CN106769550A - The experimental rig and method of Analysis of Concrete Tensile modulus under high strain-rate - Google Patents

Abstract

The present invention discloses the experimental rig and method of Analysis of Concrete Tensile modulus under a kind of high strain-rate.The problem that dynamic split tension experimental technique is present is can solve the problem that by adding shaping piece in a device and splitting pull end head, specifically, shaping piece is added in incident bar termination, the setting of shaping piece can guarantee that impact suffered by test specimen does not receive secondary reflection stress wave action, it is basicly stable that loading strain rate is met simultaneously, it is convenient that loading load is calculated；There is the rigid gasket and rigid lining bar that use cooperatively test specimen and incident bar, transmission bar contact position are symmetrically placed, the rigid gasket of setting can be concentrated when ensure that load shock test specimen with rigid lining bar and act on disk two-end-point, so as to establish a kind of test method that is very convenient, testing stretch modulus under relatively easy and success rate concrete high strain-rate high.

Description

The experimental rig and method of Analysis of Concrete Tensile modulus under high strain-rate

Technical field

The invention belongs to shock dynamics technical field, and in particular to the examination of Analysis of Concrete Tensile modulus under a kind of high strain-rate Experiment device and method.

Background technology

Concrete is a kind of heterogeneity, anisotropic material.Therefore, its stretch modulus is different from its modulus of compressibility.Together When, concrete has rate sensitiveness, and many large-scale concrete structure engineerings are subjected to the also rough dead load effect of change, The violent dynamic loading of various change is still suffered from, concrete mechanical property in a dynamic condition is substantially distinguished from static bar Part.

In order to preferably assess concrete dynamic tensile mechanical performance, it is necessary to bullet of the clear and definite concrete under high strain-rate Property modulus.At present, in addition to direct tensile test, to the Analysis of Concrete Tensile modulus measurement under dynamic condition also without more convenient Mode.But concrete dynamic direct tensile test success rate is low, and the test period is long；Brazilian tension experiment it is relatively easy and into Power is high, but existing drawing computational methods of splitting focus primarily upon static experiment, and there are the following problems for dynamic split tension experimental technique： Dynamic test stress wave receives contact surface medium Different Effects, and impact is difficult to calculate after stress wave multiple reflections；Examination is drawn according to splitting The test specimen Brazilian tension modulus that part central spot stress-strain diagram slope draws is not equal to the stretching under the conditions of its uniaxial direct tensile Modulus.

The content of the invention

For above-mentioned deficiency of the prior art, the invention provides under a kind of high strain-rate based on Brazilian disc test specimen The experimental rig and method of Analysis of Concrete Tensile modulus.The method is based on the basis of Hopkinson principle, is a kind of new concrete The test method of dynamic split tension mechanical property research, can measure stretch modulus of the concrete under the conditions of high strain-rate.

To achieve the above object, present invention employs following technical scheme：

The experimental rig of Analysis of Concrete Tensile modulus under a kind of high strain-rate, including air chamber, bullet, bearing, incident bar, transmission Bar, incident bar, transmission bar are positioned on bearing, by adjusting bearing and air chamber, make bullet, incident bar and transmission bar center pair It is accurate；Incident bar is adhesive with the first foil gauge along bar length direction at bar segment rear；Transmission bar bar segment center is glutinous along bar length direction Post the second foil gauge；Two piece of the 3rd foil gauge is pasted in Brazilian disc test specimen upper bottom surface center, and the 3rd foil gauge direction is vertical In Impact direction, second foil gauge, the first foil gauge are equal with the distance between test specimen；In test specimen and incident bar, transmission Bar contact position is symmetrically placed a rigid gasket and rigid lining bar for using cooperatively, and the spacing of the incident bar and transmission bar is lucky Pad, lining bar, Brazilian disc test specimen is set to be clamped in incident bar and transmission bar center；First foil gauge, the second strain Piece, the 3rd foil gauge are connected with deformeter bridge.In the technical scheme, the rigid gasket of setting ensure that with rigid lining bar Load can be concentrated when clashing into test specimen and act on disk two-end-point.

Preferably, the incident bar termination is equipped with shaping piece.The setting of shaping piece can guarantee that impact is not suffered by test specimen By secondary reflection stress wave action, while satisfaction loading strain rate is basicly stable, it is convenient that loading load is calculated.

