CN105547861A - Method for enhancing capability of testing modulus of elasticity and precision of Poisson's ratio of wood by four-point bent beam - Google Patents

Abstract

The invention provides a method for enhancing the capability of testing modulus of elasticity and precision of Poisson's ratio of wood by a four-point bent beam. According to the method, the bent beam is cuboid with the width of b and thickness of h; the length of load span is l; a horizontal strain gage is pasted to the central point part in the middle of the bent beam; a longitudinal strain gage is in contact with the horizontal strain gage; the length to thickness ratio l/h is 16-20; the width to thickness ratio b/h is 1-2.

Description

Method to Improve the Accuracy of Elastic Modulus and Poisson's Ratio of Timber in Four-Point Bending Beam Test

technical field

The invention relates to a method for improving the accuracy of four-point bending beam testing of wood elastic modulus and Poisson's ratio.

Background technique

GB/T1936.2-2009 Determination method of wood flexural modulus of elasticity, calculates the flexural modulus of wood by measuring the mid-span deflection of a four-point bending beam. The estimated elastic modulus formula given in the standard does not take into account the effect of shear force on mid-span deflection.

Since the elastic modulus along the grain of wood is generally an order of magnitude larger than the corresponding shear modulus, the effect of shear force on the mid-span deflection of four-point bending timber beams cannot be ignored.

Axial compression or tensile tests are commonly used to determine the Poisson's ratio of wood, and the size of the compression test piece is 20mm×20mm×30mm or 30mm×30mm×60mm. Axial compression needs to be loaded by the testing machine, and the loading requirements are centered, the surface of the test piece is flat, and the contact with the indenter of the testing machine is to reduce friction. Therefore, the axial compression test conditions are relatively harsh and difficult to achieve, so that the dispersion of test data is biased. Big.

When the four-point bending beam is used to test the elastic modulus and Poisson's ratio, although the points on the upper and lower surfaces of the bending beam can be approximately regarded as a unidirectional stress state, the ratio of transverse strain to longitudinal strain changes with the position of the point. If a cantilever beam or a four-point bending beam is used as the test piece for the static determination of Poisson's ratio, there is a problem that the cross strain rosette should be attached to the surface of the beam so that the Poisson's ratio of the material can be obtained from the measured transverse strain to longitudinal strain ratio. ? In fact, in addition to the longitudinal stress σ _x , there is also a transverse stress σ _y on the upper and lower surfaces of the four-point bending beam, but σ _y << σ _x , so it is said that the upper and lower surfaces of the beam are in an approximately unidirectional stress state. This approximation can be neglected when testing Poisson’s ratio for isotropy, but for orthotropic wood, such as spruce, even if _{σy is} only 6‰ of σx, since the modulus of elasticity along the grain is higher than that of the grain The elastic modulus is an order of magnitude larger, so it will also cause an intolerable relative error when testing Poisson's ratio.

Contents of the invention

The purpose of the invention is to provide a method capable of improving the accuracy of four-point bending beam testing of wood elastic modulus and Poisson's ratio.

The method for improving the accuracy of four-point bending beam testing wood elastic modulus and Poisson's ratio of the present invention, the bending beam is a cuboid with a width b and a thickness h, the loading span is long l, and the transverse strain gauge is attached to the middle span center point of the bending beam, The longitudinal strain gauge is in contact with the transverse strain gauge; the length-thickness ratio l/h is 16-20; the width-thickness ratio b/h is 1-2.

The above-mentioned method for improving the accuracy of four-point bending beam testing timber elastic modulus and Poisson's ratio, the loading point position is according to l/3-l/3-l/3, l/4-l/2-l/4 or l /5-3l/5-l/5 four-point bending loading.

The above-mentioned method for improving the accuracy of the four-point bending beam to test the elastic modulus and Poisson's ratio of wood, when measuring the Poisson's ratio of the chord section and radial section of the wood, the size of the bending beam is 280mm×20mm×20mm, according to l/3-l/3 –l/3 four-point bending loading, the loading span l is 240mm.

The method for improving the accuracy of the elastic modulus and Poisson's ratio of wood with four-point bending beams mentioned above, when measuring the Poisson's ratio of the cross-section of wood, the size of the bending beam is 220mm×20mm×20mm, according to l/4-l/2-l/4 Four-point bending loading, the loading span l is 240mm.

