Microstructure-based modeling of crack growth in particle reinforced composites
Introduction
Particle reinforced composites have relatively isotropic properties compared to short fiber or whisker reinforced composites. The properties of the composites can be tailored by manipulating parameters such as reinforcement particle distribution, size, volume fraction, orientation, and matrix microstructure [1], [2], [3], [4]. Metal matrix composites (MMCs), such as SiC particle reinforced aluminum, have significant advantages over conventional materials such as higher stiffness-to-weight ratio, improved resistance to high cycle fatigue and fatigue crack threshold, improved resistance to wear and reduced coefficient of thermal expansion while maintaining high thermal conductivity [1], [2], [3], [4]. Another attractive aspect of MMCs is that conventional metal working processes can be used for manufacturing.
The mechanical behavior of any material is dependent on the microstructure of the material. The introduction of reinforcement particles into a monolithic material alters the microstructure of the material and changes its mechanical properties. The addition of stiff reinforcement particles in MMCs improves the monotonic properties, such as modulus and strength, and the fatigue crack growth threshold of the composite. However, properties such as fracture toughness and fatigue crack growth resistance (in the Paris Law or steady-state regime) are inferior to that of the unreinforced alloy. The crack growth behavior in MMCs is very much dependent on reinforcement characteristics [2], [5], [6], but less dependent on matrix microstructure [7], [8]. In general, higher threshold values, ΔKth, are observed for composites than for monolithic materials [5], [6], [9]. The Paris-law slope of da/dN vs. ΔK curve for the composites is generally comparable to the unreinforced alloys. It is interesting to note that coarser particles provide better fatigue crack growth resistance, than finer particles, because of roughness-induced crack closure [6]. Furthermore, experiments on overaged and underaged composites, showed little difference in FGR resistance [7], indicating that the controlling deformation mechanisms are related to the particle characteristics and spatial distribution. The role of particle clustering on fatigue crack growth behavior has not really been quantified. The reinforcement/crack interactions are directly related to the magnitude of ΔK and/or Kmax [6], [10]. At high ΔK, the plastic zone around the crack tip is much larger than the particle size, and particle cracking takes place ahead of the crack tip. This results in planar crack growth. At low ΔK, the plastic zone is much smaller so the crack avoids the SiC particles and grows in a tortuous fashion.
Since crack growth mechanisms are very much dependent on microstructure, it follows that any modeling approach to understanding of crack growth must incorporate the microstructure. Analytical models such as the Hashin–Shtrikman (H–S) model [11], Halpin–Tsai (H–T) model [12], and Eshelby’s model [13] are typically used to compute the elastic properties of composite systems. These analyses cannot be extended to composites with irregular particle geometries and complex microstructure. Even if the particle geometries were regular, the solution for systems containing more than one particle is complex, because the distribution of particles also affects the mechanical behavior [14], [15].
Numerical modeling has been used extensively in crack growth studies [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26]. Most of the modeling has been accomplished by using the finite element method (FEM) although, in some cases, the boundary element method (BEM) has also been used. In FEM, crack growth can be achieved by two methods – the nodal release method and the re-meshing method. In the nodal release method, selected nodes are initially tied and then released when a certain criteria is satisfied, thus allowing the crack to grow. This method is suitable for modeling cracks along symmetry edges and pre-defined paths. The re-meshing method is useful to model cracks whose trajectory is not known in advance. In this method, new elements are created around the crack-tip as the crack propagates.
Existing numerical models in particle reinforced composites have not considered the explicit microstructure of the particles [16], [17], [18], [19], [20], [21], [22], [23], [24]. The reinforcement particles are generally represented as circles or in some cases as ellipses, squares, rectangles or hexagons. A unit cell approach is commonly used with a reinforcement particle embedded in the matrix [21], [22]. The stress state around the crack tip is monitored as the crack approaches the reinforcement particle [21], [22]. Particle shape effects on the crack-tip are then studied by changing the shape of the particle embedded in this unit cell [20], [21]. Standard shapes such as squares, rectangles, ellipses and hexagons are used. In some cases two particles are modeled and the influence of both particles on the crack-tip are studied [16], [17]. In more sophisticated models [16], a greater number of reinforcement particles (around 24) are taken into consideration. When more than one reinforcement particle is modeled, the shape and the size of all the particles are assumed to be identical. Particle distribution effects on crack growth are also modeled but only using particles with uniform shape and size [16], [19].
