CN117538154A - 3D printing proportioning cement stone ultra-early short-term creep test method based on pressing method - Google Patents
3D printing proportioning cement stone ultra-early short-term creep test method based on pressing method Download PDFInfo
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- 239000004568 cement Substances 0.000 title claims abstract description 166
- 239000004575 stone Substances 0.000 title claims abstract description 120
- 238000003825 pressing Methods 0.000 title claims abstract description 64
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- 238000012360 testing method Methods 0.000 claims abstract description 152
- 238000000034 method Methods 0.000 claims abstract description 51
- 235000015220 hamburgers Nutrition 0.000 claims abstract description 42
- 238000000611 regression analysis Methods 0.000 claims abstract description 9
- 239000000463 material Substances 0.000 claims description 26
- 229910001209 Low-carbon steel Inorganic materials 0.000 claims description 3
- 238000007373 indentation Methods 0.000 description 20
- 238000006073 displacement reaction Methods 0.000 description 10
- 230000006399 behavior Effects 0.000 description 8
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- 239000000203 mixture Substances 0.000 description 6
- 239000004567 concrete Substances 0.000 description 4
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- 238000004364 calculation method Methods 0.000 description 3
- 230000007423 decrease Effects 0.000 description 2
- 238000006703 hydration reaction Methods 0.000 description 2
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N3/00—Investigating strength properties of solid materials by application of mechanical stress
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
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Abstract
The invention provides a 3D printing proportioning cement stone ultra-early short-term creep test method based on a pressing method, which comprises the following specific steps: preparing a mixing ratio for testing the ultra-early creep degree of the cement stone, and preparing a cement stone test piece; performing ultra-early short-term creep test on the cement stone test piece by utilizing a pressure entering method, and recording a test result; calculating the creep degree of the cement stone test piece under the short-term constant-load control rate loading condition; obtaining the viscosity coefficient eta of the Kelvin model in the Burgers model by using the obtained test result and creep degree and utilizing unitary nonlinear regression analysis 2 And coefficient of elasticity E 2 The method comprises the steps of carrying out a first treatment on the surface of the The viscosity coefficient eta 2 And coefficient of elasticity E 2 Carrying the expression of (1) into a Burgers model to obtain a corrected Burgers model; substituting the test result into the modified Burgers model to predict the creep of the 3D printed cement stone test piece under the ultra-early short-term loading. The invention obtains the creep model of the cement stone test piece in the ultra-early stage in the time from initial setting to final setting, and has guiding significance on the 3D printing of the ultra-early-stage correlation characteristic of the cement stone.
Description
Technical Field
The invention relates to the technical field of building material testing methods, in particular to a 3D printing proportioning cement stone ultra-early short-term creep testing method based on a pressing method.
Background
The ultra-early creep refers to creep in the section from the initial setting to the final setting of the cement-based material, and deformation in the section has a critical meaning on the printing behavior of the 3D printed cement-based material. The ultra-early cement stone has the characteristics of viscosity, elasticity and plasticity, and cannot be measured by using a traditional creep degree test method.
Short term creep refers to the change in cement-based material over 5 minutes. Although the mechanical behavior of the concrete after the form removal hardening can be accurately predicted, the transformation of the mechanical property is accelerated by hydration reaction, so that the mechanical behavior of the concrete in the ultra-early stage is still difficult to accurately predict at present. The test method provided by the invention aims at monitoring creep of the cement stones in the early age.
The ultra-early creep of the cement stone can also help simulate the multi-scale response of the cement stone, and provide the inherent input characteristic for a multi-scale model for predicting the macro-scale behavior of the cement stone. Therefore, the research on the cement stone ultra-early creep degree test method and the prediction method thereof has important significance.