Beneficial effects of the present invention: the applicant finds that the longitudinal strain does not change substantially with the position on the pure bending section of four-point bending loading; but the transverse strain increases with x/l in absolute value (the x axis is Take the support point on one side of the curved beam as the origin, and extend along the length direction of the curved beam). The change characteristics of longitudinal and transverse strains lead to the fact that E can be calculated by the longitudinal strain at any point on the pure bending section, and the measured Poisson’s ratio must be estimated by the value of _-εy / _εx at the center point, otherwise it will cause large error. According to the change law of transverse strain and longitudinal strain in the pure bending section, in order to ensure the test accuracy of Poisson's ratio, the transverse strain gauge of the strain rosette is pasted on the center point of the upper and lower surfaces of the beam, and the longitudinal strain gauge should be close to the transverse strain gauge. slice paste. In addition, it shows that the size of the specimen and the position of the four-point bending loading point are also two important factors affecting the accuracy of the Poisson's ratio of wood. In the case of the length-thickness ratio l/h being 16-20 and the width-thickness ratio b/h being 1-2 Next, it is more accurate to test the elastic modulus and Poisson's ratio of wood, especially the Poisson's ratio.

Description of drawings

Figure 1 is a schematic diagram of four-point bending beam loading;

Figure 2 is the mid-span deflection when the P/2 effect l/3 is included in the shear force;

Figure 3 is a schematic diagram of the change of spruce specimen in the pure bending section -ε _y /ε _x -x/l;

Figure 4 is a schematic diagram of the change of spruce specimen in the pure bending section -ε _z /ε _x -x/l;

Figure 5 is a diagram of the strain distribution of the spruce four-point bending beam in the pure bending region;

Figure 6 is a schematic diagram of the pasting position of the rosette.

detailed description

The present invention will be described in detail below.

1 Four-point bending beam is used to determine the flexural modulus of elasticity of wood

In GB/T1936.2-2009 determination method of timber flexural elastic modulus, beams loaded by l/3, l/3, l/3 four-point bending are used as specimens, and the flexural elasticity of timber is estimated by measuring beam mid-span deflection Modulus, as shown in Figure 1.

The 1/3 span in the middle of the beam is in pure bending, that is, the shear force is zero and the bending moment is constant on all sections of the beam in this section, that is, the bending moment does not change with the position of the section; while the left and right 1/3 spans are in the transverse Force bending, that is, there is not only bending moment but also shear force on the section. In GB/T1936.2-2009 Determination Method of Timber Flexural Elasticity Modulus, only the bending moment is considered in the formula for calculating the timber elastic flexural modulus from the mid-span deflection, and the left and right l/3 are not included. The influence of mid-span shear force on beam mid-point deflection, the analysis shows that for wood, since the elastic modulus of wood along the grain is an order of magnitude larger than its shear modulus, the neglect of shear force has no effect on the test of wood flexural elastic modulus. The influence of the value is much greater than that of isotropic materials, resulting in considerable errors in the measured values of the flexural modulus of wood.

GB/T1936.2-2009 Determination method for wood flexural modulus of elasticity stipulates: four-point bending l/3-l/3-l/3 loading (Figure 1), specimen size 300mm×20mm×20mm (loading span 240mm) According to 80mm-80mm-80mm, the four-point bending l/3-l/3-l/3 loading is realized on the testing machine, the _lower limit load P = 300N, and the _upper limit load P = 700N, so △P = 400N.

The elastic modulus is calculated according to the mid-span deflection test value:

$\mathrm{<span\; class="notranslate">\; E.</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; twenty\; three</span>}{\mathrm{<span\; class="notranslate">\; \&Delta;Pl</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}}{\mathrm{<span\; class="notranslate">\; 108</span>}{\mathrm{<span\; class="notranslate">\; \&Delta;ybh</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

In the formula: △P—load increment N; △y—beam mid-span deflection increment; l—span of specimen in mm; b—width of specimen in mm; h—thickness (height) of specimen in mm. E derived unit MPa.

Equation (1) does not take into account the influence of the shear force in the beam on its mid-span deflection, but it measures the deflection under the joint action of bending moment and shear force. In this way, the flexural elastic modulus estimated by Equation (1) The amount is small.

