Development and validation of a dimensional variation measurement set-application to the plaster setting

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bEquipe Structure et Comportement Thermomécanique des Matériaux du CRISMAT, UMR 6508-CNRS, ENSICAEN, 6 Bd du Maréchal Juin, 14050 Caen Cedex 4, France

cEquipe de Biomatériaux, Faculté de Médecine Dentaire, Casablanca 20100, Morocco

dCentre Interdisciplinaire de Recherche Ions-Laser, ENSICAEN, 6 Bd du Maréchal Juin, 14050 Caen Cedex 4, France Received 27 October 2003

Abstract

A method is developed and applied to investigate the shrinkage–swelling phenomenon during the setting of plaster. It is based on an optical position-sensing device which allows for a continuous measurement of the distance to a target without contact, by means of a triangulation technique. The method is validated for two types of moulding plaster and for a building plaster blended by using different amounts of a controlled grain-size dihydrate gypsum.

Keywords: Plaster setting; Plaster seeded with gypsum grains; Dimensional variations; Contact-free measurement; Laser telemetry

1. Introduction

During and after hydration, plaster-based pastes are subject to different volume changes as a consequence of chemical and physical phenomena related to the hydration of the calcium sulfate hemihydrate [1–5]. In the shrinkage–swelling curve depicted inFig. 1, domain OA is associated with a shrinkage as the volume of the formed calcium sulfate dihydrate is lower than the volume of hemihydrate plus water system. Shrinkage ends at point A where the plaster setting begins. At point A, the increased cohesion relatively to the preceding stage is due to van der Walls forces and to hydrogen bonds with water molecules within the micropores. A noticeable swelling stage then follows (AB domain), which is associated with the mutual repulsion of the gypsum grains now in close contact and still growing. At this stage, crystallised links form due to the effect of valence forces and a continuous solid structure develops. The point B is related to the end of the setting,

∗Corresponding author. Tel.:+33-2-31452659; fax:+33-2-31951600.

E-mail address: moussa.gomina@ismra.fr (M. Gomina).

when the dimensional stability is obtained. An additional consolidation occurs during the drying stage.

An understanding of these phenomena is essential for mastering the structure of plaster, in the aim to optimise the mechanical properties by the use of additives (retarders or accelerators) or reinforcement (natural or synthetic fibres).

One issue of particular importance is the evaluation of the effects of additives on the setting of plaster, namely on the setting time and the shrinkage–swelling behaviour until the setting.

The difficulty in measuring the dimensional variation of plaster during setting lies in the poor cohesion of the samples which forbids any direct contact. Thus, up to now, two methods are commonly used:

(i) The Sahores method makes use of the hydrostatic weighing of a thin elastic waterproof membrane containing the paste (hemihydrate/water mixture). The dimensional variations of the paste induce variations in the Archimedes pressure which is a measure of the submerged volume[6].

(ii) The mercury bed method is less rigorous than the Sa- hores one. The sample floats on a mercury layer and

doi:10.1016/j.msea.2004.01.031

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Fig. 1. Diagram of a shrinkage–swelling curve and phenomenological illustration of the shrinkage and swelling stages[5].

the longitudinal variations are measured by means of a 10␮m precision gage. The friction between the sample and the bearing plate is minimised by using suitable de- moulding appliances. Due to the lack of consistency of the paste the dimensional variations cannot be measured in the early beginning of the test.

To palliate the drawbacks linked to these methods, we present herein a new method for dimensional variations measurement, which presents all the benefits peculiar to contact-free measurement techniques. To check our method, the setting of two types of industrial moulding plaster was monitored and the results were compared to data obtained from method (ii). Further, this new method is applied to investigate and discuss the influence of the concentration of gypsum grains on the setting of a building plaster.

2. Experimental methods

2.1. Dimensional variations measurement method

The method makes use of an optical position detector to monitor without any contact the distance to a target, by a triangulation technique (Fig. 2).

When a low power laser beam (2 mW; wavelength 650␮m) hits the surface of a sample at a point M, an image M is obtained at the surface of the detector by means of a concurrent lens L. This image is nearly located in the focus plane of lens L and the sidestep OM =x is related to the distance X by the relation:

x

f = Xd

D²+DX+d² (1)

If the variation of X is of the order of a few millimetres, and under the conditions X Dand X d withD = d, a linear relation can be derived:

X=x2d

f (2)

Thus, this method allows an easy determination of the vari- able position of point M through the signal delivered by the optical position detector.

2.1.1. Definition of a position sensor device (PSD) A position sensor device (PSD) is an optoelectronic com- ponent able to detect the position of a bright point on its surface. The device comprising a very large PIN junction (a few millimetres) is sketched inFig. 3(a)and its electric diagram is shown inFig. 3(b).

Fig. 2. Schematic diagram of the contact-free dimensional measurement set.

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Fig. 3. Schematic diagram of (a) a position sensor device and (b) its electric diagram.

The position of the incident bright spot barycentre relatively to the middle of the PSD is located by detecting the current balance between the two half-parts of the device.

Thus the values of the resistances R1and R2depend on the position of the incident bright point. Hence, the sidestep x can be calculated from the measured values of the currents I1and I2by using the simple relation:

I1−I2

I1+I2 =2x

L (3)

2.1.2. Laser modulation

As the device is a sensor able to work under any illumination, it is necessary to select only the light issued from the laser. The running of the device is made insensitive to any ambient or parasite illumination by modulating the intensity delivered by the laser and using a synchronous detection.

The laser source was modulated at a frequency of 4 Hz. The overall measurement set is shown inFig. 4.

2.1.3. Data acquisition

Data acquisition was performed by using an analogic dig- ital software made with Labview of National Instruments^® and operating under Windows^®.