The creep method proposed by the patent CN 112697585A is only applicable to cement stones after 28 days of age, and is not applicable to the measurement of creep of early cement stones; the patent CN 103149094A carries out an active constraint test by applying a load to a test piece and carries out a self-shrinkage test by utilizing a shrinkage compensation test piece, the method is used for measuring the cement stone creep between 20 hours and 24 hours, and although the method can test the cement stone creep earlier in age, the method still needs to disassemble a die and can not measure the ultra-early cement stone creep; patent CN 112485114A establishes a method for predicting long-term creep of set cement with age of 16h based on Maxwell model, but the method is applicable to long-term creep of set cement, but is not applicable to describing short-term loading creep of set cement.
The conventional creep test method is difficult to measure the ultra-early creep of the cement stone, so that the ultra-early short-term creep test method is needed to solve the problems.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a 3D printing proportioning cement stone ultra-early short-term creep test method based on a pressing method, which predicts the cement stone ultra-early short-term creep by using a pressing method principle and performs a pressing test by using a press. The method is characterized in that an ultra-early creep calculation method suitable for cement stones is established based on a pressing method theory, and an ultra-early creep test method and a theoretical model of the cement stones are obtained through a combined test, so that the problem of constructability performance of the 3D printed cement-based material is solved, and an inherent input characteristic is provided for a multi-scale model for predicting macro-scale behaviors of the cement-based material.
The invention provides a 3D printing proportioning cement stone ultra-early short-term creep test method based on a pressing method, which comprises the following steps of:
s1, designing a mixing ratio of the ultra-early creep degree of the cement stone based on the 3D printing matching material, and preparing a cement stone test piece;
s2, performing an ultra-early short-term creep test on the cement stone test piece by utilizing a press-in method, and recording a test result;
s3, calculating the creep degree of the cement stone test piece under the short-term constant-load control rate loading condition according to the test result obtained in the step S2 to obtain creep degree data of the cement stone, wherein the specific expression of the creep degree is as follows:
wherein: j (t) is the creep degree of the cement stone test piece, alpha is the half angle of the conical pressure head, h (t) is the pressing depth, F 0 V is poisson's ratio for initial load;
s4, utilizing the test result obtained in the step S2 and the creep degree obtained in the step S3 to analyze by utilizing unitary nonlinear regression,obtaining the viscosity coefficient eta of Kelvin model (Kelvin model) in Burgers model (Bergers model) 2 And coefficient of elasticity E 2 The expression over time is:
E 2 (t)＝ae bt
η 2 (t)＝ce -dt
wherein: a. b, c and d are parameters which influence the delay time growth rate in the corrected Kelvin model respectively;
s5, obtaining the viscosity coefficient eta from the step S4 2 And coefficient of elasticity E 2 The expression of the modified Burgers model is obtained by bringing the Burgers model into the expression of the modified Burgers model:
wherein: j (t) is creep degree of cement stone in ultra-early stage, E 1 For the elastic coefficient, η of the spring element in the modified Burgers model 1 The viscosity coefficient of the sticking kettle in the modified Burgers model is obtained;
s6, substituting the test result obtained in the step S2 into the corrected Burgers model obtained in the step S5 to obtain the 3D printing cement stone ultra-early short-term creep model.
Preferably, in step S2, the test result includes a depth-of-penetration-time curve of the set cement test piece at a different super early stage and a load-time curve of the set cement test piece at a different super early stage.
Preferably, in step S2, the accuracy of the loading pressure of the press-in method is 0.1 to 0.5N, and the accuracy of the loading speed is 0.001 to 0.005mm/m.
Preferably, in step S2, the pressing head in the pressing method is a conical pressing head with a cone half angle of 45 °, and the height of the pressing head is 10mm.
Preferably, in step S2, the material of the indenter is low carbon steel, and the elastic modulus E of the indenter i 206X 10 3 MPa, poisson ratio v of the pressure head i 0.26.
Preferably, in step S2, the press depth of the press head is 5mm when the press-in test is performed.
Preferably, in step S2, when the press-in method test is performed, the press head moves at a constant speed, the speed of the constant speed is 5mm/min, the loading time of the constant speed is 1min, and the loading time of the constant speed is 5min.