In the following, the effect of the shear force in the four-point bending beam on its mid-span deflection is taken into account, so as to modify the formula (1).

When the load P/2 (Fig. 2) is applied at the beam l/3, the deflection y(l/2) generated at the mid-span l/2 taking into account the shear force can be expressed as:

$\mathrm{<span\; class="notranslate">\; E.</span>}\mathrm{<span\; class="notranslate">\; I</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; twenty\; three</span>}}{\mathrm{<span\; class="notranslate">\; 2592</span>}}{\mathrm{<span\; class="notranslate">\; Pl</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; E.</span>}}{\mathrm{<span\; class="notranslate">\; G</span>}}\frac{{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 12</span>}}\mathrm{<span\; class="notranslate">\; P</span>}\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; k</span>}$

In the formula: I—moment of inertia of beam section; i—radius of gyration of beam section; k—section factor, for rectangular section k=0.913.

According to the principle of superposition, considering the symmetry, when P/2 acts on beams 1/3 and 2l/3 (loaded as shown in Figure 1, 1/3-l/3-l/3 four-point bending load), in the span The deflection generated at l/2 in the center is

$\mathrm{<span\; class="notranslate">\; E.</span>}\mathrm{<span\; class="notranslate">\; I</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; twenty\; three</span>}{\mathrm{<span\; class="notranslate">\; Pl</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}}{\mathrm{<span\; class="notranslate">\; 1296</span>}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; E.</span>}}{\mathrm{<span\; class="notranslate">\; G</span>}}\frac{{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 12</span>}}\mathrm{<span\; class="notranslate">\; P</span>}\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; k</span>}$

$\mathrm{<span\; class="notranslate">\; E.</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; twenty\; three</span>}{\mathrm{<span\; class="notranslate">\; Pl</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}}{\mathrm{<span\; class="notranslate">\; 1296</span>}\mathrm{<span\; class="notranslate">\; I</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 9.3913</span>}\frac{\mathrm{<span\; class="notranslate">\; E.</span>}}{\mathrm{<span\; class="notranslate">\; G</span>}}\frac{{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; l</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span>$

For a rectangular section beam with width b and height h, k=0.913, Have

$\mathrm{<span\; class="notranslate">\; E.</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; twenty\; three</span>}{\mathrm{<span\; class="notranslate">\; Pl</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}}{\mathrm{<span\; class="notranslate">\; 108</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; bh</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 0.8572</span>}\frac{\mathrm{<span\; class="notranslate">\; E.</span>}}{\mathrm{<span\; class="notranslate">\; G</span>}}\frac{{\mathrm{<span\; class="notranslate">\; h</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; l</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

Comparing formula (1) and formula (2), the second item in the right bracket of formula (2) is the percentage of mid-span deflection produced by shear force relative to bending moment. The percentage is related to the square of the beam aspect ratio and the ratio of elastic modulus to shear modulus.

The size of the test piece in the national standard GB/T1936.2-2009 satisfies l=12h, and it is substituted into formula (2) to get

$\mathrm{<span\; class="notranslate">\; E.</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; twenty\; three</span>}{\mathrm{<span\; class="notranslate">\; \&Delta;Pl</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}}{\mathrm{<span\; class="notranslate">\; 108</span>}\mathrm{<span\; class="notranslate">\; \&Delta;</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; bh</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 0.00595</span>}\frac{\mathrm{<span\; class="notranslate">\; E.</span>}}{\mathrm{<span\; class="notranslate">\; G</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

Formula (2) or formula (3) is the correction formula of formula (1) after taking into account the shear force, and the size of the correction is related to the E/G ratio and the span-thickness ratio of the beam.

For isotropic material E/G=2(1+μ), when μ=0.2-0.4, E/G=2.4-2.8, for the four-point bending beam with l/h=12, at l/3-l Under the loading mode of /3-l/3, the influence of shear force in the beam on the mid-span deflection is in the range of 1.4%-1.7%, so it can be ignored, but it is different for wood, such as spruce chord surface elastic modulus E _L =11.6GPa, and the shear modulus along the grain-chord plane G _LT =0.72GPa, so E _L /G _LT =16.1, then the percentage of mid-span deflection produced by shear force relative to bending moment is 0.00595E/G≈0.096, namely 9.6%. It is even bigger for balsa wood, because balsa wood E _L /G _LT =31.5, then 0.00595E/G≈0.187, that is 18.7%.

