Damage mechanisms in cementitious coatings on steel members under axial loading

Construction and Building Materials 90 (2015) 18–35

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Damage mechanisms in cementitious coatings on steel members under axial loading Suwen Chen a,b,⇑, Liming Jiang b,c, Asif Usmani c, Guo-Qiang Li a,b, Chu Jin b a

State Key Laboratory for Disaster Mitigation in Civil Engineering, Shanghai, China College of Civil Engineering, Tongji University, Shanghai, China c School of Engineering, The University of Edinburgh, Edinburgh, UK b

h i g h l i g h t s  Mechanical properties and bond strengths of cementitious coatings are determined.  Monotonic axial loading tests on cementitious coated steel members were conducted.  A cohesive zone finite element (CZFE) scheme for damage modelling is established.  Damage mechanisms of cementitious coatings on axially loaded steel are revealed.

a r t i c l e

i n f o

Article history: Received 19 March 2013 Received in revised form 14 February 2015 Accepted 12 April 2015 Available online 16 May 2015 Keywords: Cementitious fire protection coating Cohesive zone finite element (CZFE) Damage mechanism Axial loading Monotonic loading test Steel structure

a b s t r a c t Cementitious coatings have been widely used as fire protection for steel structures, but they are vulnerable to structural deformations or vibrations, which may lead to reduction in their effectiveness and cause severe economic loss in the event of a fire. For buildings in practice, the problem can be critical because the coatings are assumed to be in good condition as they are usually hidden underneath architectural finishes, making it difficult and expensive to carry out routine inspection. To determine the actual fire resistance of a building after a moderate or severe loading event or a relatively long period of service, it is imperative to understand the performance of the coatings and to develop effective damage estimation methodologies. Loading conditions in a real buildings can be complex, however as there is inadequate previous work in this field, it is considered more important at this stage to determine the fundamental damage mechanisms in cementitious coatings on steel members subjected to axial loading, as investigated in this paper through experimental and numerical studies. At first, tests are carried out to obtain mechanical properties of the coating and the bond properties between the coating and the steel substrate. Then, a series of monotonic loading tests are conducted on axially loaded steel members to observe damage propagation in coating specimens. Subsequently, a cohesive zone finite element (CZFE) scheme is presented for modelling the damage with both interfacial and internal damage considered. The effectiveness of the proposed CZFE scheme is validated by comparison with different numerical approaches, interlaminar stress analysis and monotonic loading tests. From monotonic loading tests and CZFE numerical analyses, damage mechanisms in cementitious coatings on axially loaded steel members are clearly revealed. Under tensile loading, the damage begins with interfacial cracks at both ends, followed by transverse cracks within the coating resulting in its ultimate fracturing into segments. Under compressive loading, the damage also initiates at the ends with interfacial cracks and propagates towards the centre until the coating completely peels off. The findings from this research build a solid foundation for estimating the damage of cementitious coatings for trusses and large space structures, as most of the structural components in these structures are axially loaded. This work also provides an effective approach for further research on understanding damage mechanisms in cementitious coatings in steel frame structures under more realistic loading conditions. Ó 2015 Elsevier Ltd. All rights reserved.

⇑ Corresponding author at: College of Civil Engineering, Tongji University, Shanghai 200092, China. Tel.: +86 21 65982975 16. E-mail address: [email protected] (S. Chen). http://dx.doi.org/10.1016/j.conbuildmat.2015.04.025 0950-0618/Ó 2015 Elsevier Ltd. All rights reserved.

S. Chen et al. / Construction and Building Materials 90 (2015) 18–35

1. Introduction Building regulations across the world require that in the event of a fire structural systems maintain integrity, insulation and stability over an adequate ‘‘length of time’’. Integrity and insulation refer to the desirability of the fire to be stopped from spreading beyond the compartment of origin, while stability alludes to the necessity of the structure itself to sustain its load-bearing function over the required period. Because of its high thermal conductivity and rapid reduction of strength and stiffness properties with temperature, steel structures are generally considered to be vulnerable to elevated temperatures such as those occurring under fire conditions. Structural steel loses roughly half its strength and stiffness at 550 °C and over 90% at temperatures above 800 °C. To address this problem the traditional practice has been to insulate steel structural members from the effect of fire for a required period of time. Cementitious fireproofing materials have been widely used as fire protective coatings on steel structures due to their durability, low density, low thermal conductivity, low cost, and non-toxic emissions upon exposure to fire. These coatings are usually made of cement mixed with aggregates such as expanded vermiculite to make them lightweight. The required thickness of cementitious coating is usually applied in-situ to structural steel members as a wet mixture. Because of their unsightly appearance, steel structural members protected in this manner end up hidden under architectural claddings and finishes. This makes it difficult and expensive to monitor the condition of the protective coatings over time or to carry out inspections after moderate or severe loading events (such as windstorms, fires or earthquakes). However, given that these coatings are cementitious and specifically designed to be lightweight, they are naturally fragile and brittle and prone to damage under deformation or vibration [1–3]. It is therefore reasonable to expect a potential reduction in the fire resistance of such buildings [4–7] after a period of use, especially if this period has included one or more of the aforementioned moderate or severe loading events. For instance, in the tragic ‘911’ event, the inadequate and damaged fire protection due to the plane impact was considered to reduce the fire resistance afterwards and therefore contribute to the eventual collapse of the World Trade Centre (WTC) towers [8,9]. Apart from the obviously damaging impact of extreme loads, relatively moderate loads such as impact, wind load or seismic action, may also induce significant monotonic and cyclic deformations in the structure and cause damage to fire protection but with limited external signs of damage. Coating damage may occur over a single significant loading event or be of a cumulative nature leading to

