Particle reinforcement of ductile matrices against plastic flow and creep

A theoretical investigation is made of the role of non-deforming particles in reinforcing ductile matrix materials against plastic flow and creep. The study is carried out within the framework of continuum plasticity theory using cell models to implement most of the calculations. Systematic results are given for the influence of particle volume fraction and shape on the overall behavior of composites with uniformly distributed, aligned reinforcement. The stress-strain behavior of the matrix material is characterized by elastic-perfectly plastic behavior or by power-law hardening behavior of the Ramberg-Osgood type. A relatively simple connection is noted between the asymptotic reference stress for the composite with the power-law hardening matrix and the limit flow stress of the corresponding composite with the elastic-perfectly plastic matrix. The asymptotic reference stress for the composite with the power-law matrix is applicable to steady-state creep. A limited study is reported on the overall limit flow stress for composites with randomly orientated disc-like or needle-like particles when the particles are arranged in a packet-like morphology.     

Computational modeling of metal matrix composite materials—II. Isothermal stress-strain behavior

The mechanical behavior of particulate reinforced metal matrix composites, in particular an SiC reinforced Al-3 wt% Cu model system, was analyzed numerically using the computational micromechanics approach. In this, the second in a series of four articles, the isothermal overall stress-strain behavior and its relation to microstructural deformation is examined in detail. The macroscopic strengthening effect of the reinforcement is quantified in terms of a hardness increment. As seen in the first article for microscale deformation, inhomogeneous and localized stress patterns develop in the microstructures. These are predominantly controlled by the positions of the reinforcing particles. Within the particles stress levels are high, indicating a load transfer from matrix to reinforcement. The higher straining that develops in the matrix grains, relative to the unreinforced polycrystal, causes matrix hardness advancement. Hydrostatic stress levels in the composite are enhanced by constraints on plastic flow imposed by the particles. Constrained plastic flow and matrix hardness advancement are seen as major composite strengthening mechanisms. The latter is sensitive to the strain hardening nature in the matrix alloy. To assess the effects of constraint more fully, simulations using external confining loads were performed. Both strengthening mechanisms depend strongly on reinforcement volume fraction and morphology. In addition, texture development and grain interaction influence the overall composite behavior. Failure mechanisms can be inferred from the microscale deformation and stress patterns. Intense strain localization and development of high stresses within particles and in the matrix close to the particle vertices indicate possible sites for fracture.     

Computational modeling of metal matrix composite materials—III. Comparisons with phenomenological models

The mechanical behavior of particulate reinforced metal matrix composites, in particular an SiC reinforced Al-3 wt% Cu model system, was analyzed numerically and analytically. In this, the third article in a series, the results of the computational micromechanics are compared with those of simpler and more approximate analytical/numerical models. The simplerapproaches considered use phenomenological theories of plasticity and power-law strain hardening. Models that predict overall composite behavior make use of a result, valid for incompressible materials in small strain, that both pure matrix material and composite harden with the same hardening exponent. Results of micromechanical simulations, with power-slip system hardening, show that in a very approximate sense over restricted strain regions, power-law slip hardening is preserved with the power-law exhonent tending to increase with volume fraction. The results of the computations presented in the previous article are compared with the predictions of one such analytical/numerical model, where the matrix hardening function is fitted to the unreinforced poyycrystal stress-strain response. This model employs the self-consistent method to quantify strengthening. There is good agreement between the computed and predicted results. Simulations are performed using existing reinforcement geometry but replacing the physically based crystal plasticity theory with the phenomenologically based J₂ flow theory. The results are in good qualitative agreement with those of the original crystal plasticity simulations at both the microscale and the macroscale. Deformation patterns in the J₂ flow theory composites are smoother and tend to be less localized than those in the crystal plasticity composites; however, these features depend strongly on volume fraction and morphology. The J₂ flow theory composites display power-law exponents whose dependence on overall strain, volume fraction and morphology are much more easily characterized than in the crystal plasticity case.     

