J. Adhesion Sci. Technol., Vol. 21, No 8, PP. 725-734(2007) Alsoavailableonline-www.brill.nl/jast Finite element analysis of load transfer at a fibre-matrix interface during pull-out loading MOHAMED KHARRAT 1, 2,* MAHER DAMMAK I ,2 and MOHAMED TRABELSI2 ent of Technology, Institut Preparatoire aux Etudes d'ingenieurs de sfax, Rte Menzel Chaker km 0.5, B.P. 805, 3018 Sfar, Tunisia 2 Laboratoire des Systemes Electromecaniques, Ecole Nationale d'Ingenieurs de sfax, Tunisia Received in final form 27 February 2007 Abstract-Load transfer ability of the fibre-matrix interface is well known to mainly control the mechanical behaviour of fibre-reinforced materials. This load transfer phenomenon is of great importance in dentistry when a post is used for fixing a ceramic crown on the tooth. The pull-out test has been well accepted as the most important micromechanical test for evaluating the interaction properties between the fibre and matrix. In this study, a finite element model is developed to analyse the pull-out process of a steel fibre from an epoxy matrix. Based on the pull-out force-displacement curves, developed in our previous experimental work, specific load transfer laws at the fibre-matrix interface have been proposed for each stage of the pull-out process, i.e., before and after fibre- matrix debonding. Predicted initial extraction forces for different implantation lengths were fitted alues and an initial interference fit of 4 um was determined. An interfacial shear trength of 21 MPa was then determined by fitting the predicted debonding forces for different implantation lengths to the experimental values. According to the load transfer laws considered analysis of the interfacial shear stress indicates that fibre-matrix debonding initiates simultaneously at both the lower and upper extremities of the interface. Keywords: Fibre; matrix; interface; friction; pull-out; debonding; finite element. 1 INTRODUCTION It is well known that the mechanical behaviour of fibre-reinforced materials mainly controlled by the load transfer ability of the fibre-matrix interface. Us of these materials in mechanical structures complicates the design problem for fatigue life, which relies on the interaction between the fibre and matrix. In order To whom correspondence should be addressed. Tel. (216)7424-1403, ext. 154; Fax: (216)7424- 6347; e-mail: Mohamed Kharrat @ipesrmutn
J. Adhesion Sci. Technol., Vol. 21, No. 8, pp. 725–734 (2007) VSP 2007. Also available online - www.brill.nl/jast Finite element analysis of load transfer at a fibre–matrix interface during pull-out loading MOHAMED KHARRAT 1,2,∗, MAHER DAMMAK 1,2 and MOHAMED TRABELSI 2 1 Department of Technology, Institut Préparatoire aux Etudes d’Ingénieurs de Sfax, Rte Menzel Chaker km 0.5, B.P. 805, 3018 Sfax, Tunisia 2 Laboratoire des Systèmes Electromécaniques, Ecole Nationale d’Ingénieurs de Sfax, Tunisia Received in final form 27 February 2007 Abstract—Load transfer ability of the fibre–matrix interface is well known to mainly control the mechanical behaviour of fibre-reinforced materials. This load transfer phenomenon is of great importance in dentistry when a post is used for fixing a ceramic crown on the tooth. The pull-out test has been well accepted as the most important micromechanical test for evaluating the interaction properties between the fibre and matrix. In this study, a finite element model is developed to analyse the pull-out process of a steel fibre from an epoxy matrix. Based on the pull-out force–displacement curves, developed in our previous experimental work, specific load transfer laws at the fibre–matrix interface have been proposed for each stage of the pull-out process, i.e., before and after fibre– matrix debonding. Predicted initial extraction forces for different implantation lengths were fitted to experimental values and an initial interference fit of 4 µm was determined. An interfacial shear strength of 21 MPa was then determined by fitting the predicted debonding forces for different implantation lengths to the experimental values. According to the load transfer laws considered, analysis of the interfacial shear stress indicates that fibre–matrix debonding initiates simultaneously at both the lower and upper extremities of the interface. Keywords: Fibre; matrix; interface; friction; pull-out; debonding; finite element. 1. INTRODUCTION It is well known that the mechanical behaviour of fibre-reinforced materials is mainly controlled by the load transfer ability of the fibre–matrix interface. Use of these materials in mechanical structures complicates the design problem for fatigue life, which relies on the interaction between the fibre and matrix. In order ∗To whom correspondence should be addressed. Tel.: (216) 7424-1403, ext. 154; Fax: (216) 7424- 6347; e-mail: Mohamed.Kharrat@ipeis.rnu.tn
