Finite Element Model for Mode II Fracture of CFRP.pdf

Finite Element Model for Mode II Fracture of CFRP-Concrete Interface using Cohesive Behavior Model Author: Mostafa Yossef Course: EM564 – Fracture and Fatigue Submitted to: Dr. Wei Hong ABSTRACT The rehabilitation and retrofit of concrete structures using externally bonded Fiber Reinforced Polymer (FRP) strips has been gaining acceptance in engineering practice. An important design issue is the interface bond performance, particularly under flexure due primarily to Mode-II fracture. Extensive research has been conducted to characterize the fracture energy release rate (G) and traction-separation law, or shear stress-slip relationship, at FRP-concrete interface. The most common experimental approach is to record the strain field on the bonded FRP strip when subjected to axial load, and this approach can be termed as strain-base method. Imani et al. (2013) presented a displacement-based method to obtain the fracture energy and tractionseparation law, by measuring the applied load and displacement at the end-notch of the test specimen, and thereby reducing the effort associated with strain-field measurements. The derivation of the displacement-based method is presented based on J-integral approach. This report/paper presents Finite Element (FE) model using ABAQUS to validate numerical model developed by Imani et al. (2013). The FE model is based on Cohesive Zone Model (CZM). A good correlation is observed between the FE results and the numerical results. 1. INTRODUCTION For the last two decades, general attention has been increased towards the function of fiber reinforced polymers (FRP) in concrete structures. There is a trend to replace the reinforcement steel in the concrete structures with FRP due to FRP’s light weight and its non-corrosion property which can provide longer life span for structures. FRP is known as high strength fibers such as (carbon, glass, aramid, etc.) embedded into resin such as (polyester, epoxy, etc.) which can achieve a strength similar to that of steel. In December 2013, annual Federal Highway Administration (FHWA) statistics revealed that 14% of all bridges in the US are structurally deficient, which amounts to 27,897,850 mi2, and

36% of the US bridges are functionally obsolete. That leads that repairing all structurally deficient bridges is a necessity to avoid catastrophic failures. For the last 100 years, steel has been widely accepted for repairing structures, although the disadvantage of the steel as a corrosive material which affect the bond between the steel plate and concrete, moreover the heavy weight of the steel comparing to FRP leads to urge of replacing the steel with FRP, specifically in repairing concrete structures. Ease and speed of construction, resistance of corrosion, low cost of application and maintenance are factors that help FRP to replace steel. Several Researches started at the late 90s to investigate the FRP-concrete fracture. Suo and Hutchinson (1990) claimed that FRP-concrete interface fracture is based on mixed mode fracture. Although, Yuan et al. (2004) concluded that if FRP and concrete are subjected to axial forces, mode II can be considered as the only mode affecting fracture, and other modes can be neglected. Extensive research has been done in this topic, Högberg (2006); Wang (2006), (2007); Xu and Needleman (1993) analyzed different fracture modes using Cohesive Zone Model (CZM). Various traction-separation law was presented including linear, bilinear, and nonlinear models. Imani et al. (2013) developed analytical model to obtain the fracture energy and tractionseparation law based on J-integral approach. This paper will present a summary for Imani et al. (2013) model, and finite element model developed to verify this model. 2. ANALYTICAL MODEL

The J-path integral introduced by Rice (1968). The J-integral is defined as:

 u   J   Wdz  T . ds  x  

(1)

Based on this equation Imani developed a relation between the load and the slip: N  A(e B  1)

(2)

relation between shear stress and load and slip was presented as follows:



h  dN  N  EA2  d  

(3)

From equation (2) and (3), relation between shear stress and slip can be presented as follows:

  A(e B  1)e B

(4)

3. EXPERIMENTAL MODEL To obtain the empirical constants A and B, an experimental tests has been conducted by Imani et al. (2013), where a concrete substrate was designed as a 13×5×4 in3 prism, and the FRP laminate to be 6.3×1.8 in2. Load and slip was measured using LVDT as shown in Figure 1. Load-slip curve was plotted as shown in Figure 2 where A, and B were obtained by regression analysis to be -2488.6 and -187.08 respectively. 4. FINITE ELEMENT MODEL A finite element model is created to validate the analytical model derived by Imani et al. (2013). Commercial finite element package ABAQUS (2013) was used to create a 2D model, where similar dimension to the experimental model has been adopted. 4.1. GEOMETRY Plain strain element with four nodes (CPE4) was chosen in both concrete and FRP parts. FRP thickness is 0.02 in and width 1.8125 in and 10.8125 in long where 4 in a free cantilever, 1.5 in as notch, and 6.3125 in long connected to the concrete. Concrete is 4 in height and 7.8125 in long, and 5 in thickness. A mesh was created that varies from 0.5 in at the edges to 0.002 in at the crack tip. Due to the large number of element created and to increase the computational time, the concrete substrate was shortened to be 7.8125 in instead of 13 in long. Figure 3 shows both experimental geometry and adopted FE mesh.

