Effective mechanical properties of self-healing cement matrices with microcapsules

    Effective mechanical properties of self-healing cement matrices with microcapsules Wenting Li, Zhengwu Jiang, Zhenghong Yang, Haitao Yu PII: DOI: Reference:

S0264-1275(16)30125-3 doi: 10.1016/j.matdes.2016.01.124 JMADE 1325

To appear in: Received date: Revised date: Accepted date:

23 September 2015 22 January 2016 26 January 2016

Please cite this article as: Wenting Li, Zhengwu Jiang, Zhenghong Yang, Haitao Yu, Effective mechanical properties of self-healing cement matrices with microcapsules, (2016), doi: 10.1016/j.matdes.2016.01.124

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ACCEPTED MANUSCRIPT Effective mechanical properties of self-healing cement matrices with microcapsules

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Wenting LI1, Zhengwu JIANG2, Zhenghong YANG3, Haitao YU4,* 1

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Key Laboratory of Advanced Civil Engineering Materials (Tongji University), Ministry of Education, Shanghai 201804, China. 2

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Key Laboratory of Advanced Civil Engineering Materials (Tongji University), Ministry of Education, Shanghai 201804, China. 3

Key Laboratory of Advanced Civil Engineering Materials (Tongji University), Ministry of Education, Shanghai 201804, China. 4

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Key Laboratory of Geotechnical and Underground Engineering of Ministry of Education, Tongji University, Shanghai, 200092, China. Email: [email protected]; Tel./Fax: 8602169580147.

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Abstract: The effective mechanical properties of matrices healed by embedded microcapsules were investigated using Eshelby theory based on the microscale healing mechanisms, reffering to the mechanical properties of the adhesive and the proportion of cracks that could be healed.

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This was determined by measuring the water absorption and vacuum saturation of precracked

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matrices. The microcapsules or cracks should not exceed 4 vol% to ensure that approx. 90% of the modulus is retained even if the cracks cannot be reattached at all. Both the healed cracks

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and unhealed cracks contribute to the anisotropy, with a greater contribution from the unhealed cracks. The elastic modulus of the adhesive has a more significant influence on the anisotropy as the applied load increases. The measured stiffness recovery indicates that the cracks were only partially healed. This value corresponds to a healing efficiency index of 0.2~0.4 for the

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present conditions.

Keywords: self-healing; microcapsule; effective mechanical properties; cement-based

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ACCEPTED MANUSCRIPT 1 Introduction Concrete is one of the most widely used construction materials. Unfortunately, it is susceptible to cracking when exposed to certain environmental conditions and external loads. This

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cracking undoubtedly compromises the performance and potential service life of concrete

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structures in terms of their mechanical and/or transport properties [1-9].

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Therefore, a bio-inspired self-healing capability has become the focus of increasing attention because it potentially enables the recovery of the structural integrity of materials [10-14]. Similar ideas have been incorporated to enhance the reliability and sustainability of concrete structures. Several approaches have been developed based on experimental explorations to

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achieve the self-healing of cement-based materials, utilizing bacteria, mineral admixtures, expansive agents, tabulated capsules or microencapsulation [15-26]. Not surprisingly, the

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liquid tightness or the transfer performance of concrete, which initially deteriorated due to the presence of microcracks, has been shown to be partially or even completely restored after crack healing by all of the previously mentioned strategies because the open paths for liquids

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can be easily disturbed and/or cut off once the cracks are filled. Accordingly, the healing efficiency has been mainly related to the recovery of transport properties because these

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properties are known to be the major factor affecting the durabilities of cement-based materials

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[15-40].

However, improvement of the mechanical performance, i.e., rebuilding the transfer of stress between failed faces, is another concern when polymers are used as the adhesive. Polymers can provide fast recovery of strength compared to other approaches. The restoration of the load

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bearing capability, even if only locally on the microscale, should improve stress redistribution and decrease further openings and the propagation of existing cracks. This also accounts for the improvement of the macroscopic mechanical properties in certain states, i.e., the initial state, and reloading after healing [28,41-45]. The effective or homogenized properties of a composite regarding its microstructure can be theoretically estimated utilizing micromechanics-based averaging or homogenization techniques in which the local effects are smeared out on the macroscale. Several classical theories have been reported in the literature [46-62]. Many of these theories are based on the pioneering work of Eshelby [48], which provided an estimation of the effective properties of such composites. Micromechanical solutions have also been employed to model microencapsulation-based self-healing cement-based composites [63-65]. The effect of the fraction of microcapsules, assumed to be voids, on the homogenized elastic properties has been numerically evaluated using the representative volume element (RVE), and the mechanical 2