19

progressive deterioration of its integrity and therefore its ability to provide the designed level of fire protection (as illustrated in Fig. 1). This deterioration represents a hidden danger to the safety of a building and its occupants in the event of a fire. Thus it is imperative to develop methodologies for estimating the in-situ condition of fire protection after a severe loading event or after a relatively long period of service. In order to achieve this goal, the performance and damage mechanisms of cementitious coatings under a variety of simple and complex loadings must be well understood. So far there has been little formal investigation of the potential fire safety risk posed by damaged cementitious fire protection as even the most fundamental failure mechanisms of such coatings have not been properly quantified, which is key purpose of the research reported in this paper. After the September 11, 2001 event, the adhesive/cohesive strengths of fibre-based spray-applied fire-resistive materials have been investigated [2] as part of WTC collapse investigation. Dwaikat and Kodur [10] present parametric studies conducted for modelling the fracture and delamination of cementitious coating on the insulated steel plates subjected to static and impact loads based on a mixed 2D cohesive zone finite element (CZFE) scheme. In order to develop a method for evaluating the damage in cementitious coatings on steel members subjected to external loading, fundamental research has been carried out in Tongji University, which includes experiments on the mechanical properties of cementitious materials and adhesion properties of the coating to steel substrate [1,11], interlaminar stress analyses on axially or flexurally loaded steel members [1,11,12], monotonic loading tests on cementitious coated steel members under axial loads and under pure bending [1,11,13,14], and detailed numerical studies [13–15]. In the numerical simulation, a cohesive zone finite element (CZFE) scheme is adopted, which employs a cohesive zone model (CZM) [16–17] in conjunction with contact pair for the interfacial crack propagation and the William-Warnke model [18] for the internal damage within the coating. This paper presents comprehensive experimental and numerical studies on damage mechanisms in cementitious coatings on steel members under axial loading. First, tests are conducted to obtain the mechanical properties of the cementitious coating to understand the behaviour of the cementitious coating itself and its adhesion to steel substrates. Then, monotonic loading tests are carried out to investigate the damage in cementitious coatings on the coated steel plates subject to pure tension and compression loadings. To analyse the damage, the CZFE scheme is adopted for modelling the tests and validated against the analytical and elastic FE solutions.

Fig. 1. Performance deterioration of cementitious fire protection over the design life.

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Fig. 2. Tests for tensile and compressive strengths of cementitious coating: (a) dimension of tensile specimen; (b) test setup for tensile strength; (c) fracturing in tensile strength test; (d) dimension of compressive specimen; (e) test setup for compressive strength; (f) crushing in compressive strength test (mm).

The modelling is to provide more detailed and deeper insights into the failure mechanisms observed in the experiments and also build a foundation to develop, with further (continuing) work, damage indices correlated to structural member stress states. From the results of loading tests and numerical analyses, the damage mechanisms in cementitious coatings on steel members under axial loading have been revealed. The revealed mechanisms build a solid foundation for estimating the damage of cementitious coatings in trusses and large space structures with axially loaded components. Furthermore, this verified numerical scheme can be adopted in further study for complex loading conditions, such as combined axial, flexural and cyclic loading.

2. Mechanical property tests for cementitious coatings Typical thick fireproof material is cementitious. In this paper, YC-1 material is adopted, which is manufactured by a factory in Shanghai. It is a mixture of vermiculite, perlite, Kaolinite, light calcium carbonate, mica, cement, and additive materials. The ratios by weight for coating and the interfacial layer are suggested as, (1) YC-1:water = 1:0.86, and (2) specific interfacial agent: YC-1:water = 1:3:2.5, respectively. In the preparation of the specimens for bond strength tests and following monotonic loading tests, the steel substrates are painted with anti-corrosion red leader primer before the interfacial layer and then the coatings, according to the real practice procedure. Tests are conducted for the following mechanical properties of cementitious coatings: (1) tensile strength ft; (2) compressive

strength fc; and adhesive strength of coating to steel substrates: (3) normal bond strength Tn; and (4) tangential bond strength Tt. The test setup and failure modes for tensile strength and compressive strength are shown in Fig. 2. For the tensile strength test, the specimen can’t be directly clamped because the strength of fireproof material is too low. Thus, we designed a new experimental way, as shown in Fig. 2b. The specimen for tensile strength is shown in Fig. 2a with end section of 90  90 mm and mid-section of 50  90 mm, where designed to be failure location. After 28 days’ curing, both ends of the specimen are respectively glued to a steel T-stub with epoxy resins and then loaded through a hinge connector, as shown in Fig. 2b. For the compressive strength test, the specimen of size 70.7  70.7  70.7 mm, according to Chinese code GB14907-2002 [19] is loaded until it is crushed as shown in Fig. 2f. To assess the performance of the coating-steel interface, bond strength tests were carried out as shown in Fig. 3. For testing the normal bond strength, the top surface of the coating block (50  50  10 mm) is glued to the steel plate with epoxy to ensure that the damage only takes place at the bottom bonding interface (Fig. 3b and c), which is processed in accordance with YC-1 product instructions. To test for the tangential bond strength, the test specimen is designed as shown in Fig. 3d. The outer bonding interfaces are designed to fail in the tests, as seen in Fig. 3e and f. The normal and tangential bond strengths are calculated using Eqs. (1) and (2), respectively.

f nb ¼

F nb Anb

ð1Þ

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S. Chen et al. / Construction and Building Materials 90 (2015) 18–35

Glued interface

Bonding interface

(a)

(b)

(c) Glued Interfaces

Bonding Interfaces

(d)

(e)

(f)

Fig. 3. Tests for normal and tangential bond strengths of cementitious coating: (a) dimension of normal bond specimen; (b) test setup for normal bond strength; (c) damage mode of normal bond-strength test; (d) dimension of tangential bond specimen; (e) test setup for tangential bond strength; (f) damage mode of tangential bond strength test.

