain relation of structural element
Technical Field
The invention relates to the field of mechanical tests, in particular to a test method for obtaining a uniaxial stress-strain relation of a structural element.
Background
The uniaxial stress-strain curve is a key link for establishing a relation between materials and mechanics, is also a basis for relating various mechanical properties (such as material strength, hardness, fatigue life and the like) of the materials, and plays an important role in the design and safety evaluation of engineering members. The conventional way to obtain the stress-strain relationship of materials is to select raw materials to process or to cut out standard tensile samples from engineering members and then to perform uniaxial tensile tests in a laboratory.
The test method and model in the prior art can only be suitable for testing one or a few components and loads, and have narrow application range and large application limitation.
Disclosure of Invention
The invention aims to provide a test method for obtaining a uniaxial stress-strain relation of a structural element, and solves the problems that the test method in the prior art is narrow in application range and large in application limitation.
The embodiment of the invention is realized by the following steps:
the embodiment of the invention provides a test method for obtaining a uniaxial stress-strain relation of a structural element, which comprises the following steps:
1) performing a monotonic load test on the object structural element, and obtaining a load P-displacement h curve of the object structural element;
2) solving the area W enclosed by the P-h curves under different displacements h, namely the deformation energy W, and obtaining a deformation energy W-displacement h curve, wherein the curve satisfies the formula (1):
W=αhm (1)
3) performing linear fitting on the W-h curve under a lnh-lnW log-log coordinate system to obtain parameters alpha and m;
4) substituting the results alpha and m obtained in the step 3) into the formula (2) to obtain constitutive relation parameters K and n of the measured structural element;
Figure BDA0001725904750000021
in the formula, v*Is a characteristic energy density and satisfies v*K/(1+ n), E is the known elastic modulus, n is the strain hardening index, K is the strain hardening coefficient, h*Is a characteristic displacement, beta1、β2、β3And beta4Is a dimensionless constant determined from the object construction elements and the corresponding experiments;
5) substituting the K and n results calculated by 4) into the formula (3) to obtain the uniaxial stress-strain relation of the tested material:
Figure BDA0001725904750000022
in the formula, σyIn order to be the nominal yield stress,
Figure BDA0001725904750000023
in one implementation of this embodiment:
the object element is a round bar, and the test is a torsional load applied to the round bar, wherein beta is1=156.4、β2=0、β3=0.04889、β4=1。
In one implementation of this embodiment:
the target member is a plate having a notch, and the test is performed by applying a tensile load to the plate having the notch, wherein beta is1=2.254、β2=-0.0483、β3=0.322、β4=1.048。
In one implementation of this embodiment:
the object elements are rings and the test is a radial compressive load applied to the rings, where beta is1=0.3791、β2=-0.08160、β3=0.144、β4=0.9184。
In one implementation of this embodiment:
the object construction element is a wafer;
the test is carried out by applying a radial compressive load to the disc, in which case beta1=0.9278、β2=-0.1703、β3=1.167、β41.129; or the test is carried out by applying a normal pressing load P to the disc, in which case beta1=0.9278、β2=-0.1703、β3=1.167、β4=1.129。
In one implementation of this embodiment:
the object structural element is a block body;
the test is as follows: applying a flat compressive load to the block, in which case beta1=13.03、β2=-0.3716、β3=0.3684、β40.8222; or the test is to apply a ball pressure load P to the block, in which case beta1=51.60、β2=-1.6708、β3=0.1578、β4=0.4333。
In one implementation of this embodiment:
the object structural element is a free beam, and the test is to apply pure bending load to the beam, wherein beta is the moment1=78.21、β2=-0、β3=0.1326、β4=1。
In one implementation of this embodiment:
the object structural element is a simply supported beam, the test is to apply bending load to the simply supported beam, and beta at the moment1=1.450、β2=-0.1014、β3=1、β4=1。
In one implementation of this embodiment:
the object structural element is a cantilever beam, and the test is to apply a bending load to the cantilever beam, at which time beta1=5.085、β2=-0.06000、β3=0.5121、β4=1。
The embodiment of the invention provides a test method for obtaining a uniaxial stress-strain relation of a structural element, which comprises the following steps:
1) performing a monotonic load test on the object structural element, and obtaining a load P-displacement h curve of the object structural element; wherein the subject construct and the corresponding assay are selected from any one of the following groups: applying a torsion load to the round rod, applying a tensile load to the plate with the notch, applying a radial compression load to the ring, applying a radial compression load to the circular sheet, applying a normal press-in load to the circular sheet, applying a flat compression load to the block, applying a ball compression load to the block, applying a pure bending load to the beam piece, applying a bending load to the simply supported beam and applying a bending load to the cantilever beam;
