CC BY
26
УДК 539 ББК В36
Рудольф Абрамович Гицелътпер,
доктор философии,
генеральный директор Союза Российских соотечественников «Золотая моя Москва»,
член международного совета российских соотечественников (Хадера, Израиль), e-mail: rudolfl94138@ mail.ru
Физико-механические свойства «RubCon»
Представлены экспериментальные результаты определения физико-механических свойств нового строительного материала - нанобетона (с наноструктурированной матрицей), названного «RubCon». Проведены исследования по изучению деформации мате-риала и оценке температурного эффекта. Представлен анализ термомеханического раз-рушения нанобетона и методов его упрочнения. Предложена методика оценки степени упрочнения нанобетона.
Ключевые слова: физико-механические свойства, «RubCon». деформация, температурный эффект, термомеханическое разрушение и упрочнение
Rudolf Abramovich Gitselter,
Doctor of Philosophy,
General Director of Russian Compatriots’ Union ”My Golden Moscow”, member of the International Board of Russian Compatriots (Hadera, Izrael),
e-mail: [email protected]
Physical-Mechanical Properties of ’’RubCon”
The article presents the experimental results of determining physical and mechanical properties of a new construction material - nanoconcrete (with the nanostructured matrix) called ’’RubCon”. The study describes the deformation of the material and the assessment of the temperature effect, analyzes the thermal and mechanical destruction of the nanoconcrete and methods of its hardening. It offers the technique of assessing the degree of nanoconcrete hardening/
Keywords: physical and mechanical properties, ’’RubCon”, deformation, temperature effect, thermal and mechanical destruction and hardening.
Stress-strain relationship at central uniaxial compression
The experimental research of RubCon deformation at uniaxial central compression carried out. The special testing module consisting from three calibrated rods allowed to provide constant deformation speed (Figure 1).
Figure 1. Draft of testing gadget: 1 - sample of RubCon; 2 - calibrated rods; 3 - plate; 4 - centering bar Characteristic pressure - deformation relationship is shown in Figure 2.
© P. А. Гицельтер, 2012
39
Relative deformation.
Figure 2. Draft of testing gadget: 1 - sample of RubCon; 2 - calibrated rods; 3 - plate: 4 - centering bar
Analytical form of this dependence may be submitted as:
a = 2.6+ 241.46- 146e2___________________________________________(1)
Let v = ct/ctr; r) = e/eR; к = Еец/сгц. On the experimental base it is believed that dependence v =
f (k, rf) looks like square parabola v = кг] — r/ 2, where cr, e are the current values of compression stress
and deformations correspondingly, <Jr,€r - coordinates of the diagram top, k - the factor describing
elastic-plastic properties of RubCon. Then, a = aR к (e/eR) - (е/ед f (2)
and t] = 0.5 к ± (k2 — Av)° J (3)
The diagram of function (3) (dashed line) in relative coordinates well coincides with experimental dependence (a continuous line) stress - strain (Figure 3).
Figure 3. Diagram of function (3)
Temperature effect
For the experiment performance the test RubCon samples in size 40 x 40 x 160 mm. were prepared. Tests were carried out in the special chamber, in the temperature range —80 °C ± +80 °C appropriated to real operation conditions of the material. During experiments the stress-strain state of samples was determined depending on temperature of environment. In particular, the changes of the module of elasticity, ultimate strength at compression and the appropriate ultimate deformations of a material at influence of temperature were determined in comparison with the similar values obtained at test of control samples at room temperature. Results of experiments at negative temperature range are illustrated in Figure 4. It is possible to see, that at the maximal negative temperature —80 °C the ultimate relative strain decreases on the average 14 % in comparison with control values, and ultimate
strength at compression and the module of elasticity, on the contrary, are increased on 19 and 35 % correspondingly. It is necessary to note thus, that change of ultimate deformations linearly depends on temperature.
Figure 4■ Influence of negative temperatures on the ratio of the module of elasticity (1), ultimate compression strength (2) and ultimate deformations at compression (3) to the siniila r values obtained at test of control
RubCon samples at room temperature
We have shown that microstructure of RubCon has elastic, elastic - plastic and viscous phases. The amount of a last in the composite is less in comparison with others and consequently deformability of RubCon at action a long-term and a short-term loadings in the greater degree is determined by elastic and elastic - plastic deformations. Increase of the RubCon strength and the module of elasticity at compression and decrease of its ultimate deformations at negative temperatures can be explain by increase of a viscous phase viscosity and partial transformation of an elastic - plastic phase of a composite in elastic. The increase of an elastic phase results to embitterment of composite and by that to changes of its stress-strain state.
