Hydraulic binder based on ground granulated blast furnace slag having improved setting improved curing

09656918 ยท 2017-05-23

Assignee

Inventors

Cpc classification

International classification

Abstract

Disclosed are a hydraulic binder composition containing at least 50% by weight of ground granulated blast furnace slag and a system for activating the slag, the system containing at least calcium sulphate, at least one product chosen from a source of Portland clinker and lime, at least one aluminum derivative and at least one alkali metal or alkaline earth metal salt; containing a ready-to-mix building material composition comprising such a hydraulic binder and aggregates of inert material capable of being agglomerated in the presence of an aqueous phase; and a process for employing the ready-to-mix composition containing a stage of mixing the said composition with water for the purpose of the preparation of a building material, such as a concrete or mortar, and in particular an adhesive mortar, pointing mortar or levelling mortar or coating.

Claims

1. A hydraulic binder composition comprising each of a-e: a) at least 50% by weight, with respect to the weight of the hydraulic binder composition, of a ground granulated blast furnace slag, b) calcium sulphate, c) at least one source of Portland clinker or lime, d) at least one aluminium derivative that is an alumina having a BET specific surface ranging from 100 to 400 m.sup.2/g, a monocalcium aluminate or a calcium sulphoaluminate, and e) at least one alkali metal or alkaline earth metal salt that is a chloride salt, bromide salt, silicate salt, nitrate salt or carboxylic acid salt, the total content of calcium sulphate, expressed as SO.sub.3 equivalent content, being at least 5% by weight, with respect to the weight of the hydraulic binder composition, the sum of the contents of c) and e) being less than 10% by weight, with respect to the weight of the hydraulic binder composition.

2. The hydraulic binder composition according to claim 1, wherein in the ground granulated blast furnace slag the amounts of calcium oxide, magnesia, alumina and silica satisfy at least one of the following three relationships: r 1 = ( CaO + MgO ) ( Al 2 O 3 + SiO 2 ) > 1.03 r 2 ( F 11 ) = ( CaO + MgO + 0.3 * Al 2 O 3 ) ( SiO 2 + 0.7 * Al 2 O 3 ) > 1.20 r 3 ( F 3 ) = ( CaO + MgO + Al 2 O 3 ) ( SiO 2 ) 1.6 , and the content of aluminium oxide (Al.sub.2O.sub.3) being less than 13% by weight of the weight of ground granulated blast furnace slag, r1, r2 and r3 corresponding to the ratios by weight relating to the amounts of calcium oxide, magnesia, alumina and silica present in the ground granulated blast furnace slag.

3. The hydraulic binder composition according to claim 1, having a Blaine specific surface of the ground granulated blast furnace slag from 7000 to 8000 cm.sup.2/g.

4. The hydraulic binder composition according to claim 1, having a maximum size of particles of the ground granulated blast furnace slag less than 45 m.

5. The hydraulic binder composition according to claim 1, comprises having a total content of ground granulated blast furnace slag(s) of 60 to 70% by weight, with respect to the weight of the hydraulic binder composition.

6. The hydraulic binder composition according to claim 1, wherein the calcium sulphate comprises at least 90% by weight of anhydrous calcium sulphate, with respect to the weight of calcium sulphate.

7. The hydraulic binder composition according to claim 1, having a total content of a source of Portland clinker, lime, or their mixture of 0.2 to 4% by weight, with respect to the total weight of the hydraulic binder composition.

8. The hydraulic binder composition according to claim 1, having a total content of aluminium derivative(s) of 0.2 to 2.1% by weight, with respect to the total weight of the hydraulic binder composition.

9. The hydraulic binder composition according to claim 1, having a total content of alkali metal or alkaline earth metal salt(s) of less than 5% by weight, with respect to the total weight of the hydraulic binder composition, the said salt(s) being calcium chloride (CaCl.sub.2), calcium formate and/or calcium acetate.

10. The hydraulic binder composition according to claim 1, wherein the carboxylic acid salts in (e) are C.sub.1-4-monocarboxylic acid salts.

11. A ready-to-mix building material composition comprising: a hydraulic binder as defined in claim 1, and aggregates of inert materials capable of being agglomerated in aqueous phase by means of the said binder in order to form an aggregated product.

12. The ready-to-mix composition according to claim 11, comprising at least one polymer in the form of a water-dispersible powder or in the form of an aqueous polymer dispersion.