2.2. Materials

The starting powders were two types of moulding plaster supplied by BPB PLACO, Centre of Vaujours in France (an

␣type termed Molda Super and a␤ type termed Molda 3

Fig. 4. Overall view of the contact-free measurement set.

Normal) and a commercially available building plaster from Morocco. The␤ type of hemihydrate plaster is commonly obtained by heating gypsum powder under air at atmospheric pressure (dry route). The rapid transformation of the gypsum results in a less crystallised structure made of micro- crystals assembled in a microporous solid, characterised by a high specific area of 8–9 m²/g. On the other hand, the ␣ type is obtained by heating the gypsum at about 120^◦C in salt solutions under atmospheric pressure or saturated water vapour pressure of 2–7 bar; fully identified and non porous crystals are obtained.

Due to the differences between the two types of hemihydrate, samples of the moulding plaster were prepared using mixing ratios (water/plaster mass ratios) of 0.39 and 0.65 for the␣and the␤type, respectively. The shrinkage–swelling behaviour was investigated on samples of standard dimen- sions 160 mm×40 mm×40 mm, first by using the mercury bed technique and then our contact-free method.

The building plaster was seeded using three concentrations (1, 3 and 6 wt.%) of dihydrate gypsum grains with size in the range 160␮m< φ <400␮m and a mixing ratio of 0.68. For the shrinkage–swelling measurements according to our method, the plaster/water blend was poured in a plastic cup (5 mm deep; 50 mm in diameter) positioned vertically under the laser beam.

3. Results and discussion

3.1. Comparison to the mercury bed method

InFig. 5are reported the shrinkage–swelling curves obtained by using the mercury bed method for the two types of moulding plaster. Due to the measurement technique, data acquisition was only possible a few minutes after the blend is poured into the mould: 15 min for the␣type and 17 min

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Fig. 5. Shrinkage–swelling curves obtained by using the mercury bed method for the two types of moulding plaster.

for the␤type. Thus, the shrinkage stage cannot be analysed.

In Fig. 5 the swelling rate is the same for both materials [7], but the setting time is longer and the long term swelling amplitude is much higher for the␣type plaster.

In the mercury bed method, the sample expands equally in all directions (isotropically). In our method, the volume change of the sample during the setting appears only along the laser beam axis as the sample is enclosed in the mould.

Thus, the expansion determined by using our method is nearly three times higher than the one obtained by the mercury bed technique. So the shrinkage–swelling values determined by our method must be divided by 3 if our results are to be compared to those obtained by using the mercury bed technique.

Consequently, the shrinkage–swelling behaviour determined by our method and the swelling measured by the mercury bed method are shown inFig. 6(a) and (b)for the Molda Super (␣ type plaster) and the Molda 3 Normal (␤ type plaster), respectively.

For both moulding plasters, the results show a fairly good agreement between the two methods regarding the long term swelling amplitude. In each figure, the differences between the two curves obtained by our method probably reflect the effects of temperature and hygrometry as the experimental setup was the same. In the case of the␤type plaster, the two families of curves are very close all along the setting. For the␣ type plaster, the lower swelling rate revealed by the mercury bed method may be an artefact due to this technique.

Effectively, when plaster is mixed with water, the ensuing hydration reaction is exothermic and the temperature rise is known to be higher for ␣ type plaster than for the ␤ type. Because the presence of the mercury bed reduces the temperature rise, it may have a more pronounced effect on the shrinkage–swelling behaviour of the␣type plaster.

3.2. Evaluation of the sensitivity of the contact-free measurement method

In the aim to evaluate the sensitivity of our method, the device was used to monitor and analyse the shrinkage–swelling behaviour of a commercial plaster seeded with different

Fig. 6. Comparison of the shrinkage–swelling behaviours obtained by the two different methods for (a) the␣type and (b) the␤type plaster.

concentrations of gypsum grains with size in the range 160␮m< φ <400␮m (Fig. 7)[8]. The shrinkage–swelling curves were analysed in term of (i) the time associated to the total dissolution of plaster, i.e. abscissa of point A in

Fig. 7. Influence of the concentration of gypsum grains on the shrinkage–swelling behaviour of plaster.

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Fig. 1; (ii) the dissolution rate, i.e. the slope of the curve between points O and A; (iii) the expansion between A and B; (iv) the total expansion by a setting time of 160 min.

InFig. 7the dimensional variations are given in term of the values relative to the initial dimension of the sample along the laser beam axis, which is 40 mm. Our method is able to distinguish between the relative total swelling of samples containing 3 and 6 wt.% of gypsum grains, i.e. 0.03%, which corresponds to a dimensional variation of 12␮m.

InTable 1are reported the main parameters we have cho- sen to evaluate the influence of the gypsum grains on the

Fig. 8. (a) Dependences of the swelling amplitude and the total dissolution time on the concentration of gypsum grains; (b) relationship between these two parameters.

concentration of an additive on the shrinkage–swelling behaviour of plaster.

4. Conclusion

A new method for measuring the shrinkage–swelling of plaster has been proposed, based on a triangulation method by laser telemetry. Experimental results on two types of moulding plasters compare fairly good with those obtained when using the standard mercury bed method. On the other hand, with the proposed contact-free method, the shrinkage associated with the dissolution of plaster and nucleation of gypsum crystals can be documented. Consequently, the sensitivity of the method was checked by investigating the influence of the concentration of gypsum grains on the setting of a building plaster. The results clearly show the reliability of our method with decisive advantages for the investigation of the shrinkage–swelling behaviour of hydraulic binders.

Acknowledgements

The authors wish to thank Mrs. Sylvie Perez, BPB Placo Central Laboratory manager at Vaujours (France), for her suggestions and advice and for providing the moulding plasters.

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