CN102901673A - Method for measuring tensile and compression elastic modulus of sheets with inconsistent tensile and compression modulus - Google Patents

Abstract

The invention discloses a method for measuring tensile and compression elastic modulus of sheets with inconsistent tensile and compression modulus. The method is characterized by comprising the steps of: preparing a test specimen of which the length-width ratio is 10 to 1 from the sheets with inconsistent tensile and compression modulus; simply supporting two ends; exerting symmetrical transverse concentrated loads to the test specimen to form a four-point curve structure, so that the middle part of the test specimen is in a pure curve stress state; attaching resistance strain gages at the upper and lower surfaces of the middle point of the test specimen; measuring the strains of the upper and lower surfaces of the test specimen through a resistance strain gauge; deducing an analytical expression of the tensile and compression modulus, and the strains, bending moments and plate thickness of the upper and lower surfaces of a pure curve beam according to plane assumption of the pure curve state beam, and calculating the tensile and compression elastic modulus of the test specimen according to the deduced analytic formula on the basis of measuring the strains of the upper and lower surfaces of the middle point of the test specimen. According to the method, the tensile and compression elastic modulus of the sheets with inconsistent tensile and compression modulus can be measured by a single test, and the method has the characteristics of being simple in method, easy to achieve and high in measurement precision.

Description

The measuring method of the tension and compression elastic modulus of the inconsistent thin plate of tension and compression modulus

Technical field

The invention provides the measuring method of the tension and compression elastic modulus of the inconsistent thin plate of a kind of tension and compression modulus, belong to technical field of measurement and test.

Background technology

Many materials all draw, press different elastic propertys showing in varying degrees in the Practical Project, such as pottery, fiberglass, plastics, reinforced concrete, graphite, powdered metallurgical material, polymeric material and fibre reinforced composites etc.It is larger that their tensile strength and compressive strength not only differ, and draws, the compression elasticity modulus also is different.Growing along with science and technology, to researching and proposing of the mechaanical property of materials higher requirement, the potentiality of the material of development of new and excavated material self-characteristic have become new research trend.

The factors such as the mechanical property of its mechanical property of fibre reinforced composites and material matrix, fortifying fibre, fiber laying, production technology are closely related, only have the test specimen to taking from the fibre reinforced composites member to detect, could record exactly the mechanical property of fibre reinforced composites member.Tensile modulus of elasticity can record by tension test at an easy rate, but because the fiber-reinforced composite thin plate is all thinner, and general compression test will cause the flexing of test specimen under very little load, is difficult to its compressive modulus of elasticity of test.

Summary of the invention

The object of the present invention is to provide the measuring method of the tension and compression elastic modulus of the inconsistent thin plate of a kind of tension and compression modulus, its technical scheme is:

The measuring method of the tension and compression elastic modulus of the inconsistent thin plate of a kind of tension and compression modulus, it is characterized in that step is followed successively by: 1) the inconsistent thin plate of tension and compression modulus is made the test specimen that length breadth ratio is 10:1, the two ends freely-supported, apply symmetric transverse centre-point load at test specimen, form the four-point bending structure, make the test specimen middle part be in the pure bending stress state; 2) stick respectively resistance strain gage in the upper and lower surface of test specimen mid point, record the strain of test specimen upper and lower surface by strainmeter; 3) according to the hypothesis of plane mechanism of pure bending state beam, derive the analytical expression of tension and compression elastic modulus and the strain of pure bending beam upper and lower surface, moment of flexure and thickness of slab; The upper and lower surface strain data of the test specimen mid point that 4) resistance strain gage is recorded, substitution step 3) analytic formula that derives calculates the tension and compression elastic modulus of test specimen.