Table 1 Test results of cementitious coating material and mechanical properties. Density (q) g/cm3

Group

Time

Curing condition

Surface treatment

A

Jan. 2009

Curing box

No

(0.086) B

Nov. 2008

Natural

No

0.59 (0.012)

C

Apr. 2009

Natural

Red lead paint

0.55 (0.017)

D

May. 2009

Natural

Red lead paint

0.64 (0.008)

0.82

Elastic modulus (Ec) MPa 18.55

Compressive strength (fc) MPa

Tensile strength (ft) MPa

Normal bond strength (fnb) MPa

Tangential bond strength (ftb) MPa

1.49

0.26

0.13

0.16

(3.298)

(0.079)

(0.027)

(0.015)

(0.042)

17.68 (1.236)

1.01 (0.156)

0.12 (0.017)

0.08 (0.014)

0.07 (0.026)

40.33 (10.187)

0.59 (0.076)

0.05 (0.005)

0.04 (0.012)

0.07 (0.016)

91.32 (8.444)

1.00 (0.082)

0.10 (0.004)

0.04 (0.008)

0.09 (0.082)

The numbers in the parentheses represent the corresponding standard deviation.

f tb ¼

F tb Altb þ Artb

ð2Þ

where fnb and ftb are the bond strengths (MPa) in normal and tangential directions; Fnb and Ftb are ultimate loads (N); Anb is the area of normal bonding interface; Altb , and Artb are the left and right areas of bonding interfaces. The mechanical properties of cementitious coating based on the test results are tabulated in Table 1. For each group, at least 5 specimens were tested. From Table 1, large variations in mechanical properties have been observed among the results obtained from different groups of specimens considering different temperature and humidity, different curing condition and different surface treatment. Nevertheless, in all groups, the results show that the normal bond strength at the coating-steel interface is weaker than the tensile strength of the coating itself, which explains that that

cracks usually initiate along the coating-steel interface. It is necessary to point out that typical thick fireproof material is cementitious and has similar composition, which means that they have similar mechanical properties. Because the specimens of group C were prepared along with the monotonic loading test specimens, thus the result of group C is selected for following numerical simulation.

3. Monotonic loading tests on cementitious coated steel members 3.1. Axial tensile loading test The damage of the cementitious coating can be assumed to only relate to the deformation of steel member. To avoid more complex

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Fig. 4. Axial tensile loading test on cementitious material coated steel plates: (a) specimen dimension; (b) test setup; (c) coating-steel interfacial cracks; (d) transverse cracks in coating.

Fig. 5. Coating strain vs. steel strain in monotonic tensile loading tests: (a) installation of strain gauges; (b) damage mode; (c) coating strain vs. steel strain.

Fig. 6. Axial tensile loading tests with different specimen size: (a) 200  60  20 mm; (b) 200  60  30 mm; (c) 400  60  20 mm; (d) 600  100  20 mm.

stress states, the coating is applied away from the edges over the central surface area of the plate, as shown in Fig. 4a. Cementitious materials are applied on both sides of the plate in a

rectangular patch of length, L of 200 mm, width, W of 60 mm, and thickness, T of 20 mm. The steel plate thickness, t for all tensile tests, is 8 mm.

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Fig. 7. Axial compressive loading test on cementitious material coated steel members: (a) specimen dimension; (b) test setup; (c) coating-steel interfacial cracks; (d) coating peeling off.

Fig. 8. Typical damaged coating-steel interface after test: (a) damaged but adhering loosely; (b) after removing the coating bulk.

Fig. 9. Cementitious coating damage mode with strain gauge applied: (a) 200  60  20 mm; (b) 200  60  30 mm.

Fig. 10. Uncoupled constitutive relationships [14]: (a) normal direction, (b) tangential direction.

As shown in Fig. 4b, axial tensile load is gradually applied on the partially coated steel plate. As the tensile load increases to reach steel strain of 0.08–0.12%, the interfacial cracks start from both ends and propagate towards the centre (Fig. 4c). This is followed

by transverse cracks in the coating (Fig. 4d). The cracks, once opened, keep getting larger until the end of the test. In another specimen, two pairs of strain gauges were installed on the steel and the coating as well as extensometer on steel

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Table 2 Data input for CZM and contact elements.

Table 5 Data Input for MKIN material model for steel.

Parameter

Kn (N mm3)

Tcn (MPa)

dcn

Kt (N mm3)

Tct (MPa)

dct

Value

16

0.04

0.005

10

0.07

0.014

Table 3 Data input for material property parameters of cementitious coating. Parameter

Ec (MPa)

m

ft (MPa)

fc (MPa)

Value

40.33

0.2

0.05

0.59

Parameter

E (GPa)

m

Ep (MPa)

fy (MPa)

Value

200

0.3

1000

315

bottom ends (Fig. 7c), and then propagate towards the centre with further increase of the load. When the steel strain reaches approximately 0.3%, cracks spreads all over the coating-steel interface but without any internal damage in the coatings. Soon after that, the coatings peel off as shown in Fig. 7d. 3.3. Results from monotonic loading tests

Table 4 Data input for MKIN material model for cementitious coating. Data No.