An analytical study of residual stress effects on uniaxial deformation of whisker reinforced metal-matrix composites

Finite element modeling was utilized to simulate the stress-strain response of discontinuous SiC whisker reinforced aluminium-matrix composites, accounting for the thermal residual stresses (TRS) generated during solution treatment. The contributions of various micro-mechanisms to overall composite strengthening and deformation, and the impact of TRS on each mechanism were explicitly evaluated. It was inferred that constrained matrix plastic flow and matrix-to-fiber load transfer are the predominant sources of strengthening, with enhanced matrix dislocation density playing a secondary role. Residual stresses were found to significantly affect each of the operative strengthening mechanisms and hence the composite properties. Comparison with experiments revealed that the trends predicted by the model are generally consistent with actual composite behavior, although the model overpredicts work hardening rate. A parametric study of the effects of whisker volume fraction, aspect ratio and spacing on tensile and compressive deformation was also conducted. The results showed that increasing volume fraction, close end-to-end spacing and large aspect ratios result in greater strength and stiffness.     

Damage due to fracture of brittle reinforcements in a ductile matrix

A micromechanical model is developed for brittle particle reinforced metal matrix composites sustaining damage. A composite with uniformly distributed damage is modelled by a three-phase damage cell consisting of a cracked particle in a cylindrical matrix cell embedded in an undamaged composite cylinder. The fraction of broken particles to all particles is taken as the ratio of the broken-particle/matrix cell volume to the whole damage cell volume. Systematic analysis is carried out for aligned spherical and cylindrical particles in an elastic-perfectly plastic matrix subject to tensile loading normal to the plane of particle cracks. The influence of damage evolution paths on the composite stress-strain behavior is investigated. Results are given for the effects of damaged particle percentage, total particle volume fraction and particle shape on the overall composite limit flow behavior. Significant reduction in composite limit flow stress may occur if most of the particles are broken. For composite with spherical reinforcement, the reduction is found to be linearly dependent on the percentage of damaged particles.     

Finite element analysis of the effect of particle alignment on the deformation behavior for a ductile matrix containing hard particles

The goal of this work is to determine the role of the particulate alignment on the overall deformation behavior of metal matrix composites. Stress–strain behavior of hard particle-ductile matrix materials were analyzed using finite elements method. The effects of volume fraction and distribution geometry of particles were investigated. The composite microstructure was assumed to be a 3-D infinite periodic array of spherical particles embedded in the matrix. Transversely aligned and staggered unit cell approximations were used for analyzing the particle distribution geometry effects. The effect of particle alignment on the overall stress–strain behavior of the composites was followed through unit cells having different aspect ratios. The strengthening and strain hardening in the hard particle-ductile matrix composite system were found to be controlled primarily by the volume percent reinforcement. Distribution geometry of reinforcement as represented by that the ratio of particle diameter to distance between nearest neighbor particles also has great effect on deformation behavior.     

Effect of fiber spatial arrangement on the transverse strength of titanium matrix composites

The transverse strength of titanium matrix composites (Ti-6Al-4V-SiC) with rectangular and hexagonal fiber arrangements was measured as a function of fiber volume fraction and cladding thickness. A net-section model was also developed to predict the strength as a function of fiber spatial arrangement. The model predictions are in good agreement with experimental results and recent finite element modeling (FEM) simulations. The data and model show that the transverse strength, for a fixed net fiber volume fraction, is strongly dependent on the cladding thickness, testing direction, and fiber spatial arrangement. The implications are particularly important for the design of rotating components such as rings or disks. For example, the transverse strength in the radial and axial directions can be tailored by using a rectangular fiber array and varying the cell aspect ratio. Another simple strategy for increasing the transverse strength, for an equivalent net fiber volume fraction, is to increase the cladding thickness. For some fiber arrangements, a locally high volume fraction composite surrounded by a thick cladding can be significantly stronger than a composite with a uniform fiber distribution.     

Micromechanical modeling of unidirectional continuous sigma fiber-reinforced Ti-6Al-4V subjected to transverse tensile loading

A micromodeling analysis of unidirectionally reinforced Ti-6-4/SM1140+ composites subjected to transverse tensile loading has been performed using the finite-element method (FEM). The composite is assumed to the infinite and regular, with either hexagonal or rectangular arrays of fibers in an elastic-plastic matrix. Unit cells of these arrays are applied in this modeling analysis. Factors affecting transverse properties of the composites, such as thermal residual stresses caused by cooling from the composite processing temperature, fiber-matrix interface conditions, fiber volume fraction, fiber spacing, fiber packing, and test temperature are discussed. Predictions of stress-strain curves are compared with experimental results. A hexagonal fiber-packing model with a weak fiber-matrix interfacial strength predicts the transverse tensile behavior of the composite Ti-6-4/SM1140+ most accurately.     

