- Email: [email protected]
epoxy composites using FEM
Computational Materials Science 64 (2012) 168–172
Contents lists available at SciVerse ScienceDirect
Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci
Analysis of microstructure damage in carbon/epoxy composites using FEM J. Bienias´ a,⇑, H. De˛bski b, B. Surowska a, T. Sadowski c a
Department of Materials Engineering, Faculty of Mechanical Engineering, Lublin University of Technology, Nadbystrzycka 36, 20-618 Lublin, Poland Department of Machine Design, Faculty of Mechanical Engineering, Lublin University of Technology, Nadbystrzycka 36, 20-618 Lublin, Poland c Department of Solid Mechanics, Faculty of Civil Engineering and Architecture, Lublin University of Technology, Nadbystrzycka 40, 20-618 Lublin, Poland b
a r t i c l e
i n f o
Article history: Received 30 October 2011 Received in revised form 13 March 2012 Accepted 15 March 2012 Available online 18 April 2012 Keywords: Carbon/epoxy composites Finite element method XFEM Interfaces Failure of composites
a b s t r a c t This work presents a numerical analysis of damage of composite materials with polymeric matrix reinforced with carbon fibres subject to static tension. Verification of numerical analyses was conducted with experimental methods – strength tests and microstructural observations. The methodologies applied were: the material damage modelling methodology based on XFEM (eXtended Finite Element Method) and contact interactions in a fibre–matrix connection layer using the CZM method (Cohesive Zone Method – Surface-based Cohesive Behaviour). ABAQUS/Standard software was the applied numerical tool. Microstructural analysis and numerical simulations indicate the fact that initiation of composite material damage takes place at the interface as a result of cracking and loss of fibre/matrix connection. This results in weakening of the composite microstructure in this area through the initiation of a reinforcement cracking process, which leads to further structural degradation, consisting in propagation of matrix cracking and, as a result, complete damage of the composite structure. The presented research of carbon/epoxy composite damage confirmed the adequacy of the prepared numerical model. Ó 2012 Elsevier B.V. All rights reserved.
1. Introduction Composite materials with polymeric matrix reinforced with carbon fibres currently constitute one of the most dominant materials applied in the aviation industry. They are characterized by high resistance and stiffness factors, low density, high fatigue resistance, chemical and corrosion resistance as well as relatively reasonable production costs [1,2]. These properties and the highly advanced degree of composite production technologies allow for application of these materials in pivotal aviation structures, quite often of a critical character; that is, skin elements, fuselage, spars, fins and planes, flaps, landing gear, and blades [3]. Very significant problems in the design of laminated composite structures are processes and mechanisms of composite damage, which are much more complex in comparison to metal materials [4]. Matrix cracking, separation of the individual layers of laminate, degradation of fibre/matrix interfaces, delaminations and cracking of reinforcing fibres are very characteristic [5]. Numerical simulations based on application of the finite element method (FEM) form a tool supporting the formation process and analysis of composite materials. These methods allow for simulation, optimization of composite structures as well as analysis of damage taking resistance criteria into account [6].
⇑ Corresponding author. Fax: +48 81 538 42 14. E-mail address: [email protected] (J. Bienias´). 0927-0256/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.commatsci.2012.03.033
This work presents a numerical analysis of damage of composite materials with polymeric matrix reinforced with carbon fibres subject to static tension. Verification of numerical analyses was conducted with experimental methods – strength tests and microstructural observations.
2. Materials and methods 2.1. Material The research subject was carbon/epoxy composite made of unidirectional prepreg tape of the HexPly system (Hexcel, USA) in [0]8 lay-out. The composite matrix was made of epoxy resin (density 1240 kg/m3; Tg: 128 °C; Rm: 64 MPa; m: 0.4; E: 5.1 (GPa), while AS7J12 K carbon fibres constituted reinforcement. The nominal content of reinforcing fibres was about 60%. Composites were made using autoclave technology. Mechanical properties were determined experimentally according to suitable objective standards for these types of materials (ISO, ASTM). Table 1 presents selected mechanical properties of the composite used in the numerical analysis. Microstructural analysis were conducted using optical (Nikon MA200, Japan) and scanning electron microscopy (Zeiss Ultra, Germany).
