This paper presents a study of the surface height irregularities of cement pastes subjected to fast dynamic fractures. The height irregularities are quantified by the values of the three-dimensional profile parameters. The studied dynamical irregularities show a similar analytical behavior to those obtained by static fractures

Ficker, T.

Acta Polytechnica

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T. Ficker

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Acta Polytechnica Vol. 51 No. 5/2011Surface Morphology of Porous Cementitious Materials Subjected toFast Dynamic FracturesT. FickerAbstractThis paper presents a study of the surface height irregularities of cement pastes subjected to fast dynamic fractures.The height irregularities are quantified by the values of the three-dimensional profile parameters. The studied dynamicalirregularities show a similar analytical behavior to those obtained by static fractures.Keywords: 3D profile analysis, fracture surfaces, cement-based materials, confocal microscopy.1 IntroductionWe have recently published several studies [1–3] onthe surface morphology of fractured specimens madefrom hydrated cement pastes. This material showsa high value of porosity, which has been proved tobe an influential factor governing the irregularities offracture surfaces.For practical surface analyses of porous materi-als, it would be valuable to know whether the sur-face height irregularities are also influenced by themethod of fracture. For this purpose we performed alarge series of experiments with cement pastes. Thismaterial was chosen because its porosity can easilybe controlled within a broad interval by means of thewater-to-cement ratio r = w/c. Correct knowledge ofthe dependence of surface roughness on the fractur-ing method may be useful for further surface studiesof fractured porous materials.2 Experimental arrangementOrdinary Portland cement CEM 42,5 I R-sc of do-mestic provenance was used to create 144 specimensof hydrated pastes with six different water-to-cementratios r (0.3, 0.4, 0.5, 0.6, 0.7, 0.8). The specimenswere rotated during hydration to achieve better ho-mogeneity. All specimens were stored for the wholetime of hydration at 100 % RH and 20 ◦C. After90 days of hydration the specimens were fracturedboth in the static regime (three-point bending tests)and also in the dynamic regime (impulse fracturescaused by a chisel and a heavy hammer). The frac-ture surfaces were then immediately used for micro-scopic analysis.The three-dimensional profile parameter Ha wasused to characterize the roughness of the fracture sur-faces of the hydrated cement pastes. In fact, Ha rep-resents the averaged ‘absolute’ height of the fracturerelief z = f(x, y)Fig. 1: 3D confocal relief of fractured cement pasteHa =1L · M∫ ∫(LM)|f(x, y)|dxdy (1)where L × M is the area of the vertical projectionof the three-dimensional fracture profile f(x, y) intothe plane xy. The parameter Ha has great statisticalrelevancy, since it is a global averaged characteris-tic covering the entire tested surface L × M . Thethree-dimensional profiles f(x, y) were created usingan Olympus Lext 3100 confocal microscope. One ofthese profiles is shown in Figure 1. The profiles areformed by software that processed a series of opticalsections created by the confocal microscope at vari-ous heights of the fracture surfaces. Approximately100 image sections were taken for each measured sur-face site, starting from the very bottom of the sur-face depressions (valleys) and proceeding to the verytop of the surface protrusions (peaks). The investi-gated area L×M = 1 280 μm× 1 280 μm (1 024 pix-els× 1 024 pixels) was chosen in five different placesof each fracture surface (in the center, and in four po-sitions near the corners of the rectangular area), i.e.each plotted point on the graphs of the profile pa-rameters corresponds to an average value composed118Acta Polytechnica Vol. 51 No. 5/2011of 60 measurements (12 samples× 5 surface measure-ments). Each measurement was performed for mag-nification 20×.3 Results and discussionIt is well known that hydrated cement is a compositematerial consisting of several solid hydrated prod-ucts and pore spaces (see the photo in Figure 2).Porosity (P ) influences most of the mechanical prop-erties of this material, and it is therefore not sur-prising that the surface irregularity (Ha) was alsofound [1–3] to be among the dependent properties.Since porosity to a large extent determines compres-sive strength, a strong functional relation betweencompressive strength σc and surface irregularity ofthe fracture surfaces was also revealedσc(Ha) = σo(HoHa − ho)ρ(2)where σo, Ho, ho and ρ are fitting parameters.Fig. 2: A photograph of the surface of a hydrated cementpasteFig. 3: Compressive strength in dependence on the heightirregularities of a surface formed in a dynamic fractureIn the present study, relation (2) is tested withspecimens fractured dynamically using a sharp chiseland a heavy hammer that simulate an impulsive load.Figure 3 shows the resulting graph σc(Ha). The dy-namical strength values in Figure 3 were evaluatedon the basis of the static values by adding correc-tions corresponding to dynamic processes [4]. Asshown in Figure 3, the experimental points are fittedwell by function (2), which means that this functionmay describe a universal behavior of the compressivestrength and the height irregularities of the surfacesformed by both the static fracture processes [3] andthe dynamic fracture processes.4 ConclusionThe experiments have proved similar behavior of theheight surface irregularities formed by static and dy-namic fractures. The fast fracture process accom-plished with the wedge-shaped chisel generates verysimilar graphs σc(Ha) to those in the case of slowfracture processes. These results have been achievedusing three-dimensional profile parameters Ha eval-uated on the basis of a reconstruction of the confocalsurface. The graphs σc(Ha) seem to be convenientcandidates for calibration curves.The properties of the surface irregularities of frac-tured cement pastes presented here may also be use-ful for morphological and structural studies of otherporous materials.AcknowledgementThis work was supported by the Ministry of theCzech Republic under Contract no. ME09046 (Kon-takt).References[1] Ficker, T., Martǐsek, D., Jennings, H. M.: Rough-ness of fracture surfaces and compressive strengthof hydrated cement pastes, Cem. Concr. Res. 40(2010) 947–955.[2] Ficker, T., Martǐsek, D., Jennings, H. M.: Sur-face roughness and porosity of hydrated cementpastes, Acta Polytechnica 51(2011), no. 3, 7–20.[3] Ficker, T.: Fracture surfaces of porous materials,Acta Polytechnica 51(2011), no. 3, 21–24.[4] Ficker, T.: Quasi-static compressive strength ofcement-based materials, Cem. Concr. Res. 41(2011) 129–132.Prof. RNDr. Tomáš Ficker, DrSc.Phone: +420 541 147 661E-mail: ficker.t@fce.vutbr.czDepartment of PhysicsFaculty of Civil EngineeringBrno University of TechnologyVeveř́ı 95, 662 37 Brno, Czech Republic119