13. A process for employing a ready-to-mix composition as defined in claim 11, comprising mixing the said composition with water to prepare a building material.

14. The process according to claim 13, comprising preparing an adhesive mortar, pointing mortar or levelling mortar or coating.

Description

EXAMPLES: FLOOR LEVELLING COATINGS

(1) Five ready-to-mix pulverulent compositions are prepared from five different hydraulic binders by mixing the different ingredients of Table 1 below.

(2) The hydraulic binder 1 (according to the invention) is prepared by mixing:

(3) a) 20 g of ground granulated blast furnace slag used according to the invention (representing 64.3% by weight of the weight of the binder),

(4) b) 10 g of synthetic calcium sulphate comprising at least 90% by weight of anhydrous calcium sulphate according to the invention (representing 32.2% by weight of the weight of the binder and corresponding to 18.9% by weight of SO.sub.3, with respect to the weight of the binder),

(5) c) 0.20 g of CEM I 52.5 R Portland cement (representing 0.6% by weight of the weight of the binder),

(6) d) 0.1 g of flash alumina with a BET specific surface ranging from 100 to 400 m.sup.2/g (representing 0.3% by weight of the weight of the binder),

(7) e) 0.8 g of CaCl.sub.2.2H.sub.2O (representing 2.6% by weight of the weight of the binder).

(8) The hydraulic binder 2 (comparative) is prepared by mixing:

(9) a) 20.56 g of ground granulated blast furnace slag used according to the invention (representing 66.1% by weight of the weight of the binder),

(10) b) 10.28 g of synthetic calcium sulphate comprising at least 90% by weight of anhydrous calcium sulphate according to the invention (representing 33.1% by weight of the weight of the binder and corresponding to 19.4% by weight of SO.sub.3, with respect to the weight of the binder),

(11) c) 0.26 g of CEM I 52.5 R Portland cement (representing 0.8% by weight of the weight of the binder).

(12) The hydraulic binder 3 (comparative) is prepared by mixing:

(13) a) 20.48 g of ground granulated blast furnace slag used according to the invention (representing 65.8% by weight of the weight of the binder),

(14) b) 10.24 g of synthetic calcium sulphate comprising at least 90% by weight of anhydrous calcium sulphate according to the invention (representing 33% by weight of the weight of the binder and corresponding to 19.4% by weight of SO.sub.3 with respect to the weight of the binder),

(15) c) 0.26 g of CEM I 52.5 R Portland cement (representing 0.8% by weight of the weight of the binder),

(16) d) 0.13 g of flash alumina with a BET specific surface ranging from 100 to 400 m.sup.2/g (representing 0.4% by weight of the weight of the binder).

(17) The hydraulic binder 4 (comparative) is prepared by mixing:

(18) a) 19.9 g of ground granulated blast furnace slag used according to the invention (representing 64% by weight of the weight of the binder),

(19) b) 9.95 g of synthetic calcium sulphate comprising at least 90% by weight of anhydrous calcium sulphate according to the invention (representing 32% by weight of the weight of the binder and corresponding to 18.9% by weight of SO.sub.3 with respect to the weight of the binder),

(20) c) 0.25 g of CEM I 52.5 R Portland cement (representing 0.8% by weight of the weight of the binder),

(21) e) 1 g of CaCl.sub.2.2H.sub.2O (representing 3.2% by weight of the weight of the binder).

(22) The hydraulic binder 5 is a reference commercial product composed, to at least 50% by weight, of Portland cement, with respect to the weight of the commercial product.

(23) The ground granulated blast furnace slag used in the examples of the present patent application exhibits the following characteristics: Particle size: D50=5 m, maximum particle size <45 m, Fineness: Blaine specific surface=7000-8000 cm.sup.2/g, Percentage of glassy phase greater than 90% by weight of the weight of the slag, Chemical composition of the slag comprising: from 33 to 37% by weight of silica (SiO.sub.2), from 9 to 13% by weight of alumina (Al.sub.2O.sub.3), from 38 to 42% by weight of calcium oxide (CaO), from 1 to 12% by weight of magnesia (MgO), less than 1% by weight of Fe.sub.2O.sub.3, less than 2% by weight of TiO.sub.2, up to 2.5% by weight of SO.sub.3, and up to 2% by weight of sulphide (S.sup.2-) ions, and the contents by weight of silica (SiO.sub.2), alumina (Al.sub.2O.sub.3), calcium oxide (CaO) and magnesium oxide (MgO) of which satisfy the following relationships:

