Soutenance mémoire
Finite element modeling of CFRP machining
Recently, many researchers have focused on investigation of CFRP machining using modeling to decrease the experiments, which are time consuming and expensive. But in the literature, very few works attempt to model the cutting forces in surface milling of fiber reinforced composites. Generally, the modeling methods of FRP machining can be classified in two general approaches: (I) theoretical and empirical models and (II) numerical models. Theoretical and empirical models were used to study the FRP milling process (Karpat, Bahtiyar et Değer, 2012; Zaghbani et al., 2012a), but using these models is very complicated because of the highly nonlinear and inhomogeneous nature of composite materials. Another problem is the lack of cutting force coefficients that are necessary for these modeling techniques, especially for modelling oblique cutting for different tool/workpiece combinations (Calzada, 2010; Kalla, Sheikh-Ahmad et Twomey, 2010). In addition, these models are not able to predict machining damages and cutting mechanism.
More recently, with the improvement in computer technology, many researchers have focused on studying composite machining by numerical methods such as finite element modeling. Finite element models are able to predict the cutting forces, chip formation mechanisms, and material damage in the machining of a complex multi-phase and anisotropic material (Calzada, 2010). In spite of existing many models for simulating CFRP orthogonal cutting, there is no finite element model for simulating the complicated surface machining process of CFRP such as the surface milling process.
Finite element formulations
For machining simulations using finite element modeling, three formulations have been used: Eulerian, Lagrangian, and Arbitrary lagrangian eulerian (ALE) .
In the Eulerian method, the mesh is spatially fixed in order to eliminate excessive element distortion, but material can flow through a meshed control volume. In this method, cutting is simulated in the steady state and therefore there is no need for chip separation criteria. The disadvantage of this method is that the initial shape of the chip and the contact conditions must be known.
In Lagrangian method, the mesh is attached to the workpiece and the elements can deform similarly to actual machining. Knowing the chip geometry is not necessary using this formulation. Lagrangian mesh always contains the same material particles. From a computational viewpoint, it is one of significant advantages of this method, especially in problems involving materials with history-dependent behaviors. The disadvantages of this method are the excessive element distortion that reduces the accuracy in large material deformation and the need for frequent remeshing.
In order to have the advantages of both Eulerian and Lagrangian approaches, the arbitrary lagrangian eulerian (ALE) method was developed. In this method, the finite element mesh is neither fixed nor attached to the workpiece material (Stein, de Borst et Hughes, 2004).
Definition of CFRP material in finite element method (FEM)
The numerical modeling of fiber reinforced composites can be classified in two general approaches: (I) micromechanical approach where the composite is modeled as multi-phase material and (II) macro mechanical approach where the composite is modeled as an equivalent homogeneous material (EHM).
The micromechanical approach was used successfully to predict cutting forces and local defects in orthogonal cutting of FRP (such as debonding) (Calzada et al., 2012; Dandekar et Shin, 2008; Nayak, Bhatnagar et Mahajan, 2005; Rao, Mahajan et Bhatnagar, 2007a; Rao, Mahajan et Bhatnagar, 2007b). Despite the advantages of the micromechanical approach, such as good accuracy of predicted cutting force and damages, it has some limitations. The micro modeling is more complex than macro modeling and needs very high calculation time and precise details of fibers, fiber matrix arrangements and their interfacial and physical properties (Dandekar et Shin, 2012). Because of these limitations, the macro mechanical modeling is preferable for modeling complex processes such as milling.
The first macro-mechanical FEM analysis of fiber-reinforced composites was developed by Arola and Ramulu (Arola et Ramulu, 1997) in 1995. The predicted values of principal cutting force agreed well with the experimental values but the predicted thrust force was much lower than experiments. The results of other studies also confirm the shortcoming of macromechanical modeling to predict the thrust forces (Arola, Sultan et Ramulu, 2002; Lasri, Nouari et El Mansori, 2009; Nayak, Bhatnagar et Mahajan, 2005; Santiuste, Soldani et Miguélez, 2010). Mkaddem et al. (Mkaddem et El Mansori, 2009; Mkaddem, Demirci et Mansori, 2008) developed a micro-macro model to get the advantages of both approaches. The composite was modeled as a homogeneous material with anisotropic effective friction coefficients. The model incorporates the adaptive mesh technique and density effect to analyse composite machining. It successfully predicted the sub-surface damages, cutting and thrust forces with lower mean errors (6% for cutting forces and 26% for thrust forces) than another macromechanical model presented by Nayak et al. (17% for cutting forces 44% for thrust forces) (Nayak, Bhatnagar et Mahajan, 2005).
