Modelling and determination of dynamic elastic modulus of magnesium based metal matrix composites

Abstract

The aim of the present study was to determine the elastic modulus of magnesium based composites containing different volume fractions of SiC particulate using an innovative suspended beam type impact based technique. This applies classical vibration theory, which relates the resonant frequency of the test specimens to the geometry and material properties of the metal matrix composites. The elastic modulus values were determined from the funda mental resonant frequency obtained from the experiment and density measurements. In addition, a finite element model was proposed for determining the dynamic elastic modulus of MMCs with different SiC reinforcement content using the first natural frequency corresponding to the flexural mode. The elastic modulus values obtained from the finite element model were in close agreement with the values obtained from the impact based experiments and in better agreement than those from theoretical methods such as the shear lag, Eshelby, and Halpin–Tsai models.     

Machining of aluminium based metal matrix composites

Although metal matrix composites (MMCs) are generally regarded as extremely difficult to machine, it is also acknowledged that their machining behaviour is not fully understood. The work reviewed here confirms this widely held view but also suggests that the machinability of these materials can be improved by appropriate selection of the reinforcing phase, its volume fraction, size, and morphology as well as the composition and hardness of the matrix material. Cemented carbide tools can be used to machine some of the less abrasive materials at slow speeds but if higher production rates are required or the more abrasive materials are to be machined, polycrystalline diamond tooling is required.     

Application of model for work hardening behaviour of SiC reinforced magnesium based metal matrix composites

Abstract

An understanding of the work hardening behaviour of particulate reinforced metal matrix composites is crucial in optimising the parameters for deformation processing of these materials. In the present study, SiC reinforced magnesium metal matrix composites were produced using a liquid phase process. The microstructure of the composite was characterised and the mechanical properties were determined. The results of the ambient temperature tensile testing on the extruded Mg and Mg/SiC specimens revealed that an increase in the weight percentage of SiC particulates in pure magnesium increases the elastic modulus, does not affect the 0·2% yield strength, and reduces the ultimate tensile strength and ductility. A modified continuum model was applied to relate the work hardening behaviour of the composites to microstructural parameters and to predict the fracture strain of the composites. The model is shown to predict the fracture strain of the composites quite accurately for all the three weight fractions of reinforcements evaluated in the present study.     

Micro-mechanical modeling the densification behavior of titanium metal matrix composites

Vacuum hot pressing has been used for the development of Ti-MMCs using foil–fiber–foil method, and a unified micro-mechanical model has been presented to determine the densification behavior. The effects of processing conditions on the consolidation, together with microstructural evolutions of the materials have been investigated. The explicit representation of fiber array, which is coupled with deformation behavior of matrix materials, is modeled in finite element simulation to determine the effect of geometrical arrangements on densification process. The approach is then used to model the densification behavior of porous plastic materials using the parameters obtained, and comparisons are made with experimental data. As shown by the results, either increasing temperature or pressure leads to increasing densification rate but the conditions should be determined by the precisely controlled geometrical arrangements with processing conditions. Further experimental investigation of the densification behavior of SiC/Ti–6Al–4V composites using thermo-acoustic emission analysis has been performed, and the results obtained are compared with the model predictions. Good comparisons are achieved.     

考虑氧化损伤的陶瓷基复合材料弹性模量多尺度预测模型

分析了化学气相渗透(CVI)工艺制备的陶瓷基复合材料的氧化损伤演化规律,基于基体的微裂纹分布规律及界面、纤维、基体等组分氧化历程,建立了考虑温度、氧化时间影响的纤维和单胞两个尺度的弹性模量预测模型。预测结果表明,碳纤维(C_f)/SiC和SiC纤维(SiC_f)/SiC复合材料的拉伸弹性模量随氧化温度升高和氧化时间的增长,下降趋势越明显。通过复合材料高温氧化后的力学性能试验,验证了弹性性能预测模型的正确性:BN界面的SiC_f/SiC材料在1000℃不同时间氧化后预测结果与试验结果误差不超过2%;PyC界面的C_f/SiC在700℃不同时间氧化后预测结果与试验结果误差不超过7%。      

In situ fibre strength determination in metal matrix composites

Single fibre fragmentation tests were performed at room temperature on SiC/Ti-6242 specimens in order to estimate the in situ fibre strength. Tensile specimens were instrumented with two acoustic emission transducers and an extensometer in order to monitor the strain at which fibre breaks occurred. Data analysis utilized Monte Carlo simulations of fibre fragmentation. The fibre/matrix stress transfer profile near a fibre break was derived using a finite element analysis. Cohesive zone model is used to describe damage of the interfacial zone. Thermally induced residual stresses and matrix plastic deformations were accounted for. The results presented in this paper show that the in situ Weibull parameters of the fibre are smaller than the reference obtained on as received fibres. Analysis of data raised questions about the validity of the Monte Carlo simulation method.     