Further, the shaping piece uses diameter 20mm, the copper sheet of thickness 2mm.

Preferably, the rigid gasket is provided with the breach for accommodating rigid lining bar just, and the rigid lining bar is straight with test specimen Contact.

Preferably, the bullet, incident bar and transmission bar, pad and lining bar use 48CrMoA round steel materials, its Young Modulus 210GPa, density 7850kg/m³, velocity of wave 5172m/s.

Further, incident bar 3200mm long, diameter 74mm, one end Diameter Gradual Change contacted with bullet are 37mm； The transmission bar is 1800mm long, the slender cylinder of diameter 74mm；The bullet diameters are 37mm, and length is 600mm；It is described Spacer thickness is 8mm, and section is the circle of diameter 74mm；The a diameter of 10mm of lining bar, length is 74mm.

The test method of Analysis of Concrete Tensile modulus, comprises the following steps under a kind of high strain-rate：

S1, placement and adjusting device：Incident bar, transmission bar are positioned on bearing, bearing and air chamber is adjusted, it is ensured that son The center alignment of bullet, incident bar and transmission bar；

S2, paste foil gauge：First foil gauge is pasted at incident bar bar segment rear, first strain length of a film side parallel to Bar length direction；Second foil gauge sticks in transmission bar bar segment center, and the second strain length of a film side is parallel to bar length direction and with the One foil gauge is maintained at same level position；3rd foil gauge is pasted in test specimen center for two pieces totally relatively, upper bottom surface each Block, the 3rd strain length of a film side perpendicular to Impact direction, as shown in Figure 2；First foil gauge, the second foil gauge, the 3rd foil gauge chi It is very little identical；

S3, placement test specimen：Incident bar, pad, lining bar, test specimen, lining bar, pad, transmission bar successively arranged in sequence are placed, Adjustment incident bar and transmission distance between tie rods, make pad, lining bar, test specimen just be clamped in incident bar and transmission bar center；

S4, connection deformeter：First, second, third foil gauge is connected with deformeter bridge；

S5, take cylindrical disc test specimen and tested, give air chamber pressurization, certain impulsive force is subject to bullet, have it There is certain stroke speed to clash into incident bar, produce stress wave, stress wave to be delivered to test specimen 8 via rod member, pad, lining bar On bring it about splitting；

S6, collection foil gauge recorded data, bring formula into and are calculated and can obtain Analysis of Concrete Tensile modulus.

Further, the computational methods of formula are in step S6：

S61, when projectile impact incident bar, rod member inside produce longitudinal direction incident compressional wave, due to different impedances, enter Ejected wave is partially reflected back incident bar in the interface that incident bar and test specimen are contacted, available based on three ripple methods：

P₁=E (ε_i+ε_r)

P₂=E ε_tr

Wherein, P₁For incident bar clashes into line load, P₂For transmission bar supports line load, unit is N/m；E is incident bar Young Modulus, E=210GPa；ε_iThe incidence wave maximum strain recorded by incident bar foil gauge；ε_rRecorded by incident bar foil gauge Back wave maximum strain, ε_trThe transmitted wave maximum strain recorded by transmission bar；

S62, incident bar clash into the difference between line load and transmission bar support line load, are mainly split pull end head to being made Into stress wave reflection influence, split the influence that pull end head is calculated test specimen impact to remove, test specimen actually is impacted Power P：

It is S63, as follows to test specimen calculation method for stress, any cross section, such as Fig. 5 on height of specimen direction are taken, section is any Cell cube stress state is as follows at position：

Wherein, σ_rIt is cell cube normal direction tension, σ_θIt is cell cube tangential stress, τ_rθIt is cell cube shearing stress, R is examination Part section radius, r, θ are the cell cube coordinates under polar coordinate system, and α is the half of the central angle corresponding to stress scope, ginseng ISRM ISRMs test specification is examined, 2 α=10 ° are taken；Such as Fig. 6, by Parameter Switch, x, y are under rectangular coordinate system Cell cube coordinate, the origin of coordinates be foil gauge central point, foil gauge centerline, when taking y=0, i.e., go up along the x-axis direction arbitrarily Some stress states are as follows：

τ_xy=0

Wherein, l is specimen thickness, l=74mm；D is that test specimen diameter of section is also 74mm；