ACCEPTED MANUSCRIPT performance in the initial state and after healing have been examined using the finite element method (FEM) [63], with the properties of the damaged elements represented by continuum elements replaced with the properties of the adhesive. However, this approach can be more accurate if the elements and the cracks healed by the adhesive are of the same order of

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magnitude in size. Therefore, a more refined mesh is necessary, considering the microcapsule

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radius is normally in the micrometer range. However, this can sharply increase the

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computational cost. Otherwise, the effective properties of the matrix after healing should be considered instead.

A two-dimensional micromechanical damage-healing model has been proposed for

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microencapsulation-based self-healing cement-based materials under tensile loading [64]. The compliance of the healing matrix has been mainly developed according to the crack length, which changes with the fracture properties of the phases and the probability of a crack hitting

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the capsules. However, the effects of the mechanical properties of the adhesive on the matrix after healing have not been considered. Herbst et al. [65] proposed a general model for local self-healing by applying an adhesive that represents the overall damage-healing of the crack

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caused by all physical mechanisms between healed contacts using the discrete element method

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(DEM) to discuss the dependence of the strength of the matrix on the adhesive. For microencapsulation-based self-healing, the adhesion is in fact mainly related to the capability

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of the adhesive to fill the cracks and its mechanical properties. Because it is such a complex process, the healing efficiency depends on many factors including the propagation of cracks to rupture the wall to release the adhesive, the crack filling mechanism under capillary action and crosslinking, and other reactions of the adhesive under certain conditions to reattach the open

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faces. The probability of a crack hitting the capsules has been discussed extensively because it is crucial for crack healing to occur [66-68]. Furthermore, the healing efficiency is supposed to be closely related, first, to the mechanical properties of each phase and, second, to the filling degree of the cracks by the adhesive as driven by the capillary effect and to the limited amount of capsules available in the system. The release of the healing agent from spherical and cylindrical microcapsules has been numerically investigated using RVE [69]. In particular, Gardner et al. [70] numerically simulated the capillary flow of cyanoacrylate in discrete cracks in cement mortar based on the Lucas-Washburn theory. These findings have provided a good base for the further exploration of the microscale healing mechanisms. Indeed, the healing of cracks is a mechanical, physical and chemical process, as described above. It is noteworthy that the actual healing efficiency also depends on local fluctuations in the contact conditions and cannot be described by a simple mathematical expression. Therefore, the dependence of the effective properties of the matrix on both the mechanical properties of 3

ACCEPTED MANUSCRIPT the adhesive and the proportion of cracks to be potentially healed, which has not been reported so far, is specifically discussed in this paper based on the Eshelby theory, assuming that the load-induced cracks are randomly and uniformly distributed in the matrix and that the adhesive, as driven by capillary action, only flows into the load-induced cracks. Moreover, not all of the

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cracks can be filled and healed even if the adhesive is sufficiently available because the

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capillary force is closely related to the size and connectivity of cracks [71-72], among other

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factors. Therefore, the proportion of cracks that can be healed has been equivalently determined as an input for the analysis by measuring the absorption resulting from the capillary effect and the vacuum saturation of the precracked matrix. The stiffness recovery was

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measured to validate the analysis.

2 Theoretical estimation of the homogenized elastic properties

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The homogenized mechanical properties were estimated by adopting the well-known Eshelby theory for the inclusion of flat ellipsoids [48]. The open cracks are characterized as a fictitious material with zero normal and shear stiffness whereas the mechanical properties of the healing

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material can be defined to represent the closed cracks. The bond between the matrix and the hardened agent is assumed to be strong enough that no cracking occurs. This is quite important

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for resistance to the reopening of cracks after healing, which is discussed in multiscale modeling [Li et al. submitted]. The cracks are all considered penny-shaped, planar and parallel

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to the z-direction for simplification, although they may not correspond to the real shapes of cracks in concrete that are irregular and have rough surfaces. The overall elastic modulus and shear modulus of the RVE were estimated assuming a dilute distribution of cracks. Interactions