Preferably, in step S4, the parameters a, b, c and d are obtained by a unitary nonlinear regression analysis, respectively.
Compared with the prior art, the invention has the following advantages:
1. the invention establishes an ultra-early creep calculation method suitable for cement stones based on the pressing method theory, and obtains the ultra-early creep test method of cement stones by combining experiments. According to the test method capable of rapidly and accurately measuring the 3D printing set cement ultra-early creep, the 3D printing set cement ultra-early creep behavior is accurately represented by constructing a set cement ultra-early creep model, theoretical support and technical support are provided for simulating the multi-scale response of the 3D printing set cement, and meanwhile the whole test process is not limited by die stripping and dimensional errors.
2. The invention derives a mathematical expression suitable for calculating the creep degree of the cement stone at the ultra-early stage under the action of one-time short-term load based on contact mechanics and linear viscoelasticity mechanics, and combines the expression with the ultra-early indentation parameter to obtain a test method capable of testing the ultra-early short-term creep of the cement stone.
3. Compared with the traditional creep degree testing method, the testing method has the advantages that the testing method is simple and convenient, the test piece does not need to be disassembled, and the test piece is not limited by size errors. Through researching the creep of the 3D printing cement stone in the ultra-early stage, the method can provide the inherent input characteristic for the multi-scale modeling of the cement stone, can be used for representing the structural deformation in the concrete printing process, and has guiding significance for researching the related characteristic of the cement stone in the ultra-early stage.
Drawings
FIG. 1 is a flow chart of a 3D printing proportion cement stone ultra-early short-term creep test method based on a pressing method;
FIG. 2 is a graph of short-term creep displacement of a pressing method in the 3D printing proportioning cement stone ultra-early-stage short-term creep test method based on the pressing method;
FIG. 3A test piece indentation method t of 1# mixing proportion in an embodiment of a 3D printing proportion cement stone ultra-early short-term creep test method based on an indentation method 0 Time-of-day displacement-time curve;
FIG. 4A test piece indentation method t of 1# mixing proportion in an embodiment of a 3D printing proportion cement stone ultra-early short-term creep test method based on an indentation method 1 Time-of-day displacement-time curve;
FIG. 5A test piece indentation method t of 1# mixing proportion in an embodiment of a 3D printing proportion cement stone ultra-early short-term creep test method based on an indentation method e Time-of-day displacement-time curve;
FIG. 6A test piece indentation method t of 1# mixing proportion in an embodiment of a 3D printing proportion cement stone ultra-early short-term creep test method based on an indentation method 2 Time-of-day displacement-time curve;
FIG. 7A test piece indentation method t of 1# mixing proportion in an embodiment of a 3D printing proportion cement stone ultra-early short-term creep test method based on an indentation method 4 Time-of-day displacement-time curve;
FIG. 8 is a graph of creep degree versus time of a 1# set test piece at different ages in an embodiment of a 3D printing proportioning set ultra-early short-term creep test method based on a pressing method;
FIG. 9 is a Burgers model E in an embodiment of a 3D printing proportioning cement stone ultra-early short-term creep test method based on a pressing method 2 A graph of change over time;
FIG. 10 shows Burgers model eta in an embodiment of the 3D printing proportioning cement stone ultra-early short-term creep test method based on the pressing method 2 A graph of change over time;
FIG. 11 is a graph of a creep model verification curve of a 3# mix proportion cement stone test piece in an embodiment of a 3D printing mix proportion cement stone ultra-early short-term creep test method based on a pressing method;
fig. 12 is a graph of model verification of creep degree of a 4# mixing ratio set test piece in an embodiment of a 3D printing mixing ratio set ultra-early short-term creep test method based on a pressing method.
Detailed Description
In order to make the technical content, the structural features, the achieved objects and the effects of the present invention more detailed, the following description will be taken in conjunction with the accompanying drawings.