Surface Morphology of Porous Cementitious Materials Subjected to Fast Dynamic Fractures

CTU Open Journal Systems (Czech Technical University, Prague / České vysoké učení technické v Praze)

Acta Polytechnica Vol. 51 No. 5/2011Surface Morphology of Porous Cementitious Materials Subjected toFast Dynamic FracturesT. FickerAbstractThis paper presents a study of the surface height irregularities of cement pastes subjected to fast dynamic fractures.The height irregularities are quantiﬁed by the values of the three-dimensional proﬁle parameters. The studied dynamicalirregularities show a similar analytical behavior to those obtained by static fractures.Keywords: 3D proﬁle analysis, fracture surfaces, cement-based materials, confocal microscopy.1 IntroductionWe have recently published several studies [1–3] onthe surface morphology of fractured specimens madefrom hydrated cement pastes. This material showsa high value of porosity, which has been proved tobe an inﬂuential factor governing the irregularities offracture surfaces.For practical surface analyses of porous materi-als, it would be valuable to know whether the sur-face height irregularities are also inﬂuenced by themethod of fracture. For this purpose we performed alarge series of experiments with cement pastes. Thismaterial was chosen because its porosity can easilybe controlled within a broad interval by means of thewater-to-cement ratio r = w/c. Correct knowledge ofthe dependence of surface roughness on the fractur-ing method may be useful for further surface studiesof fractured porous materials.2 Experimental arrangementOrdinary Portland cement CEM 42,5 I R-sc of do-mestic provenance was used to create 144 specimensof hydrated pastes with six diﬀerent water-to-cementratios r (0.3, 0.4, 0.5, 0.6, 0.7, 0.8). The specimenswere rotated during hydration to achieve better ho-mogeneity. All specimens were stored for the wholetime of hydration at 100 % RH and 20 ◦C. After90 days of hydration the specimens were fracturedboth in the static regime (three-point bending tests)and also in the dynamic regime (impulse fracturescaused by a chisel and a heavy hammer). The frac-ture surfaces were then immediately used for micro-scopic analysis.The three-dimensional proﬁle parameter Ha wasused to characterize the roughness of the fracture sur-faces of the hydrated cement pastes. In fact, Ha rep-resents the averaged ‘absolute’ height of the fracturerelief z = f(x, y)Fig. 1: 3D confocal relief of fractured cement pasteHa =1L ·M∫ ∫(LM)|f(x, y)|dxdy (1)where L × M is the area of the vertical projectionof the three-dimensional fracture proﬁle f(x, y) intothe plane xy. The parameter Ha has great statisticalrelevancy, since it is a global averaged characteris-tic covering the entire tested surface L × M . Thethree-dimensional proﬁles f(x, y) were created usingan Olympus Lext 3100 confocal microscope. One ofthese proﬁles is shown in Figure 1. The proﬁles areformed by software that processed a series of opticalsections created by the confocal microscope at vari-ous heights of the fracture surfaces. Approximately100 image sections were taken for each measured sur-face site, starting from the very bottom of the sur-face depressions (valleys) and proceeding to the verytop of the surface protrusions (peaks). The investi-gated area L×M = 1 280 μm× 1 280 μm (1 024 pix-els× 1 024 pixels) was chosen in ﬁve diﬀerent placesof each fracture surface (in the center, and in four po-sitions near