(24) r 1 = ( CaO + MgO ) ( Al 2 O 3 + SiO 2 ) > 1.03 r 2 ( F 11 ) = ( CaO + MgO + 0.3 * Al 2 O 3 ) ( SiO 2 + 0.7 * Al 2 O 3 ) > 1.20 r 3 ( F 3 ) = ( CaO + MgO + Al 2 O 3 ) ( SiO 2 ) 1.6 the sum of the contents by weight of CaO+MgO+Al.sub.2O.sub.3+SiO.sub.280% by weight, all of the percentages by weight indicated above being expressed on the basis of the total weight of the ground granulated blast furnace slag.

(25) The contents of the ingredients of Table 1 below are expressed in grams.

(26) TABLE-US-00001 TABLE 1 Ex. 1 Ex. 2 Ex. 3 Ex. 4 Ex. 5 (Inven- (Com- (Compar- (Compar- (Compar- Ingredients tion) parative 1) ative 2) ative 3) ative 4) Hydraulic 31.1 binder 1 Hydraulic 31.1 binder 2 Hydraulic 31.1 binder 3 Hydraulic 31.1 binder 4 Hydraulic 31.1 binder 5 Silica sand 34.2 34.2 34.2 34.2 34.2 (0.1-0.3 mm) Calcium 32.6 32.6 32.6 32.6 32.6 carbonate (D50 = 8 m) Polymer of 2 2 2 2 2 vinyl acetate, vinyl versatate and ethylene in the powder form Cellulose 0.1 0.1 0.1 0.1 0.1 ethers, gums, antifoam agent and colourants Total 100 100 100 100 100 weight of the pulverulent composition

(27) Each of these five compositions is subsequently mixed with water in order to form a floor coating, in a proportion of 16 g of water per 100 g of pulverulent composition. This corresponds to a degree of mixing of 16% (i.e. 0.16).

(28) Unless otherwise indicated in the present patent application, the preparation of the floor coatings and the measurement of their properties relating to the self-spreading, to the rate of setting, to the flexural strength (Fs), to the compressive strength (Cs) and to the shrinkage were carried out by observing the protocol and the operating conditions defined in the CSTB technical document relating to floor coatings, entitled modalits d'essais et contrles effectus par le fabricant, n DT7, Rvision 01 [Test methods and controls carried out by the manufacturer, No. DT7, Revised version 01].

ISeries of Tests No. 1 on the Compositions of Examples 1, 2 and 5

I.1Tests on Wet Product

(29) I.1.1Preparation of the Mixed Product (Floor Levelling Coating)

(30) Two kilograms of pulverulent composition are kneaded in a bowl with water at a degree of mixing of 16% for 1 minute using a mechanical mixer, such as is described in French Standard NF EN 1937, at slow speed (rotational speed 140 revolutions per minute (rev/min) and planetary rotational speed 62 rev/min). The wall of the receptacle and the beater of the mixer are then stripped using a spatula in order to detach the possibly agglomerated powder. The combined mixture is again kneaded for 1 minute at slow speed (rotational speed 140 revolutions per minute (rev/min) and planetary rotational speed 62 rev/min).

(31) I.1.2Measurement of the Spreading Diameter and of the Homogeneity of the Floor Levelling Coating

(32) The measurements of the spreading diameter and of the homogeneity of the floor coating at 5 minutes and at 20 minutes are carried out starting from one and the same mixed product, prepared as described above in I.1.1.

(33) Measurement at 5 Minutes (Min):

(34) After standing for 5 minutes, the mixed product is poured into a ring with a diameter of 30 mm and a height of 50 mm placed at the centre of a glass sheet. Once filled, the ring is lifted up and releases the product, which spreads over the glass sheet.

(35) After waiting for 5 minutes, the spreading diameter of the product, expressed in millimeters and measured along two perpendicular axes, is recorded and the homogeneity of the spread product is evaluated visually by noting the presence or absence of sedimentation at the circumference of the paste.

(36) The results are listed in the following Table 2 and correspond to the mean value calculated over three tests.