Influence of the increased positive temperatures in a range +20 °C + +80 °C on RubCon mechanical characteristics is shown in Figure 5.
Figure 5. Influence of positive temperatures on the ratio of the module of elasticity (1), ultimate compression strength (2) and ultimate deformations at compression (3) to the similar values obtained at test of control
RubCon samples at room temperature
Increase of temperature from +20 °C up to +50 °C has a little effect on RubCon. At the further increase of temperature, as it was possible to expect, substantial growth of ultimate deformations is observed at simultaneous drastically decrease of ultimate compressive strength and the module of elasticity. At the maximal positive temperature +80 °C deformability of RubCon grows in 2,5 times, ultimate strength is reduced on 40 %, the module of elasticity on 50 %. At rise in temperature the part of an elastic - plastic phase transfers to viscous; thus highly elastic and viscous deformations are developing
and producing the increase of RubCon deformability, decrease of its ultimate compressive strength and the module of elasticity.
These deformations have convertible character, i. e. at decrease of temperature there is a return process. The effect of temperature influence depends on its value and duration of heating or cooling. Short-term heating causes the convertible weakening of composite structure as a result of temperature binder plasticization. Result of this process is decrease of RubCon compressive strength and the module of elasticity and increase of its deformability.
Thermomechanical destruction of RubCon
As is known, load-carrying capacity of any structural materials depends on relationship of external force factors, temperature and time of their action, i. e. on strength, thermostability and durability. By this means problem of the forecast and increase of material serviceability is reduced to revealing the interrelations between aforementioned material behavior characteristics. Thermomechanical destruction is one of most practically important kinds of the high-molecular composite materials failure, accompanying with break of chemical connections. The stresses in the places of deformation grow under loading and probability of macromolecular chains change is increased as well. These chains are oriented in a direction of external force action determine the elastic deformation of molecules which changes of position may be responsible for destruction of them.
Being based on the conventional concept of S.Jurkov that mechanical failure of a polymeric material is process its thermochemical destruction, V. Jartsev put forward the formula of load-carrying capacity time border of a composite material depending on its strength and an external temperature field.
Tf = Tm * exp [(Uo — 7 * cr) (R * T) (1 — T/Trn)\ (4)
where: Tf,T,cr - time to failure (sec), temperature (°K), strength (MPa) correspondingly; rm - minimal durability of the material (sec), Uq - activation energy of a failure (thermomechanical destruction); 7 -coefficient external mechanical forces; R - universal gas constant; Tm - ultimate design temperature for the material.
The ultimate strength dependent on temperature and time of its action:
a = (1/7) * {U0 - [2.3 * R*T* lg(Tf/Tm) /1 - T/Tm]} (5)
The ultimate temperature dependent on strength and time
T = (1/Tm) + [2,3 * R* lg(Tf/Tm) /U0 - 7 * cr] (6)
Each of formulae (4)-(6) describes interrelation between stress-strain state of the composite material and time of temperature and external loading actions. Thus, for an estimation of load-carrying capacity of a composite material and its directed regulation it is necessary to know all materials physical constants. For this purpose we have undertaken an experimental research at a number of preset values of the normal stresses and temperatures time of sample destruction.
Prismatic beam samples (30x60x700 mm) of RubCon were tested for a cross, so-called "pure"bend by two equal concentrated forces symmetrically located in an average third of samples span and simultaneous temperature influence. Loading was carried out by step-by-step to the attainment of the normal stress in the middle span 5,7, 6,1 and 6,5 MPa.
For creation of the increased temperatures the special spiral heating elements, which were settled down from, two sides of a sample were used. The level of temperature heating is 60 — 105 c. During the test loading was put after the attainment of a steady in time a temperature mode. The control of temperature was made in a maximal stresses zone.
Experimental values of load-carrying capacity averaged by test results for various stresses and temperatures levels are given in Table 1.
The experimental data described are shown on Figure 6. Each line, converging a bunch of isobars family corresponds to the given level of normal stress <j\ \ 02; &3-
Table 1
Normal stress a [MPa) Temperature, T (°С) Time to failure, r/(mm)
72 527
77 340
ai = 5.65 78 132
65 83
105 3
72 552
66 340
02 = 6.07 71 215
72 74
76 56
84 42
60 300
64 256
cr3 = 6.47 67 151
78 21
Figure 6. Test results for different levels of stresses and temperatures
Values Tm and r?n can find from Figure 1. Two constants Up and 7 can be determined from an inclination of straight lines by the formula of activation energy :
U(a) = 2,3 * R * AIgT(cr)/Al/T (7)
For each given loading value it is possible to determine U(a) (Figure 7).
q N/em*
Figure 7. Relationship activation energy U and normal bending stress a
It can be see that 7 = tga and Uq is ordinate of straight line "U — a” at extrapolation to a = 0. Values of all constants calculated on the experimental database are given in the Table 2.