E and G are included in formula (3), and E can only be calculated by formula (3) after G is measured, so formula (3) is inconvenient to be used for wood test E, unless span-thickness ratio l/h=30, at this moment, for For balsa wood, the percentage of mid-span deflection caused by shear force relative to bending moment is only reduced to 2.1%.

If the measured parameters do not use the mid-span deflection, but instead use the mid-span strain, the situation will be different. Since the 1/3 span in the middle of the beam is a pure bending area, the strain is not a point concept (local concept) unlike the deflection. Although there is shear force in the left and right 1/3 spans of the four-point bending beam, it will not affect the mid-span strain , so choosing the measured value of the strain parameter to calculate the elastic modulus will improve the measurement accuracy. The formula for calculating the elastic modulus from the longitudinal strain of the pure bending 1/3 section is

$\begin{array}{cc}\mathrm{<span\; class="notranslate">\; E.</span>}<span\; class="notranslate">\; =</span>\frac{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}\mathrm{<span\; class="notranslate">\; P</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; l</span>}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; bh</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}& <span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; P</span>}\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; )</span>\end{array}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

In the formula: △P-load increment N; △ε-strain increment; l—span of specimen in mm; b—width of specimen in mm; h—thickness of specimen in mm.

2. Analysis of influence test Poisson's ratio measurement accuracy

2.1 Stress-strain relationship of wood

Wood is a positively anisotropic material. When σ _z is ignored, the stress-strain relationship can be expressed as:

${\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}}{{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}\mathrm{<span\; class="notranslate">\; x</span>}}\frac{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}}{{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}}$

${\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}}{{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}}\frac{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}}{{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}}$

$<span\; class="notranslate">\; \&Right\; Arrow;</span><span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}}{{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}\mathrm{<span\; class="notranslate">\; x</span>}}{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

Therefore, when σ _y = 0, there is -ε _y /ε _x = μ _xy , for a cantilever plate (beam), regardless of whether it is dynamic or static, on the center line of the upper and lower surfaces of the plate (beam) There must be a point where σ _y =0, but the position of the point is different.

For the four-point bending beam, the calculation result of ANSYS using Shell63 unit shows that there is no point of σ _y =0 on the center line of the upper and lower surface of the plate (beam). Therefore, the four-point bending beam used to test the wood Poisson's ratio is approximate. Its approximation depends on the specimen width-thickness ratio, length-thickness ratio and four-point bending loading method (loading point location).

2.2 Influence of specimen width-thickness ratio

Taking spruce as an example, considering that the span of the specimen is 240 mm and the thickness is 20 mm, the influence of changing the width of the specimen on -ε _y /ε _x and -ε _z /ε _x is considered. The width of the specimen is taken as 20mm, 40mm, 60mm, 80mm and 100mm respectively, and the static strain and stress are calculated by ANSYS. The ANSYS calculation adopts the shell63 unit, and the grid is divided into 30×6, and the chord surface elastic constant of the spruce is input (Table 1). When ANSYS calculates, divide the load P/2 on each node of x=l/3, x=2l/3.

Table 1 Principal elastic constants of spruce chord section

According to the static strains ε _x , ε _y , ε _z calculated by ANSYS, the -ε _y /ε _x and -ε _z of each node on the centerline of the lower surface on the pure bending section as shown in Figure 3 and 4 can be drawn The variation curve of /ε _x with x/l.

It can be seen from Figures 3 and 4 that when the width of the specimen increases, the difference between -ε _y /ε _x and the standard value of μ _LT of 0.47, and between -ε _z /ε _x and μ _LR of 0.37 becomes larger.

Figures 3 and 4 are drawn according to the output strains ε _x , ε _y , and ε _z calculated by entering the elastic constants in Table 1. Therefore, if the test piece is cut according to the chord surface or radial surface, it can pass through the chord surface The μ _LT and μ _LR can be measured by sticking the strain gauge and sticking the strain gauge at the same x position on the radial surface perpendicular to it, but two tests are required for the four-point bending, which is not as good as one test for axial tension and can be measured simultaneously Out μ _LT and μ _LR .

