# Flexible Adhesive in Composite-to-Brick Strengthening—Experimental and Numerical Study

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Laboratory Tests

#### 2.1. Materials and Specimen Preparation

^{2}, 1800 g/m

^{2}and 2000 g/m

^{2}, respectively. Additionally, pultruded CFRP laminate, also 50 mm-wide (a half of Sika CarboDur S1012 laminate) and 1.2 mm-thick, was used in the tests [43] (Figure 1d). The mechanical properties of epoxy and polyurethane adhesives were obtained from the producer’s data sheets. The main mechanical properties of the adopted materials are given in Table 1.

#### 2.2. Test Set-Ups and Experimental Procedure

#### 2.3. DIC

_{f}is the luminosity of the reference subset and μ

_{g}is the luminosity of target subset.

#### 2.4. SLST Results

_{max}, the calculated average value of the maximum force F

_{max.av}, corresponding coefficient of variation CoV, the maximum experimental tensile stress in the reinforcement σ

_{max}, exploitation ratio η. All parameters were computed with reference to the cross-sectional area of the reinforcement. The exploitation ratio η, was defined as σ

_{max}over the tensile strength of the related reinforcement (see Table 1).

## 3. Numerical Analysis

#### 3.1. Material Model Description for Polymer

_{10}and C

_{01}of the hyper-elastic material can be determined by using a uniaxial tension test. For consistency with the linear elasticity theory, in the limit of small strains, the Young’s modulus E

_{0}and the shear modulus G

_{0}can be expressed by the parameters C

_{01}and C

_{10}as follows:

#### 3.2. FEM Model Description of SLST

_{01}= 0.652 MPa and C

_{10}= 1.211 MPa, after [18]. In the case of the epoxy (Sikadur S330), the material was defined as the isotropic linear elastic (E = 4.5 GPa and ν = 0.29). The strips were modeled with C3D8R elements, and the materials were assumed to be isotropic linear elastic materials (E = 195 GPa, ν = 0.2 for SRP and E = 234 GPa, ν = 0.23 for CFRP). The brick was modeled using C3D8R elements and the isotropic linear elastic material (E = 5.76 GPa, ν = 0.2). The load of the SLST specimen was defined, as in the experiment, by the displacement rate of the strip (0.3 mm/min). The analysis for the C-E and S1/M-E specimens was linear, and for the C-PS and S1/M-PS specimens the analysis was fully nonlinear.

#### 3.3. Numerical Results for Shear Stress Distribution

_{max}for S1/M-E (Figure 15a); S1/M-PS (polyurethane PS) with F

_{max}for S-E (Figure 15b); and S1/M-PS (polyurethane PS) with F

_{max}for S1/M-PS (Figure 15c). This confirms the observations that stiff (epoxy) adhesives cause stress concentrations at the loaded end and activate the short effective bonding length.

#### 3.4. Numerical Results for Shear Strain Distribution

## 4. Discussion

#### 4.1. DIC Ability to Analyse Stiff and Flexible Adhesives in Composite Strengthening

_{max}(Figure 13 and Figure 14), allow for the observing of uneven changes in strain distributions (making failure process more understandable), which are unable to be noticed using traditional measurement devices. DIC confirms the observations obtained from strain gauges (see results for TS-1) that an effective transfer length of composites with flexible adhesive/matrix is longer than the bonding length of strengthening systems with a stiff epoxy adhesive/matrix.

#### 4.2. Differences in Work of Brick Specimens Strengthened with Composites Bonded on Stiff and Flexible Adhesives

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 1.**Textiles and laminates adopted in research: (

**a**) carbon textile; (

**b**) steel textile S1—detail; (

**c**) steel textile S2—detail; (

**d**) CFRP strip.

**Figure 3.**Manufactured single-lap shear test specimens—from left to right (3 in each group): CP-E, CP-PS, S2/S-E and S2/S-PT.