the corners of the rectangular area), i.e.each plotted point on the graphs of the proﬁle pa-rameters corresponds to an average value composed118Acta Polytechnica Vol. 51 No. 5/2011of 60 measurements (12 samples× 5 surface measure-ments). Each measurement was performed for mag-niﬁcation 20×.3 Results and discussionIt is well known that hydrated cement is a compositematerial consisting of several solid hydrated prod-ucts and pore spaces (see the photo in Figure 2).Porosity (P ) inﬂuences most of the mechanical prop-erties of this material, and it is therefore not sur-prising that the surface irregularity (Ha) was alsofound [1–3] to be among the dependent properties.Since porosity to a large extent determines compres-sive strength, a strong functional relation betweencompressive strength σc and surface irregularity ofthe fracture surfaces was also revealedσc(Ha) = σo(HoHa − ho)ρ(2)where σo, Ho, ho and ρ are ﬁtting parameters.Fig. 2: A photograph of the surface of a hydrated cementpasteFig. 3: Compressive strength in dependence on the heightirregularities of a surface formed in a dynamic fractureIn the present study, relation (2) is tested withspecimens fractured dynamically using a sharp chiseland a heavy hammer that simulate an impulsive load.Figure 3 shows the resulting graph σc(Ha). The dy-namical strength values in Figure 3 were evaluatedon the basis of the static values by adding correc-tions corresponding to dynamic processes [4]. Asshown in Figure 3, the experimental points are ﬁttedwell by function (2), which means that this functionmay describe a universal behavior of the compressivestrength and the height irregularities of the surfacesformed by both the static fracture processes [3] andthe dynamic fracture processes.4 ConclusionThe experiments have proved similar behavior of theheight surface irregularities formed by static and dy-namic fractures. The fast fracture process accom-plished with the wedge-shaped chisel generates verysimilar graphs σc(Ha) to those in the case of slowfracture processes. These results have been achievedusing three-dimensional proﬁle parameters Ha eval-uated on the basis of a reconstruction of the confocalsurface. The graphs σc(Ha) seem to be convenientcandidates for calibration curves.The properties of the surface irregularities of frac-tured cement pastes presented here may also be use-ful for morphological and structural studies of otherporous materials.AcknowledgementThis work was supported by the Ministry of theCzech Republic under Contract no. ME09046 (Kon-takt).References[1] Ficker, T., Martiˇsek, D., Jennings, H. M.: Rough-ness of fracture surfaces and compressive strengthof hydrated cement pastes, Cem. Concr. Res. 40(2010) 947–955.[2] Ficker, T., Martiˇsek, D., Jennings, H. M.: Sur-face roughness and porosity of hydrated cementpastes, Acta Polytechnica 51(2011), no. 3, 7–20.[3] Ficker, T.: Fracture surfaces of porous materials,Acta Polytechnica 51(2011), no. 3, 21–24.[4] Ficker, T.: Quasi-static compressive strength ofcement-based materials, Cem. Concr. Res. 41(2011) 129–132.Prof. RNDr. Toma´sˇ Ficker, DrSc.Phone: +420 541 147 661E-mail: ﬁcker.t@fce.vutbr.czDepartment of PhysicsFaculty of Civil EngineeringBrno University of TechnologyVeverˇ´ı 95, 662 37 Brno, Czech Republic119

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Surface Morphology of Porous Cementitious Materials Subjected to Fast Dynamic Fractures

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