1

2

3

4

5

6

Strain Stress (MPa)

0 0

0.005 0.20165

0.010 0.4033

0.02 0.53

0.03 0.58

0.04 0.59

(Fig. 5a). Coating strain vs steel strain curve is plotted in Fig. 5c, which shows that the coating strain increases linearly with steel strain and drops after the occurrence of cracks. To study the size effect upon coating damage, more axial tensile loading tests are carried out with different coating sizes, which include 200(L)  60(W)  20(T) mm, 200(L)  60(W)  30(T) mm, 400(L)  60(W)  20(T) mm, and 600(L)  100(W)  20(T) mm. Similar damage modes of the coatings in different sizes are observed and shown in Fig. 6, where all the cracks observed in the tests are sorted and numbered by time of occurrence. No. 0 represents the interfacial crack. Comparing the 20 mm thick test specimen (Fig. 6a) against the 30 mm thick one (Fig. 6b), it is observed that the interfacial crack occurs earlier for the latter with fewer transverse cracks. The reason may be that earlier occurrence of interfacial crack reduces the shear stress transferred from the steel plate resulting in fewer transverse cracks in thicker coatings. For different coating lengths of the same (20 mm) thickness (Fig. 6a, c, and d), similar damage modes are observed except that more transverse cracks occur in longer coatings. 3.2. Axial compressive loading test Fig. 7 shows the tests while the steel members are under axial compression. To avoid local and overall bucking in the steel members due to initial eccentricity, a mini-column is fabricated from 8 mm thick steel plates as illustrated in Fig. 7a. When the average strain in the steel plates reaches approximately 0.2%, coating-steel interfacial cracks appear at top and

(a)

The monotonic loading tests clearly illustrate the failure modes of cementitious coatings on steel members under axial loading. (1) Under tensile loading, interfacial cracks initiate from the ends when steel strain reaches around 0.08–0.12% and propagate towards the centre, followed by the occurrence of transverse cracks. The final failure mode is that the coating fractures into several segments but continues to adhere loosely to the steel plate (Fig. 8a). The thicker the coating is, the earlier the interfacial cracks occur and fewer transverse cracks develop. The increase of coating length increases the number of transverse cracks (suggesting that there may be a ‘‘characteristic spacing’’ between cracks when the coating fails under tensile loading). (2) Under compressive loading, interfacial cracks initiate at the ends when steel strain reaches around 0.2% and then propagates to cover the whole interface. The final failure mode is the peeling off of the coating. Further interesting facts observed from the tests are as follows, (1) The interfacial cracks do not, in fact, occur at the actual coating-steel interface but within the coating next to the interface. The reason for this may be that the coating-steel interface contains specific adhesive agents that enable good adhesion as long as the steel surface has been well treated against corrosion (Figs. 7d and 8b). (2) Some shear transfer still exists after the occurrence of the interfacial crack until the crack width reaches a critical value (Fig. 8). (3) It is difficult to accurately measure the coating strain in the tests, since the adhesive glue necessary for installing strain gauges considerably strengthens the coating performance

(b)

Fig. 11. Material model: (a) MKIN model against compressive strength test data for cementitious coating; (b) BKIN for steel.

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Fig. 12. A generic model for verification of CZFE scheme.

Fig. 13. Force/displacement relationship for COMBIN39 spring elements: (a) normal direction; (b) tangential direction.

and affects the occurrence of transverse cracks in the coatings (Fig. 9). 4. A numerical approach for modelling the damage of the coating

to pure normal or shear stress (usually being tagged as ‘single-mode delamination’), the constitutive relationship between traction (ta) and relative displacement (da) has a general expression as below, in which the subscript a can be n or t referring to normal and tangential directions respectively.

ta ¼ t a ðda Þ

4.1. Cohesive zone model A cohesive zone finite element (CZFE) scheme has been developed for the finite element analysis of delamination in laminated composites. With CZFE approach, the interface is modeled with zero-length (initial state) elements. The constitutive law of the interface is the relationship between interface tractions and relative displacements. When the cohesive zone element is subjected

0.06

ð3Þ

For the uncoupled model, two bilinear-one dimensional relationships can be assumed for normal (a = n) and tangential (a = t) direction respectively, as shown in Fig. 10 [16]. The constitutive law corresponding to Fig. 10 could be expressed from a damage mechanics perspective,

ta ¼ ua K a da ¼ ð1  da ÞK a da

ð4Þ

0.025

0.05

0.020

0.04 0.015

0.03 0.010

0.02 0.005

0.01 0.000

0.00

-0.005

-0.01 0

10

20

30

Location x (mm)

40

50

0

10

20

30

40

50

Location x (mm)

Fig. 14. Coating-steel interfacial (bond) stresses from different solutions: (a) normal direction; (b) tangential direction.

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S. Chen et al. / Construction and Building Materials 90 (2015) 18–35

Fig. 15. Damage propagation under axial tensile loading: (a) es = 0.89  103; (b) es = 1.19  103; (c) es = 1.55  103 (es is steel strain).

Fig. 16. Contact element status under axial tensile loading: (a) es = 0.67  103; (b) es = 0.84  103; (c) es = 1.19  103; (d) es = 1.55  103.

S. Chen et al. / Construction and Building Materials 90 (2015) 18–35

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Fig. 17. Normal bond stress contour plot under axial tensile loading: (a) es = 1.19  103; (b) es = 1.55  103.

Fig. 18. Interfacial (bond) stresses under axial tensile loading: (a) normal direction; (b) tangential direction.

where Ka is the initial penalty stiffness parameter, and a factor ua is applied to describe the stiffness degradation due to interfacial damage. Correspondingly damage parameter da is defined by Eq. (5). A zero value of da represents the interface is still elastic and intact while da = 1 indicates the interface is fully damaged.

da ¼

8 > > < > > :

da doa da

0 

dc a dca doa

1



06s 6s

: dt ¼ max ðjdn ðs0 ÞjÞ 0 06s 6s

if ðdoa
ð5Þ

with hdn ðs0 Þi ¼

ð8Þ

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi D2n ðs0 Þ þ D2t ðs0 Þ 06s 6s 0sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1  2  2 hdn ðs0 Þi hdt ðs0 Þi A @ þ ¼ max 06s0 6s don dot

Dm ¼ max 0

if ðda P dca Þ



0

if dn ðs0 Þ < 0

dn ðs0 Þ if dn ðs0 Þ P 0

ð6Þ

Since the actual debonding should take both the opening and the sliding modes into account [17], a modified mixed-mode constitutive relationship is presented by Alfano and Crisfield [16]. They set the ratio of relative displacement in the elastic regime to that in the softening regime to be equal for both the normal and tangential directions.

d d g ¼ 1  on ¼ 1  ot dcn dct

   1 Dm  1 dm ¼ max 1;  g Dm where Dm is calculated as below,

if ðda 6 doa Þ

where doa and dca are the elastic limit and critical failure relative displacements, and da is the maximum value of the relative displacement in the loading history (0 6 s 6 s),

8  ðhdn ðs0 ÞiÞ < dn ¼ max 0

Then a mixed-mode damage parameter dm could be introduced on the basis of the ratio parameter g.