The influence of residual stress on the yielding of metal matrix composites

A systematic numerical study of the effect of residual stresses on the yielding behavior of composites comprised of elastic particles well bonded to a ductile matrix is carried out. The calculations are made within the framework of continuum plasticity theory using cell models. An investigation is made into the roles volume fraction, particle shape, and hardening play in this interaction. A slight transient softening of the composite in both tension and compression is found, but the limit stress of the composite is unaffected by the residual stress. Thus the limit stress-strain response is symmetric in tension and compression for strains greater than a few times the matrix yield strain. A qualitative connection is made between the transient reduction in stiffness and the extent to which there was prior plastic deformation in the matrix due to residual stresses.     

Effects of thermal residual stresses and fiber packing on deformation of metal-matrix composites

The combined effects of thermal residual stresses anmd fiber spatial distribution on the deformation of a 6061 aluminum alloy containing a fixed concentration unidirectional boron fibers have been analyzed using detailed finite element models. The geometrical structure includes perfectly periodic, uniformly spaced fiber arrangements in square and hexagonal cells, as well as different cells in which either 30 or 60 fibers are randomly placed in the ductile matrix. The model involves an elastic-plastic matrix, elastic fibers, and mechanically bonded interfaces. The results indicate that both fiber packing and thermal residual stresses can have a significant effect on the stress-strain characteristics of the composite. The thermal residual stresses cause pronounced matrix yielding which also influences the apparent overall stiffness of the composite during the initial stages of subsequent far-field loading along the axial and transverse direction. Furthermore, the thermal residual stresses apparently elevate the flow stress of the composite during transverse tension. Such effects can be traced back to the level of constraint imposed on the matrix by local fiber spacing. The implications of the present results to the processing of the composites are also briefly addressed.     

Effect of temperature and strain rate on the compressive flow of aluminum composites containing submicron alumina particles

Uniaxial compression tests were conducted on aluminum composites containing 34 and 37 vol pct submicron alumina particles, to study the effect of temperature and strain rate on their flow stress. For temperatures between 25 °C and 600 °C and strain rates between 10⁻³ and 1 s⁻¹, the flow stress of the composites is significantly higher than that of unreinforced aluminum tested under similar conditions. This can be attributed to direct strengthening of the composites due to load sharing between the particles and the matrix, and an enhanced in-situ matrix flow stress resulting from a particle-induced increase in dislocation density. The composites, however, exhibit the same stress dependence on temperature and strain rate as unreinforced aluminum, indicating a common hardening mechanism, i.e., forest dislocation interactions. The forest hardening present under the explored testing conditions masks the effects of direct dispersion strengthening operative at lower deformation rates in these materials.     

Correlation of uniaxial yielding and substructure in aluminum-stainless steel composites

Stress-strain behavior and associated structural detail have been characterized in aluminum-stainless steel vacuum hot-pressed composites subjected to uniaxial tension or compression. Particular emphasis was placed on the premacroyield region. Volume fractions of reinforcement 0.041, 0.11, 0.153, 0.212, 0.248, and 0.328 have been examined with the load applied parallel to the direction of wire reinforcement. Dislocation configurations have been characterized as a function of overall composite strain, volume fraction of reinforcement, and distance into the matrix from the matrix-wire interface. In tensile loading, experimental values of the precision elastic limit, microyield stress (strain 2.5 x 10^-6) and macroyield stress (strain 1 x 10^-3) are in close agreement with values calculated from the rule of mixtures. Similar agreement is found in compression for the initial elastic modulus, however, the experimental precision elastic limit and microyield stress are higher than the calculated values by a factor ~2, and the macroyield stress is higher by a factor of 5 to 8. At a given level of strain and volume fraction of reinforcement, dislocation configurations, and dislocation densities are independent of distance from the matrix-wire interface. Alternatively, dislocation configurations and dislocation densities are essentially independent of volume fraction of reinforcement at a given level of strain. It is concluded that the matrix responds to its percentage of the applied stress as if it were the only phase present, there being no long-range matrix-wire interaction perturbing the matrix dislocation substructure. Compressive loading of composites in the direction of reinforcement constitutes a form of buckling test.     