J. Bienias´ et al. / Computational Materials Science 64 (2012) 168–172
169
Table 1 Selected mechanical properties of the composite used in the numerical analysis. Tensile ultimate strength (MPa)
Tensile elastic modulus (GPa)
Poisson’s ratio (m)
1870
130
0.32
Fig. 2. Traction–Separation failure criterion.
Fig. 1. Discrete numerical model of carbon/epoxy composite.
2.2. Numerical analysis 2.2.1. Objective and scope of numerical calculations Numerical analysis was conducted with regard to load damaging the carbon/epoxy laminate structure for the stretched sample in 0° fibre lay-out. A fragment of composite microstructure consisting of 19 carbon fibres set in the matrix of epoxy resin was analysed. The conducted calculations constitute the initial stage of laminate microstructure modelling with consideration of material damage mechanisms. The methodologies applied were: the material damage modelling methodology based on XFEM (eXtended Finite Element Method) and contact interactions in a fibre–matrix connection layer using the CZM method (Cohesive Zone Method – Surface-based Cohesive Behaviour) [7,8]. The adopted methodology enables representation of microstructure component damage conditions as well as representation of adhesive connection resistance considering its damage while loading the structure. ABAQUS/Standard software was the applied numerical tool.
2.2.2. Discrete model of laminate microstructure The prepared numerical model represented a simplified microstructure of carbon/epoxy laminate in 0° fibre lay-out. The following overall dimensions of the sample were assumed: transverse section 30 50 lm, fibre diameter 7 lm and total length of 100 lm. The scheme of fibre lay-out in the matrix was assumed on the basis of microstructure of the tested composite sample. Construction of the analytical model was based on the network of finite elements of the hexagonal type – Fig. 1. Structural body elements of C3D8 designation were used for the discretisation process – which is eight-node finite elements, with three translating freedom degrees in each node, with primary shape function. The global characteristic size of a finite element was 1.5 lm, while it was reduced to 1 lm at the edges of the fibres’ contact with the matrix. The size of the numeric model was, respectively: number of elements 74,441, number of nodes 159,122, which resulted in a solution of 425,952 equations with incremental-iterative Newton-Raphson method [6,8]. Boundary conditions were defined through fixing of frontal surfaces of carbon fibres at one end of the sample and blocking all translation freedom degrees in these nodes. The model load consisted in tensile force applied to frontal surfaces of the fibres located in the free end of the sample. The value of the force corresponded to the damaging force determined during experimental tests. 2.2.3. Definition of microstructure damage process Conducting numerical calculations considering the damage process of model components’ material structure as well as connections between them requires application of suitable numerical proce-
Fig. 3. Definition of CZM and XFEM interaction.
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J. Bienias´ et al. / Computational Materials Science 64 (2012) 168–172
Fig. 4. Failure of carbon/epoxy composite: (a) numerical analysis and (b) microstructure (cross-section).
dures containing parameters describing the mechanism of damage formation and propagation. Two methods of damage process modelling: the XFEM method – describing material structure damage and the CZM/Surface-based Cohesive Behaviour method –enabling defining fibre–matrix connection damage, were used [9–12]. A basic constitutive law used for describing the damage process in ABAQUS/ Standard software is Traction–Separation (tearing force – boundary separation value), allowing for consideration of normal interactions (tearing) as well as the effects caused by tangent interactions (shearing) in numerical analysis. Damage mechanism definition based on the above law requires an elastic range (interval O–A), determination of the damage initiation point (point A) and damage evolution parameters, consisting in gradual degradation of material rigidity or connection (interval A–B) – Fig. 2. The XFEM method was applied to describe the fibres’ structure and composite matrix damage through the proper description of material characteristics of these elements. Stress criterion was used to describe the material damage mechanism. In both cases elastic material with parameters characterizing material damage was defined as follows: Young’s modulus E = 241,000 MPa, Poisson’s ratio t = 0.26, value of stress initiating damage of material fibre rmax = 4830 MPa, value of effective separation describing damage evolution (relocation of finite element nodes as a result of material damage, measured from damage initiation point) dfn = 0.005 lm, and analogically for matrix material: Young’s modulus E = 5100 MPa, Poisson’s ratio t = 0.4, value of stress initiating damage of material fibre rmax = 64 MPa, value of effective separation describing damage evolution dm n = 0.5 lm. The CZM/Surfacebased Cohesive Behaviour method was used to define contact interactions on the surface of fibres and matrix junction. Surface contact described in this way is a combination of a classical contact
Fig. 5. Typical damage of carbon fibres: (a) FEM analysis, (b) microstructure (longitudinal-section) and (c) scanning electron microscope.
