CN108279163A - A method of based on pressure mercury experiment prediction cement-based material elasticity modulus - Google Patents
A method of based on pressure mercury experiment prediction cement-based material elasticity modulus Download PDFInfo
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- CN108279163A CN108279163A CN201810108085.3A CN201810108085A CN108279163A CN 108279163 A CN108279163 A CN 108279163A CN 201810108085 A CN201810108085 A CN 201810108085A CN 108279163 A CN108279163 A CN 108279163A
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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
- G01N3/08—Investigating strength properties of solid materials by application of mechanical stress by applying steady tensile or compressive forces
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N2203/00—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
- G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
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- G01N2203/0069—Fatigue, creep, strain-stress relations or elastic constants
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- G—PHYSICS
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- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
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Abstract
The invention discloses a kind of methods based on pressure mercury experiment prediction cement-based material elasticity modulus, include the following steps：Obtain cement-based material sample, the sample after drying is taken to carry out pressure mercury experiment, calculate the relationship between cumulative porosity rate and pore diameter, cumulative porosity rate is converted into relative compaction, relative compaction and pore diameter are indicated in log-log coordinate system, determine relative compaction and pore diameter linearly relevant region, obtain the slope of relative compaction and pore diameter linear correlation region, the characteristic parameter of cement-based material porous structure is determined with slope according to linearly related range, based on EFFECTIVE MEDIUM THEORY, the elasticity modulus of cement-based material is obtained by iterative calculation；The present invention solves the problems, such as to predict that parameter setting existing for cement-based material elasticity modulus is excessive based on aquation dynamics and mesomechanics, to establish the simple analytic method for predicting elasticity modulus by the characteristic parameter of cement-based material porous structure.
Description
Technical field
The present invention relates to inorganic non-metallic material analyses and characterization technique field, more particularly to one kind is based on pressure mercury experiment point
The method of analysis and characterization cement-based material performance indicator.
Background technology
For cement-based material, elasticity modulus (Young's modulus, body become modulus, modulus of shearing) structure design with
It occupies an important position in analysis.In view of the importance of elasticity modulus, the existing achievement in research of cement-based material proposes a variety of
Prediction technique.On the whole, current predictive method can be divided into two major classes：Analytic method and numerical method.Analytic method is based on water
Geometry, the physical features of cement-based material establish suitable mesomechanics method；Compared to analytic method, numerical method direct solution
Basic stiff equation, the powerful calculating ability dependent on computer.The experimental results show the precision of various prediction techniques
Depend primarily on the precision characterized to cement-based material porous structure.
Cement-based material porous structure shows extremely complex Heterogeneous Characteristics, usually across multiple from nanometer to micron
Scale.On nanoscale, the basic unit of about 5 nanosizeds is piled into the hydrated calcium silicate gel of porous structure；Micro-
On metrical scale, the unordered accumulation of hydrated product (hydrated calcium silicate gel, calcium hydroxide, entringite) and unhydrated clinker forms hair
Pore structure.Therefore, it for cement-based material, accurately characterizes porous structure and prediction elasticity modulus needs fundamentally to solve
Certainly Issues On Multi-scales.For example, two scale homogenization methods are a kind of common methods, aquation silicic acid of this method to nanoscale
The cement slurry of calcium gel and micro-scale uses Mori-Tanaka methods and self-consistancy theory respectively.It is worth noting that, more rulers
Degree method is carrying out needing that a large amount of parameter is arranged when scale describes from nanoscale to micro-meter scale, and comparable parameter exists
It is difficult to directly measure in experiment.In addition, multi-scale method is there are the problems such as less efficient, operability is bad, especially for
Mixed with the cement-base composite material of mineral admixture.