**Figure 4.**(

**a**) Test set-up TS-1 with supporting C-shaped steel frame; (

**b**) scheme with location of strain gauges and LVDTs, dimensions in mm.

**Figure 5.**Test set-up TS-2: (

**a**) side view; (

**b**) front view; (

**c**) detail—LVDTs. 1: Supporting L-shaped steel frame; 2. Tested specimen; 3. Loaded end of CFRP/textile; 4. LVDTs: L1—left one, L2—right one; 5. Stiffening rib; 6. Counterweight; 7. Camera for digital image correlation method (DIC); 8. Force transducer; 9. Ball-and-socket joint; 10. Aluminum guide rollers; 11. Testing frame; 12. Testing machine hydraulic clamp; 13. Aluminum section attached to loaded end of CFRP/textile; 14. LVDT holder-to-brick fastening.

**Figure 6.**(

**a**) principle of the Digital Image Correlation method; (

**b**) the artificial marker with indication of real dimensions—[30].

**Figure 7.**Possible failure modes for: (

**a**) externally bonded CFRP strips; (

**b**) textile wet lay-up systems on brick/masonry substrates.

**Figure 8.**Failure modes observed during the tests of CFRP strips: (

**a**) CP-E-2 failure mode type I; (

**b**) CP-PS-1 failure mode type I/IV; (

**c**) CP-PS-2 failure mode type III/IV; (

**d**) CP-PT-1 failure mode type I.

**Figure 9.**Failure modes observed during the tests of composites reinforced with steel textile S2: (

**a**) S2/S-E-2 failure mode type A; (

**b**) S2/S-PS-2 failure mode type A; (

**c**) S2/S-PS-5 failure mode type C; (

**d**) S2/S-PT-3 failure mode type A.

**Figure 12.**Envelope and mean distribution of strain profiles along bond at F

_{max}for tests TS-1: (

**a**) C-E specimens; (

**b**) C-PS specimens; (

**c**) S1/M-E specimens; and (

**d**) S1/M-PS specimens.

**Figure 13.**DIC (CivEng-Vision) maps of strains in y direction at 80% F

_{max}and 100% F

_{max}for specimens: (

**a**) CP-E-3; (

**b**) CP-PT-2; and (

**c**) CP-PS-2.

**Figure 14.**DIC (CivEng-Vision) maps of strains in y direction at 80% F

_{max}and 100% F

_{max}for specimens: (

**a**) S2/S-E; (

**b**) S2/S-PT-1; (

**c**) S2/S-PS-1.

**Figure 15.**Shear stress distributions computed for: (

**a**) S1/M-E with F

_{max}for S1/M-E; (

**b**) S1/M-PS with F

_{max}for S1/M-E; and (

**c**) S1/M-PS with F

_{max}for S1/M-PS.

**Figure 16.**Shear strain distributions computed for: (

**a**) S1/M-E with F

_{max}for S1/M-E; (

**b**) S1/M-PS with F

_{max}for S1/M-E; and (

**c**) S1/M-PS with F

_{max}for S1/M-PS.

**Figure 17.**Load-slip response curve provided by LVDT and DIC measurement methods in the shear bond test on: (

**a**) CFRP laminates and (

**b**) steel fiber textile S2; (RMSE—root mean square errors of LVDT and DIC comparison).

**Figure 19.**Average failure load (F

_{max,av}) versus modulus of elasticity of adopted adhesive (E

_{adh}) for various textiles/laminates (C-carbon textile, S1, S2—steel textiles, CP—CFRP strip).

**Figure 20.**Comparison of load-slip curves from experimental tests (TS-1) and numerical analysis: (

**a**) carbon fiber reinforced composite C and (

**b**) steel fiber reinforced composite S1.

**Figure 21.**Typical mean strain profiles along bonds at F

_{max}: (

**a**) experimental tests TS-1 and (

**b**) numerical analysis.

**Figure 22.**DIC (CivEng-Vision) maps of strains for specimens: (

**a**) S2/S-E-3 at a load F

_{max}(S2/S-E-3); (

**b**) S2/S-PS-1 at a load F

_{max}(S2/S-E-3); (

**c**) S2/S-PS-1 at a load F

_{max}(S2/S-PS-1).

