Investigation of interfacial fracture toughness between concrete and adhesive mortar in an external wall tile structure

ARTICLE IN PRESS International Journal of Adhesion & Adhesives 30 (2010) 1–9

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Investigation of interfacial fracture toughness between concrete and adhesive mortar in an external wall tile structure Thiti Mahaboonpachai a,n, Takashi Matsumoto b, Yohei Inaba c a

Department of Civil Engineering, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan Division of Built Environment, Hokkaido University, Kita 13, Nishi 8, Kita-ku, Sapporo 060-8628, Japan c Building Construction and Material Group, Kajima Technical Research Institute, 2-19-1 Tobitakyu, Chofu-shi, Tokyo 182-0036, Japan b

a r t i c l e in fo

abstract

Article history: Accepted 12 June 2009 Available online 7 August 2009

This paper aims to investigate interfacial fracture toughness between concrete and polymer-cement mortar (PCM) in an external wall tile structure under various shear to tensile stress ratio by using interface elements in a finite element method (FEM). A constitutive material model of interface elements was developed, and its corresponding values that have a relation to the interfacial fracture toughness were calibrated with three four-point bending set-ups and one high shear test. Then, the developed interface element was verified by applying to analyze the failure of tiles in the tiled column compression test. With this method, the interfacial fracture toughness of the current interface was successfully obtained for the whole range of the shear to tensile stress ratio. Finally, the result is further discussed with the other interfaces, consisting of cementitious materials. & 2009 Elsevier Ltd. All rights reserved.

Keywords: External wall tile structure Interface Fracture mechanics Finite element stress analysis Delamination

1. Introduction External wall tiles are commonly used as building finishing facades in Japan because of several advantages. The external wall tiles not only protect concrete walls of buildings from environmental attacks, such as, carbonation, acid rain, and weathering, but also show an aesthetic expression of the buildings. Moreover, the self-cleaning ability of glazed-surface tiles reduces a building cleaning cost that is normally considered as one of the maintenance cost during a building’s life. As a result, the total building life-cycle cost was expected to be reduced. However, the external wall tiles suffer from many problems, such as tile cracking and tile delamination. Especially, tiles falling off from high-rise buildings not only offset the potential tile advantages that might be obtained, but also cause a danger to pedestrians and the properties around that area. From field observations, the interface between concrete and adhesive mortar was mostly found as the failure location in an external wall tile structure. Therefore, most of researches were carried out to develop several types of adhesive mortar by using a standard pull-off test [1–7]. The pull-off test was also used to study the influence of workmanship on the bonding strength of tiles in the external wall tile structure [7,8]. This experiment gives a result in terms of tensile bonding strength of the interface between concrete and adhesive mortar. At the same time, some researchers investigated not only tensile bonding strength but

n

Corresponding author. Tel.: +81 3 58417455; fax: +81 3 58417496. E-mail address: [email protected] (T. Mahaboonpachai).

0143-7496/$ - see front matter & 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijadhadh.2009.06.005

also shear bonding strength of the interface, because shear stress, occurring at the interface, is also realized to be one of the factors that deteriorate the external wall tile structure [4–7]. Although tensile bonding strength and shear bonding strength are useful for ranking adhesive materials, these two parameters do not have a predictive capability for studying an interfacial crack propagation mechanism. The interfacial failure, initiated by fracture propagation, can be expected to be governed by interfacial fracture toughness than the bonding strength. The interfacial fracture toughness is the other quantity that can be not only used to quantify the performance of interfaces, but also used in a finite element method (FEM). Normally, the crack propagation in materials can be simulated by using interface elements in FEM that is a method to analyze crack propagation behavior [9–14]. For example, fracture toughness of concrete under mode I or crack-opening mode due to pure tensile stress, defined based on fracture mechanics, was experimentally investigated, and applied to define a constitutive material model of an interface element in FEM for analyzing crack-opening behavior under tensile stress condition [9]. In an external wall tile structure, the interface in the structure is subjected not only to pure tensile or shear mode, but also to mixed modes of tension and shear as exemplified by the buildings under solar radiation [15,16]. Therefore, the interfacial fracture toughness is necessary to be investigated under the whole range of shear to tensile stress ratio. A four-point bending test that was developed based on an interface fracture mechanics theory [17] is one of the experimental method for investigating the interfacial fracture toughness. The four-point bending test, consisting of symmetric and