In recent years, there is significant self-similarity characteristics for researcher's discovery cement-based material porous structure, and then develop
Go out a kind of method of geometry to describe and build the porous structure of cementitious material.This kind of method of geometry solves multi-scale method presence
It is less efficient, operability is bad the problems such as, to efficiently build cementitious material porous structure.Thin sight power is combined as a result,
Method (such as EFFECTIVE MEDIUM THEORY), the cement-based material porous structure based on this kind of method of geometry structure are also prediction cement base
The elasticity modulus of material provides a kind of feasibility.
Invention content
In view of the above problems, it solving assumed condition in the prior art present invention aims at offer one kind not conforming to
The problem of reason, parameter are difficult to measure, to establish the simple analytic method of cement-based material elasticity modulus.
In order to achieve the above object, the technical solution adopted by the present invention is as follows：One kind is based on pressure mercury experiment prediction cement base
The method of elasticity modulus of materials, this method comprises the following steps：
1) cement-based material sample is made as required, and sample is for use after freeze-drying；
2) sample for obtaining step 1) carries out pressure mercury experiment, gradually applies pressure P, obtains cumulative porosity rate f, calculates tired
Count the relationship between porosity f and hole d diameters；
3) the cumulative porosity rate f of sample is converted into relative compaction χ, relative compaction is indicated in log-log coordinate system
χ and pore diameter d；
4) relative compaction χ and pore diameter d linearly relevant region (d are determined1~d2), d1<d<d2, wherein d1It indicates
Linearly related diameter lower limit, d2It indicates the linearly related diameter upper limit, relative compaction χ and hole is calculated using least square method
The slope A in gap diameter d linear correlations region；
5) according to linearly related range (d1~d2) mathematic parameter (n, i, b) for building porous structure, n are determined with slope A
Indicate that the total number of hole phase and solid phase of the iteration member in one-dimensional square, i indicate that iterations, b indicate solid in iteration member
Body phase number；
6) it is based on EFFECTIVE MEDIUM THEORY, by porous structure characteristic parameter (n, i, b) and solid phase elasticity modulus (modulus of shearing
G0, body change modulus K0) pass through the elasticity modulus of iterative calculation acquisition cement-based material.
In the operating process of step 2) of the present invention, cement-based material hole is considered as the different cylinder of diameter, sample
Calculation formula between product cumulative porosity rate f and hole d diameters is as follows：Wherein, γsIndicate the surface of mercury
Tension, θ indicate the contact angle of mercury and pore surface.
In the operating process of step 3) of the present invention, the cumulative porosity rate f of sample is converted into the meter of relative compaction χ
It is as follows to calculate formula：χ=1-f.
In the operating process of step 4) of the present invention, relative compaction χ and pore diameter d is calculated using least square method
The calculation formula of the slope A in linearly related region is as follows：
Wherein, ∑ indicates that summation, S indicate sample size.
In the operating process of step 5) of the present invention, the n, i, b are positive integer.
In rapid operating process 5) of the present invention, the computational methods for building the mathematic parameter n and i of porous structure are as follows：
In the operating process of step 5) of the present invention, the computational methods for building the mathematic parameter b of porous structure are as follows：(b
=n3-A)。
In the operating process of the step 6) of the present invention, it is G to be tested by nano-indenter test and obtain solid phase modulus of shearing0,
It measures solid body and becomes modulus as K0。
It is described based on EFFECTIVE MEDIUM THEORY in the operating process of the step 6) of the present invention, solid phase is considered as matrix phase,
Hole is mutually considered as to distribution phase, the volume fraction c=1-b/n of hole phase3.After an iteration, the elasticity modulus of iteration phase
Calculation formula is as follows：
Wherein G1, K1For the modulus of shearing of iteration phase after 1 iteration and body change modulus.
Based on EFFECTIVE MEDIUM THEORY, iteration is mutually considered as to matrix phase, hole is mutually considered as to distribution phase, the volume point of hole phase
Number c=1-b/n3.After i iteration, the elasticity modulus calculation formula of iteration phase is as follows：
Wherein Gi, KiFor the modulus of shearing of iteration phase after i iteration and body change modulus；Gi-1, Ki-1To pass through i-1 times
The modulus of shearing of iteration phase becomes modulus with body after iteration.