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between the capsules can be neglected due to the low concentration of the self-healing microcapsules, i.e., 1 to 2 wt%, which ensures that the mechanical properties of the matrix are not weakened too much by the additional soft phase. For all estimations, the thickness of the capsule wall is ignored as the thickness is much smaller than the capsule diameter, and the volume of the healing agent to be released by a capsule is, therefore, equal to the capsule volume. Figure 1 shows a schematic of the setup of the infinite matrix containing a few microcapsules, denoted by  , and a typical n -oriented slit mesocrack (with the normal vector n ) that coincides with the semi-principal axes ( x  -direction) of the cracks with a length of 2 a0 in a 2dimensional domain with the prescribed macrostress  x . The angle between the x  -direction and the global coordinate x-axis is denoted by   .

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Figure 1. Orientation of a local crack in an infinite plane with a prescribed stress. The effective elastic stiffness

hom

for an RVE containing an isotropic linear elastic matrix s



s

 V 





s

:

, respectively, is given by [48]



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hom,



and

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and inclusions with the stiffness tensor,

where V is the volumetric fraction of microcapsules and



is the strain concentration tensor.

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 is the area average over the RVE.

(1)

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Assuming the interactions between any inclusions, referring to microcapsules and mesocracks hom

in the present study, are ignorable, the

of the system containing both microcapsules and

hom



s

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randomly distributed cracks can be written as

 V 





s

:





f

(2)

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where the additional overall elastic tensor, 

f

, due to the presence of a family of cracks has

contributions from both the unhealed and healed cracks through 

f

 Vun 

un



s

:

un

 Vh 

h



s

:

(3)

h

with V f  Vun +Vh

(4)

where V f is the volume of the load-induced cracks and is composed of unhealed and healed cracks, denoted by Vun and Vh , respectively.

un

and

h

and healed cracks, respectively. For the unhealed cracks, components of

h

are the elastic tensors for unhealed un

 0 . For the healed cracks, the

should be dependent on the properties of the cracks, i.e., the elastic

modulus E and Poisson's ratio ν (or Lamé constants λ and µ). Several elastic moduli Eh are defined to characterize the cracks healed by different adhesives, while the Poisson's ratio νh is 5

ACCEPTED MANUSCRIPT kept the same as that of the matrix. An index P is introduced to quantify the combined effects of the probability of a crack hitting the capsules, the chemical nature of the material surfaces to be bonded, etc. P is assumed to vary between 0 and 1 to account for open cracks even though

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the adhesive is available and cracks are perfectly closed by the adhesive.

h

 Vh  P 

h



s

:

h

can be related to an (interior point) Eshelby tensor



:  

s

Likewise,

un

un

un

 

s

:  

: 

s



:

s

and

un

h

h

:

:

s

s

s

 

1

can be given by











un

h





s

s

 

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Here, the associated Eshelby tensors by the transformation tensor



 

(5)

by [48]

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

:

s

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



un

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 Vun 

(6)

1

D

f

(7)

1

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

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Eq.(3) is rewritten as

un

(8) h

and

should be expressed in global coordinates (x,y)

. In the form of components for the uniformly distributed

mesocracks, it follows that [58]

1 2



2

 S pqrs Tip T jq Tkr Tls e p  eq  er  es d 

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Sijkl 

0

(9)

For a crack to heal, it is essential that the crack can break the walls of the capsules as it propagates, thereby releasing the embedded adhesive. For a crack with the unit normal vector

n in an infinite domain with the prescribed stress  x , as schematically shown in Figure 1, the stress intensity factors K I and KⅡ are given by

K I   x  a0 cos2 

(10)

and

KⅡ= x  a0 sin  cos  .

(11)

In this study, the І-mode fracture is considered to be the dominant fracture mode for the middle section, which is theoretically pure bending, in the 4-point flexure configuration. 6

ACCEPTED MANUSCRIPT The mode-І fracture toughness K IC for a crack to initiate its propagation

K I  K IC

(12)

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is determined by

(13)

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K IC   0  a0

where  0 is the critical stress required to initiate a fracture in the uniaxial tension configuration, i.e.,   0 .