ð7Þ

ð9Þ

Then the single-mode constitutive relationship (Eq. (4)) can be modified as follows for the mixed-mode delamination,

ta ¼ um K a da ¼ ð1  dm ÞK a da

ð10Þ

So far, the constitutive relationship has been built for the interfacial behaviour before cracking, then a damage law is needed to identify when the interfacial cracking occurs. In reference [16], an energy-based damage formulation is presented for mix-mode delamination since both normal and tangential energy contribute to fracture,



   Gn Gt þ ¼1 Gcn Gct

ð11Þ

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S. Chen et al. / Construction and Building Materials 90 (2015) 18–35

Fig. 19. Contour plot of first principal stress in cementitious coating under axial tensile loading: (a) es = 0.84  103; (b) es = 0.87  103; (c) es = 1.19  103; (d) es = 1.55  103.

where Gn and Gt are fracture energies calculated by the following equations,

Gn ¼

Z

t n ddn ;

Gt ¼

Z

tt ddt

ð12Þ

Meanwhile Gcn and Gct are critical fracture energies calculated in accordance with the single-mode delamination. For the bilinear traction/relative displacement relationship, the value of critical energy could be obtained by calculating the area under the bilinear curve respectively,

Gcn ¼

1 T cn dcn ; 2

Gct ¼

1 T ct dct 2

ð13Þ

where the maximum traction along normal and tangential direction (Tcn, Tct) can be set equal to normal and tangential bond strength (fnb, ftb) respectively, provided as Group C in Table 1. 4.2. Finite-element model for simulating the damage of the coating It has been understood that the damage of the coating under axial loading can be generalised as two basic types, which are (1) internal damage within the coating itself; and (2) interfacial cracking between coating and steel substrate. Therefore, a proper FE model should be able to describe the formation and propagation of both types of damage. The FE model presented in this paper is implemented with the ANSYS Version 11.0, in which a CZM model is employed in conjunction with contact pair (Conta173 and Target 171) to provide an appropriate numerical method simulating coating-steel

interfacial damage. Data input for CZM and Conta173 are shown in Table 2. Considering that cementitious coating could be treated as a weak concrete like material, and the fact that element Solid65 in ASNYS is specially developed for simulating concrete cracking and crushing, thus Solid65 with Concrete damage model is employed to address the damage of the coating itself. A crack in Solid65 element is represented through modification of the stress–strain relations by introducing a plane of weakness in a direction normal to the crack face. The data input for solid 65 is listed in Table 3. Nonlinear compressive behaviour is addressed by introducing multi-linear kinematic hardening (MKIN) material model to the Solid65 element. The data input is shown in Table 4 and in accordance with the result from the compressive strength tests, which are shown in Fig. 11a [13]. Element solid45 with bilinear kinematic hardening (BKIN) material model (Fig. 11b) is employed to simulate the steel plate. For the BKIN model, a yield stress fy and tangent modulus Ep are required to describe the post-yielding behaviour. The input data for steel material property is shown in Table 5. 4.3. Comparison and validation of CZFE scheme For handling interfacial problems, there are several different numerical approaches, such as contact analysis using zero-length spring elements, or directly coupling nodal displacement. The coating-steel interface is modeled with different approaches to validate the CZFE scheme based on a generic model

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Fig. 20. Principal stress plot in cementitious coating at different loading stages under axial tensile loading: (a) es = 0.84  103; (b) es = 0.87  103; (c) es = 1.17  103; (d) es = 1.19  103; (e) es = 1.55  103.

Fig. 21. Damage plots in cementitious coatings of different sizes under axial tensile loading: (a) 200  60  30 mm; (b) 200  60  40 mm; (c) 300  60  20 mm; (d) 400  100  20 mm.

as shown in Fig. 12. Notice that the stiffness contribution from the cementitious coating could be ignored, only one side of the coating is simulated in the finite-element model. An analytical solution for coating-steel interlaminar stress – which is initially proposed by Wang [12] in his doctoral

dissertation – is also presented. The analytical solution is based on elastic fracture mechanics with an assumption that the tangential and normal interlaminar stresses could be expressed as follows,

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S. Chen et al. / Construction and Building Materials 90 (2015) 18–35

Fig. 22. Maximum bond stresses in cementitious coatings of different thicknesses under axial tensile loading.

s0 ¼

1 X npx an sin ; l n¼1

r0 ¼

1 X npx bn cos l n¼1

ð14Þ

Fig. 24. Normal bond stress distribution in cementitious coatings of different lengths under axial tensile loading (es = 0.5  103).

ð18Þ

In numerical solutions, zero-length spring elements are commonly used for simulating single-mode interfacial behaviour in composite members, for example see COMBIN39 for steel–concrete interface [20]. Although the interfacial behaviour along normal or tangential directions can be modeled by different zero-length COMBIN39 elements, it is difficult to unify the damage status of the interface for different directions without even addressing mixed-mode delamination. In this simulation, at each pair of matching nodes, three spring elements of COMBIN39 are employed to simulate the contact in normal, longitudinal tangential and transverse tangential directions respectively. As shown in Fig. 13, the constitutive relationships of COMBIN39 elements along normal and tangential directions are set in accordance with the bond test results. Another numerical solution is obtained by simply coupling the nodal displacements at the coating-steel interface in the elastic regime, in which the interfacial (bond) stress is extracted from the stress in the coating element next to the steel. The interfacial stress distributions from different solutions are shown in Fig. 14, where all the data points are obtained along

Fig. 23. Normal Bond stress distribution in cementitious coatings of different thicknesses under axial tensile loading (es = 0.5  103).