Aiming at the ultra-early creep of the cement stone, the invention provides a 3D printing proportion cement stone ultra-early short-term creep test method based on a pressing method, which adopts a universal material tester to carry out the cement stone ultra-early creep pressing method test, adopts a 45-degree conical pressing head to press the ultra-early cement stone at a speed of 5mm/min, and has a loading time of 1min and a holding time of 5min. Based on the study of the stress and deformation problems of the linear viscoelastic half space pressed by the pressure head derived by Lee and Radok, laplace transformation is applied to derive a theoretical formula for calculating the creep degree under the constant load control loading condition, so that a theoretical foundation is laid for the ultra-early creep degree pressing test of the cement stone, and the specific implementation steps are shown in figure 1:
s1, configuring a mixing ratio of the ultra-early creep degree of the set based on the 3D printing matched material, wherein the mixing ratio refers to the proportional relation among all the constituent materials in the set, and preparing a set cement test piece.
S2, when the set cement test piece has certain hardness, performing ultra-early short-term creep test on the set cement test piece by using a pressing-in method, and recording test results, wherein the test results comprise pressing-in depth-time graphs of the set cement test piece at different ultra-early moments and load-time graphs of the set cement test piece at different ultra-early moments.
Further, in order to obtain a result of the cement stone test piece in the ultra-early short-term creep test, in the indentation method, the accuracy of the loading pressure of the pressure head is 0.1-0.5N, the accuracy of the loading speed is 0.001-0.005 mm/m, and when the indentation method test is carried out, the pressure head moves at a constant speed, the speed of the constant speed is 5mm/min, the loading time of the constant speed is 1min, the holding time of the constant speed is 5min, and the indentation depth of the pressure head is 5mm. The pressure head is conical with a cone half angle of 45 DEGThe height of the pressure head is 10mm, the material of the pressure head is low carbon steel, and the elastic modulus E i 206X 10 3 MPa, poisson ratio v i 0.26.
S3, calculating the creep degree of the cement stone test piece under the short-term constant-load control rate loading condition according to the test result obtained in the step S2, and obtaining the creep data of the cement stone, wherein the specific expression of the creep degree is as follows:
wherein: j (t) is the creep degree of the cement stone test piece, alpha is the half angle of the conical pressure head, h (t) is the pressing depth, F 0 For initial load, v is poisson's ratio.
S4, obtaining the viscosity coefficient eta of a Kelvin model (Kelvin model) in a Burgers model (Bergers model) through the test result obtained in the step S2 and the creep degree obtained in the step S3 by utilizing unitary nonlinear regression analysis 2 And coefficient of elasticity E 2 The expression over time is:
E 2 (t)＝ae bt
η 2 (t)＝ce -dt
wherein: a. b, c and d are parameters which are used for correcting the delay time increasing rate in the Kelvin model, and the parameters a, b, c and d are obtained through unitary nonlinear regression analysis.
S5, obtaining the viscosity coefficient eta from the step S4 2 And coefficient of elasticity E 2 The expression of the modified Burgers model is obtained by bringing the Burgers model into the expression of the modified Burgers model:
wherein: j (t) is creep degree of cement stone in ultra-early stage, E 1 For the elastic coefficient, η of the spring element in the modified Burgers model 1 And obtaining the viscosity coefficient of the sticking kettle in the modified Burgers model through unitary nonlinear regression analysis.
S6, substituting the test result obtained in the step S2 into the corrected Burgers model obtained in the step S5 to obtain the 3D printing cement stone ultra-early short-term creep model.
The method for testing the ultra-early short-term creep of the 3D printing proportioning cement stone based on the pressing method is further described by the following embodiment:
the specific process of the specific embodiment is realized as follows:
s1, configuring a mixing ratio for 3D printing of the ultra-early creep degree of the set cement, and preparing a set cement test piece.