Concrete prism

Constraint

FRP

Traction by MTS

Figure 1 – Test Setup (Imani, et. al 2013)

Figure 2 – Load – Slip curve (Imani, et. al 2013)

Figure 3 – (a) Experimental specimen dimensions, (b) FE meshed model 4.2. MATERIAL According to the developed analytical model derived by Imani et al. (2013), the material is assumed to be linear elastic. Young’s modulus of concrete and CFRP were taken 3,842,515 psi and 10,725,000, psi respectively. Poisson’s ratio were assumed as 0.15 and 0.3 for concrete and

CFRP respectively. The bond between the adhesive material and the concrete is taken the concrete tensile strength which is equal 620 psi as it’s lower than the strength of the adhesive material strength and most likely the bond will fall at. Table 1 shows a summary of the material properties that has been used in this model. Table 1 – Material Properties used in FE model Concrete

CFRP

Modulus (psi)

3,842,515 (26.5 GPa)

10,725,000 (74 GPa)

Poisson's ratio

0.15

0.3

4.3. FRACTURE MODEL The fracture model used is Cohesive Zone Model (CZM) where cohesive behavior interaction was chosen in ABAQUS to represent mode II fracture between the concrete and the CFRP interfaces. ABAQUS divides the cohesive model into three parts: Traction-separation behavior, damage initiation, and damage evolution. The empirical constant values of A and B were adopted from the experimental and substituted in equation (4) and traction-separation curve was plotted as shown in Figure 4. The initial slope of the curve (K) was calculated as 155,089 lbf/in3. For the damage initiation part, maximum shear was taken as 620 psi which explained previously as the bond strength between concrete and CFRP. Finally for damage evolution section, Gf was calculated according to equation (5) equal 6.22 Ibf/in which is derived also by Imani et al. (2013), and exponential softening was adopted to simulate the same softening as Figure 4.

1 N max 2 Gf  t 2 2 AE (5)

700

Shear Stress (psi)

600 500 400 300 K

200 100 0 0

0.01

0.02

0.03

0.04

Slip (in) Figure 4 – Traction separation curve obtained by analytical model derived by Imani et al. (2013) 4.4. ANALYSIS

The model was run using implicit dynamic analysis due to the conversions problem that faced the same model when it was run as general static analysis. 3000 lb ramp load was applied at the end of the FRP and the concrete part were restrained from the left and right side. Maximum increment step was set as 0.001 to capture the change in slip and shear stress at small load rating. 5. RESULTS AND DISCUSSION For 583 step, the loading stop at maximum load 2717.7 lb. load and slip at the crack tip values were exported and plotted verses the load-slip curve obtained from equation (2) using the same empirical constant values obtained from the experimental as shown in Figure 5. A good correlation was achieved between both curves. Figure 6 shows the traction separation curve exported from the FE model verses the tractionseparation curve obtained from equation (4). Both curves shows a good correlation between the analytical model and FE results. Shear stress is plotted with the distance away from the crack tip as shown in Figure 7. It can be noticed that the curve follows one over square root the distance away from the crack tip.

Moreover, intermediate step was chosen to show the scalar stiffness degradation as shown in Figure 8, where the process zone is shown as green and cyan colors.

3000 2500

Load ( lbf)

2000 1500 1000

FE Theoritical Equation

500 0 0

0.005

0.01

0.015

0.02

0.025

Slip (in)

Figure 5 – Load-Slip at the crack tip for FE and analytical results 800 700

Shear Stress (psi)

600

Theoretical Eq.

500

FE

400 300 200 100 0 0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

Slip (in)

Figure 6 – Shear Stress – Slip at the crack tip of both FE and analytical results

600

Shear Stress (psi)

500

400

300

200

100

0 0

1

2

3

4

5

6

7

Distance from the crack tip (in)

Figure 7 – Shear Stress verses distance away from the crack tip

Figure 8 – Scalar Stiffness Degradation 6. CONCLUSION AND RECOMMENDATIONS In this paper, a FE model is proposed to obtain the traction-separation law for FRP-concrete bonded interface. This model has validated successfully the analytical model derived by Imani et al. (2013) to evaluate the interfacial behavior. The model can be used in further research

including plastic behavior of concrete where concrete damaged plasticity can be adopted to simulate the actual behavior of the concrete. Also further research is needed to study the factors affecting the empirical constants and whether it can be obtained numerically or not. 7. REFERENCES Högberg, J. L. (2006). “Mixed mode cohesive law.” International Journal of Fracture, 141(3-4), 549–559. Imani, F. S., Ray, I., Chen, A., and Davalos, J. F. (2013). “Exploratory Study on Mode II Fracture Evaluation of CFRP-Concrete Interface by a Displacement-based Approach.” Proceedings of American Society for composites 2013 Twenty-Eighth Technical Conference, State College, Pennsylvania. Rice, J. R. (1968). “A Path Independent Integral and the Approximate Analysis of Strain Concentration by Notches and Cracks.” Journal of Applied Mechanics, 35(2), 379. Suo, Z., and Hutchinson, J. W. (1990). “Interface Crack between Two Elastic Layers.” International Journal of Fracture, 43, 1–18. Wang, J. (2006). “Debonding of FRP-plated reinforced concrete beam, a bond-slip analysis. I. Theoretical formulation.” International Journal of Solids and Structures, 43(21), 6649– 6664. Wang, J. (2007). “Cohesive zone model of FRP-concrete interface debonding under mixed-mode loading.” International Journal of Solids and Structures, 44(20), 6551–6568. Xu, X.-P., and Needleman, A. (1993). “Void nucleation by inclusion debonding in a crystal matrix.” Modelling and Simulation in Materials Science and Engineering, 1(2), 111–132. Yuan, H., Teng, J. G., Seracino, R., Wu, Z., and Yoa. J. (2004). “Full-range Behavoir of FRP-toConcrete Bonded Joints.” Engineering Structures, 26, 553–565.