Fig. 25. CZFE model for simulating cementitious coating damage in compressive loading case.

where the parameters an and bn are determined by applying mechanical equilibriums and the minimum energy principle. Wang [12] proposed his analytical solution for the interfacial stresses as below.

an ¼ C

2

C¼

h

n cos np ; n4 þ 2gn2 þ p2

bn ¼

pan n Ehs sIs  EhccIc 2l

1 Es I s

 P i 1 an c 1 þ 2h n¼1 n cos np hs h  i p2 h2c 1 h2s hs þ E1s hhcs 12 þ 3h þ 15h 2 5Ec c 4l4

hc N

þ Ec1Ic

ð15Þ

1

p bhs Es l þ pEs

ð16Þ

c

1

p2 ¼

p2 h2c 4l4

g¼

1 3



h

1 5Ec



2

p

þ E1s

ð17Þ

c

  hs 1 c s  2u  2u þ 6h þ uEcc  uEss Gs Ec Es c h  i p2 h2c 1 h2s hs þ E1s hhcs 12 þ 3h þ 15h 2 5Ec c 2l4

1 Gc



 c þ E1s 2h hs  i h2s hs 1 hs þ þ 15h 2 hc 2 3hc

1 Ec





c

S. Chen et al. / Construction and Building Materials 90 (2015) 18–35

31

Fig. 26. Contact element status under axial compressive loading: (a) es = 1.82  103; (b) es = 2.30  103; (c) es = 3.62  103.

Fig. 27. Interfacial (bond) stresses in a 150  60  20 mm coating model under axial compressive loading: (a) normal direction; (b) tangential direction.

the centroidal axis of the interface, with half of length (0–50 mm) being depicted due to the symmetry. From Fig. 14a, normal interfacial (bond) stress curves are generally of the same shape with maximum normal interfacial stress locating at the very end of the interface, however differences can be seen near the end (40–50 mm) of the interface. It is noticed that there is a 10 mm (35–45 mm) compressive (negative) zone for the analytical solution, but all the numerical approaches did not model this phenomenon, which is due to the chosen discretization and can be improved with finer mesh. Since negative normal bond stress will not cause debonding and affect the damage mode, it is acceptable to use current mesh scheme. For the tangential interfacial stress, results from different solutions also have similar shapes except the difference at the end of the interface, as plotted in Fig. 14b. For the analytical solution,

the interfacial stress ideally drops to zero at the end. However, boundary conditions could not be precisely satisfied in FE analyses given the continuity limitation of displacement shape function in elements and the presence of a singularity at the corner of coating-Steel interface. Finer mesh may help but cannot fundamentally solve this problem.

5. Results from the simulations for axial monotonic loading tests 5.1. Under axial tensile load The damage propagation in the cementitious coating (200  60  20 mm) is shown in Fig. 15, where the cracks in

32

S. Chen et al. / Construction and Building Materials 90 (2015) 18–35

Fig. 28. Principal stresses and cracks in coating elements at different loading stages under axial compressive loading.

Solid65 elements are plotted in red, and the deformation has been amplified 50 times. From the simulation results, it can be found that the damage (es = 0.84  103) appears at both ends of the interface, which is represented by the delamination of the contact elements (near interface) as shown in Fig. 16b. As the steel strain increases to 0.89  103, it is noticed that delamination does not propagate along the interface to the centre, instead by a set of short diagonal cracks occurring in the Solid65 elements as shown in Fig. 15a. Then the short diagonal cracks propagate towards the centre until the steel strain increases to 1.19  103 as depicted in Fig. 15b, where the first pair of transverse cracks forms in cementitious coating(solid65 elements) (Fig. 17a). As the tensile load continues increasing, the short diagonal cracks in the bottom coating elements continue to spread along the interface, which is followed by the second pair of transverse cracks when the steel strain reaches 1.55  103 (Figs. 15c and 17b). The damage seems to have been adequately simulated for this test. The interfacial (bond) stresses at different loading stages are plotted in Fig. 18, which provides a straightforward way to see the stress or traction in the contact elements. While the steel strain es is 0.52  103, the interface is still elastic. As es increases to 0.67  103, the CZM based contact element at the end of the

interface comes to the end of its elastic regime response. The traction and relative displacements along normal and tangential directions can be obtained from the analysis output, which are normal traction (interfacial stress) rn = 0.036 MPa, tangential traction (interfacial stress) st = 0.026 MPa, the open gap in normal direction dn = 2.53  103, and the tangential slip dt = 2.01  103. Then the damage parameter dm corresponding to es = 0.67  103 could be calculated as 0.998.

Dm ¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  2  2ffi hdn i D2n þ D2t ¼ þ hddott i don rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi    ffi 2:53103 2:5103

2

3

2

þ 2:0110 7:0103 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 ¼ 1:012 þ 0:287 ¼ 1:052 ¼

dm ¼

  1 Dm  1 ¼ 0:998  g Dm

ð19Þ

ð20Þ

Corresponding to the contact status depicted in Fig. 16b (es = 0.84  103), interfacial (bond) stresses in the debonded contact elements drop to zero in both normal and tangential directions, as shown in Fig. 18.

Fig. 29. Coating strain vs. steel strain for compressive loading case.

S. Chen et al. / Construction and Building Materials 90 (2015) 18–35

Fig. 30. Tangential bond stress distribution in cementitious coatings of different thicknesses under axial compressive loading (es = 2.0  103).