After i iteration, iteration mutually represents the overall construction of studied cement-based material porous structure, thus water
It is respectively G that the modulus of shearing and body of cement-based material entirety, which become modulus,i, Ki。
The advantage of the invention is that：The present invention compared with the prior art in deposited based on aquation dynamics and mesomechanics method
The excessive problem of parameter setting, efficiently structure cement-based material porous structure on the basis of establish prediction elasticity modulus solution
Analysis method.
The pressure mercury experiment of the method application of the present invention is a kind of general technological means in cement-based material research, according to this
The experimental data that pressure mercury experiment measures finally obtains the gross data of cement-based material elasticity modulus by the processing to data,
Compared with the test value finally measured by the data, the gross data of cement-based material elasticity modulus of the invention with most
The data of whole measurement are essentially identical, greatly reduce the workload finally measured, method of the invention is efficient, is suitable for
Across comparison between different personnel's results of study.
Iterative calculation is carried out using unified mathematical formulae in overall flow in the method for the present invention, is not conformed to without containing any
The assumed condition of reason is difficult to the experiment parameter measured, to developing the efficient construction method of porous structure, establishing elasticity modulus
Simple analytic method is of great significance for cement-based material performance study.
Description of the drawings
Fig. 1 is that cement-slag slurry presses mercury experimental data figure in present example；
Fig. 2 is the data analysis figure that cement-slag slurry presses mercury experiment in present example；
Fig. 3 is the mathematic parameter schematic diagram that cement-slag slurry porous structure is built in present example；
Fig. 4 is the illustraton of model that cement-slag slurry porous structure is built in present example；
Fig. 5 is the iteration schematic diagram that cement-slag slurry elasticity modulus is predicted in present example；
Fig. 6 is the comparison of cement-slag slurry Elastic modulus prediction value and ultrasonic test value in present example.
Specific implementation mode
The present invention is described in further detail with specific implementation mode for explanation below in conjunction with the accompanying drawings.
The cement-based material referred in the embodiment of the present invention is mainly by cement and mineral admixture (such as granulated blast-furnace mine
Slag) plus the preparation of water mix.Cement-based material porous structure after maintenance hardening includes gel pore and pore.Cement-based material
Hole be presented as complicated geometrical morphology and random spatial distribution.Press mercury experiment since principle and equipment are relatively simple, quilt
It is widely used in the distribution of pores characterization of cement-based material, is a kind of routine test means of cement-based material research field.
Embodiment 1：A kind of method of structure cement-based material porous structure as shown in Fig. 1,2,3 and 4, including it is as follows：
1) cement-based material sample is obtained, it is freeze-dried：
By cement, slag powders and water mix, conserved 28 days in standard curing room.Take the cement-slag slurry after maintenance small
Block (about 0.5cm3) several, freezing (about 2~3min) in liquid nitrogen atmosphere is placed it in, is then placed in vacuum drying chamber and is taken out very again
Sky, per the weight for recording loss of moist for 24 hours, until reaching 0.01%/day, entire drying process lasts about 1 week.
2) take it is dry after sample carry out pressure mercury experiment, gradually apply pressure, calculate cumulative porosity rate and pore diameter it
Between relationship：
The sample after drying is taken to carry out pressure mercury experiment, impressed pressure P ranging from 0~206MPa obtain cumulative porosity rate f,
That is f (P)；Cement-based material hole is considered as the different cylinder of diameter, calculates the cumulative porosity rate f and pore diameter d of sample
Between relationship, i.e. f (d), computational methods are as follows：
Wherein γs=0.48N/m indicates that the surface tension of mercury, θ=140 ° indicate the contact angle of mercury and pore surface.
Obtain the mercury pressuring data (cumulative porosity rate and pore diameter) of the cement-slag slurry sample measured shown in Fig. 1.