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Then, Eq.18 can be written as

(14)

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0 . x

cos 2  

This gives the critical orientation for the cracks to be activated, denoted by  cr ,

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0 r

(15)

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cos 2 cr 

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Taking advantage of the axial symmetry, the cracks oriented only in [0,  cr ] in the first quadrant can be activated to propagate and be potentially healed. un

Therefore,

h Sijkl 

 /2

2

 

h

can be rewritten as [58]

 S pqrs Tip T jq Tkr Tls e p  eq  er  es d 

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un Sijkl 

and

2



(16)

cr

cr

0

 S pqrs Tip T jq Tkr Tls e p  eq  er  es d 

(17)

The transformation matrix is given by [58]  cos T    sin 

sin    cos 

The components of the Eshelby tensor depend on the crack aspect ratio c/a0 and can be found in detail in [58].

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ACCEPTED MANUSCRIPT Crack healing can only occur if the shell of the capsules can be ruptured by the propagating cracks and the released adhesive can fill the cracks. Therefore, the volumetric fraction of the healed cracks Vh is related to the two mechanisms through (18)

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Vh  f cr ,  

where  characterizes the filling ability of the adhesive due to capillary flow, which is mostly

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influenced by the crack size, connectivity, etc. [71-72], and thus cannot be described by an explicit mathematic formula. However, it can be determined by experiments assuming the cracks are randomly and uniformly distributed in the matrix. This gives the volumetric

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proportion of cracks absorbing adhesive due to capillary force with respect to the total volume of cracks, i.e., Vw Vf

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

(19)

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where Vw and V f are the crack volumes determined by absorption and vacuum saturation,

Eq.(18) becomes

  

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Vh  cr  Vw     V f Vf 2

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respectively, as reported in the experimental section below.

(20)

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The capsule breakage is greatly dependent on the mechanical fracture properties of the capsule int  s , the matrix K IC , and, most of all, the interface K IC between the capsule and the matrix as K IC

described by

int s min  K IC ,K IC   KIC .

(21)

Assuming this precondition is fulfilled in the present study, the healing efficiency is then closely related to the proportion of cracks filled by the adhesive as influenced by both the crack extension and the capillary flow. The parametric study of

hom

has been performed following Eq.(2)~(20) and considering the

elastic properties of the adhesive as they relate to



, the volume of the microcapsules V ,

the total volume of the induced cracks V f , the volume of healed cracks Vh (related to Vw and

 cr ), the level of load applied  /  0 (which determines  cr ), and the healing index P . For 8

ACCEPTED MANUSCRIPT this, V f and Vh (or Vw ) need to be known, and they have been equivalently determined by vacuum saturation and water absorption, respectively, as described in the following.

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3 Experimental program

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Cement paste specimens containing microcapsules were used to verify the theoretical estimations. For comparison, specimens without microcapsules were prepared to determine the

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filling capability of the adhesive due to capillary action. In general, the same specimens should be used for all tests. Indeed, the release of the adhesive occurred instantaneously once the capsules were broken. Therefore, the specimens with microcapsules could not be used for the absorption test right after flexural loading because it takes time for the side surfaces to become

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sealed prior to the absorption tests [73]. Furthermore, water was used instead for the absorption tests because the epoxy resin will lose its flowability over time when exposed to atmosphere

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although it has a low viscosity (1.2×10-3 Pa·s at 25°C), which is similar to that of water. It should be noted that viscosity is not the only factor that affects capillary flow.

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3.1 Materials

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The poly(styrene-divinylbenzene) (St-DVB) microcapsules were previously prepared in the laboratory. These capsules enclosed the epoxy resin (E) that was used as the adhesive to achieve self-healing [74]. In general, benzylalcohol (BA) was used as the reactive St-DVB

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diluent. Monomers of styrene (St), divinylbenzene (BPO) and benzoylperoxide (BP) were the polymerization triggers. Additional surfactants, including sodium dodecylbenzene sulfonate (SDBS), octylphenol ethoxylate (OP-10) and potassium peroxydisulfate (PP), were also