(37) Measurement at 20 Minutes (Min):

(38) After standing for 20 minutes, it is evaluated visually on the mixed product whether the latter has remained homogeneous, that is to say whether there has not been sedimentation of its ingredients at the bottom of the bowl.

(39) The product is subsequently mixed manually with three turns of a blade before being poured into a ring of the same size as described above. The measurement of the spreading diameter of the product is carried out as above, 5 minutes after having lifted up the ring.

(40) The results are listed in the following Table 2 and correspond to the mean value calculated over three tests.

(41) I.1.3Measurement of the Setting Time (Vicat)

(42) The measurements of the initial set and final set time of the floor coating are carried out starting from one and the same mixed product, prepared as described above in I.1.1.

(43) The measurements of the initial set and final set time of the floor coating are carried out with a Vicat apparatus as described in Standard EN 13454-2.

(44) The mixed product is poured into a standardized mould which is filled in order to carry out the measurements. The mould used is a rubber mould in the form of a truncated cone having upper and lower internal diameters of 7 cm and 8 cm respectively and provided, at its base, with a removable glass sheet which is broader than the rubber mould and which has a thickness of at least 2.5 mm.

(45) The set time is determined by the observation of the penetration of a needle with a diameter of 1.13 mm into the mixed product, under a load of 300 grams, corresponding to the weight specific to the Vicat apparatus.

(46) The initial set corresponds to the time at the end of which the needle ceases to sink in under the effect of the load applied and halts at a distance of 4 mm1 mm from the bottom of the mould, counting from the start of kneading of pulverulent composition with water.

(47) In order to determine the final set the mould is inverted, after having determined the initial set of the product, and the glass sheet is removed in order to carry out the measurements of sinking of the needle on the face of the product which has been in contact with the glass sheet. The measurements of the sinking of the needle are carried out at different points of the surface of the product.

(48) The final set corresponds to the time at the end of which the needle now for the first time only penetrates 0.5 mm into the product, counting from the start of kneading of pulverulent composition with water.

(49) The results, expressed in minutes, are listed in the following Table 2 and correspond to the mean value calculated over three tests.

I.2Tests on Cured Product

(50) I.2.1Preparation of the Test Specimens

(51) The mixed product prepared above in I.1.1 starting from 2 kg of pulverulent composition and water at a degree of mixing of 16% is used to prepare the test specimens which will be used for the tests which follow on the cured floor coating.

(52) The mixed product is poured into each of the three rectangular compartments of a mould, making possible the simultaneous preparation of three test specimens of parallelepipedal shape with a height of 16 cm and having, for base, a square with a side length of 4 cm.

(53) Before removing from the mould, the test specimens are stored, covered with a glass sheet, at 23 C. and 50% relative humidity.

(54) 24 hours after start of the kneading with water, the test specimens are removed from the mould.

(55) Once removed from the mould, and between two measurements, the test specimens are stored at 23 C. and 50% relative humidity.

(56) I.2.2Measurement of the Flexural Strength (Fs)

(57) The flexural strength tests were carried out at 24 hours, 7 days and 28 days after pouring the test specimens, using a flexural and compressive strength testing machine, such as is described in French Standard NF EN 196-1. The device for the flexural strength test comprises two support rolls placed in parallel on one and the same horizontal plane at a distance of 100 mm from one another and a third parallel roll (known as loading roll) surmounting the other two and placed equidistantly from the other two rolls. The three rolls are made of steel and each has a diameter of 10 mm and a length of 48 mm. The test specimen is placed in the apparatus, so as to be held therein by the three rolls, the axes of the three rolls being perpendicular to the length of the test specimen and the axis of the loading roll coinciding with the middle of the length of the test specimen.

(58) A load is applied to the upper lateral face of the test specimen by vertically dropping the loading roll and then the roll is placed back in its initial position. As long as the test specimen does not break, this stage is repeated by applying a greater load. The load applied is gradually increased at a loading rate of 50 newtons per second (N/s) (50 N/s10 N/s) until the test specimen breaks.

(59) The flexural strength corresponds to the force necessary to break the test specimen and is expressed in megapascals (MPa).

(60) The results are listed in the following Table 2 and correspond to the mean value calculated over three tests.

(61) I.2.3Measurement of the Compressive Strength (Cs)

(62) The compressive strength tests were carried out on the two halves of each of the test specimens broken according to the protocol for the flexural strength tests described above. In total, six tests are thus carried out for each age of the building material (24 hours, 7 days, 28 days).