For realizing goal of the invention, described a kind of application of pure bending test is measured the method for the inconsistent thin plate tension and compression of tension and compression modulus elastic modulus, in step 3) in, from pure bending state beam, get a length and be little section of dx, relative rotation between little section two end section is d θ, the neutral line subsequent corrosion is ρ, is the normal strain ε of any point of y apart from coordinate on the cross section then _xFor

${\mathrm{\ϵ}}_x=\frac{(\mathrm{\ρ}+y)\mathrm{d\θ}-\mathrm{\ρd\θ}}{\mathrm{\ρd\θ}}=\frac{y}{\mathrm{\ρ}}---\left(1\right)$

According to the bilinearity characteristics of different modulus at the neutral point broken line, obtain normal stress σ by Hooke's law _x:

$\begin{array}{cc}{\mathrm{\&sigma;}}_x=E_T\&CenterDot;\frac{y}{\mathrm{\&rho;}}& y\&GreaterEqual;0\\ {\mathrm{\&sigma;}}_x=E_C\&CenterDot;\frac{y}{\mathrm{\&rho;}}& y<0\end{array}---\left(2\right)$

Wherein, E _TBe tensile modulus of elasticity, E _CBe compressive modulus of elasticity;

If the width of pure bending state beam is b, highly be h, the stretch section height is h _T, the compression section height is h _C, and h is arranged _T+ h _C=h,

Can get the F that vertically makes a concerted effort by the equation of static equilibrium _xAnd moment M _y:

$\begin{array}{cc}\mathrm{\&Sigma;}{F}_x=0& {\&Integral;}_{-h_C}^0{E}_C\&CenterDot;\frac{y}{\mathrm{\&rho;}}\&CenterDot;b\&CenterDot;\mathrm{dy}+{\&Integral;}_0^{h_T}{E}_T\&CenterDot;\frac{y}{\mathrm{\&rho;}}\&CenterDot;b\&CenterDot;\mathrm{dy}=0\\ \mathrm{\&Sigma;}{M}_y=M& {\&Integral;}_{-h_C}^0{E}_C\&CenterDot;\frac{y}{\mathrm{\&rho;}}\&CenterDot;b\&CenterDot;\mathrm{ydy}+{\&Integral;}_0^{h_T}{E}_T\&CenterDot;\frac{y}{\mathrm{\&rho;}}\&CenterDot;b\&CenterDot;\mathrm{ydy}=M\end{array}---\left(3\right)$

Integral formula (3):

$E_T=\frac{h_C^2}{h_T^2}{E}_C---\left(4\right)$

$E_C=\frac{3\mathrm{\&rho;M}}{b\&CenterDot;h_C^3}-\frac{E_T{h}_T^3}{h_C^3}---\left(5\right)$

With formula (4) substitution formula (5):

$E_C=\frac{3\mathrm{\&rho;M}}{{\mathrm{bh}}_C^2(h_C+h_T)}---\left(6\right)$

By formula (1), can try to achieve maximum tension line strain ε _XmaxWith maximum compression line strain ε _XminRespectively on the upper and lower surface of pure bending state beam, and

${\mathrm{\&epsiv;}}_{x\max }=\frac{h_T}{\mathrm{\&rho;}}---\left(7\right)$

With

${\mathrm{\&epsiv;}}_{x\min }=-\frac{h_C}{\mathrm{\&rho;}}---\left(8\right)$

With formula (7), formula (8) and h _T+ h _C=h simultaneous solution:

$h_T=\frac{{\mathrm{\&epsiv;}}_{x\max }}{{\mathrm{\&epsiv;}}_{x\max }-{\mathrm{\&epsiv;}}_{x\min }}h,$ $h_C=\frac{{-\mathrm{\&epsiv;}}_{x\min }}{{\mathrm{\&epsiv;}}_{x\max }-{\mathrm{\&epsiv;}}_{x\min }}h,$ $\mathrm{\&rho;}=\frac{h}{{\mathrm{\&epsiv;}}_{x\max }-{\mathrm{\&epsiv;}}_{x\min }}---\left(10\right)$

With formula (10) substitution formula (6) and formula (4):