S64, test specimen center foil gauge measured value are equal to the calculated value of following theoretical formula, because of the compression on y-axis direction It is the twice of tension on x-axis direction, thus it is very important because of the stretch modulus that poisson effect causes；Diametrically horizontal direction On, in the range of foil gauge, the test specimen Brazilian tension dependent variable ε of the 3rd foil gauge measurement_tEqual to following theoretical formula：

Wherein, L takes the half of strain leaf length, E_tIt is Analysis of Concrete Tensile modulus, v is test specimen Poisson's ratio；Abbreviation is final to be obtained Go out test specimen stretch modulus：

Wherein, Brazilian tension modulus E_s=2P/ π Dl ε_tDetermined by surveyed stress-strain diagram, wherein stress σ_t=2P/ π Dl, takes the linear slope over 10 of stress-strain diagram, or take E_s=[(1/2) σ_t,max]/ε_t, wherein σ_t,max/ 2 take stress-strain diagram The half of middle maximum stress, ε_tIt is then corresponding elongation strain amount when reaching maximum stress half.

The beneficial effects of the present invention are：

The present invention combines Hopkinson principle and one-dimensional elastic wave is theoretical, adds shaping piece and splits by experimental rig Pull end head (i.e. pad and lining bar), shaping piece can guarantee that impact suffered by test specimen not by secondary reflection stress wave action, while full Foot loading strain rate is basicly stable, convenient that loading load is calculated；The rigid gasket of setting can be protected with rigid lining bar Card load can be concentrated when clashing into test specimen and act on disk two-end-point, it is to avoid stress disperses, and improve the accuracy of experiment；Can pass through Formula calculates test specimen stretch modulus；So as to solve the presence of dynamic split tension experimental technique：Dynamic test stress Ripple receives contact surface medium Different Effects, and impact is difficult to calculate after stress wave multiple reflections；Test specimen central spot is drawn to answer according to splitting The test specimen Brazilian tension modulus that stress-strain curve slope draws is not equal to the problem of the stretch modulus under the conditions of its uniaxial direct tensile.And And establish a kind of experiment dress that is very convenient, testing stretch modulus under relatively easy and success rate concrete high strain-rate high Put and corresponding test method.

Brief description of the drawings

Fig. 1 is structure scheme of installation of the invention.

Fig. 2 is the enlarged drawing of incident bar end in Fig. 1.

Fig. 3 is to split the enlarged drawing at pull end head (i.e. pad and lining bar) place in Fig. 1.

Fig. 4 is that the 3rd foil gauge pastes mode figure on test specimen in the present invention.

Fig. 5 is any element stress view in Brazilian disc test specimen.

Fig. 6 is the plane positioning schematic diagram of any cell cube in Brazilian disc test specimen.

The implication of label symbol is as follows in figure：

1- air chamber 2- bullet 3- bearing 4- incident bars the first foil gauges of 5-

The foil gauge 8- test specimen 9- transmission bar 10- lining bars of 6- rigid gaskets 7- the 3rd

11- the second foil gauge 12- shaping pieces

Specific embodiment

Below in conjunction with the accompanying drawing in the embodiment of the present invention, the technical scheme in the present invention is clearly and completely retouched State.The following examples are only intended to illustrate the technical solution of the present invention more clearly, and guarantor of the invention can not be limited with this Shield scope.

The experimental rig of Analysis of Concrete Tensile modulus under a kind of high strain-rate

As shown in Figures 1 to 3, including air chamber 1, bullet 2, bearing 3, incident bar 4, transmission bar 9, incident bar 4, transmission bar 9 are put It is placed on bearing 3, by adjusting bearing 3 and air chamber 1, is directed at bullet 2, incident bar 4 and the center of transmission bar 9；Transmission bar bar is long 1800mm, the bar segment center of transmission bar 9 is adhesive with the second foil gauge 11 along bar length direction；Incident bar 4 is along bar length direction in distance The first foil gauge 5 is adhesive with the 900mm of bar segment end；The center of Brazilian disc test specimen 8 is relative to paste two piece of the 3rd foil gauge, the The direction of three foil gauge 7 is perpendicular to Impact direction；The distance between second foil gauge 11, the first foil gauge 5 and test specimen 8 phase Deng；There is the rigid gasket 6 and rigid lining bar 10 that use cooperatively test specimen and incident bar 4 and the contact position of transmission bar 9 are symmetrically placed, The spacing of the incident bar 4 and transmission bar 9 makes pad 6, lining bar 10, test specimen 8 be clamped in incident bar 4 and transmission bar 9 just At the heart；First foil gauge 5, the second foil gauge 11, the 3rd foil gauge 7 are connected with deformeter bridge.First foil gauge 5, The two foil gauges 11, size of the 3rd foil gauge 7 are identical.