(63) A test specimen half is sandwiched between the two parallel movable plates of the measuring device, so that the side faces of the test specimen half are centred and in contact with the movable plates. Each plate has a length of 40 mm and a width of 40 mm.

(64) A load is applied to the test specimen half by exerting a compressive force using the two movable plates and the compressive strength of the test specimen half is simultaneously measured. The load applied is gradually increased at a loading rate of 2400 N/s200 N/s and the value of the compressive strength (expressed in MPa) is recorded continuously, until rupture, that is to say until the moment when the resistance opposed by the test specimen half is zero.

(65) The results are listed in the following Table 2 and correspond to the mean value calculated over six tests for each age (24 h, 7 d, 28 d).

(66) I.2.4Measurement of Shrinkage

(67) The measurements of shrinkage were carried out on a series of three test specimens prepared as described above in I.2.1.

(68) The measurements of shrinkage were carried out using a deformeter as described in French Standard NF P15-433 and a rod with a length of 16 cm made of invar acting as reference.

(69) The initial length of each of the test specimens is measured from the removal of the tests specimens from the mould, i.e. 24 hours after the beginning of the kneading of the pulverulent composition with water.

(70) After the measurement, the test specimens are again stored under the same conditions as described above in 1.2.1.

(71) The final length of the test specimens is subsequently measured at 28 days, that is to say 28 days after the start of the kneading of the pulverulent composition with water.

(72) The shrinkage, as being the difference between the final length and the initial length of the test specimen, everything divided by the length of the reference (16 cm), is then calculated for each test specimen.

(73) The results, expressed in micrometers per meter (m/m), are listed in the following Table 2 and correspond to the mean shrinkage value calculated over the three test specimens.

Results of the Series of Tests No. 1 on the Compositions of Examples 1, 2 and 5

(74) TABLE-US-00002 TABLE 2 Ex. 2 Ex. 5 Properties of the Ex. 1 (Comparative (Comparative floor coating (Invention) 1) 4) Spreading diameter after 150 150 150 standing for 5 min (mm) Sedimentation after no no no standing for 5 min (mm) Spreading diameter after 150 150 135 standing for 20 min (mm) Sedimentation after no no no standing for 20 min (mm) Vicat initial set (min) 230 300 230 Vicat final set (min) 270 330 270 Cs 24 h (MPa) 8 6 2 Fs 24 h (MPa) 2 2 0.5 Cs 7 d (MPa) 35 30 10 Fs 7 d (MPa) 5 5 2 Cs 28 d (MPa) 40 35 20 Fs 28 d (MPa) 6 6 5 Shrinkage at 28 days <1500 <2000 <2000 (m/m)
These test results show that: the floor coating according to the invention (ex. 1) does not sediment and exhibits a good property of self-spreading over time, the floor coating according to the invention (ex. 1) has very good short-term compressive mechanical strengths while having a suitability for the use desired for its employment. The comparative floor coatings (ex. 2 and 5) do not make it possible, for equivalent set times, to obtain satisfactory short-term compressive mechanical strengths, the kinetics of the mechanical strengths of the floor coating according to the invention are also better, with respect to the reference floor coating, the floor coating according to the invention exhibits better flexural strength values than the reference floor coating. The flexibility of the cured floor coating according to the invention makes it possible to gain in particular in durability when the floor is subjected to deformations or vibrations, the floor coating according to the invention exhibits a reduced shrinkage and thus an improved dimensional stability, with respect to the comparative floor coatings. In particular, no cracking is observed on the cured product of the invention.

IISeries of Tests No. 2 on the Compositions of Examples 1 to 4

(75) Measurement of the Set Time and of the Total Heat of Hydration (by Isothermal Calorimetry)

(76) The measurements of set time and of total heat of hydration are carried out on a sample of 7.5 grams of mixed product, prepared as described above in I.1.1.

(77) The sample is introduced into a thermally sealed ampoule. The ampoule is introduced into a TAM Air isothermal calorimeter regulated at 23 C., having a thermally sealed reference ampoule containing water. The amount of water present in the reference ampoule is calculated in a way well known to a person skilled in the art so that the heat capacity of the measurement ampoule containing the mixed product is equal to the heat capacity of the reference ampoule. Isothermal calorimetry makes it possible to measure the differences in heat between the sample and the reference.