Table 2
Constant Load-carrying capacity parameters
Uo(kJ/mol) Tm(sec) Г (kJrnrn/rnolN) Tm(W3/°K) Tf(sec) a(MPa) T(°K)
293.9 0.025 25.7 2.15 104'1 5.65 352
From Table 2 follows, that Up value is close to activation energy of chemical connections break, resulting to formation free macroradicals [5]. The temperature Tm corresponds to initial temperature of rubber decomposition. Value of a structural - mechanical constant 7 corresponds to complex composite materials on the rubber and phenol-formaldehyde resin base. It should be noted, that experimentally received minimal time of destruction rm is in 100 times exceeds the period of atoms fluctuation of a hard body. Such sharp increase rTO is obviously connected to a plenty quantity of filler in the RubCon material (about 90%), resulting to a complex way of a crack development at destruction.
The resulting values of constants allow to define the key parameters of load-carrying capacity of the researched composition in the given range of loadings, temperatures and operation time.
Obviously, for increase of load-carrying capacity of a material it is necessary to increase constants Tm, Tm and Up and to reduce 7. It is known, that the increase Uo is promoted by increase of a degree of filling and its uniformity. Introduction in a composition the special additives (plasticizers, antioxidants and others), and also the manufacturing process and material structure will have essential influence on constants Tm, Trn and Up.
It is known also [6] that for various kinds of plastics the ratio between design bending stress and tension stress is 0,5-0,87 i. e. "jbend/ltens ~ 0, 5 — 0,87. Ratio between design compression and tension stresses is. Icomprhtens ~ 0,95.
The knowledge of these relationships and constants will allow to forecast the borders of RubCon load-carrying capacity and by their directed regulation increase its durability.
Strength of reinforced RubCon RubCon with steel ribbed reinforcement
Joint work of reinforcement and polymer concrete matrix
The joint work of a steel reinforcement and composite matrix depends on:
- Coefficients of linear expansion of polymer concrete and steel reinforcements;
- The friction forces arising owing to reinforcing draft in the process of composite hardening and shrinkage;
- Mechanical bond of a reinforcement and a matrix;
- Adhesion of a metal reinforcement to a matrix.
The listed above factors in turn are determined with physical-mechanical characteristics of a composite material, a cross section and diameter of reinforcement rods, technology of preparation and placement of a composite mix, thickness of a composite protection layer etc.
a. Coefficient of thermal linear expansion of RubCon
It has been known that the average coefficient of thermal linear expansion is equal to the relation of a sample length increment AI in temperature interval [ti, ^2] to size of this interval t\ — £2 • The average coefficient of linear expansion of RubCon was determined with test unit Figure 8.
Heating of a RubCon sample was made with speed not exceeding 1,5 =b 0,5 °C/min in a range
h =23 °C + t2 = 120 °C.
Measurements of elongation of test samples in the size 40 x 40 x 160mm during heating were carried out in a thermostatic mode. The average coefficient of linear thermal expansion a was calculated with the following formula:
a = l/lp(Al/At)____________________________________________________(8)
where: Ip - initial length of a sample measured at temperature 23 °C, mm; AI - increment of length of
a sample in the temperature interval borders [ti, £2]5 mm; At = t2 — t\.
As the a result of the carried out researches it is established, that for RubCon samples
a = 1,35* 10~5(1/°C)___________________________________________(9)
We shall note, that the coefficient of linear expansion of steel is equal a = 1.2 -7- 1.3 * 10~5(1/°C)
at the same temperature range. Thus, in the reinforced building RubCon structures in all range of an
operational temperature there will be no additional internal temperature stresses.
Figure 8. Test unit for determination of coefficient linear expansion of RubCon: 1 - indicator; 7 - leg of indicator; 8 - thermometer
b. Shrinkage stress of RubCon matrix
Dependence of internal shrinkage stresses of RubCon matrix on time of its manufacturing was determined with the help of the special device (Figure 9).
4-
7
4-
350
/
Figure 9. Test device for determination of shrinkage stress of RubCon matrix:
1 - rigid frame; 2 - steel substrate; 3 - layer of RubCon; 4 - indicator; 5 - stand; 6 - holder
The RubCon layer thickness of 10 mm was put on a surface of a steel console plate in the size 350 x 20 x 2 mm. Then the device was located in drying cabinet where at temperature 120 °C RubCon was hardened. By means of the dial type indicator displacements of the free end of a console substrate were fixed during RubCon vulcanization. Initial indication was made after 2 hours after isothermal exposure of the sample, that is at the moment of the vulcanization beginning and further at regular time intervals.