Wherein, the incident bar termination is equipped with shaping piece 12；Shaping piece uses diameter 20mm, the copper sheet of thickness 2mm.

Specifically, the rigid gasket 6 is provided with the breach for accommodating rigid lining bar 10 just, the rigid lining bar 10 and examination The directly contact of part 8；Breach is cambered surface breach.

Bullet 2, incident bar 4 and transmission bar 9, pad 6 and lining bar 10 use 48CrMoA round steel materials, its Young's modulus 210GPa, density 7850kg/m³, velocity of wave 5172m/s.

Incident bar 4 3200mm long, diameter 74mm, one end Diameter Gradual Change contacted with bullet 2 are 37mm；The transmission bar 9 It is 1800mm long, the slender cylinder of diameter 74mm；The a diameter of 37mm of the bullet 2, length is 600mm；The thickness of the pad 6 It is 8mm, section is the circle of diameter 74mm；The a diameter of 10mm of lining bar 10, length is 74mm.

The test method of Analysis of Concrete Tensile modulus under a kind of high strain-rate

Comprise the following steps：

S1, placement and adjusting device：Incident bar 4, transmission bar 9 are positioned on bearing 3, bearing 3 and air chamber 1 is adjusted, protected Card bullet 2, incident bar 4 and the centering of transmission bar 9；

S2, paste foil gauge：First foil gauge 5 paste incident bar 4 along bar length direction at the 900mm of bar segment end, The bar length direction in edge long of first foil gauge 5；Second foil gauge 11 sticks in the bar segment center of transmission bar 9, and the second foil gauge 11 is grown Edge bar length direction is simultaneously maintained at same level position, the second foil gauge 11, the first foil gauge 5 and test specimen 8 with the first foil gauge 5 The distance between it is equal；Totally two pieces of relative pasting record ginseng to 3rd foil gauge 7 at the center of test specimen 8 (each one piece of tow sides) Number, the side long of the 3rd foil gauge 7 perpendicular to Impact direction, as shown in Figure 4；First foil gauge 5, the second foil gauge the 11, the 3rd are strained The size of piece 7 is identical；

S3, placement test specimen：By incident bar 4, pad 6, lining bar 10, test specimen 8, lining bar 10, pad 6, transmission bar 9 successively sequentially Arrangement is placed, and adjusts incident bar 4 and the spacing of transmission bar 9, pad, lining bar, test specimen is just clamped in incident bar 4 and transmission bar 9 centers；

S4, connection deformeter；Above-mentioned all of foil gauge is connected with deformeter bridge；

In S5, the experiment, take cylindrical disc test specimen and tested, pressurizeed to air chamber 1, certain punching is subject to bullet 2 Power is hit, makes it have certain stroke speed to clash into incident bar 4, produce stress wave, stress wave is via rod member 4, pad 6, pad Bar 10, is delivered to and splitting is brought it about on test specimen 8；

S6, collection foil gauge recorded data, bring formula into and are calculated the concrete that can obtain under high strain-rate Stretch modulus.

Wherein, the computational methods of formula are in step S6：

S61, when projectile impact incident bar, rod member inside produce longitudinal direction incident compressional wave, due to different impedances, enter Ejected wave is partially reflected back incident bar in the interface that incident bar and test specimen are contacted, available based on three ripple methods：

P₁=E (ε_i+ε_r)

P₂=E ε_tr

Wherein, P₁For incident bar clashes into line load, P₂For transmission bar supports line load, unit is N/m；E is incident bar Young Modulus, E=210GPa；ε_iThe incidence wave maximum strain recorded by incident bar foil gauge；ε_rRecorded by incident bar foil gauge Back wave maximum strain, ε_trThe transmitted wave maximum strain recorded by transmission bar；