In this embodiment, in order to facilitate verification of test data, five different set cement samples were prepared and numbered, wherein the mix proportion of the set cement was used to compare with the mix proportion of the 3D printed set cement, and the specific mix proportion components are shown in table 1.
TABLE 1
Mixing raw materials according to the mixing ratio in the step S1, pouring the cement stone into a cylindrical die with the diameter of 160mm and the height of 70mm to prepare cement stone test pieces, preparing 6 groups of 1# cement stone test pieces, wherein the age is the initial setting time t 0 Half of the initial setting time t 1 Time t of final setting e Two hours t after final setting 2 1 cement stone test piece respectively, the age is 4 hours t after final setting 4 2 cement stone test pieces; 4 groups of 2# cement stone test pieces are prepared, and the age is the initial setting time t respectively 0 First 1h, initial setting time t 0 After 1h, final setting time t e 0.5 hour t after final setting e The method comprises the steps of carrying out a first treatment on the surface of the 3 groups of 3# cement stone test pieces and 4# cement stone test pieces are respectively prepared, and the age is the initial setting time t 0 Time t of initial setting 0 1h after and at final setting time t e 。
S2, firstly, performing indentation test tests of different indentation rates and different holding times on the cement stone test piece, exploring the influence of the indentation test piece loading rate on indentation displacement, and determining the optimal loading speed and holding time of the cement stone test piece through analysis test results.
The specific operation process for determining the optimal loading speed and the loading time of the cement stone test piece is as follows:
the test piece of cement stone with the 1# mixing ratio is loaded at the speeds of 5mm/30s, 5mm/5s and 5mm/min respectively at the early age of 7h, and then is carried for 5min, and the experimental result is shown in figure 2. It can be seen that the displacement-time curve of 5mm/5s loading speed is significantly higher than the other two, whereas the curves of 5mm/30s loading speed and 5mm/min loading speed are closer. The method shows that the loading speed is too high, and when the loading speed is 5mm/5s, the method is not suitable for the ultra-early test of the pressing method, and meanwhile, the sensitivity of the ultra-early test is lost in consideration of the too low loading speed. The impact of 5mm/30s and 5mm/min loading rates on the indentation test will also be discussed.
Carrying out a short-term creep press-in test on the 1# mixing ratio test piece by a press-in method, wherein the age is respectively the initial setting time t0 and the initial final setting time half time (half) t 1 Time t of final setting e Two hours t after final setting 2 T 4 hours after final setting 4 5 time points. The loading path 1 is used for loading for 30s at a constant speed of 5mm/30s, and when the displacement is 5mm, the load is increased, and the constant force is kept for loading for 1min. The loading path 2 is used for loading at a constant speed of 5mm/min for 1min, and when the displacement is 5mm, the load is increased, and the constant force is kept for 10min. The test results are shown in fig. 3 to 8.
The displacement curve with the holding time of 10min can show that the loading time is about 5min, the displacement curve is basically a straight line, the creep degree change rule of the cement stone after holding for 5min tends to be stable, and the creep degree change rule can be used for describing the creep change rule in the 3D printing process and providing assistance for structural deformation, so that the 5min is used as the holding time of the cement stone. As can be seen from FIG. 3, the loading rate of the press-in is 5mm/30s, and the larger the load required for 5mm.
As can be seen from fig. 4, 5, 6 and 7, as the age increases, the displacement decreases, and the curve trend for loading 30s and 1min becomes closer. The longer the age, the smaller the influence of the loading rate of the cement paste indentation test on the test result. Through the analysis, the loading time of the cement paste ultra-early short-term creep is 1min, the constant-speed loading speed is 5mm/min, and the 5min is selected as the most suitable loading time of the cement paste short-term creep.