**Figure 23.**DIC (CivEng-Vision) maps of strains for specimens: (

**a**) S2/S-E-3 at a load F

_{max}(S2/S-E-3); (

**b**) S2/S-PT-1 at a load F

_{max}(S2/S-E-3); (

**c**) S2/S-PT-1 at a load F

_{max}(S2/S-PT-1).

**Figure 24.**DIC (CivEng-Vision) maps of strains for specimens: (

**a**) CP-E-3 at a load F

_{max}(CP-E-3); (

**b**) CP-PS-2 at a load F

_{max}(CP-E-3); (

**c**) CP-PS-2 at a load F

_{max}(CP-PS-2).

**Figure 25.**DIC (CivEng-Vision) maps of strains for specimens: (

**a**) CP-E-3 at a load F

_{max}(CP-E-3); (

**b**) CP-PT-2 at a load F

_{max}(CP-E-3); (

**c**) CP-PT-2 at a load F

_{max}(CP-PT-2).

Material/Mechanical Property | Value |
---|---|

Clay Brick ^{1.} | |

compressive strength | 19.8 N/mm^{2} |

flexural strength | 3.66 N/mm^{2} |

splitting tensile strength | 2.46 N/mm^{2} |

Young’s modulus | 5760 N/mm^{2} |

Epoxy adhesive/Sikadur 330/ ^{2} | |

tensile strength | 30 N/mm^{2} |

Young’s modulus | 4500 N/mm^{2} |

strain at peak load | 0.90% |

Epoxy adhesive/Sikadur 30 Normal/ ^{2} | |

tensile strength | 26 N/mm^{2} |

Young’s modulus | 11,200 N/mm^{2} |

Polyurethane adhesive/PS/ ^{2} | |

tensile strength | 2.5 N/mm^{2} |

Young’s modulus | 16 N/mm^{2} |

strain at peak load | 45% |

Polyurethane adhesive/PT/ ^{2} | |

tensile strength | 20 N/mm^{2} |

Young’s modulus | 700 N/mm^{2} |

strain at peak load | 10% |

Carbon textile/FIDCARBON UNI 320 HT240/ ^{1} | |

tensile strength | 2735 N/mm^{2} |

Young’s modulus | 234,000 N/mm^{2} |

nominal thickness | 0.170 mm |

CFRP plate/Sika CarboDur S1012/ ^{2} | |

tensile strength | 2900 N/mm^{2} |

Young’s modulus | 165,000 N/mm^{2} |

plate thickness | 1.2 mm |

Steel textile S1/FIDSTEEL 3X2-B 12-12-500/ ^{1} | |

tensile strength | 2997 N/mm^{2} |

Young’s modulus | 195,000 N/mm^{2} |

nominal thickness | 0.231 mm |

Steel textile S2/Kerakoll GeoSteel G2000/ ^{3} | |

tensile strength | 3083 N/mm^{2} |

Young’s modulus | 183,000 N/mm^{2} |

nominal thickness | 0.254 mm |

Notation | No. of Specimens | Description of Strengthening System | Test Set-Up |
---|---|---|---|

C-E | 5 | carbon fiber textile embedded in epoxy based matrix Sikadur 330 | TS-1 |

C-PS | 5 | carbon fiber textile embedded in polyurethane PS matrix | TS-1 |

S1/M-E | 5 | steel fiber textile S1 embedded in epoxy based matrix Sikadur 330—glass mesh side towards the substrate | TS-1 |

S1/M-PS | 4 | steel fiber textile S1 embedded polyurethane PS matrix—glass mesh side towards the substrate | TS-1 |

CP-E | 3 | pultruded CFRP laminate bonded using epoxy based adhesive Sikadur 30 | TS-2 |

CP-PS | 3 | pultruded CFRP laminate bonded using polyurethane PS adhesive | TS-2 |

CP-PT | 3 | pultruded CFRP laminate bonded using polyurethane PT adhesive | TS-2 |

S2/S-E | 3 | steel fiber textile S2 embedded in epoxy based matrix Sikadur 30—steel cords side towards the substrate | TS-2 |

S2/S-PS | 3 | steel fiber textile S2 embedded polyurethane PS matrix—steel cords side towards the substrate | TS-2 |