3) cumulative porosity rate is converted into relative compaction, indicates that relative compaction and hole are straight in log-log coordinate system
Diameter：
The cumulative porosity rate f of sample is converted into relative compaction χ, i.e. χ=1-f.Phase is indicated in log-log coordinate system
To compactness χ and pore diameter d.
4) relative compaction and pore diameter linearly relevant region are determined, is calculated using least square method relatively closely knit
The slope of degree and pore diameter linear correlation region：
Determine relative compaction and pore diameter linearly relevant region (d1~d2), i.e. log χ=Alogd+B, d1<d<
d2, wherein d1Indicate linearly related diameter lower limit (d1=5nm), d2Indicate the linearly related diameter upper limit (d2=320nm), such as
Shown in Fig. 2.Relative compaction and pore diameter linear correlation region (d are calculated using least square method1~d2) slope A, calculate
Method is as follows：
It is calculated：A=0.0608.
5) according to linearly related range (d1~d2) mathematic parameter (n, i, b) for building porous structure is determined with slope A,
Middle positive integer n indicates phase (including hole phase and solid phase) of the iteration first (by hole phase and solid phase composition) in one-dimensional square
Number, positive integer i indicate that iterations, positive integer b indicate solid phase number in iteration member, as shown in Figure 3.
6) determine that the mathematic parameter n and i of structure porous structure, computational methods are as follows：
Wherein d1=5nm indicates linearly related diameter lower limit, d2=320nm indicates the linearly related diameter upper limit, A=
0.0608 indicates the slope of relative compaction and pore diameter linear correlation region.Result of calculation is：N=4, i=3.
7) determine that the mathematic parameter b of structure porous structure, computational methods are as follows：
(b=n3-A)
Wherein A=0.0608 indicates the slope of relative compaction and pore diameter linear correlation region；Result of calculation is：b
=60；It is visualized based on MATLAB software realization porous structures, as shown in Figure 4.
8) after i=3 iterative calculation, computational methods are as follows：
Wherein shear modulus G0=11.2GPa, body become modulus K0=31.3GPa, parameter c=1-b/n3=5/64；Iteration mistake
Journey is as shown in Figure 5.
9) prediction result of the elasticity modulus of cement-slag slurry sample is：Young's modulus=20.1GPa, modulus of shearing=
7.7GPa, body become modulus=17.0GPa.Simultaneously using ultrasonic method test verification the method for the present invention, Comparative result such as Fig. 6 institutes
Show.
From in embodiment the result shows that：The gross data of the cement-based material elasticity modulus of the present invention passes through with final
The data of ultrasonic measuring are essentially identical, and in actual mechanical process, method through the invention can obtain final products
Elasticity modulus, without the work finally measured, because measuring, work itself is time-consuming and laborious, and the cost of measurement is larger, because
This greatly reduces the workload finally measured, method of the invention be it is efficient, simultaneously, can by prediction data with most
Whole data carry out across comparison, facilitate the across comparison between different personnel's results of study.
It should be noted that above-mentioned is only presently preferred embodiments of the present invention, protection model not for the purpose of limiting the invention
It encloses, the arbitrary combination made on the basis of the above embodiments or equivalents all belong to the scope of protection of the present invention.
Claims (10)
1. a kind of method based on pressure mercury experiment prediction cement-based material elasticity modulus, makes cement matrix sample, obtains sample
The characteristic parameter of porous structure, which is characterized in that by the characteristic parameter (n, i, b) and solid phase of cement matrix sample porous structure
Elasticity modulus (G0, K0) by iterative calculation, obtain the elasticity modulus of cement-based material；
Wherein n indicates that the total number of hole phase and solid phase of the iteration member in one-dimensional square, i indicate that iterations, b expressions change
Dai Yuanzhong solid phase numbers, G0And K0It is tested and is obtained by nano-indenter test, G0Indicate modulus of shearing, K0Indicate that body becomes modulus.