When the 1# cement stone test piece prepared in the step S1 is initially set, performing ultra-early creep test on the 1# cement stone test piece, using an INSTRON-5928 type press machine as an experimental instrument, wherein the loading pressure precision is 0.1N, the loading speed precision is 0.001-0.005 mm/m, using a conical pressure head with a cone half angle of 45 degrees as a pressure head, aligning the cone tip of the pressure head with cement stone to be tested, loading for 1min at a constant speed of 5mm/min, holding for 5min after reaching a press-in depth of 5mm, recording test data, and testing a press-in depth-time curve graph of the cement stone test piece at different ultra-early moments and a load-time curve graph of the cement stone test piece at different ultra-early moments.
S3, deducing a calculation model of the creep degree of the cement stone under the constant load control rate loading condition according to the test result obtained in the step S2:
for the conical pressure head with the conical half angle of 45 degrees adopted in the embodiment, the classical Sneddon formula is adopted for analyzing and solving the elastic pressing of the conical pressure head, and the relational expression between the pressing load F and the pressing depth h is obtained as follows:
e and v are respectively the elastic modulus and Poisson's ratio of the cement stone test piece, and alpha is the half angle of the pressure head.
According to theory of material mechanics and contact mechanics, the following expression can be obtained by transforming the relational expression between the pressing load F and the pressing depth h:
in the test of the pressing method, the linear displacement rate is used for controlling the loading of the pressing head, and the relation between the pressing load F and time is as follows:
F(t)＝F 0 H(t)
wherein: f (F) 0 For initial loading, H (t) is a Heaviside function.
Through the deduction, the creep degree of the cement stone test piece under the short-term constant-load control rate loading condition is obtained, and the concrete expression is as follows:
wherein: j (t) is the creep degree of the cement stone test piece, alpha is the half angle of the conical pressure head, h (t) is the pressing depth, F 0 For initial load, v is poisson's ratio.
In this embodiment, for different test ages, taking 5min of loading as an abscissa, loading end time of loading for 1min as a starting point, and end time of loading for 5min as an end point, and taking a creep degree calculated value of a pressing-in method as an ordinate. And calculating creep degree-time curves of the cement stone test piece in the ultra-early stage at different moments in the short-term loading (5 min) process.
In order to verify the accuracy of the test method, a cement stone test piece with the mixture ratio of No. 1 and No. 2 is taken for creep test, and the age is t 4 The creep degree of the cement stone is tested by adopting a traditional creep degree testing method by adopting a 1# mixing proportion cement stone test piece at moment and a 2# mixing proportion cement stone test piece with the age of 0.5h after final setting; and carrying out creep test on the 2# mixing proportion cement stone test piece with the age of 1h before initial setting, 1h after initial setting and the final setting time by adopting a pressing method.
The traditional creep testing experimental instrument adopts a universal material tester INSTRON-5928, and the whole process of the material creep test is in a creep standard curing roomAnd (3) carrying out a stress-strain method on the cement stone test piece after the cement stone test piece is demolded, wherein the temperature is 20+/-2 ℃ and the humidity is greater than or equal to 95%, the loading time is 1min, the loading displacement is 0.3mm, and the holding time is 5min. Age t 4 The test result of the conventional creep degree test method of the cement stone test piece with the mixing ratio of No. 1 at the moment is shown in FIG. 8.
As can be seen from fig. 8, t 4 The creep degree test result of the traditional method almost coincides with the creep degree test result of the pressing method at the moment, which shows that neglecting plasticity can be carried out through constant loading, and the ultra-early creep degree of the viscoelastic plastic material is measured. The displacement-time test result of the ultra-early cement stone short-term pressing method can calculate the creep compliance-creep degree through the viscoelasticity assumption of the pressing method; in addition, it is evident that the creep profile decreases progressively as age increases. The maximum creep degree before the early stage set cement is initially set is indicated, and the creep degree is gradually reduced.
S4, severe hydration reaction still occurs in the cement-based material at the ultra-early stage, so that the trend of the variation of the ultra-early stage creep degree of the cement-based material with time is predicted more accurately in order to more accurately and reasonably reflect the characteristic of the variation of the ultra-early stage cement-based material with time, and the Burgers model needs to be corrected.