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obtained for encapsulation. All of the solvents were of analytical grade. All of the paste specimens were made with ordinary Portland cement (Type I) and tap water from the lab. 3.2 Preparation of microcapsules [74] The epoxy was first mixed with BA (14 wt%) in a 250-ml three-neck round-bottomed flask for dilution. A aqueous surfactant solution of SDBS (4 wt%) and OP (4 wt%) and 2.8 times the amount of epoxy were added to the flask and mechanically stirred to form a well-dispersed solution. The solution was gradually heated to 75°C and maintained at this temperature for 1 h. While still at this temperature, the mixture of St, BPO and BP was then added to this solution. Air in the container was then replaced by argon through an opening in the flask with the help of a vacuum pump. The temperature was maintained for 5 h for synthesis. PP (1 wt%) was then added and allowed to react for 3 more hours. In this way, a microcapsule emulsion with a concentration of 30% by mass was obtained. The typical proportion of epoxy resin to St-DVB 9

ACCEPTED MANUSCRIPT is 9:1 by mass. The microcapsules are 50~500 µm in diameter with the most likely size of 200 µm. 3.3 Preparation of self-healing cement paste containing microcapsules

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Cement paste with 0.42w/c was used as the host matrix material. Up to 2 wt% of

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microcapsules was added to the cement paste, which is equivalent to approximately 4 vol%.

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Specimens without microcapsules were prepared for reference. The prism specimens with dimensions of 40 mm × 40 mm × 160 mm were cast and cured under standard conditions (20°C ± 2°C, ≥95% RH) until 90 d prior to the test.

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3.4 Testing procedures

The flexural strength, denoted by f, was first measured via the 4-point bending test according

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to ASTM C348 [75]. The remaining specimens were preloaded at a certain level of f, i.e., 0% (intact), 30% and 60%, respectively, to induce internal cracks. The healed cracks and ruptured microcapsules were observed to ensure that the preload is high enough to induce the healing

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mechanism [74]. Then, the load was removed, and the specimens were set aside in a room

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(18~25°C, 60~70% RH) for 1 d to allow the healing to occur. The specimens were reloaded the following day until failure, and the load-displacement curve was recorded for the initial

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state and after the healing of the cracks. The reference specimens were grouped into two collections: one for reloading to measure the mechanical response as described above and the other where the middle sections (40 mm × 40 mm × 40 mm) were cut for absorption tests in accordance with ASTM C1585 [73]. After that, the specimens were dried at 50°C for 2 d

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before the vacuum saturation measurements. A schematic illustration of the test setup is shown in Figure 2. The cubic blocks were placed in the container with the sides that experienced the tensile stressed submerged in water for the water absorption tests. Overviews of the different tests series are given in Table 1.

(a)

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ACCEPTED MANUSCRIPT Figure 2. Schematic illustration of the test setup for (a) the 4-point bending test and (b) the water absorption measurements. Table 1 Overview of the different flexural loading test series. Number of specimens 4* 10** 10** 4* 10** 10**

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Fraction of Level of load microcapsules (%f) (wt%) AH0f0 0 0 Reference AH0f30 specimens (no 0 30 microcapsules) AH0f60 0 60 AH2f0 2 0 Specimens with AH2f30 2 30 microcapsules AH2f60 2 60 * ** for absorption. 6 for reloading and 4 for absorption. Description

4 Results and discussion

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4.1 Experimental results

The water absorbed in volume per exposed surface area versus the square root of time is

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plotted in Figure 3 for two preload levels, i.e., 30%f and 60%f. The curves can be divided into

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two distinct stages, i.e., the initial absorption within the first 6 h and the secondary absorption after 6 h. Not surprisingly, a higher preload led to more absorbed water, particularly for the secondary absorption. It should be noted that the polymeric healing agent can flow from the

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stress-ruptured reservoir into discrete cracks due to capillary action, followed by polymerization of the healing agent, which reattaches to the failed surfaces. It usually requires a certain amount of time for the process to complete. The epoxy resin used in the present study

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can solidify within 1 d [74]. Furthermore, the resins released from the capsules preferentially flowed into the voids with smaller widths because the capillary force increases with decreasing void radius. Considering the instantaneous and limited release of the adhesive, only the initial absorption within the first 6 h of the formation of the cracks was considered as the maximum absorptivity that the healing agent can achieve. It is noteworthy that part of the agent will be absorbed by the pores of the matrix; this effect was taken into account by comparing with the reference, as explained in the following. The total void volume was measured with respect to the size of the specimen using the vacuum saturation technique, as shown in Figure 4. The volume of the voids increased with the applied load because more cracks were induced as the load increased. The void volume includes both the induced cracks and the initial void volume. For the theoretical experiment, it is assumed that the initial volume voids remains the same for all specimens, and thus, the water absorbed by the cracks can be determined by subtracting the amount of water absorbed by the reference 11

ACCEPTED MANUSCRIPT sample (without the application of an external load) from the value obtained for the cracked

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specimens.