In order to more clearly illustrate the influence of the width of the specimen on the accuracy of Poisson’s ratio of the tested wood, take spruce, l/3–l/3–l/3 four-point bending load, load P=400N, and four-point bending loading span l=240mm ,h=20mm, the ANSYS calculation results of two specimen widths of b=60mm and 20mm illustrate the influence of σ _y ≠0 on the test accuracy of Poisson's ratio of wood.

Consider the point in the span

When b=60mm,

Calculated according to ANSYS σ _x ＝3.965MPa, σ _y ＝0.0227MPa, σ _y /σ _x ＝0.0057

Since the spruce E _x =11.6GPa, E _y =0.5GPa, μ _xy =0.47, μ _yx =0.02,

Therefore -ε _y /ε _x = 0.339 (ANSYS calculated value 0.338);

When b=20mm,

Calculated according to ANSYS σ _x ＝11.994MPa, σ _y ＝0.0037532MPa, σ _y /σ _x ＝0.00031357

Since the spruce E _x =11.6GPa, E _y =0.5GPa, μ _xy =0.47, μ _yx =0.02,

Therefore -ε _y /ε _x = 0.463 (ANSYS calculated value 0.463);

2.3 Influence of specimen length-thickness ratio

The width and thickness of the spruce specimens were kept constant, and 20mm was taken, and the length of the specimens was changed, and the length-thickness ratios were 12, 15, 16, 18 and 20, respectively. The values of -ε _y /ε _x and -ε _z /ε _x calculated in the span are shown in Table 2.

Table 2 Effect of aspect ratio (width 20mm unchanged)

Spruce specification values μ _LT = 0.47, μ _LR = 0.37.

In short, for spruce, when a 240mm×20mm×20mm specimen is used and the l/3-l/3-l/3 loading method is used, the -ε _y /ε _x and -ε _z /ε _x calculated at the mid-span are consistent with the specification There is still a difference of 1.5% in the value (see the second row of Table 2); it is also known from Table 2 that when l/h=18, this is equivalent to the length-thickness ratio of the pure bending section being equal to 6, _-εy /εx= _0.469 ,- ε _z /ε _x = 0.370, which is almost equal to the standard value of spruce, which indicates that increasing the length-thickness ratio of the purely curved section can improve the accuracy of testing Poisson's ratio.

2.4 The effect of four-point bending loading point position

The size of the test piece is 300mm×20mm×20mm unchanged (loading span 240mm), change l/3-l/3-l/3, l/4-l/2-l/4 and l/5-3l/5-l Under the conditions of three four-point bending loading such as /5, the -ε _y /ε _x and radial section of wood chord section are calculated for six species of spruce, beech, scotch pine, balsa, mahogany and ash -ε _z /ε _x . The calculation results are shown in Table 3. From the data in Table 3, it can be seen that under the four-point bending load of l/4-l/2-l/4, the difference between the spruce -ε _y /ε _x and -ε _z /ε _x calculated through the mid-span and the standard value decreases to 0.6%.

Table 3. Effect of Four-Point Bending Loading Point Position

From Table 3, under l/3-l/3-l/3 loading, except spruce, the calculated values of -ε _y /ε _x and -ε _z /ε _x of other tree species differ from their normative values by less than 1% In this sense, the Poisson's ratio of wood can also be tested by the l/3-l/3-l/3 four-point bending loading method, but in order to improve the test accuracy, it is recommended to use l/4-l/2-l/ 4 The four-point bending loading method is used for measurement.

In fact, the impact of the position of the loading point on the test accuracy of Poisson's ratio is related to the ratio of σ _y /σ _x . For spruce, according to ANSYS calculation results:

When l/3-l/3-l/3 load σ _y /σ _x =3.13×10 ^-4 ,

When l/4-l/2-l/4 load σ _y /σ _x = 1.09×10 ^-4 ;

When l/5-3l/5-l/5 is loaded σ _y /σ _x =6.21×10 ^-5 .

That is, the smaller the ratio of σ _y /σ _x , the closer the calculated value of -ε _y /ε _x in the span is to the Poisson's ratio.