(78) As the hydration reaction of the hydraulic binder, which is responsible for the setting and the curing of the binder, is exothermic, the differences in heat brought about by this reaction are monitored as a function of the time by isothermal calorimetry, in order to evaluate the reactivity of the binder on contact with water.

(79) The curve of heat flow given off by the mixed product (in watts per gram of product) and the curve of heat given off by the mixed product (in Joules per gram of product) are plotted as a function of the time elapsed, counting from the preparation of the mixed product (up to approximately 72 hours), for each floor coating tested.

(80) The curve of heat flow given off by the mixed product as a function of the time, represented by FIG. 1, illustrates the kinetics of hydration of the different floor coatings tested (FIG. 1).

(81) The curve of heat given off by the mixed product as a function of the time, represented by FIG. 2, makes it possible to determine the value of the initial set and final set of the product by looking for the inflection points. However, this proves to be difficult in practice. Consequently, the first derivative d(q)/d(t) of the curve of heat flow given off by the mixed product as a function of the time is plotted in FIG. 3 for each of the floor coatings tested, in order to more accurately identify the initial set and final set values of each of these products.

(82) The initial set (Ins) and final set (FiS) are identified using FIG. 3, and thus the total heat given off by the product 72 hours after its hydration.

(83) The initial set value corresponds to the time elapsed, counting from the preparation of the mixed product, at which the maximum of the derivative d(q)/d(t) is reached. The final set value corresponds to the time elapsed, counting from the preparation of the mixed product, at which the value of the derivative d(q)/d(t) is zero.

(84) The initial set and final set of the binder make it possible to characterize the rate of setting of the binder and thus the reactivity of the latter on contact with water. In particular, the initial set of the binder corresponds to the moment, counting from the start of the mixing with water, when the product suddenly thickens and begins to heat up while the final set of the binder, which coincides with the start of the curing of the binder, corresponds to the moment, counting from the start of the mixing with water, when the product becomes stiff and ceases to be deformable. The emission of heat begins to slow down from this moment.

(85) The total heat given off by the product during its hydration is correlated with the mechanical properties developed by the product during its hydration.

(86) The total heat given off by the product, measured after 72 hours of hydration, thus makes it possible to characterize the degree of stiffness achieved by the product.

(87) In fact, the greater the kinetics of the hydration reaction and the greater the total heat of hydration of the product, the greater the activation of the binder.

(88) The result are collected in the following Table 3 and are illustrated by the calorimetry curves represented in FIGS. 1 to 3.

Results of the Series of Tests No. 2 on the Compositions of Examples 1 to 4

(89) TABLE-US-00003 TABLE 3 Ex. 2 Ex. 3 Ex. 4 Ex. 1 (Comparative (Compar- (Compar- (Invention) 1) ative 2) ative 3) InS (hours) 3.2 6.5 4.7 5.1 FiS (hours) 5.3 8.9 6.9 7.1 Total heat of 45.4 37.3 37.6 45.3 hydration after 72 h (J/g)

(90) The floor coating according to the invention (ex. 1), comprising a four-component activation system, exhibits a set time which is lower and a total of heat of hydration after 72 h which is greater than the values found for the comparative floor coatings (ex. 2 to 4) comprising, at a comparable content, an activation system having two or three components only.

(91) These test results thus show that the floor coating according to the invention (ex. 1) exhibits an improved rate of setting and makes it possible to achieve, beyond 72 h of hydration, an improved mechanical strength, with respect to the comparative floor coatings (ex. 2 to 4), which exhibit a different activation system.

(92) The preceding examples can be repeated with similar success by substituting the generically or specifically described reactants and/or operating conditions of this invention for those used in the preceding examples.

(93) From the foregoing description, one skilled in the art can easily ascertain the essential characteristics of this invention and, without departing from the spirit and scope thereof, can make various changes and modifications of the invention to adapt it to various usages and conditions.

BRIEF DESCRIPTION OF THE FIGURES

(94) FIG. 1 illustrates the kinetics of hydration of the different floor coatings tested.

(95) FIG. 2 makes it possible to determine the value of the initial set and final set of the product by looking for the inflection points.

(96) FIG. 3 represents more accurate initial set and final set values.