Figure 4 Relative void volume as determined

absorption.

by the vacuum saturation technique.

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Figure 3 Effect of the applied load on water

Figure 5 shows the result for the cracks filled within the first 6 h, assuming that the initial void volume remains the same for the specimens prior to loading. Pre-loading with 30%f and 60%f

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led to a similar absorption performance up to 40 s1/2. The specimens pre-loaded with 60%f exhibited a higher absorptivity after that. This result illustrates the common combined effect of

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cracks induced by the two levels of load, i.e., the amount and size, on the absorption at a certain stage. A further increase of the load led to the continuous growth of the cracks as well

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as the initiation of new cracks. This contributed to a higher absorptivity over time. An unexpected decrease in the amount of absorbed water was observed in the interval from 40 to 60 s1/2. This can possibly be attributed to a deviation in the initial void volume from that of the reference. Further work is in progress to better understand this result.

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ACCEPTED MANUSCRIPT Figure 5 Amount of water absorbed by the induced cracks within the first 6 h. Table 2 summarizes the volumetric fraction of the added cracks as determined after 6 h of

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water absorption and using the vacuum saturation technique for analysis. The difference

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between the two results is considered to be the volume of the unhealed cracks.

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Table 2 Volumetric fraction of induced cracks used as input for the analysis. 30%f 0.006437 (0.016161)1

60%f 0.011541 (0.021265)

0.014301 (0.035465)

0.024331 (0.045495)

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Description ( Vw ) Volume obtained after 6 h of water absorption ( V f ) Volume by using the vacuum saturation

1 The value between the brackets denotes the sum of the cracks and the initial void space.

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4.2 Theoretical estimation

Table 3 lists the mechanical properties used as input parameters for the analysis. Unless stated

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otherwise, the fracture toughness K IC and the crack aspect ratio b / a0 are taken as 1.002MPa  m for plane strain and 0.01, respectively. It should be noted that the size

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follows a normal distribution, and the microcapsules with 150~200 µm take a proportion of approximately 70% by volume, although the full distribution was 50~500 µm in diameter. A

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single size (i.e., 200 µm) was used in the model because the microcapsules with the largest size are supposed to have the most compromised mechanical properties. Therefore, the analytical results could provide a lower limit for the mechanical properties of the matrices, which can be used as criteria in material design. Table 3 Mechanical properties of each phase used as input for analysis. Elastic modulus (MPa) Poisson’s ratio Host matrix 15000 (Es) 0.25 (νs) Cracks healed by the 3080 (Eh) 0.25 (νh) adhesive Unhealed cracks 0 (Eun) 0 (νun) Adding the microcapsules can influence the mechanical properties of the matrix material. Figure 6 shows the normalized Young’s modulus obtained by the theoretical prediction for V f  0 . The theoretical result is in good agreement with the experimental result and correctly 13

ACCEPTED MANUSCRIPT reproduces the trend of a diminishing Young’s modulus as the volumetric fraction of the microcapsules increases. According to this result, the microcapsule content should be below 4

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vol% to ensure that at least 90% of the Young’s modulus of the matrix is retained.

Figure 6 Comparison of the estimated Young’s modulus with the corresponding values obtained from the experiments.

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Figure 7 shows the effect of load-induced cracks on the anisotropy for V  0 . The ratio of the direct stiffness components in the x- and y-directions, i.e., (

hom

)22 / (

hom

)11 , is plotted versus

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the applied load (  ) and normalized to the critical load (  0 ), i.e., the load leading to fracture at θ=0, for the various Young’s moduli of the healing agent with respect to the Young’s

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modulus of the cement matrix, i.e., the Eh/Es ratio. The plot exhibits two distinct trends with a remarkable turning point at  /  0 of approximately 1~2. The value of (

hom

)22 / (

hom

)11

remains one when the applied load does not exceed the critical load because crack propagation is not initiated. Thus, the specimen remains in an isotropic state as long as the cracks are randomly oriented. Both crack generation and healing contribute to the anisotropy of the material. A sharp increase in (

hom

)22 / (

hom

)11 can be observed once  /  0  1 within a comparatively short range up to a

peak value, followed by its decrease with an increase of  /  0 . Furthermore, a closer look at the plot shows that the curves obtained for Eh/Es ≥0.4 exhibit a progressive transition. Eh/Es ≤ 0.3 results in remarkable anisotropy as demonstrated by the deviation of ( 14

hom

)22 / (

hom

)11

ACCEPTED MANUSCRIPT from one, where the recovered Young’s modulus becomes so insignificant that the