M. Kharrat et al Crown Dental po Cement Aveolar bon Figure 1. Schematic drawing of an endodontically-treated tooth with a dental post. to determine this interaction several micromechanical tests which. in general use composite model specimens containing a single fibre, have been developed [1-4]. Based on how the external load is applied to the composite specimen, micromechanical tests can be divided into two groups. The first group in which the external load is directly applied to the fibre includes the micro-indentation test, the push-out test and the pull-out test. In the second group the external load is applied to the matrix and includes the fragmentation test and the broutman test. there has been extensive discussion in the literature about the choice of an appropriate micromechanical test for interface characterization [4 ]. The pull-out test has been well accepted as the most suitable micromechanical test for evaluating the bond quality at the fibre-matrix interface [4-7]. In addition to its relative simplicity of sample preparation and measurement, this test is expected to provide realistic investigation of interfacial adhesion for composites with both ductile and brittle matrices In prosthetic dentistry, a ceramic crown is fixed by placing a dental post within the tooth root using cement. The visible part of the post is then bonded to the crown with a resin core(Fig. 1). When forces are applied to the crown, they are transferred to the dentin through the core and the post. Stress concentration at the end of the post often initiates root fracture [8]. This phenomenon depends on the post-core and post-tooth root interaction. The pull-out test can also be used to evaluate the retentive strength of the post to the tooth root and to the core foundation [9] Experimental pull-out force-displacement curves are used to determine the intrin sic properties of the fibre-matrix interface. For this purpose, several analytical mod- els based on elastic (shear-lag) and frictional load transfer considerations between
726 M. Kharrat et al. Figure 1. Schematic drawing of an endodontically-treated tooth with a dental post. to determine this interaction, several micromechanical tests, which, in general, use composite model specimens containing a single fibre, have been developed [1–4]. Based on how the external load is applied to the composite specimen, micromechanical tests can be divided into two groups. The first group in which the external load is directly applied to the fibre includes the micro-indentation test, the push-out test and the pull-out test. In the second group the external load is applied to the matrix and includes the fragmentation test and the Broutman test. There has been extensive discussion in the literature about the choice of an appropriate micromechanical test for interface characterization [4]. The pull-out test has been well accepted as the most suitable micromechanical test for evaluating the bond quality at the fibre–matrix interface [4–7]. In addition to its relative simplicity of sample preparation and measurement, this test is expected to provide realistic investigation of interfacial adhesion for composites with both ductile and brittle matrices. In prosthetic dentistry, a ceramic crown is fixed by placing a dental post within the tooth root using cement. The visible part of the post is then bonded to the crown with a resin core (Fig. 1). When forces are applied to the crown, they are transferred to the dentin through the core and the post. Stress concentration at the end of the post often initiates root fracture [8]. This phenomenon depends on the post-core and post-tooth root interaction. The pull-out test can also be used to evaluate the retentive strength of the post to the tooth root and to the core foundation [9]. Experimental pull-out force–displacement curves are used to determine the intrinsic properties of the fibre–matrix interface. For this purpose, several analytical models based on elastic (shear-lag) and frictional load transfer considerations between