Elastic modulus and vibration damping in Iron/Copper- and steel-based metal matrix composites

Measurements were made of the dynamic flexural modulus, dynamic Young's modulus, damping, strain amplitude, and the strain amplitude dependence of damping in iron/copper- and steel-based metal matrix composites. Comparisons were made concerning the steel matrix specimens before and after heat treatment. The flexural modulus tests were performed using the Grindosonic technique, while the Young's modulus, damping, strain amplitude, and the strain amplitude dependence of damping were determined using the piezoelectric ultrasonic composite oscillator technique (PUCOT). Metallographic studies utilizing chemical etching, optical and electron microscopy, and microhardness testing were performed to assess the distribution of the fibres in the composites. The variation of dynamic Young's modulus with respect to percentage copper in the composites followed the rule of mixtures.     

The elastic and compressive properties of hybrid metal matrix composites/hexagonal prismatic cellular solids

An analysis is presented of the elastic and compressive properties of hybrid metal matrix composite (MMC) materials containing a uniform distribution of hexagonal prismatic cells which form closely spaced arrays separated by thin walls. The cell walls are considered to be reinforced by chopped fibers, whiskers, or particulates, thus forming a MMC. Exact derivations of the moment of inertia, elastic moduli, and compressive strength are presented, and approximations to these expressions are discussed. Results of these analyses are applied to the calculations of elastic moduli, flexural rigidity, and compressive strength of a square beam. Comparisons are made between the cases of unreinforced aluminum and steel cell walls and the cases of graphite chopped fiber reinforced aluminum and tungsten chopped fiber or whisker reinforced steel. The axial modulus and flexural rigidity of this type of structure made from Gr/Al composite are superior to unreinforced steel cellular structures only when the volume fraction of reinforcement exceeds about 30%. The material with reinforced cell walls is distinctly superior to its unreinforced counterpart by a factor of 4·3 at 50 volume percent graphite chopped fiber in aluminum.     

Elastic constants determination of thin cold-rolled stainless steels by dynamic elastic modulus measurements

Temperature dependence of elastic constants of thin cold-rolled stainless steel has been measured by using the acoustic resonance method. Identification of the vibration mode has been examined numerically and experimentally. The elastic constants at room temperature have also been measured by the pulse echo method. In addition, the texture effect on the elastic constants has been analysed by assuming the specimen has orthorhombic structure.     

Strain gradients and continuum modeling of size effect in metal matrix composites

Summary Constitutive modeling for the particle size effect on the strength of particulate-reinforced metal matrix composites is investigated. The approach is based on a gradient-dependent theory of plasticity that incorporates strain gradients into the expression of the flow stress of matrix materials, and a finite unit cell technique that is used to calculate the overall flow properties of composites. It is shown that the strain gradient term introduces a spatial length scale in the constitutive equations for composites, and the dependence of the flow stress on the particle size/spacing can be obtained. Moreover, a nondimensional analysis along with the numerical result yields an explicit relation for the strain gradient coefficient in terms of particle size, strain, and yield stress. Typical results for aluminum matrix composites with ellipsoidal particles are calculated and compare well with data measured experimentally.     

Effective elastic modulus and micro-structure damage of particle-reinforced composites

A new analysis method of effective elastic modulus for composites has been developed by combining Eshelby’s equivalent inclusion method and self-consistent method. The equations obtained can describe the evolution of debonding damage of the composites with multi-phase particles and single-phase particles. Based on the incremental relation between particles and the matrix, the incremental constitutive relations of composite, matrix, particles and voids have been developed. Numerical analysis has been conducted for Ramburg–Qsgood function incorporating with equivalent elastic modulus obtained. The constitutive equation curves for different particle volume fractions can describe the influence of debonding damage on effective elastic modulus of the composites. Numerical results of the present study have a better agreement with the experimental results.     

Microstructure-based modeling of the deformation behavior of particle reinforced metal matrix composites

A review is provided of the use of analytical models and two dimensional (2D) and three dimensional (3D) microstructure based FEM models to accurately predict the properties of particle reinforced composite materials. It is shown that analytical models do not account for the microstructural factors that influence the mechanical behavior of the material. 2D models do capture the anisotropy in deformation behavior induced by anisotropy in particle orientation. The experimentally-observed dependence of Young's modulus and tensile strength is confirmed by the 2D microstructure-based numerical model. However, because of the 2D stress state, a realistic comparison to actual experimental values is not possible. A serial sectioning process can be used to reproduce and visualize the 3D microstructure of particle reinforced metal matrix composites. The 3D microstructure-based FEM accurately represents the alignment, aspect ratio, and distribution of the particles. Comparison with single particle and multiparticle models of simple shape (spherical and ellipsoidal) shows that the 3D microstructure-based approach is more accurate in simulating and understanding material behavior.     