(

hom

)22 / (

hom

)11 ratio is strongly dependent on  /  0 . When Eh/Es =0.4, a critical hom

)22 / (

hom

)11

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combination of crack generation and healing is passed, as indicated by (

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decreasing to approximately one with  /  0  10 , beyond which a healing agent with a higher

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Young’s modulus (Eh/Es ≥0.5) contributes to the recovered modulus and anisotropy due to the increasing mismatch between the Young’s moduli of the two phases.

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Figure 8 shows the effects of crack healing on the anisotropy. The volumetric fraction of cracks in the matrix is assumed to be equal to that of the microcapsules, i.e., Vf=Va, for the case of the

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maximum healing capability that is dependent on the amount of healing agent available. One striking feature is that the healed cracks do not influence (

hom

)22 / (

hom

)11 as much as the

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total cracks, or rather the prehealing cracks, with increasing Vf. The specimen remains isotropic

(

hom

)22 / (

hom

TE

up to 10% Vf when all of the cracks are healed, and then, a minor decrease in

)11 can be observed as Vf increases further. The (

hom

)22 / (

hom

)11 ratio exhibits

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considered.

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a greater change when Vf increases to more than 5% if only the prehealing cracks are

Figure 7 Anisotropic trend changes under the

Figure 8 Anisotropic trend as a function of

applied load for adhesives with different

the number of cracks for different healing

mechanical properties.

conditions.

15

ACCEPTED MANUSCRIPT Figure 9 shows the bulk modulus and shear modulus normalized to the corresponding values of the cement matrix, i.e., K/Ks and µ/µs, for the assumed minimum and maximum healing

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efficiencies, i.e., the cracks either remain all open or are all closed. The volumetric fractions of

IP

the cracks and the microcapsules are assumed to be equal. Both the bulk modulus and the shear

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modulus cannot be perfectly restored even if all cracks are healed. As expected, if the cracks remain all open, the mechanical characteristics exhibit a certain decrease in value, with the bulk modulus showing a much greater reduction than the shear modulus. For the healing agent

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used in the present work, the volumetric fraction of microcapsules or cracks should not exceed

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4 vol% to ensure that the remaining modulus is higher than approx. 90%, even if the cracks cannot be reattached at all. If the volume of the cracks is higher than that of the adhesive

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D

provided by the capsules, a further decrease of the mechanical characteristics will result.

(a)

(b)

Figure 9 Estimated modulus for various assumed healing efficiencies: (a) the bulk modulus, (b) the shear modulus. Figure 10 shows the stiffness normalized to that of the host matrix with microcapsules only, denoted by (C hom )11 /(C hom, )11 , for various healing efficiency ratios. It shows the upper and lower bounds of (C hom )11 /(C hom, )11 , which correspond to P = 1 and P = 0, respectively. The embedded plot on the right shows the healing index corresponding to the maximum healing efficiency, where the maximum volume of the healing cracks should not exceed the volume of the available adhesive, which is equivalent to the volume of the added microcapsules, i.e., 4 16

ACCEPTED MANUSCRIPT vol% (Va), because the simulation of the thickness of the capsule wall is ignored. Thus, the healing volume is kept at 4 vol% when the volume of cracks exceeds that of microcapsules, i.e.,

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for Vf > Va. The same assumption is made for P = 0.7, where the volume of the cracks is more

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than that of the microcapsules as the total volume of cracks increases to approximately 6 vol%,

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beyond which the upper bound should be considered a limit of the restored Young’s modulus instead of its linear extension as highlighted by the green dashed line in Figure 10.