S62, incident bar clash into the difference between line load and transmission bar support line load, are mainly split pull end head to being made Into stress wave reflection influence, split the influence that pull end head is calculated test specimen impact to remove, test specimen actually is impacted Power P：

It is S63, as follows to test specimen calculation method for stress, any cross section on height of specimen direction is taken, as shown in figure 5, section Any position cell cube stress state is as follows：

Wherein, σ_rIt is cell cube normal direction tension, σ_θIt is cell cube tangential stress, τ_rθIt is cell cube shearing stress, R is examination Part section radius, r, θ are the cell cube coordinates under polar coordinate system, and α is the half of the central angle corresponding to stress scope, ginseng ISRM ISRMs test specification is examined, 2 α=10 ° are taken；Such as Fig. 6, by Parameter Switch, x, y are under rectangular coordinate system Cell cube coordinate, the origin of coordinates be foil gauge central point, foil gauge centerline, when taking y=0, i.e., go up along the x-axis direction arbitrarily Some stress states are as follows：

τ_xy=0

Wherein, σ_xIt is cell cube x-axis direction tension, σ_yIt is cell cube y-axis direction tension, τ_xyBe cell cube cut should Power, l is specimen thickness, l=74mm；D is all 74mm for test specimen diameter of section；

S64, test specimen center foil gauge measured value should be equal to following theoretical calculation formula, because the compression on y-axis direction is x The twice of tension on direction of principal axis, thus it is very important because of the stretch modulus that poisson effect causes；Diametrically level is AB in Fig. 4 On direction, in the range of foil gauge, the test specimen Brazilian tension dependent variable ε of the 3rd foil gauge measurement_tEqual to following theoretical formula：

Wherein, L takes the half of strain leaf length, E_tIt is Analysis of Concrete Tensile modulus, v is test specimen Poisson's ratio；Abbreviation is final to be obtained Go out test specimen tensile modulus of elasticity：

Brazilian tension modulus E_s=2P/ π Dl ε_tDetermined by surveyed stress-strain diagram, wherein stress σ_t=2P/ π Dl, taking should The linear slope over 10 of stress-strain curve；Or, take E_s=[(1/2) σ_t,max]/ε_t, wherein σ_t,max/ 2 take maximum in stress-strain diagram The half of stress, ε_tIt is then that stress reaches corresponding elongation strain amount during maximum stress half.

The above is only the preferred embodiment of the present invention, it is noted that for the ordinary skill people of the art For member, on the premise of the technology of the present invention principle is not departed from, some improvement and deformation can also be made, these improve and deform Also should be regarded as protection scope of the present invention.

Claims (8)

1. under a kind of high strain-rate Analysis of Concrete Tensile modulus experimental rig, it is including air chamber (1), bullet (2), bearing (3), incident Bar (4), transmission bar (9), incident bar (4), transmission bar (9) are positioned on bearing (3), by adjusting bearing (3) and air chamber (1), It is directed at bullet (2), incident bar (4) and transmission bar (9) center；It is characterized in that：The incident bar (4) is along bar length direction in bar The first foil gauge (5) is adhesive with section rear, the transmission bar (9) is adhesive with the second strain along bar length direction in bar segment center Piece (11)；Two piece of the 3rd foil gauge (7) is pasted relatively in Brazilian disc test specimen (8) center, the 3rd foil gauge (7) direction is vertical In Impact direction, second foil gauge (11), the first foil gauge (5) are equal with the distance between test specimen (8)；In test specimen (8) It is symmetrically placed with incident bar (4), transmission bar (9) contact position to have the rigid gasket (6) and rigid lining bar (10), institute for using cooperatively State the spacing of incident bar (4) and transmission bar (9) make just pad (6), lining bar (10), test specimen (8) be clamped in incident bar (4) and Transmission bar (9) center；First foil gauge (5), the second foil gauge (11), the 3rd foil gauge (7) and deformeter bridge connect Connect.

2. under a kind of high strain-rate according to claim 1 Analysis of Concrete Tensile modulus experimental rig, it is characterised in that：Institute State incident bar (4) termination and be equipped with shaping piece (12).

3. under a kind of high strain-rate according to claim 2 Analysis of Concrete Tensile modulus experimental rig, it is characterised in that：Institute Shaping piece (12) is stated using diameter 20mm, the copper sheet of thickness 2mm.