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asymmetric loading set-ups, can be used to investigate the interfacial fracture toughness for the whole range of shear to tensile stress ratio, which occurs at the interface between two materials. One drawback of this method is the difficulty to obtain the interfacial fracture toughness between two cementitious materials at high shear to tensile stress ratio, because the failure sometimes does not occur at the interface [18]. To overcome this drawback, the current research performs the finite element (FE) analysis by applying the interface element, having a relationship to the interfacial fracture toughness, to calibrate with the fourpoint bending tests and the high shear test in order to investigate the interfacial fracture toughness. Then, the interfacial fracture toughness, covering the whole range of phase angles, is successfully obtained. This paper aims to investigate the interfacial fracture toughness between concrete and polymer-cement mortar (PCM) that is commonly used as adhesive mortar for an external wall tile structure in Japan, and also to propose a method to investigate the interfacial fracture toughness between two cementitious materials. With this method, not only the interfacial resistance of the interface can be quantified in terms of the interfacial fracture toughness for the whole range of shear to tensile stress ratio, but also the constitutive material model of the interface element in FEM can be developed simultaneously. In what follows, the interface element and its constitutive material model are, firstly, developed in FEM. Then, each parameter in the constitutive material model is calibrated with four experiments that generate a different shear to tensile stress ratio at the interface. Three experiments are prepared based on the interface fracture mechanics approach, and the other one is modified from the test method for shear strength of steel fiberreinforced concrete in Japan Society of Civil Engineers (JSCE) standard [19]. Next, the interface element is verified with another experiment, namely the tiled column compression test, that is designed to have a failure at the interface between concrete and PCM. In this experiment, the compressive force is applied on the concrete specimen, attached with tiles, and strain responses on the tile surfaces are monitored in order to check a damage condition at the interface between concrete and PCM. The purposes of this experiment are not only to verify the interface element, but also to show an example of utilization of the developed interface element. Finally, the value of the interfacial fracture toughness of the interface between concrete and PCM in the external wall tile structure, which is obtained from FEM calibrated with the experiments in this study, is further compared with the ones of the interfacial fracture toughness of the other interfaces that were tested, and calculated directly from the interface fracture mechanics theory [18].

2. Development of the interface element In this section, a constitutive material model of interface elements, developed in this study, is described, and the values of parameters in the constitutive material model are determined by calibrating with four experiments. The first three experiments are four-point bending tests that consist of a symmetric loading set-up, two asymmetric loading set-ups, and the fourth one is the so-called high shear test that is developed from the test method for shear strength of steel fiber-reinforced concrete in JSCE standard [19]. 2.1. Constitutive material model of the interface element An interface element in Fig. 1(a), having zero thickness in n-direction, is developed from a four-node solid element, and can be applied to analyze interfacial stress by embedding the interface

element between two standard four-node elements in FEM. Normally, stress that occurs inside the interface element is calculated from relative displacements between two bordering elements [9–14]. In this study, the interface element is developed for analyzing stress under mixed modes of a shear to normal stress condition. Before crack initiation, the interface element is assumed to have high stiffness in order to prevent separation of two bordering elements. Moreover, the high stiffness is also provided for preventing node inter-penetration when the interface element is under compression. The cracking surface shown in Fig. 1(b) is proposed to be the criterion for interfacial crack in this study. Under the tension–shear mode, the elliptic cracking surface in Eq. (1) is proposed to be the cracking initiation criterion [20].  2  2 s1 t1 þ ¼1 ð1Þ