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The (C hom )11 /(C hom, )11 ratio estimated according to the filling degree, which is determined by measuring the water absorption and vacuum saturation and listed in Table 2,

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agrees well with the stiffness recovery obtained experimentally with a certain standard deviation as marked by the error bar. Furthermore, the results, as determined either

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theoretically or experimentally, are close to the values obtained for P = 0.4 and 0.2, highlighted

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by the red dashed line and the blue dashed line, respectively. This indicates that the induced cracks were only partially healed depending on the limited flow of the healing agent and its

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mechanical properties and corresponding to a healing efficiency P of 0.2~0.4 for the conditions

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in the present study.

Figure 10 Comparison of the estimated stiffness with the experimental values. 5 Conclusions The dependence of the effective properties of microencapsulation-based self-healing cement matrices on the mechanical properties of the adhesive and the proportion of the cracks to be 17

ACCEPTED MANUSCRIPT healed has been investigated in this study by employing the Eshelby theory. The proportion of the cracks to be healed, determined by both of the flowability of the adhesive through capillary action and the total volume of the load-induced cracks in the system, was determined by measuring the water absorption and vacuum saturation of precracked specimens. The stiffness

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recovery was experimentally determined to validate the analysis. The following conclusions

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can be drawn:

1. For the healing agent used in the present work, the microcapsules or cracks should not exceed 4 vol% to ensure that approx. 90% of the modulus remains even if the cracks

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cannot be reattached at all.

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2. Both types of cracks, i.e., healed and unhealed, contribute to the anisotropy of the matrix. With an increasing volumetric fraction of cracks, the healed cracks do not influence the hom

)22 / (

hom

)11 ratio as much as the prehealed cracks.

D

(

TE

3. The elastic modulus of the adhesive exhibits a more significant influence on the anisotropy with increasing  /  0 . The case where  /  0  10 and Eh/Es=0.4 passes a critical

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combination of crack generation and healing. 4. The stiffness estimated using the filling proportion determined by the absorption and

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vacuum saturation measurements is in good agreement with that determined by the experiments. This result indicates that the cracks were partially healed depending on the limited flow of the healing agent and its mechanical properties and corresponding to a healing efficiency index P of 0.2~0.4 for the present conditions. Acknowledgements

The authors gratefully acknowledge the financial support provided by the National Natural Science Foundation of China (51308407, 51208296), the Opening Funds of State

Key

Laboratory

of

High

Performance

Civil

Engineering

Materials

(2014CEM009), the Fundamental Research Funds for the Central Universities 18

ACCEPTED MANUSCRIPT (2013KJ095), the Open Funding of the Key Laboratory of Advanced Civil Engineering Materials of Jiangsu (CM2014-02), and the National Key Project of Scientific and

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Technical Supporting Programs of China (No. 2014BAL03B02).

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[71] Hall C, Hoff WD. Water in porous materials. In: Water-Transport in Brick, Stone and Concrete, Taylor & Francis, Abingdon, Oxon, 2002: 29–41.doi: 10.4324/9780203301708_chapter_2 [72] Hanžič L, Kosec L, Anžel I. Capillary absorption in concrete and the lucas-washburn equation. Cem Concr Compos 2010; 32(1): 84–91. doi: doi:10.1016/j.cemconcomp.2009.10.005 [73] ASTM C1585-04. Standard test method for measurement of rate of absorption of water by hydraulic-cement concretes. West Conshohocken, PA: ASTM International, 2004. [74] Li W, Jiang Z, Yang Z, Zhao N, Yuan W. Self-healing efficiency of cementitious materials containing microcapsules filled with healing adhesive: mechanical restoration and healing process monitored by water absorption. PLoS ONE 2013; 8(11): e81616. doi: 10.1371/journal.pone.0081616 [75] ASTM C348-08. Standard Test Method for Flexural Strength of Hydraulic-Cement Mortars. West Conshohocken, PA: ASTM International, 2008. [76] El-Hadek MA, Tippur HV. Simulation of porosity by microballoon dispersion in epoxy and urethane: mechanical measurements and models. J Mater Sci 2002;37(8):1649-60.doi: 10.1023/A:1014957032638

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Graphical Abstract

24

ACCEPTED MANUSCRIPT Highlights 1. A framework for modeling the effective mechanical properties of microencapsulation-based

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self-healing matrices was proposed.

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2. Capsules or cracks should not exceed 4 vol% to ensure 90% of the modulus preserved. 3. Both crack generation and healing contribute to the anisotropy of cement matrices.

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4. Elastic modulus of adhesive has a more significant influence on the anisotropy as applied load increases.

25