4. under a kind of high strain-rate according to claim 1 Analysis of Concrete Tensile modulus experimental rig, it is characterised in that：Institute State rigid gasket (6) and be provided with the breach for accommodating rigid lining bar (10), breach is cambered surface breach；The rigid lining bar (10) and examination Part (8) directly contact.

5. under a kind of high strain-rate according to claim 1 Analysis of Concrete Tensile modulus experimental rig, it is characterised in that：Institute State bullet (2), incident bar (4) and transmission bar (9), pad (6) and lining bar (10) and use 48CrMoA round steel materials, its Young Modulus 210GPa, density 7850kg/m³, velocity of wave 5172m/s.

6. under a kind of high strain-rate according to claim 5 Analysis of Concrete Tensile modulus experimental rig, it is characterised in that：Institute Incident bar (4) 3200mm long, diameter 74mm is stated, one end Diameter Gradual Change contacted with bullet (2) is 37mm；The transmission bar (9) It is 1800mm long, the slender cylinder of diameter 74mm；The a diameter of 37mm of the bullet (2), length is 600mm；The pad (6) Thickness is 8mm, and section is the circle of diameter 74mm；Lining bar (10) a diameter of 10mm, length is 74mm.

7. under a kind of high strain-rate Analysis of Concrete Tensile modulus test method, it is characterised in that comprise the following steps：

S1, placement and adjusting device：Incident bar (4), transmission bar (9) are positioned on bearing (3), bearing (3) and air chamber is adjusted (1), it is ensured that the center alignment of bullet (2), incident bar (4) and transmission bar (9)；

S2, paste foil gauge：First foil gauge (5) is pasted at incident bar (4) bar segment rear, the first foil gauge (5) side long Along bar length direction；Second foil gauge (11) sticks in transmission bar (9) bar segment center, and the second foil gauge (11) side long is parallel to bar Length direction is simultaneously maintained at same level position with the first foil gauge (5), second foil gauge (11) and the first foil gauge (5) away from It is equal with a distance from the stickup of test specimen (8)；3rd foil gauge (7) is pasted in test specimen (8) center, the 3rd foil gauge for two pieces totally relatively (7) side long is perpendicular to Impact direction；First foil gauge (5), the second foil gauge (11), the 3rd foil gauge (7) size are identical；

S3, placement test specimen：By incident bar (4), pad (6), lining bar (10), test specimen (8), lining bar (10), pad (6), transmission bar (9) arranged in sequence is placed successively, adjusts incident bar (4) and transmission bar (9) spacing, has made pad (6), lining bar (10), test specimen (8) just Incident bar (4) and transmission bar (9) center are clamped in well；

S4, connection deformeter：First foil gauge (5), the second foil gauge (11), the 3rd foil gauge (7) and deformeter bridge are connected Connect；

S5, take cylindrical disc test specimen and tested, give air chamber (1) pressurization, certain impulsive force is subject to bullet (2), make it Incident bar (4) is clashed into certain stroke speed, stress wave is produced, stress wave is via rod member (4), pad (6), lining bar (10), it is delivered on test specimen (8) and brings it about splitting；

S6, collection foil gauge recorded data, substitute into formula and are calculated the Analysis of Concrete Tensile that can obtain under high strain-rate Modulus.

8. under a kind of high strain-rate according to claim 7 Analysis of Concrete Tensile modulus test method, it is characterised in that step The computational methods of formula are in rapid S6：

S61, when bullet (2) clash into incident bar (4) when, rod member inside produce longitudinal direction incident compressional wave, due to different impedances, Incidence wave is partially reflected back incident bar (4) in the interface that incident bar (4) and test specimen (8) are contacted, available based on three ripple methods：

P₁=E (ε_i+ε_r)

P₂=E ε_tr

Wherein, P₁For incident bar clashes into line load, P₂For transmission bar supports line load, unit is N/m；E is incident bar Young mould Amount, E=210GPa；ε_iThe incidence wave maximum strain recorded by incident bar foil gauge；ε_rBy incident bar foil gauge record it is anti- Ejected wave maximum strain, ε_trThe transmitted wave maximum strain recorded by transmission bar；

The influence that pull end head is calculated test specimen impact is split in S62, removal, tries to achieve the actual suffered impact P of test specimen：