J. Bienias´ et al. / Computational Materials Science 64 (2012) 168–172
171
Fig. 6. Failure at the carbon fibres/matrix interfaces: (a) numerical analysis and (b) microstructure (SEM).
problem, acting in the case of pressure, and the properties of adhesive connection or layers, in the case of tearing away or shearing of the joined surfaces or layers. The elastic behaviour of contact required determining the joint rigidity for three directions of interactions, which means tearing away and shearing in two directions. In the analysed case we applied a method of automatic definition of joint rigidity with computer software, determined with the Penalty method on the basis of mutual rigidities of the joined elements, that is fibres and matrix. The connection between fibres and matrix of the following mechanical properties: value of stress initiating connection damage rmax = 64 MPa, value of effective separation describing damage evolution dcon = 1.5 lm, was defined. The areas of the numerical model which was used for defining the CZM and XFEM methods was presented in Fig. 3. 3. Results and discussion The conducted numerical calculations considering modelling techniques enabling analysis of the investigated damage of carbon–epoxy laminate microstructure in 0° lay-out allowed for identification and evaluation of damage of the sample subject to tensile load. Fig. 4 presents a general view of the deformed sample model of microstructure in conditions of damaging load. It was found, while analysing the obtained model deformation form, that in the case of load value corresponding to 94% of damaging load (determined during experimental tests), reinforcing fibres as well as matrix material were damaged. The analysis of numerical model sensitivity was performed for various values of effective separation of fibres as well as of matrix.
In case of resin, the increase of the values of effective separation m dm n = 1 and their reduction dn = 0.05 (maintaining the constant value for fibres dfn = 0.005) caused the reduction of the degree of microstructure damage evidenced by the lack of complete ruptures in carbon fibres – small micro-ruptures were observed in about 60% of fibres only. The increase of the values of effective separation for fibres (dfn = 0.01, dfn = 0.0075) caused the reduction of the degree of microstructure damage reducing the number of completely ruptured fibres while the reduction of the degree of microstructure damage dfn = 0.001 resulted in significantly limited degree of microstructure damage and complete ruptures of fibres were eliminated. Performed analysis of numerical model sensitivity to the values of effective separation, characterizing the damage evolution process indicated relevant impact of assumed value of effective separation on the degree of microstructure damage in composite material at assumed (constant) value of the external load. Therefore this value may constitute a parameter controlling the damage evolution process in individual components of the model in order to enable its calibration in relation to the real structure. The values of effective f separation dm n = 0.5 and dn = 0.005 assumed in calculations ensure the adequacy of elaborated numerical model in qualitative approach (significant degree of damage in individual microstructure components evidenced by the rupture in the matrix as well as in the fibres) and in quantitative approach ensuring high consistency of breaking load in relation to experimental studies. The elaborated numerical model considers the composite microstructure with parallel orientation of fibres in the direction 0°. Making the assumptions, we idealize the real structure of composite matrix fibres to a certain extent, because the fibres are not
172
J. Bienias´ et al. / Computational Materials Science 64 (2012) 168–172