3 Four-point bending beam testing of wood flexural modulus of elasticity and Poisson's ratio Patch position

3.1 Longitudinal and transverse strain distribution of four-point bending beam

Spruce specimen 300mm×20mm×20mm (span 240mm), l/3-l/3-l/3 four-point bending load, P=400N. The transverse strain and longitudinal strain of the pure bending section calculated by ANSYS are shown in Table 4 (the input values calculated by ANSYS are shown in Table 1).

Table 4 The estimated value of E and the calculated value of -εy/εx of spruce at different positions

From the data in Table 4, it can be seen that the longitudinal strain basically does not change with the position on the pure bending section loaded by four-point bending; but the transverse strain increases with the increase of x/l in absolute value. The change characteristics of longitudinal and transverse strains lead to the fact that E can be calculated by the longitudinal strain at any point on the pure bending section, and the measured Poisson’s ratio must be estimated by the value of _-εy / _εx at the center point, otherwise it will cause large error.

When the spruce beam is loaded in l/3-l/3-l/3 four-point bending, the longitudinal strain ε _x and transverse strain ε _y of the pure bending section, that is, the middle 1/3 section, are relative to the ε _x and ε y of the mid-span The distribution of the ratio of εy with _x /l is shown in Fig. 5. It can be seen from Figure 5 that ε _x (x/l)/ε _x (0.5)-x/l basically does not change, its value changes from 0.999 to 1, while ε _y (x/l)/ε _y (0.5)-x/ l changes from 0.903 to 1.

3.2 Calculation formula of flexural modulus of test and patch position

Calculation formula for measured elastic modulus

l/3-l/3-l/3 loading: $\mathrm{E.}=\frac{\left(\mathrm{\&Delta;}P\right)l}{\left({\mathrm{\&Delta;\&epsiv;}}_x\right){\mathrm{bh}}^2}---\left(6a\right)$

l/4-l/2-l/4 loading: $\mathrm{E.}=\frac{3\left(\mathrm{\&Delta;}P\right)l}{4\left({\mathrm{\&Delta;\&epsiv;}}_x\right){\mathrm{bh}}^2}---\left(6b\right)$

l/5-3l/5-l/5 loading: $\mathrm{E.}=\frac{3\left(\mathrm{\&Delta;}P\right)l}{5\left({\mathrm{\&Delta;\&epsiv;}}_x\right){\mathrm{bh}}^2}---\left(6c\right)$

In the formula: △P—load increment; △ε _x —strain increment of mid-span longitudinal sheet.

It can be seen from Figure 5 that there is no special requirement for the attachment position of the longitudinal strain gauge for measuring E in the pure bending section, as long as it is in the pure bending section, it is recommended to stick it near the mid-span of the beam.

3.3 Test rosette paste position of wood Poisson's ratio

It can be seen from Figure 5 that the ratio of ε _y /ε _x varies with x/l in the pure bending section, from 0.419 to 0.463 (the standard value of spruce μ _LT is 0.47), so the sticking strain rosette for measuring Poisson’s ratio μ The location should be in the middle of the beam span. Therefore, the Poisson's ratio is estimated by the ratio of the transverse strain to the longitudinal strain increment at the mid-span:

According to the change law of transverse strain and longitudinal strain in the pure bending section, in order to ensure the test accuracy of Poisson's ratio, the transverse strain gauge of the strain rosette is pasted on the center point of the upper and lower surfaces of the beam, and the longitudinal strain gauge should be close to the transverse strain gauge. paste, as shown in Figure 6.

To test the Poisson's ratio of the wood, a strain rosette is pasted on the center point of the upper and lower surfaces of the four-point bending beam, and the longitudinal strain gauge and transverse strain gauge are respectively according to the half-bridge method.

3.4 Recommended four-point bending beam size and its loading point location

According to the above analysis, it is recommended that the specimen size for testing the elastic modulus and Poisson’s ratio of the chord surface or radial surface be 280mm×20mm×20mm (the span of the four-point bending loading is 240mm, and the four-point bending loading method is l/3-l/3- l/3 or l/4-l/2-l/4.

The size of the specimen for testing the elastic modulus and Poisson's ratio is 220mm×20mm×20mm (the span of four-point bending loading is 180mm), and the four-point bending loading method is l/4-l/2-l/4.