As a result of the propagation of debonding, the stresses in coating (Solid65) elements vary at the different loading stages, which can be well represented by the plot of the principal stresses in the Solid65 elements shown in Figs. 19 and 20. When the steel strain reaches 0.84  103, the value of first principal stress decreases to nearly zero in the bottom elements at both ends because the loss of shear from delamination of contact elements (Figs. 19a and 20a). Meanwhile, the maximum principal stress occurs in the bottom elements adjacent to the debonded contact elements. When the maximum principal stress is equal to or larger than the tensile strength of cementitious material, a set of tensile cracks initiate in the bottom solid65 elements, which represents the second type of interfacial damage. It may be noticed that when the steel strain increases from 0.84  103 to 1.17  103, the direction of the maximum first principal stress in the bottom solid65 elements continuously inclines to parallel with the coating-steel interface (Fig. 20c), which results in the first pair of transverse cracks in the solid65 elements as the steel strain reaches 1.19  103 (Figs. 19c and 20d). Similarly, the second set of transverse cracks in the coating could be seen at the centre of the coating (es = 1.55  103) (Figs. 19d and 20e). As discussed above, the damage of cementitious coating under tensile loading could be simulated reasonably well using the CZFE scheme, being represented by debonding contact elements

33

and tensile cracks in Solid65 elements. The damage on the coating-steel interface is simulated not only by the CZM based delamination in contact elements, but also by a set of short diagonal cracks in the bottom Solid65 elements. Further numerical work is carried out for damage simulation of tests comparing different coating sizes (Fig. 21). Firstly, damage plots in Fig. 21a and b show that fewer transverse cracks occur in the thicker coatings, where greater interfacial damage in CZM based contact elements can be found. This phenomenon agrees well with test results shown in Fig. 6. Parametric study (Fig. 22) shows the relationship between the maximum bond stresses (at the end of the interface) and the thickness of the coatings. Generally in the thicker coatings the interface gets debonded earlier due to higher bond stress at the ends (Fig. 23). However in the coatings of thickness larger than 50 mm, coating thickness does not affect the bond stress as strongly as it does in the thinner coatings (Saint–Venant’s principle). But it is necessary to point out that installation of steel mesh is usually required to strength the coating’s integrity when the thickness is equal to or lager than 40 mm. Secondly, for different lengths of coatings, similar damage mode is observed (Fig. 21) except that more transverse cracks are observed in longer coatings, which can also be observed from the normal bond stress distributions as shown in Fig. 24. 5.2. Under axial compressive load Through simulating the compressive loading case with the CZFE model shown in Fig. 25, the development of damage is found only in the vicinity of the coating-steel interface, which agrees with the test results of the compressive loading cases. The development of contact status on the interface is plotted in Fig. 26. As the axial compressive load increases, the interface gradually develops delamination from the both ends and moves towards the centre. This is because the maximum tangential bond stress, forming at the ends of the interface in the compressive loading cases, dominates the damage mechanism since the interface is under compression at the ends along the normal direction (Fig. 27a). In Fig. 27b, the variation of tangential bond stress in the contact delamination can be easily tracked at different loading stages. The maximum tangential stress forming at the ends continues to increase until the elastic response of the interface ends, which is followed by the CZM-based delamination and final peeling off. To further demonstrate this mechanism, the vector plots of principal stresses in solid65 elements are presented in Fig. 28a and b. Fig. 28c illustrates the short diagonal cracks in the bottom solid65 elements. Now comparing the Fig. 28b and c with

Fig. 31. Tangential bond stress distribution in cementitious coatings of different lengths under axial compressive loading: (a) es = 1.0  103; (b) es = 2.0  103.

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S. Chen et al. / Construction and Building Materials 90 (2015) 18–35

the contact status plotted in Fig. 26b, it can be observed that the contact delamination accompanies the short diagonal cracks seen in the Solid65 elements. As the compressive load increases, the interface cracks spread towards the centre. Fig. 29 illustrates the coating strain developing against the steel strain, obtained from the simulation results and experimental data. The coating strains are measured at the outer surface of the coating, and the data from 12 strain gauges on the specimens on each side of the columns is plotted in Fig. 29. In order to investigate how the coating size influences the damage propagation in compressive loading cases, FE models are built in different sizes which varies in the length and thickness of the coatings. Similar to the phenomenon from the tensile loading cases, earlier interfacial damage occur in thicker coatings. Fig. 30 illustrates the tangential bond stress distributions in coatings whose thicknesses are 20, 30, and 40 mm, respectively. When steel strain reaches 2.0  103, the 20 mm thick coatings still maintains an elastic coating-Steel interface, whereas the interfaces for 30 and 40 mm specimens have started to crack with the 40 mm specimen having the longer crack. Tangential bond stresses for different coating lengths are illustrated in Fig. 31. Different lengths do not cause significant difference as long as the coating is long enough to transfer the shear stress, which in this study is found to be around 100 mm.