perfectly parallel in a real structure. Assumed boundary and initial conditions will be adequate in case of models with small angle of fibres deviation from the direction 0o while the parallel orientation of fibres in the matrix is not required. Therefore the elaborated numerical model is not a fully universal model, because the construction of a separate discrete model and the definition of adequate boundary conditions would be required in case of a significant change of fibres orientation configuration in the scope of large angles, e.g. 30° or 45°. Other parameters of the model, i.e. amongst others the definition of material models or definition of procedures describing the damage process (XFEM, CZM) are identical to those applied in case of the model elaborated for an ideal configuration 0°. The evaluation of the character of composite structure damage indicates the presence of numerous transverse cracks (toward tensile force direction). Cracks of individual fibres were noted as well as warp and fibre/matrix division surface degradation. Fig. 5 presents the typical character of damage – transverse cracks of carbon fibres obtained during numerical analyses and microscopic observations. Damage – degradation of composite materials also occurs at the fibre/matrix interfaces (Fig. 6) [5,10]. Numerous points of initiation and cracks (adhesion loss), which can constitute an easy way of composite degradation (cracks running along the fibre/matrix boundary) were observed at the interfaces. Apart from the component kind and characteristics, the interfaces is the main factor determining the properties of composite material. It directly influences the quality of connection of the reinforcing phase with matrix, the composite cracking mechanism and cracking of the individual components [5]. 4. Summary Describing damage of composite materials is a complex problem, necessitating thorough and detailed research and application of modern tools and research methods. Microstructural analysis and numerical simulations – FEM, allowed for identification of the damage mechanism of the investigated composite material. The conducted verification of the results of numerical calculations demonstrated high conformity of the simulation with experimental results, both qualitatively and quantitatively. The obtained forms of composite microstructure damage were convergent –
transverse cracks of the reinforcing fibres, degradation of fibre/matrix interface. This allowed for identification of initiation points, damage character and its further propagation. Microstructural analysis and numerical simulations indicate the fact that initiation of composite material damage takes place at the interface as a result of cracking and loss of fibre/matrix connection. This results in weakening of the composite microstructure in this area through the initiation of a reinforcement cracking process, which leads to further structural degradation, consisting in propagation of matrix cracking and, as a result, complete damage of the composite structure. The presented research of carbon/epoxy composite damage confirmed the adequacy of the prepared numerical model, thus opening the possibility for further research in this field. Acknowledgements This research was supported by the European Union within the 7th Framework Programme, call FP7-REGPOT-2009-1, Grant Agreement No. FP-7 24547. References [1] P. Morgan, Carbon Fibers and Their Composites, Taylor and Francis Group, New York, 2005. [2] D.D.L. Chung, Carbon Fiber Composites, Butterworth-Heinemann, Boston, 1994. [3] W.T. Freeman, The use of composites in aircraft primary structure, Compos. Part B – Eng. 3 (1993) 767–775. [4] B. Harris, Fatigue in Composites, CRC Press, Boca Raton, 2000. [5] E.S. Greenhalgh, Failure Analysis and Fractography of Polymer Composites, CRC Press, Cambridge, 2009. [6] E Rusin´ski, J. Czmochowski, T. Smolnicki, Zaawansowana metoda elementów skon´czonych w konstrukcjach nos´nych, Oficyna Wydawnicza Politechniki Wrocławskiej, Wrocław, 2000 (in Polish). [7] G. Alfano, M.A. Crisfield, Int. J. Numer. Meth. Eng. 50 (2001) 1701–1736. [8] Abaqus HTML documentation, v. 6.10, 2010. [9] J.X. Shi, D. Chopp, J. Lua, N. Sukumar, T. Belytschko, Eng. Fract. Mech. 77 (2010) (2010) 2840–2863. [10] E. Giner, N. Sukumar, J.E. Tarancón, F.J. Fuenmayor, Eng. Fract. Mech. 76 (2009) (2009) 347–368. [11] N. Sukumar, N. Moës, B. Moran, T. Belytschko, Int. J. Numer. Meth. Eng. 48 (2000) (2000) 1549–1570. [12] R. Kregting, Cohesive zone models – towards a robust implementation of irreversible behavior, MT05.11, 2005.