s0

t0

where s1 and t1 are cracking stress under mixed modes of tension and shear, respectively. s0 and t0 are tensile and shear bonding strength under pure tensile and shear stress conditions. Furthermore, shear bonding strength (t0) is assumed to be the crack initiation criterion when the interface element is under the compression-shear mode. Fig. 1(c) shows the relationship between stress and relative displacement in this study. Both normal stress (sn) and shear stress (t) are dependent on relative displacement in normal direction (dn), namely n-direction, and in sliding direction (dt), namely t-direction, respectively. It can be seen that the proposed cracking stress in each mode is used as the crack initiation criterion of the interface element. After crack initiation, tensile and shear stresses decrease or undergo a softening process as shown in Fig. 1(c) when the interface element is under the tension–shear mode. The interface element fails when maximum relative displacement (dn0 or dt0) is attained. In other words, maximum relative displacement is defined as the crack propagation criterion of the interface element. Under the fracture process of the interface element, the area under the relation between stress and relative displacement is assumed to be equal to the critical energy release rate or fracture toughness [9–14]. In other words, the maximum relative displacement of interface element can be defined from the mentioned assumption. Therefore, under the tension–shear mode, maximum relative displacement in each direction can be determined by assuming that the area under two softening curves is equal to the interfacial fracture toughness as shown in Eq. (2). 1 1 s1 dn0 þ t1 dt0 ¼ GðcÞ 2 2

ð2Þ

where dn0 and dt0 are maximum relative displacement in n and t directions, respectively, and s1 and t1 are cracking stress determined from Eq. (1). G(c) is the interfacial facture toughness at a different level of shear to tensile stress ratio. From Eq. (2), maximum relative displacement, dn0 and dt0, can be obtained when the other parameters are known. The shear to tensile stress ratio is defined as phase angle (c) as given in Eq. (3). 01 of phase angle means pure tensile condition, and the phase angle increases when the shear to tensile stress ratio increases. The maximum value of the phase angle is equal to 901, indicating pure shear condition. tanðcÞ ¼

t1 s1

ð3Þ

In this study, Eqs. (1)–(3) are used to define the constitutive material model of the interface element under tension–shear mode, because the interfacial fracture toughness has been derived

ARTICLE IN PRESS T. Mahaboonpachai et al. / International Journal of Adhesion & Adhesives 30 (2010) 1–9

Compression-shear mode n

τ

τ0

t

Zero thickness

Tension-shear mode Cracking stress ( σ 1 ,τ 1)

σ0

Interface element

3

σn

Cracking surface

τ σn τ1 σ1

δcrack

δn0

δcrack δt0 Shear stress under tension τ Compression

δn

δt

τ0

Normal stress δcrack

δt0

δt

Shear stress under compression Stress-relative displacement relation Fig. 1. An interface element and its constitutive material model.

in terms of bonding strength (s0 and t0), maximum relative displacement (dn0 and dt0), phase angle, and interfacial fracture toughness under pure tensile condition as a function shown in Eq. (4)[20].

GðcÞ ¼ f ðs0 ; t0 ; dn ; dt ; Gð0o ÞÞ

ð4Þ

From Eq. (4), the relationship shows that both magnitude and tendency of the interfacial fracture toughness against the phase angle are changed when the parameters changes. It has been found that the interfacial fracture toughness, derived from the elliptic cracking surface in Eq.(1), can denote the tendency that shows the increase of interfacial fracture toughness when phase angle increases, and then slowly increase at high phase angle under the condition that shear bonding strength is higher than the tensile bonding strength. This tendency is, sometimes, observed in the interface between concrete and PCM [20,21]. On the other hand, the interfacial fracture toughness derived form linear cracking surface can denote only the exponential change of the interfacial fracture toughness when phase angle increases. Therefore, Eqs. (1)–(3) are proposed for the interface element under mixed modes of tension and shear in this study. Under the compression-shear mode, shear stress after crack initiation is dependent not only on relative displacement but also on compressive stress as shown in Fig. 1(c). Eq. (5) shows the shear stress after the crack initiation as a function of relative displacement and compressive stress in this study.

t ¼ f ðdt ; sn Þ

ð5Þ

The shear stress, occurring due to the friction between two smooth concrete surfaces, is assumed to be 0.4sn. In other words, the shear stress of the interface element under compression is dependent on the compressive stress (sn) [22]. After crack propagation, normally the propagated crack surfaces between two cementitious materials are not completely smooth. There are some small portions left on two cracked surfaces. Therefore, due to the surface roughness, 10% of cracking stress is assumed to transfer via the propagated crack surface between two materials. 2.2. Calibration of the interface element In this part, the value of each parameter in the constitutive material model of the interface element that represents the interface between concrete and PCM is determined. With the assumed parameter values, the developed interface element is applied to determine the maximum capacity of the beams that composed of two materials, concrete and PCM in FEM, and then the analysis results are compared with the experimental results. The value of each parameter is seeked until the maximum capacity of the beams in four experimental set-ups can be reproduced in the FE analysis. Three of four cases are four-point bending tests, and the other case is a high shear test. Each case was designed to have different shear to tensile stress ratio or phase angle at the interface. 2.2.1. Experimental method Two types of beam configurations, consisting of two materials that are concrete and PCM, were prepared as shown in Fig. 2(a)