$E_T=\frac{3({\mathrm{\&epsiv;}}_{x\max }-{\mathrm{\&epsiv;}}_{x\min })\&CenterDot;M}{b\&CenterDot;{\mathrm{<figure-callout\; id="2"\; label="h"\; filenames="HDA00002242449800012.png,HDA00002242449800013.png"\; state="\{\{state\}\}">h</figure-callout>}}^2\&CenterDot;{\mathrm{\&epsiv;}}_{x\max }^2},$ $E_C=\frac{3({\mathrm{\&epsiv;}}_{x\max }-{\mathrm{\&epsiv;}}_{x\min })\&CenterDot;M}{b\&CenterDot;{\mathrm{<figure-callout\; id="2"\; label="h"\; filenames="HDA00002242449800012.png,HDA00002242449800013.png"\; state="\{\{state\}\}">h</figure-callout>}}^2\&CenterDot;{\mathrm{\&epsiv;}}_{x\min }^2}---\left(11\right)$

Formula (11) has been set up the strain stress of the drawing of tension and compression elastic modulus different materials, compression elasticity modulus and cross section moment M, specimen width b, height of specimen h and test specimen upper and lower surface _XmaxAnd ε _XminBetween relation.

For realizing goal of the invention, the measuring method of the tension and compression elastic modulus of the inconsistent thin plate of described a kind of tension and compression modulus is in step 4) in, specimen width b, height of specimen h are known really quantitative, treat the length l between the freely-supported of test specimen two ends ₀, lateral symmetry load p and action of lateral load point position l ₁After determining, the cross section moment M=P of test specimen mid point * l ₁Also be known quantity, on the basis of the upper and lower surface strain that records the test specimen mid point, can calculate according to the analytic formula (11) that derives the tension and compression elastic modulus of test specimen.

The present invention compared with prior art, its advantage is:

1, flexing can not occur in this method test specimen in test process, has solved the measurement problem that is difficult to carry out compressive modulus of elasticity that causes owing to thin plate test specimen generation flexing in the compression test process;

2, can measure once by single test the tension and compression elastic modulus of the inconsistent thin plate of tension and compression modulus;

3, have method simple, realize easily, characteristics that measuring accuracy is high.

Description of drawings

Fig. 1 is the front view of standard specimen of the present invention;

Fig. 2 is the vertical view of standard specimen of the present invention;

Fig. 3 is test specimen four-point bending structural representation of the present invention;

Fig. 4 is the front view that test specimen posts the resistance strain gage paster among the present invention;

Fig. 5 is the vertical view that test specimen posts the resistance strain gage paster among the present invention;

Fig. 6 is the schematic diagram that the present invention tests.

Among the figure: 1, the test specimen strong point 2, test specimen 3, resistance strain gage 4, strainmeter 5, computer

Embodiment

The invention will be further described below in conjunction with accompanying drawing:

Among Fig. 1,2, for guaranteeing test condition standard, consistent, test result is accurate, at first needs the thin plate of taking from the fibre reinforced composites member is made standard specimen 2, and standard specimen 2 length are l, and width is b, highly is h, and length breadth ratio is 10:1.

Among Fig. 3, standard specimen 2 two ends by the test specimen strong point 1 freely-supported, are applied symmetric transverse centre-point load P at test specimen 2, two load p are l-2l apart ₁, make test specimen 2 form the four-point bending structure, test specimen 2 middle parts just are in the pure bending stress state like this.

Among Fig. 4,5, two resistance strain gages 3 are affixed on respectively the center on test specimen 2 upper and lower surfaces, namely are positioned at the l/2 place of test specimen 2 length directions, the b/2 place of Width.

Among Fig. 6, thin plate is made standard specimen 2, the test specimen strong point 1 freely-supported is passed through at two ends, and posts resistance strain gage 3 in the upper and lower surface of test specimen 2, and the output terminal of resistance strain gage 3 connects computer 5 through strainmeter 4.Apply symmetric transverse centre-point load P at test specimen 2, two load p are at a distance of l-2l ₁, standard specimen 2 occurs bending and deformation, and causes the distortion of test specimen 2 upper and lower surface resistance strain gages 3, and then has changed the resistance value of resistance strain gage 3, by computer 5 and strainmeter 4, can measure the strain value ε of standard specimen 2 upper and lower surfaces _XmaxAnd ε _XminSubstitution analytic formula (11) calculates the tension and compression elastic modulus of test specimen.