2) solving the area W enclosed by the P-h curves under different displacements h, namely the deformation energy W, and obtaining a deformation energy W-displacement h curve, wherein the curve satisfies the formula (1):
W=αhm (1)
3) performing linear fitting on the W-h curve under a lnh-lnW log-log coordinate system to obtain parameters alpha and m;
4) substituting the results alpha and m obtained in the step 3) into the formula (2) to obtain constitutive relation parameters K and n of the measured structural element;
Figure BDA0001725904750000041
in the formula, v*Is a characteristic energy density and satisfies v*K/(1+ n), E is the known elastic modulus, n is the strain hardening index, K is the strain hardening coefficient, h*Is a characteristic displacement, beta1、β2、β3And beta4Dimensionless constants determined by the subject's constitution and test for drinking, are taken from table 1 below:
Figure BDA0001725904750000042
Figure BDA0001725904750000051
table 1;
5) substituting the K and n results calculated by 4) into the formula (3) to obtain the uniaxial stress-strain relation of the tested material:
Figure BDA0001725904750000052
in the formula, σyIn order to be the nominal yield stress,
Figure BDA0001725904750000053
the test method for obtaining the uniaxial stress-strain relationship of the structural element disclosed in the embodiment of the invention can obtain the uniaxial stress-strain relationship of the material of the structural element to be tested through a test load-displacement curve under the load of pulling/bending and the like of the object structural element comprising a round rod, a block, a beam, a plate, a ring, a wafer, a block and the like. Compared with the prior art, the method has the advantages that applicable objects are enlarged on one hand, the existing block ball pressing and ring radial compression are enlarged into various objects such as round rod torsion, stretching of a plate with a notch, ring radial compression, normal pressing of a wafer, a pure curved beam, cantilever beam bending, simple supported beam bending, block ball pressing and block flat pressing, and the application range is greatly increased; on the other hand, the method unifies the analysis method for obtaining the uniaxial stress-strain relation of the measured material through different object load-displacement curves, the same theoretical model and analysis steps are adopted, and compared with the prior art, the theoretical model is simpler and has fewer parameters.
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In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the embodiments will be briefly described below, it should be understood that the following drawings only illustrate some embodiments of the present invention and therefore should not be considered as limiting the scope, and for those skilled in the art, other related drawings can be obtained according to the drawings without inventive efforts.
FIG. 1 illustrates the manner in which torsional loads are applied to a round bar;
FIG. 2 illustrates the manner in which a tensile load is applied to a panel having a gap;
FIG. 3 illustrates the manner in which radial compressive loads are applied to the ring;
FIG. 4 illustrates the manner in which radial compressive loads are applied to the disc;
FIG. 5 illustrates the manner in which a flat compressive load is applied to a block;
FIG. 6 illustrates the manner in which ball pressure loads are applied to the blocks;
FIG. 7 illustrates the manner in which pure bending loads are applied to the beam;
FIG. 8 illustrates the manner in which a normal press-in load is applied to the disc;
FIG. 9 illustrates the manner in which bending loads are applied to a simply supported beam;
FIG. 10 illustrates the manner in which bending loads are applied to a cantilever beam;
fig. 11-16 sequentially show uniaxial stress-strain relationship diagrams of the material of the measured object component obtained under six tests of applying a flat compression load to the block, applying a spherical compression load to the block, applying a radial compression load to the ring, applying a radial compression load to the wafer, applying a normal press-in load to the wafer, and applying a bending load to the cantilever beam.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, 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 some, but not all, embodiments of the present invention. The components of embodiments of the present invention generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations.
Thus, the following detailed description of the embodiments of the present invention, presented in the figures, is not intended to limit the scope of the invention, as claimed, but is merely representative of selected embodiments of the 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.
It should be noted that: like reference numbers and letters refer to like items in the following figures, and thus, once an item is defined in one figure, it need not be further defined and explained in subsequent figures.
