Finite element delamination study of adhesively-bonded patchs used to repairs damaged jute fiber/polypropylene composites
A.Mokhtari1, M.Ould Ouali2, N.Tala-ighil1, A.Brick Chaouche1 1Welding and NDT Research Centre (CSC), PB 64 CHERAGA - ALGERIA.
2Laboratoire Elaboration, Caractérisation des Matériaux et Modélisation. Université Mouloud Mammeri de Tizi-Ouzou, BP 17 RP, 15000 Tizi-Ouzou.
*Corresponding author: [email protected]
Abstract
In this work, the mechanical behavior of repaired specimens is studied from both experimental and numerical viewpoints. Tensile testing of the specimens with defect, without defect and repaired is carried out.
The finite element method (FEM) model is utilized to simulate the mechanical behavior of the repaired specimen during the test. Cohesive Zone Model (CZM) was used to simulate the inter-laminar fracture of the composite, with the capability of simulating the damage initiation and evolution mechanisms of adhesives. The validations of the numerical results were carried out with the experimental results and are show to be in a good agreement.
Key words: PP/jute composite, damage, adhesive bonding, cohesive element.
1. Introduction
The composites reinforced natural fibers have a great potential as alternatives to traditional reinforcements such as glass fibers, for applications mainly in the automotive and packaging fields, for which the driving forces are primarily reduction of cost and of environmental impact. These composites are exposed at the damage (as an external shock), which do not significantly reduces the strength of these structures, that makes repairing very advantageous for cost saving and repair of these structures should be evaluated.
Most of the approaches for these structures are based on Finite Element Modeling coupled with strength of materials or fracture criteria, which have some limitations. The Cohesive Zone Methods are an appealing alternative to these methods, overcoming their limitations and exploiting their advantages, it can be applied to both linear and non-linear fracture mechanics and critical fracture criteria is defined as part of the element degradation properties. In composite laminates, the delamination between plies is the most common failure mode and it occur due to the presence of matrix cracks; the fracture of the adhesive layer is modeled by the traction–
separation laws [5–8]. The failure mechanism of a traction–separation law involves a three step process: Damage initiation, damage evolution and element removal [9]. This method is widely used to model delamination at the substrate/adhesive interface in bonded joints [10], but also to model interlaminar cracks in laminates [11].
In this study, we present experimental and numerical results concerning the tensile behavior of Composites reinforced natural fibers Double-strap repairs. The failure load with and without the defects and repair were considered. The patch detachment has been observed in the specimens repaired. In order to account for this behavior, Cohesive Zone Model (CZM) damage was used to simulate the inter-laminar fracture. A stress
analysis was performed to identify the critical regions of the repaired composite, leading to damage initiation.
Thereafter, the cohesive damage model is used to predict the failure modes and repair strengths of the adhesive layer. The resultants were compared with the experimental ones.
2. Theory of cohesive element model
Cohesive Elements Model (CZM) implemented in Abaqus [1], simulates the damage along this path by specification of a traction-separation response between initially coincident nodes on either side of the predefined crack path. In most of the CZM, the traction-separation relation for the interfaces are such that with increasing interfacial separation, the traction across the interface reaches a maximum (crack initiation), the decreases (softening) and finally, the crack propagates permitting a total de-bond of the interfaces. The whole failure response and crack propagation can thus be simulated. The theoretical is well described in [1] and [2]. The use of cohesive elements together with a bilinear traction separation law (Figure 1) is outlined below.
Figure 1. Schematic of a CZM for failure prediction of adhesively bonded joints.
The initial response of cohesive element is assumed to be linear until a damage initiation criterion is met (till point A). The penalty stiffness of the bi-linear traction-separation law is defined as
, (1)
Damage initiation criterion determined by the quadratic nominal stress was applied to predict the onset of the damage process at the interface. The damage initiates when the quadratic stress criterion (equation (2)) reaches a critical value ( 1). The strength of composite in the normal and shear directions are used as input data.
, , , (2)
Once the damage initiation criterion of the cohesive element is satisfied, the stiffness of the element is degraded. Equation (3) represents the stress composants of the traction-separation law are affected by the damage variable of the cohesive element.
A
B
!
"#$%
0
Delamination Initiation
Delamination propagation
"
Softening
" 1 ' ! , ( 1,2,3 (3) Where D is damage variable, which represented the overall damage in the material and captured effects all active mechanisms. It initially had a value of 0 when the interface is undamaged. After the initiation of damage, damage variable D evolved from 0 to 1 upon further loading (D =1 when the interface is fully damaged).
+,,, - +,,.+,,/
+,,- +,,, . +,,/ (4)
Where 0#$%referred to the maximum value of the effective displacement attained during the loading history. 0 and 0 1ere the effective displacement at complete failure and effective displacement at the effective displacement at damage initiation, respectively. The effective displacement was defined as [4].