2. the method as described in claim 1 based on pressure mercury experiment prediction cement-based material elasticity modulus, which is characterized in that institute
The method stated includes the following steps：
1) cement-based material sample is made as required, and sample is for use after freeze-drying；
2) sample for obtaining step 1) carries out pressure mercury experiment, gradually applies pressure P, obtains cumulative porosity rate f, calculates and add up hole
Relationship between gap rate f and hole d diameters；
3) the cumulative porosity rate f of sample is converted into relative compaction χ, in log-log coordinate system indicate relative compaction χ with
Pore diameter d；
4) relative compaction χ and pore diameter d linearly relevant region (d are determined1~d2), d1<d<d2, wherein d1Indicate linear
Relevant diameter lower limit, d2It indicates the linearly related diameter upper limit, calculates relative compaction χ using least square method and hole is straight
The slope A in diameter d linear correlations region；
5) according to linearly related range (d1~d2) with slope A determine cement-based material porous structure characteristic parameter (n, i,
b)；
6) it is based on EFFECTIVE MEDIUM THEORY, by porous structure characteristic parameter (n, i, b) and solid phase elasticity modulus (G0, K0) by repeatedly
In generation, calculates the elasticity modulus for obtaining cement-based material.
3. the method as claimed in claim 2 based on pressure mercury experiment prediction cement-based material elasticity modulus, which is characterized in that institute
In the operating process for stating step 2), cement-based material hole is considered as the different cylinder of diameter, sample cumulative porosity rate f and hole
Calculation formula between gap d diameters is as follows：
Wherein, γsIndicate that the surface tension of mercury, θ indicate the contact angle of mercury and pore surface.
4. the method as claimed in claim 2 based on pressure mercury experiment prediction cement-based material elasticity modulus, which is characterized in that institute
In the operating process for stating step 3), the calculation formula that the cumulative porosity rate f of sample is converted into relative compaction χ is as follows：χ=1-
f。
5. the method as claimed in claim 2 based on pressure mercury experiment prediction cement-based material elasticity modulus, which is characterized in that institute
In the operating process for stating step 4), the oblique of relative compaction χ and pore diameter d linear correlations region is calculated using least square method
The calculation formula of rate A is as follows：
Wherein, ∑ indicates that summation, S indicate sample size.
6. the method as claimed in claim 2 based on pressure mercury experiment prediction cement-based material elasticity modulus, which is characterized in that institute
In the operating process for stating step 5), the n, i, b are positive integer.
7. the method as claimed in claim 6 based on pressure mercury experiment prediction cement-based material elasticity modulus, which is characterized in that institute
It states in rapid operating process 5), the computational methods of the characteristic parameter n and i of cement-based material porous structure are as follows：
The computational methods of the characteristic parameter b of cement-based material porous structure are as follows：
(b=n3-A)。
8. the method as claimed in claim 2 based on pressure mercury experiment prediction cement-based material elasticity modulus, which is characterized in that institute
It states in rapid operating process 6), solid phase is considered as matrix phase, hole is mutually considered as to distribution phase, the volume fraction c=of hole phase
1-b/n3, after an iteration, the elasticity modulus calculation formula of iteration phase is as follows：
Wherein G1, K1Become modulus for the modulus of shearing and body of iteration phase after 1 iteration.
9. the method as claimed in claim 8 based on pressure mercury experiment prediction cement-based material elasticity modulus, which is characterized in that warp
After crossing i iteration, the elasticity modulus calculation formula of iteration phase is as follows：
Wherein Gi, KiBecome modulus for the modulus of shearing and body of iteration phase after i iteration；Gi-1, Ki-1For iteration phase after i-1 iteration
Modulus of shearing and body become modulus.
10. the method as claimed in claim 9 based on pressure mercury experiment prediction cement-based material elasticity modulus, which is characterized in that
After i iteration, iteration is mutually the overall construction of studied cement-based material porous structure, finally obtains cement matrix
The shear modulus G of materialiBecome modulus K with bodyi。
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