The test piece of the principal elastic constant can be reduced to 180mm×20mm×20mm (the length of the test piece is 220mm).

4 Static test of wood elastic modulus and Poisson's ratio

The elastic modulus and Poisson's ratio of Sitka spruce, Chinese pine and poplar are measured by four-point bending beam. For Sitka spruce, the elastic modulus and Poisson's ratio are also determined by axial tensile test, so as to compare with the four-point bending measurement results. A comparison is made to verify the correctness of the four-point bending test method for wood elastic modulus and Poisson's ratio given in this paper.

4.1 Four-point bending

Specimens: Sitka spruce radial-cut specimens with nominal size 300mm×12.2mm×12.2mm, quantity 5; Chinese pine string-cut specimens with nominal size 300mm×12.2mm×12.2mm, quantity 5. The span of both is 240mm, l/3-l/3-l/3 four-point bending loading method; the nominal size of the Sitka spruce cross-cut test piece is 220mm×12.2mm×12.2mm, the quantity is 4, and the span is 200mm, l/4 -l/4-l/4 four-point bending loading method; loading: weight.

Radial section and radial section test piece: lower limit load 4.165N, upper limit load 16.66N;

The lower limit load of the cross-section test piece is 1.019N, and the upper limit load is 2.783N.

Three tests were carried out on each specimen, and the average value of the second and third test values was taken as the measured value of the elastic modulus and Poisson's ratio of the specimen.

Poisson's ratio and modulus of elasticity were calculated as follows:

In the formula: if b-mm, h-mm, △P-N, ε-με, then the unit of E is MPa.

4.2 Axial stretch

Specimens: Sitka spruce diameter-cut specimens, nominal size 300mm×40mm×12.2mm, quantity 3, are from the same Sitka spruce slab (large slab size 625mm×107mm×12.2mm) with the four-point bending test piece The tensile test piece of the material is used, so the test piece number is the same as that of the four-point bending test piece.

Stick a strain rosette on the two surfaces of the tensile test piece respectively, the transverse and longitudinal plates on both sides are connected in series respectively, the longitudinal plates connected in series are connected to the bridge boxes A and B of the first channel, and the transverse plates connected in series are connected to the bridge box A of the second channel , B; another test piece is used for the compensating plate, the longitudinal plates in series are connected to one-channel bridge boxes B, C, and the transverse plates in series are connected to two-channel bridge boxes B, C. This connection method is to eliminate the bending strain caused by tension misalignment, and ensure that the measured strain is only the strain caused by axial tension. The output of the strain gauge is connected to the YD-25A dynamic and static strain gauge, and the output of the transverse gauge of the strain gauge is respectively connected to the first channel and the second channel of the collection box.

Loading: The testing machine is continuously loaded, the output of the strain gauge is connected to the dynamic strain gauge, the output of the strain gauge is connected to the acquisition box, and the longitudinal strain and transverse strain data are recorded through special software and computer.

Data processing: Tensile loading from the lower limit load 2kN to the upper limit load 3.5kN, record the corresponding time, read the lateral strain and longitudinal strain values from the lower limit load to the upper limit load from the archive file of the collected data, take several sets of data, and verify them After the linearity of , Poisson's ratio can be determined from the slope. Poisson's ratio and elastic modulus can also be simply calculated as follows:

In the formula: if b-mm, h-mm, △P-N, ε-με, then the unit of E is MPa.

4.3 Elastic modulus and Poisson's ratio test of Sitka spruce and Chinese pine

The static test values of elastic modulus and Poisson's ratio of four-point bending and tensile tests of Sitka spruce and Chinese pine are shown in Table 5.

Table 5 Static test values of elastic modulus and Poisson's ratio of Sitka spruce and Chinese pine (four-point bending beam span 240mm, 180mm)

From the data in Table 5, it can be seen that the elastic modulus and Poisson's ratio of the radial section of Sitga spruce tested by four-point bending and axial tension tests are very consistent. Although the number of tests is small, it also shows the four points given in this paper. The method of flexural testing of elastic modulus and Poisson's ratio is reliable and has sufficient precision.