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40 15 cm

5

10

ψ = 0°

simulate

30 cm

5 Top view

Symmetric loading set-up in four-point bending test

1 plastic tape 10

ψ = 30° 5

simulate

Front View

ψ = 60°

For four-point bending test

Asymmetric loading set-up in four-point bending test 15

10

15

simulate

10

ψ ≈ 90° Top view High-shear loading set-up

plastic tape 10

Fig. 3. Modeling of the experiments for investigation of interfacial fracture toughness.

5 Front View Unit: centimeter

For high shear test

Table 1 Material properties.

Fig. 2. Beam specimen.

Material

Young’s modulus (GPa)

Poisson’s ratio

and (b). The first type in Fig. 2(a), having concrete on the left-hand side and PCM on the right-hand side, was used for the symmetric and the asymmetric four-point loading tests in Fig. 3(a) and (b). For the other material configuration in Fig. 2(b), having concrete between PCM, was used for the high shear test in Fig. 3(c). PCM was cast against concrete substrate after concrete had experienced 35 days of age that consisted of 28-day water curing and 7-day air curing processes. Before casting PCM, the smooth surface of concrete was treated by using water jet in order to remove the dirt from the surface. Then, plastic tape with 5 cm in length was attached at the bottom half of the bonded area to serve as an artificial crack, and it was used to ensure that the failure would occur at the interface. After casting PCM, the specimens were cured for additional 28 days in water. In total, the specimens had 63 days of age before conducting the experiment. Material properties of both normal concrete and PCM, having 4% of polymer content, at 63 days are given in Table 1. For the symmetric four-point bending test, the loading configuration was set as shown in Fig. 3(a) in order to generate 01 of phase angle at the artificial crack tip along the interface. In Fig. 3(b), there were two cases of the asymmetric four-point bending test having different loading set-ups or different values of S, A, and B that were calculated based on the standard testing method [17]. It can be seen that by changing the values of A, B, and S the phase angle at the interface could be changed. In this experiment, the values of A, B, and S were approximately equal to 6.9, 15.6, and 2.4 cm for 301 of phase angle, and equal to 5.2, 17.2, and 0.7 cm for 601 of phase angle, respectively. For the other loading set-up in Fig. 3(c), although it is not a standard test to investigate the interfacial fracture toughness, high phase angle, approximately 901, was expected along the interface. Displacement control was applied to all types of the experiments with

Concrete PCM

30.7 21.6

0.207 0.212

0.005 mm/s loading speed. Finally, the maximum loading capacity of each specimen was recorded.

2.2.2. FE modeling for calibrating the interface element and the calibration results The FE analysis was performed to determine the maximum loading capacity of each loading set-up in order to calibrate the parameter values of the constitutive material model of the interface element as mentioned previously. Since the experiments were designed to have the failure at the interface between two materials, the failure of the beams in FEM is also dependent on the properties of interface elements, namely bonding strength and maximum relative displacement in tension and shear. These four parameters in the constitutive material model of the interface element were obtained so that the maximum loading capacity of all cases could be reproduced in FEM. A plane strain condition was assumed in this analysis. For the symmetric and the asymmetric four-point bending test, the same specimen geometry and the same loading condition was modeled as shown in Figs. 3(a) and (b). For the high shear test, having the boundary condition as shown in Fig. 3(c), the half beam analysis was performed in FEM because of the symmetric condition. Twenty interface elements, having 2.5 mm in length in t-direction, were embedded between concrete and PCM elements above the initial crack tip. Low value of cracking relative displacement, dcrack, in comparison with the maximum relative displacement, dn0 and dt0, has to be provided in order to have a high stiffness for the interface elements. In this study, 0.000001 mm of the cracking relative displacement, dcrack, was given for the interface elements.