In reality, the particle microstructure is quite complex. Particles vary considerably in size, aspect ratio, and have irregular shapes. Particle distribution is important since any given microstructure is likely to contain “particle clusters”. Therefore, in order to understand the true behavior of the composite, the complex microstructure of the composite has to be taken into account. Numerical methods such as FEM or BEM have the ability to capture the complex geometry of the reinforcement particles and hence could be exploited for such studies. Wulf and co-workers [25], [26], [27], [28] were able to simulate ductile failure in Al(6061)/SiC using an advanced finite element method. Multiphase elements were used in conjunction with an automatic element elimination technique to simulate the stages of ductile fracture. Even though an “actual” microstructure was not used, their simulated microstructure contained 32 irregular SiC particles with complex shapes. In conventional single-phase elements the phase boundaries are simulated by element edges. In contrast, the multiphase element can be assigned to different materials when a phase boundary runs across it. A regular finite element mesh is created independent of the microstructural geometry. The complex microstructure geometry is then superimposed on this mesh and the material properties of the different phases are assigned to the integration points. Therefore, the primary advantage of using the multiphase element is that the need for a complex mesh can be avoided. However, it is likely that the microstructural geometry will change depending on the position of the integration points in the multiphase elements, especially if the mesh is coarse. Also, as a consequence of the different material properties in the multiphase elements, the stress concentration effects are reduced and stress discontinuities are not as clear. Thus, the element-averaged results obtained in simulations with the use of multiphase elements will differ from those of conventional single-phase elements. In the element elimination technique, an element is removed from the simulation based on certain damage criteria. When an element is removed the shape of the crack faces is affected. During the element elimination process the element is deleted completely. Therefore, with multiphase elements, sections of the particle and the matrix are removed, affecting not only the crack faces but also the geometry of the microstructure. Another limitation of multiphase elements is that occurrences at phase boundaries such as debonding cannot be simulated [29].
Chawla and co-workers [30], [31], [32], [33] and Gokhale and co-workers [34], [35] used the finite element method to study the mechanical behavior of MMCs using a microstructure-based model. Chawla and co-workers [31] used micrographs of Al–SiC MMCs to create numerical models with approximately 800 particles and simulate the mechanical behavior in two dimensions (2D). A serial sectioning based procedure was also used to obtain the complex microstructure of the reinforcement particle in three dimensions (3D). The mechanical behavior of the composite predicted by these 3D microstructure-based models correlated well with experimental results [30], [33]. They also showed that analytical models and numerical models using a unit cell approach were not as accurate as the microstructure-based models. Most of their focus up to this point has been on simulating the tensile behavior of MMCs. Modeling of crack growth in MMCs with an actual microstructure has not yet been conducted.
In this paper, we have used numerical modeling to study crack growth in particle reinforced composites by taking into account the complex geometry of the reinforcement particles and their distribution. We have chosen a SiC particle-reinforced Al matrix composite as a model system, although the results presented here are applicable to any particle reinforced system, where the particle is much stiffer than the matrix. The influence of reinforcement particle size, particle shape, and particle distribution on crack growth was studied. The key parameters influencing crack growth were identified. It was assumed that all reinforcement particles were perfectly bonded to the matrix and free of flaws. The matrix material was assumed to be free of flaws and behaved elastically. The reinforcement particles are treated as 2D entities and therefore subsurface crack–particle interaction is ignored. Interfacial decohesion (not an issue in Al–SiC systems formed through powder metallurgy process, because of the strong particle/matrix interface) and particle fracture have not been considered in the current models.