In the description of the present invention, it should be noted that, if the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer", etc. indicate orientations or positional relationships based on the orientations or positional relationships shown in the drawings or the orientations or positional relationships that the products of the present invention are usually placed in when used, the terms are only used for convenience of describing the present invention and simplifying the description, and do not indicate or imply that the devices or elements indicated must have a specific orientation, be constructed in a specific orientation, and be operated, and thus, should not be construed as limiting the present invention. Furthermore, the appearances of the terms "first," "second," and the like in the description of the present invention are only used for distinguishing between the descriptions and are not intended to indicate or imply relative importance.
Furthermore, the terms "horizontal", "vertical" and the like when used in the description of the present invention do not require that the components be absolutely horizontal or overhanging, but may be slightly inclined. For example, "horizontal" merely means that the direction is more horizontal than "vertical" and does not mean that the structure must be perfectly horizontal, but may be slightly inclined.
In the description of the present invention, it should be further noted that unless otherwise explicitly stated or limited, the terms "disposed," "mounted," "connected," and "connected" should be interpreted broadly, and may be, for example, fixedly connected, detachably connected, or integrally connected; can be mechanically or electrically connected; they may be connected directly or indirectly through intervening media, or they may be interconnected between two elements. The specific meanings of the above terms in the present invention can be understood in specific cases to those skilled in the art.
Examples
The embodiment of the invention provides a test method for obtaining a uniaxial stress-strain relation of a structural element, which comprises the following steps:
1) performing a monotonic load test on the object structural element, and obtaining a load P-displacement h curve of the object structural element;
2) solving the area W enclosed by the P-h curves under different displacements h, namely the deformation energy W, and obtaining a deformation energy W-displacement h curve, wherein the curve satisfies the formula (1):
W=αhm (1)
3) performing linear fitting on the W-h curve under a lnh-lnW log-log coordinate system to obtain parameters alpha and m;
4) substituting the results alpha and m obtained in the step 3) into the formula (2) to obtain constitutive relation parameters K and n of the measured structural element;
Figure BDA0001725904750000081
in the formula (I), the compound is shown in the specification,v*is a characteristic energy density and satisfies v*K/(1+ n), E is the known elastic modulus, n is the strain hardening index, K is the strain hardening coefficient, h*Is a characteristic displacement, beta1、β2、β3And beta4Is a dimensionless constant determined from the object construction elements and the corresponding experiments;
5) substituting the K and n results calculated by 4) into the formula (3) to obtain the uniaxial stress-strain relation of the tested material:
Figure BDA0001725904750000082
in the formula, σyIn order to be the nominal yield stress,
Figure BDA0001725904750000083
wherein the subject construct and the corresponding test are selected from any one of the following groups: torsional loading of the round bar (loading is shown in fig. 1), tensile loading of the plate with the notch (loading is shown in fig. 2), radial compressive loading of the ring (loading is shown in fig. 3), radial compressive loading of the disc (loading is shown in fig. 4), normal compressive loading of the disc (loading is shown in fig. 8), flat compressive loading of the block (loading is shown in fig. 5), spherical compressive loading of the block (loading is shown in fig. 6), pure bending loading of the beam member (loading is shown in fig. 7), bending loading of the simply supported beam (loading is shown in fig. 9) and bending loading of the cantilever beam (loading is shown in fig. 10), and under different tests, β is1、β2、β3And beta4The values of (b) can be taken from table 1.
Figure BDA0001725904750000091
TABLE 1
Fig. 11 to 16 sequentially show uniaxial stress-strain relationships of materials of the measured object structural element obtained in six tests of applying a flat compression load to the block, applying a spherical compression load to the block, applying a radial compression load to the ring, applying a radial compression load to the wafer, applying a normal press-in load to the wafer, and applying a bending load to the cantilever beam.