Contents lists available at SciVerse ScienceDirect
Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci
Analysis of microstructure damage in carbon/epoxy composites using FEM J. Bienias´ a,⇑, H. De˛bski b, B. Surowska a, T. Sadowski c a
Department of Materials Engineering, Faculty of Mechanical Engineering, Lublin University of Technology, Nadbystrzycka 36, 20-618 Lublin, Poland Department of Machine Design, Faculty of Mechanical Engineering, Lublin University of Technology, Nadbystrzycka 36, 20-618 Lublin, Poland c Department of Solid Mechanics, Faculty of Civil Engineering and Architecture, Lublin University of Technology, Nadbystrzycka 40, 20-618 Lublin, Poland b
a r t i c l e
i n f o
Article history: Received 30 October 2011 Received in revised form 13 March 2012 Accepted 15 March 2012 Available online 18 April 2012 Keywords: Carbon/epoxy composites Finite element method XFEM Interfaces Failure of composites
a b s t r a c t This work presents a numerical analysis of damage of composite materials with polymeric matrix reinforced with carbon fibres subject to static tension. Verification of numerical analyses was conducted with experimental methods – strength tests and microstructural observations. The methodologies applied were: the material damage modelling methodology based on XFEM (eXtended Finite Element Method) and contact interactions in a fibre–matrix connection layer using the CZM method (Cohesive Zone Method – Surface-based Cohesive Behaviour). ABAQUS/Standard software was the applied numerical tool. Microstructural analysis and numerical simulations indicate the fact that initiation of composite material damage takes place at the interface as a result of cracking and loss of fibre/matrix connection. This results in weakening of the composite microstructure in this area through the initiation of a reinforcement cracking process, which leads to further structural degradation, consisting in propagation of matrix cracking and, as a result, complete damage of the composite structure. The presented research of carbon/epoxy composite damage confirmed the adequacy of the prepared numerical model. Ó 2012 Elsevier B.V. All rights reserved.
1. Introduction Composite materials with polymeric matrix reinforced with carbon fibres currently constitute one of the most dominant materials applied in the aviation industry. They are characterized by high resistance and stiffness factors, low density, high fatigue resistance, chemical and corrosion resistance as well as relatively reasonable production costs [1,2]. These properties and the highly advanced degree of composite production technologies allow for application of these materials in pivotal aviation structures, quite often of a critical character; that is, skin elements, fuselage, spars, fins and planes, flaps, landing gear, and blades [3]. Very significant problems in the design of laminated composite structures are processes and mechanisms of composite damage, which are much more complex in comparison to metal materials [4]. Matrix cracking, separation of the individual layers of laminate, degradation of fibre/matrix interfaces, delaminations and cracking of reinforcing fibres are very characteristic [5]. Numerical simulations based on application of the finite element method (FEM) form a tool supporting the formation process and analysis of composite materials. These methods allow for simulation, optimization of composite structures as well as analysis of damage taking resistance criteria into account [6].
⇑ Corresponding author. Fax: +48 81 538 42 14. E-mail address: [email protected] (J. Bienias´). 0927-0256/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.commatsci.2012.03.033
This work presents a numerical analysis of damage of composite materials with polymeric matrix reinforced with carbon fibres subject to static tension. Verification of numerical analyses was conducted with experimental methods – strength tests and microstructural observations.
2. Materials and methods 2.1. Material The research subject was carbon/epoxy composite made of unidirectional prepreg tape of the HexPly system (Hexcel, USA) in [0]8 lay-out. The composite matrix was made of epoxy resin (density 1240 kg/m3; Tg: 128 °C; Rm: 64 MPa; m: 0.4; E: 5.1 (GPa), while AS7J12 K carbon fibres constituted reinforcement. The nominal content of reinforcing fibres was about 60%. Composites were made using autoclave technology. Mechanical properties were determined experimentally according to suitable objective standards for these types of materials (ISO, ASTM). Table 1 presents selected mechanical properties of the composite used in the numerical analysis. Microstructural analysis were conducted using optical (Nikon MA200, Japan) and scanning electron microscopy (Zeiss Ultra, Germany).