Section snippets
Materials and experimental procedure
The Al/SiC composites were fabricated using a powder metallurgy process. Pure Al and SiC particulate powders were mixed and blended using a V-cone blender. The powder mixture was cold compacted in a uniaxial press at 550 ± 20 MPa, and sintered at 493 ± 2 °C for 60 ± 1 min in a vacuum of 5 ± 2 μPa. The sintered composites were then sectioned and polished. Extreme care was taken during metallographic sample preparation to minimize the extent of particle fracture due to polishing. Optical micrographs were
Quantifying particle clustering in discontinuously reinforced composites
The mechanical behavior of MMCs is very much dependent on the microstructural homogeneity of the reinforcement particles [14], [15]. In particular, “particle clusters” have been shown to act as defects or stress concentration sites for crack nucleation. Thus, the ability to quantify the size and distribution of particle clusters and their effect on crack growth behavior is extremely important. Several techniques have been used to quantify SiC particle clustering in metal–matrix composites [15],
Conclusions
We have employed clustering analysis techniques to quantify the degree of clustering in SiC particle reinforced aluminum alloy matrix composites. Verification of the applicability of techniques was conducted on several composites, where the degree of clustering was tailored by systematically varying the Al:SiC particle size. It appeared that a minimum in particle clustering took place for particle size ratios of about one. Thus, when processing these composites, to minimize the degree of
Acknowledgements
The authors are grateful for financial support from the Office of Naval Research (Dr. A.K. Vasudevan, Program Manager, contract # N000140110694). The authors thank the creators of FRANC2D/L software, Dr. R.J. Fields (NIST) for providing the SiC particle reinforced Al matrix composite samples, and Dr. J.J. Williams for assistance with clustering analysis. We acknowledge useful discussions with Dr. P. Peralta, Arizona State University.
References (62)
- et al.
Fatigue behavior of discontinuously reinforced metal matrix composites
- et al.
A variational approach to the theory of the elastic behaviour of multiphase materials
J Mech Phys Solid
(1963) - et al.
Multi-scale characterization of spatially heterogeneous systems: implications for discontinuously reinforced metal–matrix composite microstructures
Mater Sci Eng A
(2001) - et al.
Numerical modelling of particle distribution effects on fatigue in Al–SiCp composites
Mater Sci Eng
(2001) - et al.
Finite element simulation to investigate interaction between crack and particulate reinforcements in metal–matrix composites
Mater Sci Eng
(1995) - et al.
Micromechanical simulation of crack growth in WC/Co using embedded unit cells
Comput Mater Sci
(1998) The interaction between a crack and an inclusion
Int J Eng Sci
(1972)- et al.
Micromechanical investigation of the fatigue crack growth behaviour of Al–SiC MMCs
Int J Fatig
(2004) - et al.
Simulation of crack propagation in alumina particle-dispersed SiC composites
J Eur Ceram Soc
(1999) - et al.
FE-simulation of crack paths in the real microstructure of an Al(6061)/SiC composite
Acta Mater
(1996)
Finite element modeling of crack propagation in ductile fracture
Comput Mater Sci
Simulation of experimental force–displacement curves by a finite element elimination technique
Comput Mater Sci
Computational mesomechanics of particle-reinforced composites
Comput Mater Sci
3D-finite-element-modeling of microstructures with the method of multiphase elements
Comput Mater Sci
Three-dimensional (3D) microstructure visualization and finite element modeling of the mechanical behavior of SiC particle reinforced aluminum composites
Scripta Mater
Effect of particle orientation anisotropy on the tensile behavior of metal matrix composites: experiments and microstructure-based simulation
Mater Sci Eng A
Digital image analysis and microstructure modeling tools for microstructure sensitive design of materials
Int J Plasticity
Micromechanics of complex three-dimensional microstructures
Acta Mater
Effects of matrix microstructure and particle distribution on fracture of an aluminum metal matrix composite
Mater Sci Eng A
Quantitative characterization of spatial clustering in three-dimensional microstructures using two-point correlation functions
Acta Mater
Mechanical behavior and microstructure characterization of sinter-forged SiC particle reinforced aluminum matrix composites
J Light Met
A finite element calculation of stress intensity factors by a modified crack closure integral
Eng Fract Mech
Interactive finite element analysis of fracture processes: an integrated approach
Theor Appl Fract Mech
Fracture problems in composite materials
Eng Fract Mech
Basic role of a hard particle in a metal matrix subjected to tensile loading
Acta Metall Mater
The deformation of discontinuously reinforced MMCs – II. The elastic response
Acta Metall Mater
Effective elastic response of two-phase composites
Acta Metall Mater
Weibull modeling of particle cracking in metal matrix composites
Acta Metall Mater
Effects of particle morphology and spacing on the strain fields in a plastically deforming matrix
Acta Mater
Composite materials – science and engineering
Metal matrix composites
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