Instantiation numerical value is: material for test is that carbon fiber strengthens unidirectional laying thin plate, test specimen 2 thickness h=4.12mm, and the length and width of test specimen 2 is respectively l=300mm, b=30mm; Test specimen 2 bearing length l ₀=250mm, action of lateral load point position l ₁=86mm, transverse load P=1.1kN; Two resistance strain gages 3 are affixed on respectively the center on test specimen 2 upper and lower surfaces, namely are positioned at the 150mm place of test specimen 2 length directions, the 15mm place of Width; Measured the maximum stretching strain ε of test specimen 2 upper surfaces by strainmeter 4 _Xmax=9667 * 10 ^-6, the maximum compressive strain ε of test specimen lower surface _Xmin=-10705 * 10 ^-6With above-mentioned numerical value substitution (11), can calculate tensile modulus of elasticity and compressive modulus of elasticity is respectively:

$E_T=\frac{3(9667+10705)\&times;94.6\&times;{10}^{-6}}{0.03\&times;{0.00412}^2\&times;{9667}^2\&times;{10}^{-12}}=121.4\mathrm{GPa}$

$E_C=\frac{3(9667+10705)\&times;94.6\&times;{10}^{-6}}{0.03\&times;{0.00412}^2\&times;{(-10705)}^2\&times;{10}^{-12}}=99\mathrm{GPa}.$

Claims (3)

1. the measuring method of the tension and compression elastic modulus of the inconsistent thin plate of tension and compression modulus, it is characterized in that step is followed successively by: 1) the inconsistent thin plate of tension and compression modulus is made the test specimen that length breadth ratio is 10:1 (2), the two ends freely-supported, apply symmetric transverse centre-point load at test specimen (2), form the four-point bending structure, make test specimen (2) middle part be in the pure bending stress state; 2) stick respectively resistance strain gage (3) in the upper and lower surface of test specimen (2) mid point, record the strain of test specimen (2) upper and lower surface by strainmeter (4); 3) according to the hypothesis of plane mechanism of pure bending state beam, derive the analytical expression of tension and compression elastic modulus and the strain of pure bending beam upper and lower surface, moment of flexure and thickness of slab; The upper and lower surface strain data of test specimen (2) mid point that 4) resistance strain gage (3) is recorded, substitution step 3) analytic formula that derives calculates the tension and compression elastic modulus of test specimen (2).

2. the measuring method of the tension and compression elastic modulus of the inconsistent thin plate of a kind of tension and compression modulus as claimed in claim 1, it is characterized in that: in step 3) in, from pure bending state beam, get a length and be little section of dx, relative rotation between little section two end section is d θ, the neutral line subsequent corrosion is ρ, is the normal strain ε of any point of y apart from coordinate on the cross section then _xFor

${\mathrm{\&epsiv;}}_x=\frac{(\mathrm{\&rho;}+y)\mathrm{d\&theta;}-\mathrm{\&rho;d\&theta;}}{\mathrm{\&rho;d\&theta;}}=\frac{y}{\mathrm{\&rho;}}---\left(1\right)$

According to the bilinearity characteristics of different modulus at the neutral point broken line, obtain normal stress σ by Hooke's law _x:

$\begin{array}{cc}{\mathrm{\&sigma;}}_x=E_T\&CenterDot;\frac{y}{\mathrm{\&rho;}}& y\&GreaterEqual;0\\ {\mathrm{\&sigma;}}_x=E_C\&CenterDot;\frac{y}{\mathrm{\&rho;}}& y<0\end{array}---\left(2\right)$

Wherein, E _TBe tensile modulus of elasticity, E _CBe compressive modulus of elasticity;

If the width of pure bending state beam is b, highly be h, the stretch section height is h _T, the compression section height is h _C, and h is arranged _T+ h _C=h,

Can get the F that vertically makes a concerted effort by the equation of static equilibrium _xAnd moment M _y:

$\begin{array}{cc}\mathrm{\&Sigma;}{F}_x=0& {\&Integral;}_{-h_C}^0{E}_C\&CenterDot;\frac{y}{\mathrm{\&rho;}}\&CenterDot;b\&CenterDot;\mathrm{dy}+{\&Integral;}_0^{h_T}{E}_T\&CenterDot;\frac{y}{\mathrm{\&rho;}}\&CenterDot;b\&CenterDot;\mathrm{dy}=0\\ \mathrm{\&Sigma;}{M}_y=M& {\&Integral;}_{-h_C}^0{E}_C\&CenterDot;\frac{y}{\mathrm{\&rho;}}\&CenterDot;b\&CenterDot;\mathrm{ydy}+{\&Integral;}_0^{h_T}{E}_T\&CenterDot;\frac{y}{\mathrm{\&rho;}}\&CenterDot;b\&CenterDot;\mathrm{ydy}=M\end{array}---\left(3\right)$

Integral formula (3):

$E_T=\frac{h_C^2}{h_T^2}{E}_C---\left(4\right)$

$E_C=\frac{3\mathrm{\&rho;M}}{b\&CenterDot;h_C^3}-\frac{E_T{h}_T^3}{h_C^3}---\left(5\right)$

With formula (4) substitution formula (5):

$E_C=\frac{3\mathrm{\&rho;M}}{{\mathrm{bh}}_C^2(h_C+h_T)}---\left(6\right)$

By formula (1), can try to achieve maximum tension line strain ε _XmaxWith maximum compression line strain ε _XminRespectively on the upper and lower surface of pure bending state beam, and

${\mathrm{\&epsiv;}}_{x\max }=\frac{h_T}{\mathrm{\&rho;}}---\left(7\right)$

With

${\mathrm{\&epsiv;}}_{x\min }=-\frac{h_C}{\mathrm{\&rho;}}---\left(8\right)$

With formula (7), formula (8) and h _T+ h _C=h simultaneous solution:

$h_T=\frac{{\mathrm{\&epsiv;}}_{x\max }}{{\mathrm{\&epsiv;}}_{x\max }-{\mathrm{\&epsiv;}}_{x\min }}h,$ $h_C=\frac{{-\mathrm{\&epsiv;}}_{x\min }}{{\mathrm{\&epsiv;}}_{x\max }-{\mathrm{\&epsiv;}}_{x\min }}h,$ $\mathrm{\&rho;}=\frac{h}{{\mathrm{\&epsiv;}}_{x\max }-{\mathrm{\&epsiv;}}_{x\min }}---\left(10\right)$

With formula (10) substitution formula (6) and formula (4):

$E_T=\frac{3({\mathrm{\&epsiv;}}_{x\max }-{\mathrm{\&epsiv;}}_{x\min })\&CenterDot;M}{b\&CenterDot;h^2\&CenterDot;{\mathrm{\&epsiv;}}_{x\max }^2},$ $E_C=\frac{3({\mathrm{\&epsiv;}}_{x\max }-{\mathrm{\&epsiv;}}_{x\min })\&CenterDot;M}{b\&CenterDot;h^2\&CenterDot;{\mathrm{\&epsiv;}}_{x\min }^2}---\left(11\right)$

Formula (11) has been set up the strain stress of the drawing of tension and compression elastic modulus different materials, compression elasticity modulus and cross section moment M, test specimen (2) width b, test specimen (2) height h and test specimen (2) upper and lower surface _XmaxAnd ε _XminBetween relation.

3. the measuring method of the tension and compression elastic modulus of the inconsistent thin plate of a kind of tension and compression modulus as claimed in claim 1, it is characterized in that: in step 4) in, test specimen (2) width b, test specimen (2) height h are known really quantitative, treat the length l between the freely-supported of test specimen (2) two ends ₀, lateral symmetry load p and action of lateral load point position l ₁After determining, the cross section moment M=P of test specimen (2) mid point * l ₁Also be known quantity, on the basis of the upper and lower surface strain that records test specimen (2) mid point, can calculate according to the analytic formula (11) that derives the tension and compression elastic modulus of test specimen (2).

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