0 2 34 3 (5)
The damage evaluation is governed by a damage parameter which describes the rate of stiffness softening after damage initiation ( ). The damage propagation ( ) is studied in terms of energy release rate and toughness. The energy-based mixed mode delamination growth law suggested by Benzeggagh-Kenane criteria [3], given in Equation (6) was used in this work.
56 556' 56 ! -789+ :7; /< 6 , 1(=> 3?0$@ 55 555 (6) Where 5 55 555 , A is a material parameter (A is chosen 1.45). 56, 556 and 6 are the fracture energies for mode I, mode II, and mixed mode loading respectively. 5, 55 and 555are the strain energy release rates for the mode I, mode II, and mode III respectively. In this criterion, fracture energy for first shear (mode II) and second shear directions (mode III) are the same, 556 555 .
3. Problem description
The material under study is a jute fabric reinforced polypropylene (PP) composite. One stacking sequence was used for composite plate, namely [0°, 90°]2S where (0°,90°) represents one layer of fabric. The manufacturing of specimens was produced by compression molding process at a temperature of 210°C and a pressure of 10 bars. This pressure is applied to force the material into contact with all mold areas, while heat and pressure are maintained until the molding material has cured. The advantage of this method is its ability to mold fairly intricate parts. All the fibers are aligned from the tension direction. The geometry of the repairs jute/PP laminate specimen is detailed in Figure (2). The thickness of the jute/PP laminate is 4.8 mm and thickness of the patch is 2 mm. The ply thickness is 1.2 mm, the length of the plate is 280 mm, and the width is 30 mm, and the diameter of the hole is 8 mm. The patch is quasi-isotropic with the lay-up [0°, 90°]2S . The ply thickness is 0.5 mm, the length of the plate is 30 mm, and the width is 30 mm. The patch is glued over the surface of the composite.
Figure 2. Geometry and dimensions of the specimen 4. Numerical simulation
Standard experimental tests (tension test) were carried with repair jute/PP specimens. The elastic properties and strengths, of the PP/jute laminate obtained experimentally, are presented in Table 1. The elastic properties of the patch laminate obtained experimentally, are presented in Table 2. The material parameters for the cohesive layer are reported in Table 3.
Table 1. PP/Jute – Mechanical properties
BCC (MPa) BDD(MPa) ECD(MPa) FCD
PP/Jute 1912 1878 979.8 0.27
Table 2. Material data of verre/epoxy– Mechanical properties
BCC (GPa) BDD(GPa) ECD(GPa) FCD
Verre/epoxy 45 12 4.5 0.34
Table 3. Cohesive layer properties
Strength data Critical energy release rate GH IJK! LM IJK! ENO P/RD! ENNO P/RD!
32 16 300 700
The numerical models presented below, reproduce the geometry of specimens that were tested. The objective is to determine the delamination onset and growth of adhesively-bonded patch observed
Side view
u
Cohesive surface Parch 1
Parch 2
4.8 mm 2 mm
hole imposed displacement
Top view
280 mm
30 mm
30 mm x
experimentally. The model was divided into 3 different parts: patch 1, patch 2 and a composite laminate with a circular hole (figure 2). The patch and the laminate with a hole were joined by cohesive surface. The cohesive surface is the simpler and less costly computationally contrary to cohesive elements. The cohesive elements needed to reproduce the adhesively-bonded patch delamination are implemented in Abaqus [1]. The elements type and the elements number used for the simulation are reported in Table 4.
Table 4. Elements type and number
Cohesive surface Jute/PP laminate with a hole Verre/Epoxy laminate (patchs) Element type Cohesive COH3D8 Elements C3D8 Elements C3D8
Number --- 4032 1445
The mesh parts and the assembly considered in the model are shown in figure 3.
Figure 3. Mesh of the whole model
All the models were meshed with three dimensional reduced integration elements (C3D8). The cohesive surface is used to contact between the patch and the laminate, was meshed with three dimensional elements (COH3D6). The contacts were defined with a coarse mesh to decrease the computing time. The laminate is fixed on one side and is subjected on the other side to a horizontal imposed displacement u of 2 mm. Damage models where material softening occurs are often generating convergence difficulties in standard ABAQUS. Therefore, it is useful to include artificial damping in the model in order to overcome these problems. In all models, a damping value of 3.10-4 was used. By comparison of the viscous damping energy with the total strain energy, it was verified that the artificial damping does not yields inaccurate solutions.
5. Results and discussion
5.1. The stress-strain curve of the laminate
The stress-strain curves are also compared with experimental results. Figure 4 gives the stress-strain results obtained experimentally of the laminate with and without defect (hole). Maximum stresses are 36 MPa for specimen without hole and 24 MPa for specimen with hole.