Friction at the tool/workpiece interface
Friction is another important parameter in machining simulation. An accurate modeling of the coefficient of friction allows for accurate prediction of cutting forces and temperature distributions. Mahdi and Zhang (Mahdi et Zhang, 2001a) assumed that tool-workpiece friction is negligible but in most researches, a Coulomb friction law has been used to describe the contact between tool and workpiece.
In some researches, the coefficient of friction was assumed constant and equal to 0.3 (Arola et Ramulu, 1997; Rao, Mahajan et Bhatnagar, 2008; Rao, Mahajan et Bhatnagar, 2007b; Rentsch, Pecat et Brinksmeier, 2011), 0.4 (Arola, Sultan et Ramulu, 2002), or 0.5 (Lasri, Nouari et El Mansori, 2009; Santiuste, Soldani et Miguélez, 2010). Nayak and Bhatnagar (Nayak, Bhatnagar et Mahajan, 2005) and Mkaddem (Mkaddem et El Mansori, 2009; Mkaddem, Demirci et Mansori, 2008) used various friction coefficients for different fibre orientations to improve the predicted cutting forces in orthogonal cutting of FRP materials.
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Table des matières
INTRODUCTION
CHAPTER 1 CHALLENGE DESCRIPTION, OBJECTIVES AND ORIGINAL
CONTRIBUTIONS
1.1 Challenge description
1.2 Research objectives
1.3 Original contributions
CHAPTER 2 LITERATURE REVIEW
2.1 Carbon fiber reinforced plastics
2.2 Surface milling of CFRP
2.2.1 Milling Geometry
2.2.2 Chip formation mechanism
2.2.3 Cutting forces in CFRP machining
2.2.4 Machining Induced Damage and Surface Integrity
2.2.5 Cutting temperature in CFRP milling
2.3 Finite element modeling of CFRP machining
2.3.1 Finite element formulations
2.3.2 Definition of CFRP material in finite element method (FEM)
2.3.3 Friction at the tool/workpiece interface
2.3.4 Failure criteria and chip formation
2.4 Summary
CHAPTER 3 EFFECT OF CUTTING TOOL LEAD ANGLE ON MACHINING
FORCES AND SURFACE FINISH OF CFRP LAMINATES
3.1 Abstract
3.2 Introduction
3.3 Materials and methods
3.4 Results
3.4.1 Effects of feed rate and cutting speed on surface roughness
3.4.2 Effects of feed rate and cutting speed on cutting force
3.4.3 Effects of lead angle on surface roughness and cutting force
3.5 Conclusions
3.6 Acknowledgment
3.7 References
CHAPTER 4 EXPERIMENTAL INVESTIGATION OF THE CUTTING
TEMPERATURE AND SURFACE QUALITY DURING MILLING
OF UNIDIRECTIONAL CFRP
4.1 Abstract
4.2 Introduction
4.3 Methodology
4.4 Results and discussion
4.4.1 Effects of cutting speed on the cutting force and cutting temperature
4.4.2 Effects of fibers orientation on the cutting temperature and cutting
force
4.4.3 Effects of fibers orientation and cutting speed on surface quality
4.5 Conclusion
4.6 Acknowledgments
4.7 References
CHAPTER 5 FINITE ELEMENT ANALYSIS OF SURFACE MACHINING OF
CARBON FIBER REINFORCED COMPOSITES
5.1 Abstract
5.2 Introduction
5.3 Experimental procedure
5.3.1 Composite Materials
5.3.2 Milling process
5.4 Numerical modeling
5.4.1 Geometry, contact, meshing and analysis
5.4.2 Contact modeling
5.4.3 Failure criteria
5.5 Results and discussion
5.5.1 Chip formation
5.5.2 Cutting forces
5.5.3 Surface integrity
5.6 Conclusion
5.7 Acknowledgments
5.8 References
CONCLUSION
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