To explore the super early elastic coefficient E of the cement stone 2 And coefficient of viscosity eta 2 And (3) carrying out displacement test on test pieces with different ages according to the change rule of time, and carrying out the obtained test results into a formula (11) to obtain a creep degree curve. And meanwhile, carrying out unitary nonlinear regression analysis on the cement paste ultra-early creep test data measured in the step S2 by utilizing a Burgers model to obtain the figures 9 and 10.
As can be seen from fig. 9 and 10, E of the cement-based material 2 η 2 Meets the development rule of an exponential function in the ultra-early stage, so E is 2 (t) and eta 2 And (t) correcting the Burgers model in the following modes, wherein the specific expression is as follows:
E 2 (t)＝ae bt
η 2 (t)＝ce -dt
wherein: a. b, c, d are parameters affecting the delay time growth rate in the modified Kelvin model, respectively.
S5, for cement-based materials at an ultra early stage, the cement-based materials generally show viscoelastic properties, namely, aggregate inside the materials and gel which is not hydrated yet show elastic properties; the hydrated gel exhibits viscous behavior upon viscous flow when subjected to a load, and gradually hardens and develops elastic behavior as age increases. The Burgers creep model is formed by connecting a Kelvin model and a Maxwell model in series. When the material is loaded, the instantaneous elastic deformation thereof is caused by the spring element E 1 The viscous deformation is represented by eta 1 、η 2 Co-representation, where η 1 The non-recoverable deformation represented is represented by E 2 And eta 2 The recoverable deformations of the common representation are represented.
The total deformation of the set test piece is expressed as:
ε t ＝ε 1 +ε 2 +ε 3
constitutive equation of the Burgers model can be written as:
from this, the creep prediction expression of the Burgers model can be deduced:
wherein: j (t) is the creep degree of the set cement, E 1 And E is 2 Elastic coefficients, eta, of two spring elements in Burgers model 1 And eta 2 The viscosity coefficients of two kettles in the Burgers model are respectively.
The viscosity coefficient eta obtained in the step S4 2 And coefficient of elasticity E 2 Is brought into the Burgers model to obtain a modified expressionThe expression of the Burgers model is:
wherein: j (t) is creep degree of cement stone in ultra-early stage, E 1 And E is 2 (t) the spring coefficients, η, of the two spring elements in the modified Burgers model, respectively 1 And eta 2 (t) are the viscosity coefficients of the two sticking kettles in the modified Burgers model, respectively.
S6, substituting the test result obtained in the step S2 into the corrected Burgers model obtained in the step S5 to predict creep of the 3D printing cement stone under ultra-early short-term loading.
In order to verify the accuracy of the modified Burgers model, ultra-early test data of the cement stones with the proportions of 1# and 2# and 3# and 4#, which are measured in the test, are taken, verified by a method of unitary nonlinear regression analysis, and compared with the fitting results of the conventional common models such as a Van derpel model, a Kelvin model and the like, and the verification results are shown in figure 11. As can be seen from fig. 11, the modified Burgers creep model herein predicts the ultra-early short-term loading creep of the set cement more accurately.
The 3D-printed set cement is prepared according to the 8# mixing ratio shown in table 1 and subjected to creep test by a pressing method to obtain creep data of the 3D-printed set cement, and the 3D-printed set cement is predicted according to S4, S5 and S6, and the prediction result is shown in fig. 12. As can be seen from FIG. 12, the prediction model provided by the method has high accuracy on the creep of the 3D printing set cement, and can well describe the ultra-early creep of the 3D printing set cement.
The feasibility of the testing method is verified by comparing the testing results of the traditional creep degree testing method and the testing method and comparing the testing results of cement stones with different mixing ratios. Compared with the traditional method, the method is simple and convenient, is not limited by size errors, can help solve the ultra-early configurable performance problem of the cement stone and provide necessary parameters for the numerical simulation of cement-based materials.