Finite element analysis of load transfer during a pull-out process the fibre and matrix have been developed [5, 6, 10]. For the same purpose, finite el- ement models have also been developed [ll, 12]. To analyse the effect of specimen size on the interfacial shear and normal stresses, Yang et al. [ll] developed a 2-D finite element model using ANSYS program. For simplicity, the effects of thermal residual stress and friction between crack faces have been ignored by these authors They concluded that both normal and shear interfacial stresses concentrations exist near the fibre ends whose values are affected by the length of the fibre embed- ded in the matrix and the thickness of the matrix around the fibre. To analyse the crack bridging ability in laminated composites with through-thickness reinforce- nent (TTR), Meo et al. [12] developed a finite element model. A specific contact frictional law has been used to describe the several phases of the pull-out process In their work, Meo et al. carried out a parametric study to investigate the effect of the contact frictional law parameters on the simulated pull-out force-displacement curve Experimental characterization of the fibre-matrix interface for a steel/epoxy composite system has been developed using the pull-out test in our previous work [10]. The objective of this study was to develop a finite element model for the analysis of the experimental results. A specific load transfer law at the fibre-matrix interface has been proposed for each stage of the pull-out process, i.e., before and after fibre-matrix debonding. Using this finite element model. the interfacial shear trength has been determined and the interfacial stresses have been analysed 2. EXPERIMENTAL The composite model specimen used in the pull-out experiment [10] was made from stainless steel fibre embedded in a cylindrical epoxy matrix with different implantation lengths(the length of the fibre embedded in the matrix). To carry out the pull-out experiments, an apparatus mounted on a standard traction-compression machine was designed [10]. The top surface of the matrix cylinder was not permitted to move with respect to the pull-out test apparatus(Fig. 2). A monotonic displacement with a constant speed of 5 mm/min was applied to the end of the steel fibre. Typical pull-out force versus displacement curve for 10 mm implantation length is shown in Fig 3. The features of this curve are outlined as follows [ 5] In the initial quasi-linear region, the fibre extends as the force rises. When the maximum force Fa(debonding force)is reached the fibre debonds from the matrix along the full embedded length. This is followed by a sudden drop of the force to initial Fi (initial extraction force)required for pulling out the debonded fibre fron the matrix. After that the force continues to decrease while the extracted length increases until the whole fibre is extracted from the matrix FINITE ELEMENT MODELLING A 2-D axisymmetric finite element was used in the pull-out simulation, where a
Finite element analysis of load transfer during a pull-out process 727 the fibre and matrix have been developed [5, 6, 10]. For the same purpose, finite element models have also been developed [11, 12]. To analyse the effect of specimen size on the interfacial shear and normal stresses, Yang et al. [11] developed a 2-D finite element model using ANSYS program. For simplicity, the effects of thermal residual stress and friction between crack faces have been ignored by these authors. They concluded that both normal and shear interfacial stresses concentrations exist near the fibre ends whose values are affected by the length of the fibre embedded in the matrix and the thickness of the matrix around the fibre. To analyse the crack bridging ability in laminated composites with through-thickness reinforcement (TTR), Meo et al. [12] developed a finite element model. A specific contact frictional law has been used to describe the several phases of the pull-out process. In their work, Meo et al. carried out a parametric study to investigate the effect of the contact frictional law parameters on the simulated pull-out force–displacement curve. Experimental characterization of the fibre–matrix interface for a steel/epoxy composite system has been developed using the pull-out test in our previous work [10]. The objective of this study was to develop a finite element model for the analysis of the experimental results. A specific load transfer law at the fibre–matrix interface has been proposed for each stage of the pull-out process, i.e., before and after fibre–matrix debonding. Using this finite element model, the interfacial shear strength has been determined and the interfacial stresses have been analysed. 