6. Conclusions Experiments and numerical simulations have been carried out to investigate the damage mechanisms in cementitious coatings on axially loaded steel members. Tests were also carried out to determine the mechanical properties of cementitious coating and its bond properties with steel substrates. Even though the mechanical properties depend on the products that we used, other thick fireproof coatings may exhibit similar mechanical properties as most of thick fireproof coatings are cementitious and have similar compositions. The main findings from this work are as follows: (1) The CZFE scheme developed is effective in modelling the interfacial cracking as well as the cracking within the coatings. (2) Under tensile loading, damage initiates at both ends with cracks in the coatings close to the steel-coating interface and followed by periodic transverse cracks with a characteristic spacing between them until the final fracture of the coatings. (3) Under compressive loading, damage also initiates with the occurrence of cracks in the coatings close to the steel-coating interface at the ends. These cracks occur because the tangential bond stress exceeds the strength. These cracks continue to propagate towards the centre until the final failure when the coating completely peels off from the steel substrate. (4) It is also found that the thicker the coating is, the earlier the interfacial cracks occur, resulting in increasing characteristic spacing between transverse cracks, which suggests that thicker coatings may be more susceptible to damage under axial loadings. The aim of this research has so far been to understand and quantify the nature of the cementitious fire proofing damage under relatively simple monotonic and quasi-static loading leading to simple stress states (axial compression, axial tension). The findings from this paper build a solid foundation for developing an assessment method to determine the condition of cementitious coatings in structures with axially loaded components, such as trusses and

many large space structures. There are however significant limitations in directly applying the conclusions of this paper to real structures (even if the components are under axial loading) as the tests were carried out on a rectangular patch of cementitious material on a steel substrate, while real structural components are likely to be fully encased in the material. The computational modelling approach however validated under the more idealised conditions of the tests can now be used to model structural steel members fully encased in cementitious fire proofing. For many other structures with more complex loading conditions, considerable further work needs to be conducted to establish how the basic failure mechanisms of cementitious coatings identified so far manifest themselves when the coatings are subjected to cyclic and dynamic loading with possible torsional components and correspondingly complex stress states. Furthermore, a great deal of variability in the properties of cementitious coatings has been observed in the experiments, which points to the desirability of a probabilistic framework for using this data as a basis for a methodology to determine damage magnitudes under realistic loading conditions. The authors are currently working on such a framework. Acknowledgements The authors would like to thank former students, Mr. Zhao Sheng, Mr. Zhang Zhi-Ling and Mr. Dong Zhao-Hai, and technical staffs in the Laboratory in College of Civil Engineering in Tongji University for their help with experiments. Financial supports from the Natural Science Foundation of China (Grant No. 50808143) and Key innovative Research Project of Shanghai Municipal Education Commission (Grant No. 09ZZ37) to this study are gratefully acknowledged. References [1] Chen SW, Jin C, Li GQ. A study on damage mechanism of thick fireproof coating for steel member subjected to monotonic loading. In: Structures in fire: proceedings of the sixth international conference; 2010, p. 130. [2] Tan KT, White CC, Hunston DL. An adhesion test method for spray-applied fire resistive materials. Fire Mater 2011;35:245–59. [3] Braxtan NL, Pessiki S. Bond performance of SFRM on steel plates subjected to tensile yielding. J Fire Protect Eng 2011;21(1):37–55. [4] Ryder NL, Wolin SD, Milke JA. An investigation of the reduction in fire resistance of steel columns caused by loss of spray-applied fire protection. J Fire Protect Eng 2002;12(1):31–44. [5] Milke JA, Ryder N, Wolin S. Analyses of the impact of loss of spray-applied fire protection on the fire resistance of steel columns. In: Fire safety scienceproceedings of the seventh international symposium; 2003. [6] Wang WY, Li GQ. Behavior of steel columns in a fire with partial damage to fire protection. J Constr Steel Res 2009;65(6):1392–400. [7] Keller WJ, Pessiki S. Effect of earthquake-induced damage to spray-applied fire-resistive insulation on the response of steel moment-frame beam-column connection during fire exposure. J Fire Protect Eng 2012;22(4):271–99. [8] Lee G, Vladimir R, Tong M, Chen SW. From the world trade centre tragedy to development of disaster engineering for landmark buildings: an extension of the performance-based earthquake engineering approach. In: MCEER special report series: engineering and organizational issues related to the world trade centre terrorist attack, vol. 4; 2003. [9] NIST, Final report on the collapse of the world trade center towers, NCSTAR; 2005. [10] Dwaikat M, Kodur V. Modeling fracture and delamination of spray-applied fire-resisting materials under static and impact loads. J Eng Mech 2011;137(12):901–10. [11] Jin C. Research on the failure mode and damage mechanism of the thick fireproof coating for steel member under monotonic loading (MSc thesis). College of Civil Engineering, Tongji University (in Chinese); 2011. [12] Wang WY. Damage mechanism of fire protection on steel columns under earthquake and influence of damage on the fire (PhD dissertation). College of Civil Engineering, Tongji University (in Chinese); 2008. [13] Jiang LM. Numerical simulation and study on the damage of the thick fireproof coating for steel member under monotonic loading (MSc thesis). College of Civil Engineering, Tongji University (in Chinese); 2012. [14] Chen SW, Jiang LM, Li GQ. Experimental and numerical damage mechanism investigation of thick fireproof coatings for steel members subjected to

S. Chen et al. / Construction and Building Materials 90 (2015) 18–35 monotonic loading. Behaviour of Steel Structures in Seismic Areas, STESSA 2012. Santiago, Chile; 2012. [15] Chen SW, Jiang LM, Usmani AS, Li GQ. A numerical approach for damage simulation of spray-applied fire-resisting materials on the axially loaded steel members. In: First international conference on performance-based and lifecycle structural engineering (PLSE 2012), Hong Kong, China, Dec. 5–7; 2012. [16] Alfano G, Crisfield MA. Finite element interface models for the delamination analysis of laminated composites: mechanical and computational issues. Int J Num Methods Eng 2001;50(7):1701–36.

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[17] Tvergaard V. Predictions of mixed mode interface crack growth using a cohesive zone model for ductile fracture. J Mech Phys Solids 2004;52(4):925–40. [18] William KJ. Constitutive model for the triaxial behaviour of concrete. IABSE; 1974. [19] GB14907-2002. Fire resistive coating for steel structure (in Chinese). [20] Li A. Nonlinear numerical simulation of bonded steel-concrete composite beams by finite element analysis. In: 2011 international conference on electric technology and civil engineering (ICETCE); 2011, p. 6702–5.