Displacement of the free end of a steel plate - substrate occurs owing to shrinkage stresses in a RubCon layer. Knowing value of this displacement it is possible to determine shrinkage stresses with the
Q'sh = {4A * Es * k [/s + Ibc (Erc/-^s)1) /Frc * Iec * fa + Irc)____________________(10)
where: A - displacement of free end of steel console substrate; Es,Erc ~ modulus of elasticity of steel substrate and RubCon layer correspondingly; k = 1 + (Es/ErcIrc ~ moments of inertia of steel substrate and RubCon layer correspondingly, Frc, Irc ~ area and length of RubCon layer correspondingly. ts,tRc - thickness of steel substrate and RubCon layer correspondingly.
From the experimental results it may be deduced that at hardening of RubCon polymer matrix initial shrinkage stresses are, a8h <1,6 MA. It is worth nothing that shrinkage stress of other kinds of polymer concrete it is much more, for example, 8 + 12 MPa for furfurolacetate concrete, 10 MPa for epoxy concrete and 5 -7- 6 for polyester concrete. By this means the value of shrinkage stress of RubCon is insignificant
in comparison with compression strength of the material and practically does not influence on structures behavior under loading. On the other hand, initial compressing stresses are of important concern in the joint work of RubCon and steel reinforcement. Shrinkage stresses compress a reinforcement bar with the results that there are an additional bond forces between reinforcement bar and matrix.
c. Mechanical bond and adhesion between steel reinforcement and RubCon matrix Forces of mechanical bond between steel reinforcing bar and RubCon matrix were experimentally determined with the help of the device (Fig. 10). Some series of prismatic reinforced RubCon samples were produced. Reinforcement was the ribbed steel bar 08mm. The height of samples or depth of a reinforcement anchorage was equaled from 35 up to 120 mm, that is (4.3 -f- 15)0; thickness of protection layer was 8,16 and 24 mm (1,2 and 3) 0. Displacements of a reinforcing bar relatively the end face of RubCon prism and load were measured during the tests. Results of tests are shown in Fig. 10, 11.
0 0,0)5 0.01 0,015 11,02 0,025 0.03 chbs am
Elongation of free and ot feiniwcament bat, «m*
Figure 10. Draft of test gadget and displacements of non-loaded end of reinforcement bar in dependence of height of anchorage (a) and thickness of protection layer (b): 1, 2, 3 - a = 60 mm, b=8, 16, 24 mm correspondingly; 4, 5, 6 - a = 80 mm, b=8,16,24 mm correspondingly; 7, 8 - a = 120 mm, b=8, 16, 24 mm
correspondingly
Destruction of samples with depth of anchorage 35 and 40 mm (Figure 11) occurred as a result of shear of reinforcement bar and the subsequent splitting of the RubCon prisms. At depth of anchorage 45 and 50 mm destruction occurred owing to the reinforcement rupture. The initial displacements of a non-loaded end of reinforcement bars were marked at stress up to 50 MPa at all tested samples. Destruction of samples with depth of anchorage 60,80 and 120 mm (Figure 10) occurred as a result of reinforcement bar rupture. The initial displacements of a non-loaded end of reinforcement bars were marked at stress 50+200 MPa. As this take place the final displacements of bars didn’t depend on thickness of a protection layer .
We can make conclusion that minimal thickness of a protection layer of a reinforced RubCon structures should be not less than one diameter of a reinforcement bar The average bond stress between steel reinforcement and RubCon matrix can be determined from the formula:
Tb = ar * Ar/u * lr_____________________________________________(11)
where <7,-, Ar, lr - ultimate normal stress , cross section area and anchorage length (depth) of reinforcement bar correspondingly; u = ird - perimeter reinforcement bar with diameter d. Dependence of average bond stress t„ on anchorage depth of reinforcement bar Zrlr is shown in Figure 12.