Cast metal matrix composites

Abstract

Metal matrix composites have been available in certain forms for at least two decades, e.g. boron fibre reinforced aluminium and various dispersed phase alloys and cermets. Recently, a range of alumina and silicon carbide fibres, whiskers, and particles with diameters <20 μm have become available. The possibilities of incorporating these materials into metals to improve stiffness, wear resistance, and elevated temperature strength without incurring weight penalties have attracted the attention of design engineers in the aerospace and automobile industries. The aim of the present paper is to outline the manufacturing processes for such composites, in particular those based upon liquid metal technology, e.g. squeeze casting and spray forming. Some of the mechanical and physical properties which have been determined for these materials are described. An analysis of how matrix alloy selection may influence tensile and fracture behaviour of short fibre and particle reinforced composites is attempted.

MST/770     

Analytical modeling of damping at micromechanical level in particulate-reinforced metal matrix composites

A new model for calculating the damping capacity of particulate-reinforced metal matrix composites (PMMCs) is proposed based on the assumption that the energy loss mainly results from the anelasticity of the particulate and matrix and the micro-plasticity of the matrix under small strain amplitude. Finite element method (FEM) with a multi particle model has been adopted. The results show that the energy loss in the loading direction can represent the total energies consumed in the composites. Moreover, the results calculated with the new model show good coincidence to the Granato–Lücke theory, which demonstrates the feasibility of damping calculation with the method.     

颗粒增强镁基复合材料的研究现状

综述了颗粒增强镁基复合材料常用的基体合金,常用的增强相及其镁基复合材料的制备技术、组织和性能等,并对颗粒增强镁基复合材料的发展进行了展望.     

Fatigue of metal matrix composites

One unidirectional and two laminated 6061-0 A-B composite plates were tested under various cyclic loading conditions. Three types of material response to cyclic loading were identified; No evidence of damage at relatively low cyclic loads, damage accumulation caused primarily by growth of long matrix cracks parallel to the fibers in off-axis layers at higher loads, and sudden localized failure of the fibers. Quantitative analysis of the results shows that the extent of internal damage, demonstrated by a reduction in axial elastic modulus, depends on the applied stress range and is independent of mean stress. The stress range at which damage first starts to appear coincides with the shakedown range of the laminate.

---

Résumé On a testé sous des conditions de contrainte cyclique variable des plaques constituées d'une part par des alliages 6061-0 A-B unidirectionnels et d'autre part du même alliage composite bilaminé. On a identifié trois types de réponse du matériau aux contraintes cycliques, à savoir la non-évidence d'un dommage pour des cycles de charge à faible amplitude relative, une accumulation du dommage causé principalement par la croissance de longues fissures matricielles parallèles aux fibres dans les couches éloignées du plan médian à des contraintes plus élevées, et une fissure soudainement localisée des fibres. L'analyse quantitative des résultats montre que 1'extension du dommage interne telle qu'elle est dóntree par une réduction du module axial d'élasticité, dépend de l'amplitude des contraintes appliquées et est indéndante de la contrainte moyenne. L'amplitude de contrainte auquelle un dommage commence à apparaître coíncide avec l'amplitude de l'adaptation plastique du laminé telle qu'établie par le théorème de Melan.

     

Analysis of effective elastic modulus for multiphased hybrid composites

Short fiber reinforced composites inherently have fiber length distribution (FLD) and fiber orientation distribution (FOD), which are important factors in determining mechanical properties of the composites. Since the internal structure has a direct effect on the mechanical properties of the composites, a Micro-CT was used to observe the three dimensional structure of fibers in the composites and to acquire FLD and FOD. It was successful to investigate FLD, FOD, and fiber orientation states and to predict the elastic modulus of the hybrid system. Since hybrid composites used in this study consist of three phases of particles, glass fibers, and matrix, theoretical hybrid modeling is required to consider reinforcing effects of both particles and glass fibers. Interaction between the particles and matrix was considered by using a perturbed stress–strain theory, the Tandon–Weng model. In addition, the laminating analogy approach (LAA) was used to predict the overall elastic modulus of the composite. Theoretical prediction of hybrid moduli indicated that there was a possibility of poor adhesion between glass fibers and matrix. The poor interfacial adhesion was confirmed by morphological experiments. This theoretical and experimental platform is expected to provide more insightful understanding on any kinds of multiphased hybrid composites.     

Thermal expansion characteristics of cast Cu based metal matrix composites

Like any other metal/alloy, copper and its alloys also soften at elevated temperatures. Reinforcing with ceramic or carbon fibres is one of the suggested solutions to overcome this. Very limited literature is available on Cu based metal matrix composites (MMCs); none of these pertain to liquid phase fabrication. Hence, a systematic investigation was carried out on MMCs based on copper, with alumino-silicate fibres and carbon fibres as reinforcements. The MMCs thus produced exhibit a uniform distribution of reinforcement in the matrix. Coefficient of thermal expansion (CTE) values are lower than that of pure copper.