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Elastic behavior was assumed for concrete and PCM elements with the material properties given in Table 1. In the calibration process, firstly, the parameters of the constitutive material model of the interface elements were assumed to predict the maximum loading capacity of the symmetric four-point bending test. In this loading configuration, the capacity of the maximum loading is mainly dependent on the tensile bonding strength (s0) and maximum relative displacement in n-direction (dn0). The tensile bonding strength was defined from the standard pull-off provided from the product data sheet. Then, the maximum relative displacement dn0 was seeked until the maximum loading capacity between the experiment and FEM agreed with each other. In the same way, shear bonding strength and maximum relative displacement in shear direction were also seeked by analyzing the high shear test. With these two loading configurations, four parameters were roughly obtained. Finally, the interface element with the obtained properties was applied to predict the maximum loading capacity of the other two loading configurations. During this process, the values of each parameter were adjusted until the maximum loading capacity in FEM agreed with the experiment. With the parameter values shown in Table 2, the maximum loading capacity of four models in FEM is compared with the experimental results as shown in Table 3. Table 3 shows the calibration result that is the comparison of the maximum loading capacities between the experiment and the FE analysis for all cases. In the experiment, there were four specimens for the symmetric loading set-up of four-point bending test that generated 01 phase angle at the interface above the initial crack tip. In this case, three of four specimens have approximately 1 kN of the loading capacity, and another one shows 0.436 kN. For the

Table 2 Constitutive material model of the interface elements. Tensile bonding strength, s0 Shear bonding strength, t0 Maximum relative displacement in normal direction, dn0 Maximum relative displacement in shear direction, dt0 Cracking relative displacement, dcrack

2.5 MPa 5.6 MPa 0.002 mm 0.006 mm 0.000001 mm

5

asymmetric loading set-up, six specimens for two loading configurations (three for each one) that generated different phase angles above the initial crack tip at the interface were used. In the first loading configuration, giving 301 of phase angle, the maximum loading capacity is about 5.7 kN from three specimens, and in the other loading configuration (601 of phase angle), two of three specimens are 8.2 kN and one specimen shows 6.3 kN. Finally, there were five specimens for the high shear test that shows the maximum loading capacity in the range of 19–34 kN. In FE analysis, the maximum loading capacities of the beams are 0.94, 4.77, 8.58, and 29.4 kN, and phase angles of each beam are 2.071, 26.561, 60.941, and 85.001 for each case, respectively. Based on Eq. (3), the phase angle of each beam in the FE analysis shown in Table 3 was calculated from the cracking stress, s1 and t1, of the interface element above the initial crack tip during the occurring of crack initiation of the interface element. It can be seen that by having the interfacial properties of the interface elements in Table 2, the FE analysis results agree well with the experimental results in terms of the maximum loading capacity of the beams. In other words, the constitutive material model of the interface elements with the proposed constitutive material model, and its corresponding values can be used to perform the external wall tile delamination analysis in the future, if the same materials, concrete and PCM, are used. Moreover, this calibration method, including FE analysis and four experiments, can be applied to determine the constitutive material model of the interface element for other interfaces.

3. Verification of the interface element In this section, the constitutive material model of the interface elements, developed from Section 2, is verified in order to ensure that it can be utilized in the future. The experiment that is the tiled column compression test was designed for this purpose. The experiment was also designed to have a failure at the interface between concrete and PCM. Thereby, the behavior of the tile failure, mainly dependent on the interfacial properties of the interface between concrete and PCM, from both the experiment and the FE analysis can be compared. The strain histories on tile

Table 3 Calibration results. Experiment

FEM

Type of loading

No.

P (kN)

Model

Phase angle (deg.)

s1 (MPa)

t1 (MPa)

P (kN)

Phase angle ¼ 01

1 2 3 4 Avg.

1.185 1.077 1.041 0.436 0.935

1

2.07

2.49

0.09

0.94

Phase angle ¼ 301

1 2 3 Avg.

5.705 5.554 5.924 5.728

2

26.56

2.46

1.23

4.77

Phase angle ¼ 601

1 2 3 Avg.

8.278 8.282 6.38 7.647

3

60.94

1.95

3.51

8.58

High shear test

1 2 3 4 5 Avg.