The above examples are only illustrative of the preferred embodiments of the present invention and are not intended to limit the scope of the present invention, and various modifications and improvements made by those skilled in the art to the technical solution of the present invention should fall within the scope of protection defined by the claims of the present invention without departing from the spirit of the present invention.
Claims (8)
1. The 3D printing proportioning cement stone ultra-early short-term creep test method based on the pressing method is characterized by comprising the following steps of:
s1, designing a mixing ratio of the ultra-early creep degree of the cement stone based on the 3D printing matching material, and preparing a cement stone test piece;
s2, performing an ultra-early short-term creep test on the cement stone test piece by utilizing a press-in method, and recording a test result;
s3, calculating the creep degree of the cement stone test piece under the short-term constant-load control rate loading condition according to the test result obtained in the step S2 to obtain creep degree data of the cement stone, wherein the specific expression of the creep degree is as follows:
wherein: j (t) is the creep degree of the cement stone test piece, alpha is the half angle of the conical pressure head, h (t) is the pressing depth, F 0 V is poisson's ratio for initial load;
s4, obtaining the viscosity coefficient eta of the Kelvin model in the Burgers model by using the test result obtained in the step S2 and the creep degree data obtained in the step S3 through unitary nonlinear regression analysis 2 And coefficient of elasticity E 2 The expression over time is:
E 2 (t)＝ae bt
η 2 (t)＝ce -dt
wherein: a. b, c and d are parameters which influence the delay time growth rate in the corrected Kelvin model respectively;
s5, obtaining the step S4Coefficient of viscosity eta 2 And coefficient of elasticity E 2 The expression of the modified Burgers model is obtained by bringing the Burgers model into the expression of the modified Burgers model:
wherein: j (t) is creep degree of cement stone in ultra-early stage, E 1 For the elastic coefficient, η of the spring element in the modified Burgers model 1 The viscosity coefficient of the sticking kettle in the modified Burgers model is obtained;
s6, substituting the test result obtained in the step S2 into the corrected Burgers model obtained in the step S5 to obtain the 3D printing cement stone ultra-early short-term creep model.
2. The 3D printing proportioning cement stone ultra-early short-term creep test method based on the pressing method according to claim 1, wherein in step S2, the test result includes a pressing depth-time curve of the cement stone test piece at different ultra-early time and a load-time curve of the cement stone test piece at different ultra-early time.
3. The 3D printing proportioning cement stone ultra-early short-term creep test method based on the pressing method according to claim 1, wherein in step S2, the accuracy of the loading pressure of the pressing method is 0.1-0.5N, and the accuracy of the loading speed is 0.001-0.005 mm/m.
4. The 3D printing proportioning cement stone ultra-early short-term creep test method based on the pressing method according to claim 1 or 3, wherein in the step S2, the pressing head is a conical pressing head with a cone half angle of 45 degrees, and the height of the pressing head is 10mm.
5. The method for testing ultra-early short-term creep of 3D printing proportioning set cement based on pressing method according to claim 1 or 3, wherein in step S2, the material of the pressing head is low carbonSteel, elastic modulus E of the indenter i 206X 10 3 MPa, poisson ratio v of the pressure head i 0.26.
6. The method for testing ultra-early short-term creep of 3D printing proportioning set cement based on the pressing method according to claim 1 or 2, wherein in step S2, the pressing depth of the pressing head is 5mm when the pressing method test is performed.
7. The 3D printing proportioning cement stone ultra-early short-term creep test method based on the pressing method according to claim 1 or 2, wherein in the step S2, when the pressing method test is performed, the pressing head moves at a constant speed, the speed of the constant speed is 5mm/min, the loading time of the constant speed is 1min, and the holding time of the constant speed is 5min.
8. The method for testing the ultra-early short-term creep of the 3D printing proportioning cement set based on the pressing method according to claim 1, wherein in the step S4, parameters a, b, c and D are obtained through unitary nonlinear regression analysis respectively.
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