5 Conclusion

5.1 According to the static stress and strain analysis of the ANSYS shell6.3 unit, there is no point where σ _y = 0 exists in the four-point bending beam. For the wood with positive anisotropy, the value of -ε _y /ε _x on the bending beam loaded at four points is always smaller than the Poisson’s ratio, and the Poisson’s ratio can be estimated with sufficient accuracy by using the center point -ε _y /ε _x on the upper or lower surface of the beam mid-span by using an appropriate specimen size or four-point bending loading method;

5.2 The recommended sample size for measuring the Poisson’s ratio of the chord section and radial section of wood is 280mm×20mm×20mm, and the four-point bending load is carried out according to l/3-l/3-l/3, and the four-point bending loading size is 240mm×20mm×20mm ; The recommended sample size for Poisson’s ratio measurement on the cross section is 220mm×20mm×20mm, according to l/4–l/2–l/4 four-point bending loading, and the four-point bending loading size is 200mm×20mm×20mm;

5.3 Four-point bending beam test Poisson's ratio, the strain gauge is attached to the center point of the middle span, and the transverse piece is aligned with the center point;

5.4 The four-point bending beam is suitable for testing 9 principal elastic constants of wood E _L , E _T , E _R , μ _LT , μ _LR , μ _RT , μ _TL , μ _RL , μ _TR ;

5.5 Measure the Poisson's ratio of wood by four-point bending beam, and use the testing machine to load or weight to load. The recommended lower limit load of the testing machine is 300N, and the upper limit load is 700N; when the weight is loaded, the upper and lower limit load values are designed so that the strain difference of the longitudinal sheet should not be less than 100με.

In summary, since the elastic modulus along the grain of wood is generally an order of magnitude larger than the corresponding shear modulus, the effect of shear force on the mid-span deflection of four-point bending timber beams cannot be ignored. Mid-span deflection measurements allow for a more accurate deduction of the timber's modulus of elasticity. According to the static stress and strain calculation of ANSYS, although there is no point where the transverse stress σ _y = 0 in the four-point bending beam, using the appropriate specimen size and the position of the four-point bending loading point, the center points of the upper and lower surfaces of the beam span The -ε _y /ε _x measurement value has sufficient accuracy to estimate the Poisson's ratio of wood; the Poisson's ratio is tested by four-point bending beam, and the cross strain flower is attached to the center point of the upper and lower surfaces of the pure bending section, so that the transverse strain gauge is aligned with the center point position, the longitudinal strain gauge is pasted close to the transverse strain gauge; the four-point bending beam is suitable for testing 9 principal elastic constants such as the elastic modulus and Poisson's ratio of wood. In addition, for four-point bending beams, especially wooden beams can be loaded by testing machine or by weights. For 300mm×20mm×20mm oak wood specimens, l/3-l/3-l/3 span l= 240mm four-point bending load, according to our test, that is, the Poisson’s ratio of the two loading methods of the testing machine and the weight is consistent. In this sense, for wood, the four-point bending of the weight can be used Beam test Poisson's ratio, weight loading is simple, easy to implement, and has its advantages.

Claims (4)

1. improve the method for four_point bending beam test modulus of elasticity of wood and Poisson ratio precision, described bent beam is the rectangular parallelepiped of wide b, thick h, load the long l of span, it is characterized in that: transverse strain sheet is attached to the centre of bent beam across center position, and longitudinal strain sheet contacts with transverse strain sheet; Slenderness ratio l/h is 16 ~ 20; Flakiness ratio b/h is 1 ~ 2.

2. the method improving four_point bending beam test modulus of elasticity of wood and Poisson ratio precision as claimed in claim 1, is characterized in that: described loading Position loads by l/3-l/3-l/3, l/4-l/2-l/4 or l/5-3l/5-l/5 four-point bending.

3. the method improving four_point bending beam test modulus of elasticity of wood and Poisson ratio precision as claimed in claim 2, it is characterized in that: when surveying timber tangential section, radial longitudinal section Poisson ratio, bent beam size 280mm × 20mm × 20mm, load by l/3 – l/3 – l/3 four-point bending, loading span l is 240mm.

4. the method improving four_point bending beam test modulus of elasticity of wood and Poisson ratio precision as claimed in claim 2, it is characterized in that: when surveying wood transverse section Poisson ratio, bent beam size 220mm × 20mm × 20mm, load by l/4 – l/2 – l/4 four-point bending, loading span l is 240mm.