23 19.1 34.4 28.55 33.6 27.73

4

85.00

0.48

5.49

29.4

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surfaces from both the experiment and the analysis at various locations were compared, because the change of strain responses on tile surfaces was expected when there was damage occurring at the interface.

was also attached at concrete surfaces in three sides of the specimen, and was used to monitor the strain on concrete in order to prevent the failure of concrete due to compressive force. Finally, the compressive force was applied on the top of concrete until the interfacial failure of tiles was clearly observed.

3.1. Experimental method 3.2. FE modeling Fig. 4 shows the experimental configuration of the tiled column compression test. Seven of glazed-surface tiles, having a square shape with 45 mm in length each side, were attached on three sides of concrete surfaces by using PCM as the adhesive as shown in the figure. Before the tile attachment, plastic tape with 50 mm in length was used as an artificial crack in order to ensure that the failure will occur along the interface between concrete and PCM, and the location of plastic tape is also shown in the figure. The material properties of concrete and PCM are the same as Section 2, and given in Table 1. Five strain gauges, namely A, B, C, D, and E, were attached on the tile surfaces in order to measure the local strain on tile surfaces at different positions as shown in Fig. 4, because the change of strain on the tile surfaces was expected when there was damage at the interface. The other strain gauge location, namely L,

Experiment

FE model

5 A B C

Plastic tape

D 40

E simulate

L A

A

10

1

3

Surface number Unit: centimeter

2 Fig. 4. Experiment and analysis of compressive test on concrete specimen attached with tiles.

Half of the specimen was modeled with the boundary conditions shown in Fig. 4 by assuming the plane strain condition. 106 interface elements with 2.5 mm in length that have the same material properties in Table 2 were embedded between concrete and PCM elements. The material properties of the concrete and PCM elements are the same as the previous analysis, and given in Table 1. For the tiles, element size was made small enough to compute the local strain on tile surfaces. Namely, along the tile surfaces, the element size was 2.5 mm in a vertical direction of tiles. For tile properties, 49 GPa of Young’s modulus and 0.18 of Poisson’s ratio were used in this analysis. 3.3. Results and discussion Strain histories on tile surfaces from both the experiment and the analysis were plotted against the load as shown in Fig. 5. The strain histories on the tile surfaces in Fig. 5(a)–(c) are from the experiment, and the one in Fig. 5(d) is from the FE analysis. The positive value of strain on tile surface in the plot indicates compressive strain in this study. During the experiment, the strain on tile surfaces was initially under the compression as shown in Fig. 5(a)–(c), because the compressive force was transferred from concrete to the tile surfaces via the PCM layer. The compressive strain at all strain gauge locations increased when the applied force increases until 200 kN approximately. Then, the compressive strain on strain gauge A did not increase, but started to gradually reverse to zero. After that, the strain gauges B and C also started reversing to zero during 250–300 kN. The interfacial delamination could be clearly observed when the applied compressive load on concrete was approximately 350 kN. At this time, the strain on tile surfaces at locations D and E suddenly reversed to zero. Although the interfacial damage could not be visually inspected during conducting the experiment, the strain histories from strain gauge location A, B, and C, show that the strain started reversing to zero when the applied force was during 200–300 kN as shown in the figure. The change of strain responses implies that there was damage occurred at the interface under the strain gauge locations. The FE analysis results can be used to confirm this experiment. From the FE analysis, the strain histories on the tile surfaces are shown in Fig. 5(d). The strain histories, for example, at three locations that are A, B, and E are described. The maximum strain at location A was 77–109 m when the load was 256–288 kN in the experiment, and equal to 84 m when the load was 170 kN in the FE analysis. At location B, the maximum strain was 211–352 m when the load was 256–298 kN in the experiment, and equal to 309 m when the load was 202 kN in the FE analysis. Finally, the maximum strain at location E was 733–935 m when the load was 331–366 kN in the experiment, and equal to 907 m when the load was 368 kN in the FE analysis. The strain on tile surfaces at locations A and B reaches the maximum value at a bit lower loading levels in comparison with the experiment, because elastic behavior is assumed for concrete, PCM, and tile elements in this study. In other words, all of the damages that are possible in the concrete and the PCM during conducting the experiment are lumped into the interface elements. As a result, deformation in terms of relative displacement of the interface elements in the FE analysis is