$P=P_1+\frac{P_1-P_2}{2}$

It is S63, as follows to test specimen calculation method for stress, take any cross section on height of specimen direction, section any position unit Body stress state is as follows：

${\mathrm{\σ}}_r=-\frac{2P}{\mathrm{\π}}\{\mathrm{\α}+\underset{n=1}{\overset{n=\mathrm{\∞}}{\Σ}}\[1-(1-\frac{1}{n}){\left(\frac{r}{R}\right)}^2\]{\left(\frac{r}{R}\right)}^{2n-2}sin2n\mathrm{\α}cos2n\mathrm{\θ}\}$

${\mathrm{\σ}}_{\mathrm{\θ}}=-\frac{2P}{\mathrm{\π}}\{\mathrm{\α}-\underset{n=1}{\overset{n=\mathrm{\∞}}{\Σ}}\[1-(1+\frac{1}{n}){\left(\frac{r}{R}\right)}^2\]{\left(\frac{r}{R}\right)}^{2n-2}sin2n\mathrm{\α}cos2n\mathrm{\θ}\}$

${\mathrm{\τ}}_{r\mathrm{\θ}}=-\frac{2P}{\mathrm{\π}}\{\underset{n=1}{\overset{n=\mathrm{\∞}}{\Σ}}\[1-{\left(\frac{r}{R}\right)}^2\]{\left(\frac{r}{R}\right)}^{2n-2}sin2n\mathrm{\α}cos2n\mathrm{\θ}\}$

Wherein, σ_rIt is cell cube normal direction tension, σ_θIt is cell cube tangential stress, τ_rθIt is cell cube shearing stress, R is that test specimen cuts Radius surface, r, θ are the cell cube coordinates under polar coordinate system, and α is the half of the central angle corresponding to stress scope, reference ISRM ISRMs test specification, takes 2 α=10 °；By Parameter Switch, x, y are the cell cube under rectangular coordinate system Coordinate, the origin of coordinates is foil gauge central point, and foil gauge centerline when taking y=0, i.e., goes up any point stress along the x-axis direction State is as follows：

${\mathrm{\σ}}_x=\frac{2P}{\mathrm{\π}Dl}\[\frac{16D^2{x}^2}{{(4x^2+D^2)}^2}-1\]$

${\mathrm{\σ}}_y=\frac{2P}{\mathrm{\π}Dl}\[\frac{4D^2{x}^2}{{(4x^2+D^2)}^2}-1\]$

τ_xy=0

Wherein, σ_xIt is cell cube x-axis direction tension, σ_yIt is cell cube y-axis direction tension, τ_xyIt is cell cube shearing stress, l is Specimen thickness, D is test specimen diameter of section；

S64, test specimen center foil gauge measured value are equal to the calculated value of following theoretical formula, because the compression on y-axis direction is x-axis The twice of tension on direction, thus it is very important because of the stretch modulus that poisson effect causes；Diametrically in horizontal direction, strain In the range of piece, the test specimen Brazilian tension dependent variable ε of the 3rd foil gauge measurement_tBy following theoretical formula method：

${\mathrm{\ϵ}}_t=\frac{1}{2L}{\∫}_{-L}^L\frac{1}{E_t}(-{\mathrm{\σ}}_x+{\mathrm{\ν\σ}}_y)dx=\frac{1}{E_{t}L}{\∫}_0^L(-{\mathrm{\σ}}_x+{\mathrm{\ν\σ}}_y)dx$

Wherein, L takes the half of strain leaf length, E_tIt is required Analysis of Concrete Tensile modulus, v is test specimen Poisson's ratio；Abbreviation finally draws Analysis of Concrete Tensile modulus：

$E_t=E_s\{(1-\frac{D}{L}\arctan \frac{2L}{D})(1-\mathrm{\ν})+\frac{2D^2(1+\mathrm{\ν})}{4L^2{D}^2}\}=A^{*}{E}_s$

Brazilian tension modulus E_s=2P/ π Dl ε_tDetermined by surveyed stress-strain diagram, wherein stress σ_t=2P/ π Dl, taking stress should The linear slope over 10 of varied curve；Or, take E_s=[(1/2) σ_t,max]/ε_t, wherein σ_t,max/ 2 take maximum stress in stress-strain diagram Half, ε_tIt is then corresponding elongation strain amount when reaching maximum stress half.