It is possible to see, that at depth 45 mm Tb = maxTb = 27,9 4- 28,6 MPa. One of the important factors of RibCon and steel reinforcement joint work is an adhesive bond between these materials which are caused by forces of intermolecular interaction. As have shown [9] the adhesion of RubCon to steel is equal 12,1 MPa, that makes approximately 0,8 from RubCon tensile strength . It is necessary to note,
Elongation of free end of reinforcemewnt bar, mm
Figure 11. Displacements of non-loaded end of reinforcement bar in dependence of height of anchorage (a) and thickness of protection layer (b): 1, 2, 3 - a = 35 mm, b=8, 16, 24 mm correspondingly; 4, 5, 6- a = 40 mm, b=8, 16, 24 mm correspondingly; 7,8,9- a = 45 mm, b=8, 16, 24 mm correspondingly; 10, 11, 12- a = 50 mm,
b=8, 16, 24 mm correspondingly
40 45 50 Б0 70 80 90 100 110 120
Length of the reinforcement anchorage, mm
Figure 12. Dependence of average bond stress ?b on anchorage depth of reinforcement bar lr
that this value approximately in 10 times exceeds adhesion of furfurolacetate polymer concrete or usual cement concrete. Such high adhesion of RubCon matrix to steel reinforcement apparently connected with a nature of diene oligomer used as binder.
Load-carrying capacity at eccentric compression load
Experimental researches of the eccentrically compressed elements capacity was carried out on samples in the size 100 x 100 x 500 mm reinforced by longitudinal rods 08 mm and stirrups 05 mm.
As a result of regression analysis of the experimental data mathematical model was obtained:
Nu = 3200e(°>23'1-2’15) (12)
where Nu - limiting compressive load (kN), /x - is percent of reinforcing (%), - is initial load eccentricity (cm).
From the consideration of the response surface (Figure 13), it can be seen that capacity of the investigated samples depends from eccentricity to a greater extent than from the reinforcement.
The analysis of (13) shows, that the increase initial eccentricity of loading drastically reduces the loading capacity of a eccentric compressed element from RubCon on the equation of power function. It is possible to note the "weak"dependence of the loading capacity on reinforcing percents.
Figure 13. Relationship between compressive strength, percent of reinforcing and eccentricity
Design model for eccentric compressed elements from RubCon (Figure 14) was developed in view:
- Hypothesis of flat sections;
- Physical non-linearity of material;
- Work of the tension zone in a condition approached to destruction is insignificant;
- Position of forces system resultant is constant during all loading process.
Exhaustion of loading capacity comes at achievement of a maximum on the diagram "bending moment - curvature".
Let’s write down the equilibrium equations of normal section of an eccentric compressed RubCon short column (without buckling) at loading approached to destruction:
2 = 0, N - Nk + as As = 0;
(13)
M0 = 0, Ne — NKzK = 0.
(14)
In view of nonlinear dependence between stress and strain we have:
X
N - b j a(y)dy + as As = 0;
0
___________x______________________
ne - xkb j a{y)dy = 0.
(15)
(16)
where y - the current coordinate of height of cross section, z- shoulder of internal force pair the forces, equal:
J a(y)edy
i u
zK = ho-----------------,
/ <J{y)dy
Q
Normal stress in compressed zone may be computed from the formula uniaxial compression:
21
(16)
a = a д
к
with
x — у ho — x
^ky = £fc--------------, £s = -----------
(17)
(18)
Substituting (17) and (18) in equilibrium equations (14) and (15) we have:
2~
N -bRK
eKx - у eRx
eKx - у
6rX
dy + EsAseK
hn — x
= 0;
(19)
Figure 14- Model of slress-slrain state oi’ eccentrically compressed element
Ne — bRK
eKX - у tRX
tKx - у
tRX
dyx
( X f k(e«X~y) \ tRV ) ( eKx-y\2 \ ) ydy^
X ho — U = 0 (20)
X Г
\ I 0 k( e"x~y ) \ J ґ \ tRX ) dy J
Supposing that loss of load capacity of a eccentric compressed element is determined by maximal
(21)
bending moment, we shall add the third equation, describing condition of a maximum:
dM
deh
= 0,
k
£Kx ~ У
£rX
- у
єкх
dyx
or
h0 -
k (
€RX
-Л)
ydy\
\
f
€rX
£кХ-У
eRx
dy
>= 0
(22)
/
After integration and transformations the equations (17),(18) and (20) we shall write down as: N-hJtx <3e^~e^ + asAs = 0
at „ bRK 12h0eReKx-4h0el+elx2-4eReKx2 _ ^ (23)
12 eR
6h0-2x
,tfv tR 4ha-x
We obtained the system of three equations with three unknown, which can be solved analytically, where: N - is limiting compressive load; b - width of cross section of sample; RK - compressive strength of RubCon; x - distance from the most compressed fiber to neutral axis of the cross section; ед - deformation corresponding to maximal stress from diagram ”<x — e”; eK - deformation of extreme compressed fiber; as
- tension stress; As - area of tension zone of cross section; ho - distance between centers of longitudinal reinforcements.
Results of experiment are in close agreement with calculated the formula (23).
Статья поступила в редакцию 20.01.2012 г.