J. Bienias´ et al. / Computational Materials Science 64 (2012) 168–172
169
Table 1 Selected mechanical properties of the composite used in the numerical analysis. Tensile ultimate strength (MPa)
Tensile elastic modulus (GPa)
Poisson’s ratio (m)
1870
130
0.32
Fig. 2. Traction–Separation failure criterion.
Fig. 1. Discrete numerical model of carbon/epoxy composite.
2.2. Numerical analysis 2.2.1. Objective and scope of numerical calculations Numerical analysis was conducted with regard to load damaging the carbon/epoxy laminate structure for the stretched sample in 0° fibre lay-out. A fragment of composite microstructure consisting of 19 carbon fibres set in the matrix of epoxy resin was analysed. The conducted calculations constitute the initial stage of laminate microstructure modelling with consideration of material damage mechanisms. The methodologies applied were: the material damage modelling methodology based on XFEM (eXtended Finite Element Method) and contact interactions in a fibre–matrix connection layer using the CZM method (Cohesive Zone Method – Surface-based Cohesive Behaviour) [7,8]. The adopted methodology enables representation of microstructure component damage conditions as well as representation of adhesive connection resistance considering its damage while loading the structure. ABAQUS/Standard software was the applied numerical tool.
2.2.2. Discrete model of laminate microstructure The prepared numerical model represented a simplified microstructure of carbon/epoxy laminate in 0° fibre lay-out. The following overall dimensions of the sample were assumed: transverse section 30 50 lm, fibre diameter 7 lm and total length of 100 lm. The scheme of fibre lay-out in the matrix was assumed on the basis of microstructure of the tested composite sample. Construction of the analytical model was based on the network of finite elements of the hexagonal type – Fig. 1. Structural body elements of C3D8 designation were used for the discretisation process – which is eight-node finite elements, with three translating freedom degrees in each node, with primary shape function. The global characteristic size of a finite element was 1.5 lm, while it was reduced to 1 lm at the edges of the fibres’ contact with the matrix. The size of the numeric model was, respectively: number of elements 74,441, number of nodes 159,122, which resulted in a solution of 425,952 equations with incremental-iterative Newton-Raphson method [6,8]. Boundary conditions were defined through fixing of frontal surfaces of carbon fibres at one end of the sample and blocking all translation freedom degrees in these nodes. The model load consisted in tensile force applied to frontal surfaces of the fibres located in the free end of the sample. The value of the force corresponded to the damaging force determined during experimental tests. 2.2.3. Definition of microstructure damage process Conducting numerical calculations considering the damage process of model components’ material structure as well as connections between them requires application of suitable numerical proce-
Fig. 3. Definition of CZM and XFEM interaction.
170
J. Bienias´ et al. / Computational Materials Science 64 (2012) 168–172
Fig. 4. Failure of carbon/epoxy composite: (a) numerical analysis and (b) microstructure (cross-section).
dures containing parameters describing the mechanism of damage formation and propagation. Two methods of damage process modelling: the XFEM method – describing material structure damage and the CZM/Surface-based Cohesive Behaviour method –enabling defining fibre–matrix connection damage, were used [9–12]. A basic constitutive law used for describing the damage process in ABAQUS/ Standard software is Traction–Separation (tearing force – boundary separation value), allowing for consideration of normal interactions (tearing) as well as the effects caused by tangent interactions (shearing) in numerical analysis. Damage mechanism definition based on the above law requires an elastic range (interval O–A), determination of the damage initiation point (point A) and damage evolution parameters, consisting in gradual degradation of material rigidity or connection (interval A–B) – Fig. 2. The XFEM method was applied to describe the fibres’ structure and composite matrix damage through the proper description of material characteristics of these elements. Stress criterion was used to describe the material damage mechanism. In both cases elastic material with parameters characterizing material damage was defined as follows: Young’s modulus E = 241,000 MPa, Poisson’s ratio t = 0.26, value of stress initiating damage of material fibre rmax = 4830 MPa, value of effective separation describing damage evolution (relocation of finite element nodes as a result of material damage, measured from damage initiation point) dfn = 0.005 lm, and analogically for matrix material: Young’s modulus E = 5100 MPa, Poisson’s ratio t = 0.4, value of stress initiating damage of material fibre rmax = 64 MPa, value of effective separation describing damage evolution dm n = 0.5 lm. The CZM/Surfacebased Cohesive Behaviour method was used to define contact interactions on the surface of fibres and matrix junction. Surface contact described in this way is a combination of a classical contact
Fig. 5. Typical damage of carbon fibres: (a) FEM analysis, (b) microstructure (longitudinal-section) and (c) scanning electron microscope.