ARTICLE IN PRESS

400

400

300

300 A

B

C

L

100

D

E

L

1800

0 -200

A

B

C

100

D

E

300 800 1300 Compressive Strain ()

300 800 1300 Compressive Strain ()

400

400

300

300 A

100

E

0 -200

300 800 1300 Compressive Strain ()

1800

Experiment on surface 2

B

D

L

1800

Experiment on surface 3

Load (kN)

Load (kN)

Experiment on surface 1

200

7

200

200

0 -200

Load (kN)

Load (kN)

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E

L

D C

200

A

B

100 0 -200

A

B

C

D

E

L

300 800 1300 Compressive Strain ()

1800

FE analysis

Fig. 5. Strain histories on tile surface from experiments and FE analysis.

Shear stress (MPa)

A

8 6 4 2 0 -2 -4 -6 -8

B

C

D

106 kN 213 kN 298 kN

E

360 kN

400 kN

In summary, the constitutive material model of the developed interface elements could be verified by this experiment, because the results in terms of strain histories from both the experiment and the analysis agreed well with each other. Moreover, the interfacial crack propagation mechanism could be explained by using the interface elements. With these achievements, it can be seen that the interface element can be further utilized in order to analyze the cause of the external wall tile delamination in the future.

4. Interfacial fracture toughness

53 kN

0

50 100 150 200 Distance along the interface element (mm) Fig. 6. Interfacial shear stress along the interface elements.

probably larger than in the experiment. Although the maximum levels of strain in each location occurs at the bit lower loading level in the FE analysis, the tendencies of the strain responses at all locations agrees well with the experimental results. From the FE analysis, the interfacial failure mechanism of this experiment can be explained. Fig. 6 shows the interfacial shear stress at six different loading levels that are 53, 106, 213, 298, 360, and 400 kN. From the plot, the movement of maximum shear stress location implies that the interfacial crack propagated when the load increases. For example, the maximum shear stress level moved from A to B (the strain gauge locations) when the load was during 106–213 kN. As a result, the compressive force transferred via the PCM layer reduced due to the occurrence of interfacial crack represented by the interface elements. Consequently, the strain on tile surface reversed to zero because the tile was elastic.

Based on the interface fracture mechanics approach, the experimental results from the symmetric and the asymmetric four-point bending tests can be directly used to calculate the interfacial fracture toughness. The interfacial fracture toughness is written as a function of material properties and a critical stress intensity factor as shown in Eq. (6)[17].

G ¼ f ðE1 ; E2 ; u1 ; u2 ; Kc Þ

ð6Þ

where G is the interfacial fracture toughness. E and u are Young’s modulus and Poisson’s ratio, respectively. The subscript 1 and 2 are belonging to material 1 and 2 in the specimen that are concrete and PCM in this study. Kc is the critical complex stress intensity factor of the interface, calculated from the geometric correction factor for the four-point bending test, the critical nominal stress at the crack tip, and the initial crack length [17]. Although the asymmetric loading set-up can be theoretically used to obtain the interfacial fracture toughness for the whole range of phase angles by changing the loading set-ups, the failure of specimen composed of cementitious materials may occur at the other locations, especially at high phase angle [18]. Fig. 7 shows the modes of failure that can occur from the four-point bending test. Mode A is defined when the interfacial crack clearly propagates along the interface. Mode B is defined when the interfacial crack propagates along the interface until one point

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Concrete

toughness equal to 2–24 J/m2 when phase angle is 0–751, and the interface between concrete and engineered cementitious composites (ECC) has the interfacial fracture toughness equal to 3–34 J/m2 when phase angle is 0–601. Based on those values, the interface between concrete and PCM in the external wall tile structure is quite week, especially at high degree of phase angle, and the result also implies that this interface is possible to be harmful under high shear condition such as the shear stress that occurs from thermal expansion mismatch among the materials under the solar radiation.

PCM Mode A

Concrete

PCM Mode B

Concrete

PCM

5. Concluding remarks

Mode C Fig. 7. Modes of failure.