2. EXPERIMENTAL The composite model specimen used in the pull-out experiment [10] was made from stainless steel fibre embedded in a cylindrical epoxy matrix with different implantation lengths (the length of the fibre embedded in the matrix). To carry out the pull-out experiments, an apparatus mounted on a standard traction-compression machine was designed [10]. The top surface of the matrix cylinder was not permitted to move with respect to the pull-out test apparatus (Fig. 2). A monotonic displacement with a constant speed of 5 mm/min was applied to the end of the steel fibre. Typical pull-out force versus displacement curve for 10 mm implantation length is shown in Fig. 3. The features of this curve are outlined as follows [5]: In the initial quasi-linear region, the fibre extends as the force rises. When the maximum force Fd (debonding force) is reached the fibre debonds from the matrix along the full embedded length. This is followed by a sudden drop of the force to the initial Fi (initial extraction force) required for pulling out the debonded fibre from the matrix. After that, the force continues to decrease while the extracted length increases until the whole fibre is extracted from the matrix. 3. FINITE ELEMENT MODELLING A 2-D axisymmetric finite element was used in the pull-out simulation, where a
M. Kharrat et al Pull-out force Steel fibre 囫H Epoxy matrix Figure 2. Schematic representation of the experimental pull-out test configuration. Displacement(mm) Figure 3. Experimental pull-out force-displacement curve for 10 mm implantation length [10]. Fd debonding force; Fi. initial extraction force. steel fibre of 1. 2 mm in diameter was embedded in an epoxy cylinder of 30 mm outside diameter and 20 mm length. The implantation length L of the fibre in the matrix was varied in the range of 4-12 mm, while the non-embedded length of fibre( the surface of the matrix cylinder and the point of loading)was kept at 28 mm. As we do not expect large deformations in the fibre or the matrix
728 M. Kharrat et al. Figure 2. Schematic representation of the experimental pull-out test configuration. Figure 3. Experimental pull-out force–displacement curve for 10 mm implantation length [10]. Fd, debonding force; Fi, initial extraction force. steel fibre of 1.2 mm in diameter was embedded in an epoxy cylinder of 30 mm outside diameter and 20 mm length. The implantation length L of the fibre in the matrix was varied in the range of 4–12 mm, while the non-embedded length of fibre (between the surface of the matrix cylinder and the point of loading) was kept at 28 mm. As we do not expect large deformations in the fibre or the matrix
Finite element analysis of load transfer during a pull-out process Properties of steel fibre and epoxy matrix used Elastic modulus(MPa) Poissons coefficient Epoxy matrix 4080±180 Araldite LY 556 with Aradur 917 and DY070(Huntsman) Steel fibre X2CrNiMo17-12(316L) =0 Figure 4. Axisymmetric finite element mesh for pull-out loading. I/1, radial direction: 2, axial direction; F, pull-out force. during pull-out loading, both fibre and matrix are assumed to be linear elastic. Their material properties are given in Table 1 For each implantation length, an axisymmetric nonlinear finite element model was developed using the ABAQUS program(ABAQUS 6.4, 2003). Small displacement conditions were considered for this model. Therefore, we chose to limit the analysis of the pull-out process to the beginning of the extraction process(F= Fi). The model subdivision used for calculations is shown in Fig 4. The model consists of 760 8-node elements and 84 6-node elements. a total of 2747 nodes were used in his model
Finite element analysis of load transfer during a pull-out process 729 Table 1. Properties of steel fibre and epoxy matrix used Elastic modulus (MPa) Poisson’s coefficient Epoxy matrix 4080 ± 180 0.3 Araldite LY 556 with Aradur 917 and DY070 (Huntsman) Steel fibre 200 000 0.22 X2CrNiMo17-12 (316L) Figure 4. Axisymmetric finite element mesh for pull-out loading. u1, radial direction; u2, axial direction; F, pull-out force. during pull-out loading, both fibre and matrix are assumed to be linear elastic. Their material properties are given in Table 1. For each implantation length, an axisymmetric nonlinear finite element model was developed using the ABAQUS program (ABAQUS 6.4, 2003). Small displacement conditions were considered for this model. Therefore, we chose to limit the analysis of the pull-out process to the beginning of the extraction process (F = Fi). The model subdivision used for calculations is shown in Fig. 4. The model consists of 760 8-node elements and 84 6-node elements. A total of 2747 nodes were used in this model