J. Bienias´ et al. / Computational Materials Science 64 (2012) 168–172
171
Fig. 6. Failure at the carbon fibres/matrix interfaces: (a) numerical analysis and (b) microstructure (SEM).
problem, acting in the case of pressure, and the properties of adhesive connection or layers, in the case of tearing away or shearing of the joined surfaces or layers. The elastic behaviour of contact required determining the joint rigidity for three directions of interactions, which means tearing away and shearing in two directions. In the analysed case we applied a method of automatic definition of joint rigidity with computer software, determined with the Penalty method on the basis of mutual rigidities of the joined elements, that is fibres and matrix. The connection between fibres and matrix of the following mechanical properties: value of stress initiating connection damage rmax = 64 MPa, value of effective separation describing damage evolution dcon = 1.5 lm, was defined. The areas of the numerical model which was used for defining the CZM and XFEM methods was presented in Fig. 3. 3. Results and discussion The conducted numerical calculations considering modelling techniques enabling analysis of the investigated damage of carbon–epoxy laminate microstructure in 0° lay-out allowed for identification and evaluation of damage of the sample subject to tensile load. Fig. 4 presents a general view of the deformed sample model of microstructure in conditions of damaging load. It was found, while analysing the obtained model deformation form, that in the case of load value corresponding to 94% of damaging load (determined during experimental tests), reinforcing fibres as well as matrix material were damaged. The analysis of numerical model sensitivity was performed for various values of effective separation of fibres as well as of matrix.
In case of resin, the increase of the values of effective separation m dm n = 1 and their reduction dn = 0.05 (maintaining the constant value for fibres dfn = 0.005) caused the reduction of the degree of microstructure damage evidenced by the lack of complete ruptures in carbon fibres – small micro-ruptures were observed in about 60% of fibres only. The increase of the values of effective separation for fibres (dfn = 0.01, dfn = 0.0075) caused the reduction of the degree of microstructure damage reducing the number of completely ruptured fibres while the reduction of the degree of microstructure damage dfn = 0.001 resulted in significantly limited degree of microstructure damage and complete ruptures of fibres were eliminated. Performed analysis of numerical model sensitivity to the values of effective separation, characterizing the damage evolution process indicated relevant impact of assumed value of effective separation on the degree of microstructure damage in composite material at assumed (constant) value of the external load. Therefore this value may constitute a parameter controlling the damage evolution process in individual components of the model in order to enable its calibration in relation to the real structure. The values of effective f separation dm n = 0.5 and dn = 0.005 assumed in calculations ensure the adequacy of elaborated numerical model in qualitative approach (significant degree of damage in individual microstructure components evidenced by the rupture in the matrix as well as in the fibres) and in quantitative approach ensuring high consistency of breaking load in relation to experimental studies. The elaborated numerical model considers the composite microstructure with parallel orientation of fibres in the direction 0°. Making the assumptions, we idealize the real structure of composite matrix fibres to a certain extent, because the fibres are not
172