S2/S-PT | 3 | steel fiber textile S2 embedded polyurethane PT matrix—steel cords side towards the substrate | TS-2 |

Type of Composite | Specimen | Failure Mode | F_{max} (kN) | F_{max.av} (kN) | CoV (%) | σ_{max} (MPa) | η (-) |
---|---|---|---|---|---|---|---|

CFRP | C-E-1 | A | 6.32 | ||||

C-E-2 | A | 7.71 | |||||

C-E-3 | A | 8.85 | 7.03 | 17.3 | 852 | 0.31 | |

C-E-4 | A | 6.05 | |||||

C-E-5 | A | 6.23 | |||||

CFRPU | C-PS-1 | - ^{1} | 12.73 | ||||

C-PS-2 | - ^{1} | 14.40 | |||||

C-PS-3 | C | 11.64 | 12.40 | 12.8 | 1503 | 0.55 | |

C-PS-4 | A | 10.18 | |||||

C-PS-5 | A | 13.05 | |||||

SRP | S1/M-E-1 | A | 6.66 | ||||

S1/M-E-2 | A | 5.76 | |||||

S1/M-E-3 | A | 6.91 | 6.78 | 9.6 | 597 | 0.20 | |

S1/M-E-4 | A | 7.53 | |||||

S1/M-E-5 | A | 7.02 | |||||

SRPU | S1/M-PS-1 | C | 11.06 | ||||

S1/M-PS-2 | A | 12.31 | 12.02 | 7.7 | 1059 | 0.35 | |

S1/M-PS-3 | A | 13.18 | |||||

S1/M-PS-4 | A | 11.53 | |||||

CFRP | CP-E-1 | I | 13.69 | ||||

CP-E-2 | I | 12.64 | 13.51 | 5.9 | 135 | 0.05 | |

CP-E-3 | I | 14.20 | |||||

CFRPU | CP-PS-1 | I/IV | 21.44 | ||||

CP-PS-2 | III/IV | 24.45 | 22.35 | 8.2 | 224 | 0.08 | |

CP-PS-3 | I | 21.16 | |||||

CFRPU | CP-PT-1 | I | 17.42 | ||||

CP-PT-2 | I | 16.62 | 17.48 | 5.1 | 175 | 0.06 | |

CP-PT-3 | I | 18.39 | |||||

SRP | S2/S-E-1 | A | 8.83 | ||||

S2/S-E-2 | A | 8.32 | 8.46 | 3.8 | 655 | 0.21 | |

S2/S-E-3 | A | 8.23 | |||||

SRPU | S2/S-PS-1 | C(D) | 15.80 | ||||

S2/S-PS-2 | A | 15.58 | |||||

S2/S-PS-3 | C | 16.07 | 15.16 | 6.6 | 1174 | 0.38 | |

S2/S-PS-4 | C | 14.75 | |||||

S2/S-PS-5 | C | 13.61 | |||||

SRPU | S2/S-PT-1 | A | 13.15 | ||||

S2/S-PT-2 | A | 14.31 | 13.81 | 4.3 | 1070 | 0.35 | |

S2/S-PT-3 | A | 13.96 |

^{1}Non-standard failure mode due to shear failure of the brick.

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Kwiecień, A.; Krajewski, P.; Hojdys, Ł.; Tekieli, M.; Słoński, M. Flexible Adhesive in Composite-to-Brick Strengthening—Experimental and Numerical Study. *Polymers* **2018**, *10*, 356.
https://doi.org/10.3390/polym10040356

**AMA Style**

Kwiecień A, Krajewski P, Hojdys Ł, Tekieli M, Słoński M. Flexible Adhesive in Composite-to-Brick Strengthening—Experimental and Numerical Study. *Polymers*. 2018; 10(4):356.
https://doi.org/10.3390/polym10040356

**Chicago/Turabian Style**

Kwiecień, Arkadiusz, Piotr Krajewski, Łukasz Hojdys, Marcin Tekieli, and Marek Słoński. 2018. "Flexible Adhesive in Composite-to-Brick Strengthening—Experimental and Numerical Study" *Polymers* 10, no. 4: 356.
https://doi.org/10.3390/polym10040356