In summary, the test method for obtaining the uniaxial stress-strain relationship of the structural element disclosed in the embodiment of the present invention can obtain the uniaxial stress-strain relationship of the measured structural element material through the test load-displacement curve under the load of pulling/bending the target structural element including the round rod, the block, the beam, the plate, the ring, the wafer, the block, and the like. Compared with the prior art, the method has the advantages that applicable objects are enlarged on one hand, the existing block ball pressing and ring radial compression are enlarged into various objects such as round rod torsion, stretching of a plate with a notch, ring radial compression, normal pressing of a wafer, a pure curved beam, cantilever beam bending, simple supported beam bending, block ball pressing and block flat pressing, and the application range is greatly increased; on the other hand, the method unifies the analysis method for obtaining the uniaxial stress-strain relationship of the measured material through different object load-displacement curves, the same theoretical model and analysis steps are adopted, and the theoretical model is simpler than the prior art scheme and has fewer parameters, so that simple structural elements which easily obtain the load-displacement curves can predict the uniaxial stress-strain relationship of the material through the technical scheme.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (4)

1. A test method for obtaining a uniaxial stress-strain relation of a structural element is characterized by comprising the following steps:
1) applying a monotonic load test to the object structural element and obtaining a load P-displacement h curve of the object structural element;
2) solving the area W enclosed by the P-h curves under different displacements h, namely the deformation energy W, and obtaining a deformation energy W-displacement h curve, wherein the curve satisfies the formula (1):
W=αhm (1)
3) performing linear fitting on the W-h curve under a lnh-lnW log-log coordinate system to obtain parameters alpha and m;
4) substituting the results alpha and m obtained in the step 3) into the formula (2) to obtain constitutive relation parameters K and n of the measured structural element;
Figure FDA0002989492030000011
in the formula, v*Is a characteristic energy density and satisfies v*K/(1+ n), E is the known elastic modulus, n is the strain hardening index, K is the strain hardening coefficient, h*Is a characteristic displacement, beta1、β2、β3And beta4Is a dimensionless constant determined from the object construction elements and the corresponding experiments;
5) substituting the K and n results calculated by 4) into the formula (3) to obtain the uniaxial stress-strain relation of the tested material:
Figure FDA0002989492030000012
in the formula, σyIn order to be the nominal yield stress,
Figure FDA0002989492030000013
2. the test method for obtaining the uniaxial stress-strain relationship of a structural element according to claim 1, wherein:
the object element is a round bar, and the test is a torsional load applied to the round bar, wherein beta is1=156.4、β2=0、β3=0.04889、β4=1。
3. The test method for obtaining the uniaxial stress-strain relationship of a structural element according to claim 1, wherein:
the target member is a plate having a notch, and the test is performed by applying a tensile load to the plate having the notch, wherein beta is1=2.254、β2=-0.0483、β3=0.322、β4=1.048。
4. A test method for obtaining a uniaxial stress-strain relation of a structural element is characterized by comprising the following steps:
1) performing a monotonic load test on the object structural element, and obtaining a load P-displacement h curve of the object structural element; wherein the subject construct and the corresponding assay are selected from any one of the following groups: the method comprises the following steps of applying torsion load to a round rod, applying tensile load to a plate with a notch, applying radial compression load to a ring, applying radial compression load to a circular sheet, applying normal pressing load to the circular sheet, applying flat compression load to a block, applying spherical compression load to the block, applying pure bending load to a beam piece, applying bending load to a simply supported beam and applying bending load to a cantilever beam;
2) solving the area W enclosed by the P-h curves under different displacements h, namely the deformation energy W, and obtaining a deformation energy W-displacement h curve, wherein the curve satisfies the formula (1):
W=αhm (1)
3) performing linear fitting on the W-h curve under a lnh-lnW log-log coordinate system to obtain parameters alpha and m;
4) substituting the results alpha and m obtained in the step 3) into the formula (2) to obtain constitutive relation parameters K and n of the measured structural element;
Figure FDA0002989492030000021
in the formula, v*Is a characteristic energy density and satisfies v*K/(1+ n), E is the known elastic modulus, n is the strain hardening index, K is the strain hardening coefficient, h*Is a characteristic displacement, beta1、β2、β3And beta4Is made of an objectThe values of the building elements and the corresponding experimentally determined dimensionless constants are taken from table 1 below:
Figure FDA0002989492030000022
Figure FDA0002989492030000031
table 1;
5) substituting the K and n results calculated by 4) into the formula (3) to obtain the uniaxial stress-strain relation of the tested material:
Figure FDA0002989492030000032
in the formula, σyIn order to be the nominal yield stress,
Figure FDA0002989492030000033
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