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perfectly parallel in a real structure. Assumed boundary and initial conditions will be adequate in case of models with small angle of fibres deviation from the direction 0o while the parallel orientation of fibres in the matrix is not required. Therefore the elaborated numerical model is not a fully universal model, because the construction of a separate discrete model and the definition of adequate boundary conditions would be required in case of a significant change of fibres orientation configuration in the scope of large angles, e.g. 30° or 45°. Other parameters of the model, i.e. amongst others the definition of material models or definition of procedures describing the damage process (XFEM, CZM) are identical to those applied in case of the model elaborated for an ideal configuration 0°. The evaluation of the character of composite structure damage indicates the presence of numerous transverse cracks (toward tensile force direction). Cracks of individual fibres were noted as well as warp and fibre/matrix division surface degradation. Fig. 5 presents the typical character of damage – transverse cracks of carbon fibres obtained during numerical analyses and microscopic observations. Damage – degradation of composite materials also occurs at the fibre/matrix interfaces (Fig. 6) [5,10]. Numerous points of initiation and cracks (adhesion loss), which can constitute an easy way of composite degradation (cracks running along the fibre/matrix boundary) were observed at the interfaces. Apart from the component kind and characteristics, the interfaces is the main factor determining the properties of composite material. It directly influences the quality of connection of the reinforcing phase with matrix, the composite cracking mechanism and cracking of the individual components [5]. 4. Summary Describing damage of composite materials is a complex problem, necessitating thorough and detailed research and application of modern tools and research methods. Microstructural analysis and numerical simulations – FEM, allowed for identification of the damage mechanism of the investigated composite material. The conducted verification of the results of numerical calculations demonstrated high conformity of the simulation with experimental results, both qualitatively and quantitatively. The obtained forms of composite microstructure damage were convergent –
transverse cracks of the reinforcing fibres, degradation of fibre/matrix interface. This allowed for identification of initiation points, damage character and its further propagation. Microstructural analysis and numerical simulations indicate the fact that initiation of composite material damage takes place at the interface as a result of cracking and loss of fibre/matrix connection. This results in weakening of the composite microstructure in this area through the initiation of a reinforcement cracking process, which leads to further structural degradation, consisting in propagation of matrix cracking and, as a result, complete damage of the composite structure. The presented research of carbon/epoxy composite damage confirmed the adequacy of the prepared numerical model, thus opening the possibility for further research in this field. Acknowledgements This research was supported by the European Union within the 7th Framework Programme, call FP7-REGPOT-2009-1, Grant Agreement No. FP-7 24547. References [1] P. Morgan, Carbon Fibers and Their Composites, Taylor and Francis Group, New York, 2005. [2] D.D.L. Chung, Carbon Fiber Composites, Butterworth-Heinemann, Boston, 1994. [3] W.T. Freeman, The use of composites in aircraft primary structure, Compos. Part B – Eng. 3 (1993) 767–775. [4] B. Harris, Fatigue in Composites, CRC Press, Boca Raton, 2000. [5] E.S. Greenhalgh, Failure Analysis and Fractography of Polymer Composites, CRC Press, Cambridge, 2009. [6] E Rusin´ski, J. Czmochowski, T. Smolnicki, Zaawansowana metoda elementów skon´czonych w konstrukcjach nos´nych, Oficyna Wydawnicza Politechniki Wrocławskiej, Wrocław, 2000 (in Polish). [7] G. Alfano, M.A. Crisfield, Int. J. Numer. Meth. Eng. 50 (2001) 1701–1736. [8] Abaqus HTML documentation, v. 6.10, 2010. [9] J.X. Shi, D. Chopp, J. Lua, N. Sukumar, T. Belytschko, Eng. Fract. Mech. 77 (2010) (2010) 2840–2863. [10] E. Giner, N. Sukumar, J.E. Tarancón, F.J. Fuenmayor, Eng. Fract. Mech. 76 (2009) (2009) 347–368. [11] N. Sukumar, N. Moës, B. Moran, T. Belytschko, Int. J. Numer. Meth. Eng. 48 (2000) (2000) 1549–1570. [12] R. Kregting, Cohesive zone models – towards a robust implementation of irreversible behavior, MT05.11, 2005.