Figure 4. Experimental results for specimens with and without hole.
Figure 5 compared between experimental and numerical results obtained for repaired specimen with hole.
The numerical and experimental results are in good agreement.
Figure 5. A comparison between experimental and numerical results obtained for repaired specimen with hole.
The numerical results above verify that the model has enough accuracy to predict the delamination of adhesively-bonded patch of the composite structure reinforced natural fibers repairs under dynamic loading.
5.2. Damage analysis of the laminate
The damage occurred due to cohesive crack propagation in the repairs laminate (figure 6a). The propagation damage of the patch detachment observed in the specimens repaired is showed in figures 6b and 6c.
The parameter criterion CSDMG corresponds to the scalar stiffness degradation for cohesive surfaces for the hole damage of laminate (CSDMG = 0 relating to the undamaged material and CSDMG = 1 to complete failure).
The numerical results obtained for the damage evolution (patch detachment) correspond to the experimental observation of this phenomenon.
0 5 10 15 20 25 30 35 40
0 0.5 1 1.5 2
Strain (%)
Specimen with hole
Specimen without hole
0 5 10 15 20 25 30 35
0 0.5 1 1.5 2
Strain (%)
Numerical results Experimental
results
Figure 6. Propagation damage in the adhesive layer for a double-lap joint using CZM:
(a) damage initiation, (b) and (c) damage propagation to the inner region of the bond.
The patch damage started at locations where there are high strain concentrations. As this initial damage is very local it is assumed to hardly affect the overall stiffness. Due to this, the damage evolution speeds will be very low just after damage initiation. Only when the amount of damage becomes significant, the speed of damage evolution will increase rapidly. This means that the process of damage progression takes place relatively slow, and that there is a large difference between the composite strain at which patch damage is initiated and the strain at which it completely fails.
6. Conclusion
In this work, an experimental characterization of the mechanical response fiber-reinforced composites of jute under tension load was done. The onset and the growth of the delamination in notched repair laminates have been investigated and simulated using finite element analysis.
The Cohesive Zone Model (CZM) has been used to model the delamination onset and growth between the observed delaminated patch/composite. The model performance was evaluated by comparing with the experimental results, in terms of equivalent stiffness, of failure load of repairs and the failure of the patch.
The experimentally observed failures modes were also reproduced in the numerical analysis, in terms of the failure onset and progression in path/composite interface until failure.
REFERENCES
[1] ABAQUS version 6.7-1. ”User manual” Abaqus Inc., 2007
[2] Camanho, P.P.; Davila, C.G. Mixed-Mode Decohesion Finite Elements for the Simulation of Delamination in Composite Materials; NASA/TM-2002–211737, pp. 1–37, 2002
(a) (b)
(c)
[3] Benzeggagh, M. L.; Kenane, M. Measurement of Mixed-Mode Delamination Fracture Toughness of Unidirectional Glass/Epoxy Composites with Mixed-Mode Bending Apparatus; Composites Science and Technology, vol. 56, pp. 439–449, 1996
[4] Jiang, W.G.; Hallett, S.R.; Green, B.G.; Wisnom, M.R. A concise interface constitutive law for analysis of delamination and splitting in composite materials and its application to scaled notched tensile specimens;
International Journal for Numerical Methods in Engineering 69, 1982–1995. 2007
[5] Li, S; Thouless, M.D.; Waas, A.M.; Schroeder, J.A.; Zavattieri, P.D. Mixed-mode cohesive-zone models for fracture of an adhesively bonded polymer–matrix composite; Eng Fract Mech 73(1):64–78. 2006
[6] Shet, C.; Chandra, N. Analysis of energy balance when using cohesive zone models to simulate fracture processes; J Eng Mater Technol, 124(4):442–50. 2002
[7] De Moura, MFSF; al. Cohesive and continuum mixed-mode damage models applied to the simulation of the mechanical behaviour of bonded joint; Int J Adhes Adhes 28(8):419–26. 2008
[8] Alfano, M.; Furgiuele, F.; Leonardi, A.; Maletta, C. Paulino G.H. Mode I fracture of adhesive joints using tailored cohesive zone models; Int J Fract, 157(1–2):193–204. 2009
[9] ABAQUS. “Analysis users manual version 6.10,” Dassault Systemes Corp., 2013
[10] Crocombe, A.; al. Predicting the residual strength for environmentally degraded adhesive lap joints;
International Journal of Adhesion and Adhesives 26 : 325-336. 2006
[11] Ortiz, M.; Pandolfi, A. Finite-deformation irreversible cohesive elements for three-dimensional crack- propagation analysis; International Journal for Numerical Methods in Engineering 44, 1267–1282. 1999