Interfacial fracture toughness (J/m2)

20 Experiment Finite Element Analysis

15

10

×2

5

×2 ×2

0 0

20

40 60 Phase angle (degree)

80

Fig. 8. Interfacial fracture toughness.

(more than 10 mm from the initial crack tip) and then kinks out to the PCM. The reason is maybe due to the change of a stress field when the interfacial crack approached the top part of the beam near the loading point. Mode C, the crack directly initiates from the initial crack tip towards the PCM, and it usually occurs at high phase angle. The mode C failure is not considered as interfacial fracture, and also is not included in the evaluation of the interfacial fracture toughness. In this study, the interfacial fracture toughness could be experimentally obtained until the phase angle was 601 as shown in Fig. 8, because mode C started to occur at this phase angle. On the other hand, the interfacial fracture toughness at the whole range of phase angles could be obtained from the interface elements in FEM. The interfacial fracture toughness in Eq. (2) and the phase angle in Eq. (3) were obtained after the calibration. Fig. 8 also shows the obtained interfacial fracture toughness from the FE analysis in comparison with the one obtained from the interface fracture mechanics approach. It can be seen that the interfacial fracture toughness at 841 of phase angle could be obtained, and at the other three cases of phase angle that are 01, 301, and 601 of phase angle, the FE analysis agrees well with the interface fracture mechanics approach. With this method, the interfacial fracture toughness between concrete and PCM in the external wall tile structure is shown to be 2–16 J/m2 when the phase angle is in the range of 0–841. The interfacial fracture toughness of the other interfaces between cementitious materials [18] is selected to be compared with this interface. For example, the interface between concrete and fiber-reinforced concrete (FRC) has the interfacial fracture

In this study, the interfacial fracture toughness between concrete and PCM was investigated for the whole range of shear to tensile stress ratio (phase angle) by using the interface elements in FEM. Although there is a standard test method based on fracture mechanics approach, it is difficult to use this standard test to investigate the interfacial fracture toughness between two cementitious materials at high phase angle practically. Therefore, the constitutive material model of the interface elements was defined, and its corresponding parameter values, having a relation to the interfacial fracture toughness, were calibrated with four experiments that have different phase angle at the interface. Regarding the calibration of the interface element, the value of each parameter in the proposed constitutive material model of the interface element was calibrated by analyzing the beam-loading capacity under four different loading set-ups. The maximum loads of the beams from the FE analysis and the experiment were compared. The interface elements with 5.6 MPa of shear bonding strength, 2.5 MPa of tensile bonding strength, 0.006 mm of maximum relative displacement in the shear direction, and 0.002 mm of maximum relative displacement in the normal direction could reproduce the maximum loading capacity between the FE analysis and the experiment for all cases. Next, the interface element was applied to analyze the failure of tiles in the tiled column compression test developed in this study. The experiment was designed for not only to verify the interface element, but also to use it as an example of the model utilization. In this part, the strain histories on tile surfaces in the experiment could be reproduced in the FE analysis by using the developed interface element. Moreover, interfacial crack propagation behavior could be explained by observing the interfacial shear stress along the interface elements in the FE analysis. After calibration and verification of the interface element, the interfacial fracture toughness was obtained from the FEM for the whole range of phase angles. In this study, the four-point bending tests were prepared to investigate the interfacial fracture toughness at 01, 301, and 601 of phase angle only, and the results of interfacial fracture toughness from both methods during the 0–601 of phase angle agreed well with each other. With the proposed method, the interfacial fracture toughness between concrete and PCM in the external wall tile structure is equal to 2– 16 J/m2 when the phase angle is in the range between 01 and 841. If it is compared with the ones of the other interfaces between cementitious materials that normally have a value higher than 20 J/m2 when phase angle is higher than 701, it can be seen that the interface between concrete and PCM is quite weak, showing the possibility to fail under high shear stress condition. For example, the thermal expansion mismatch among materials that induce shear stress at the interface could be harmful to the external wall tile structure. In the future, the developed interface element can be used to analyze such a condition in order to check the shear stress level at the interface, and to develop a durable adhesive material for the external wall tile structure.

ARTICLE IN PRESS T. Mahaboonpachai et al. / International Journal of Adhesion & Adhesives 30 (2010) 1–9

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