不同陶瓷颗粒增强铁基复合材料力学性能的研究(英文)

Mechanical properties of iron matrix composites reinforced by different types of ceramic particles(SiC,Cr3C2,TiC and Ti(C,N)) prepared by the two-stage resistance sintering were studied experimentally.It was found that tensile strength of SiC/Fe composite shows the highest among the four types of composites.The elongation of all the composites decreases as increasing of reinforcement volume fraction.The stress-strain curves of the composites were simulated by Eshelby approach modeling to reveal the strengthening mechanisms.The modeling and microstructure observations suggest that the strengthening mechanism of the iron matrix composites relies not only on load sharing of the reinforcements but also on reinforcement increasing matrix strength.     

The influence of particle distribution on the mechanical response of a particulate metal matrix composite

A self-consistent model, based on Eshelby's equivalent inclusion method, has been developed to predict to flow of a particulate-reinforced alloy. The model gives excellent agreement with the measured elastic moduli for Al/SiC composites. Beyond the elastic limit, the model predicts an increase in the initial work hardening rate with increasing particle content. At large strains (above about 1%) the stress-strain behaviour of the composite is parallel to that of the unreinforced alloy. The results agree well with those obtained by Bao et al. [G. Bao, J. W. Hutchinson and R. M. McMeeking, Acta metall. mater.39, 1871 (1991)] using finite element methods, indicating that solutions based on average stress fields around particles do capture the essential features of composite strengthening. However, the current treatment can be readily extended to treat the effect of an inhomogeneous particle distribution on strength. As the degree of particle clustering increases, an increase in the rate of initial work hardening is predicted. Moreover, the strengthening ratio is increased substantially by clustering.     

The strength of metal matrix composites

There is intensive interest in metal matrix composites (MMCs) for automotive components, and the first production applications in Japan use discontinuous fibers as the reinforcements. These fibers are randomly oriented, resulting in an MMC with isotropic properties. However, there are conflicting reports on the tensile strengths attainable. In some cases, the strength increases with increasing volume fraction(V _f) of fibers, while in other cases, there is little or no benefit. A simple method is proposed to calculate the strength of this type of MMC. It is shown that the fibers oriented perpendicular to the stress direction play a key role, and the strength depends upon the strength of the interfacial bond. Upper and lower limits of the composite strength are calculated. If the bond strength is larger than the matrix strength, the composite strength has a maximum value which increases withV _f. If the bond strength is weaker than the matrix, the composite strength has a minimum value which is either weakly dependent or even independent ofV _f. These calculations are in good agreement with examples taken from the literature of aluminum composites reinforced with either A1₂O₃, graphite, or SiC. The strength of the matrix alloy is shown to be a very important parameter: weak alloys are easily strengthened, while in certain cases, strong alloys may be weakened.     

Strengthening of a particulate metal matrix composite by quenching

The strengthening of a particulate metal matrix composite due to quenching was studied both experimentally and theoretically. The strengthening was attributed to two mechanisms: punched-out dislocations due to CTE mismatch strain and back stress. Both mechanisms were analyzed by theoretical modeling leading to a good agreement between the experimentally observed strengthening and the prediction by the models. A parametric study revealed that the volume fraction of particulate, quenching temperature and its temperature differential and particulate size are the major variables influencing the increase in composite flow stress.     

Influence of elastic inclusion morphology and matrix hardening behavior on bauschinger effect in metal matrix composites

Finite element modeling based on axisymmetrical cells was performed for relating the Bauschinger effect (BE) in metal matrix composites (MMCs) to the reinforcement volume fraction and shape, matrix hardening behavior, and plastic prestrain levels. It was found that elastic inclusions in MMCs introduce a significant BE, which is ascribed to the residual phase stresses in the component phases. The BE introduced by cylindrical inclusions is more significant than that of spherical ones and increases rapidly with increasing the aspect ratio of the cylindrical inclusion. The volume fraction of the elastic inclusion has a strong effect on BE. The hardening behavior of the matrix has a weak effect on BE. The BE increases with increasing plastic prestrain level.     

纤维类型和涂层对纤维增强MoSi2复合材料弯曲性能的影响

以短切碳纤维(Cf)和碳化硅纤维(SiCf)为增强相,并用化学气相渗透法对部分纤维进行炭涂层处理,采用热压法制备了4种纤维增强MoSi2基复合材料(SiCf-MoSi2、SiCf/C-MoSi2、Cf-MoSi2和Cf/C-MoSi2),研究了纤维类型及表面炭涂层对MoSi2基复合材料弯曲性能的影响.结果表明纤维的加入明显提高了MoSi2的抗弯强度,加入5%SiCf和5%Cf的复合材料的强度比纯MoSi2分别提高了9.0%和22.8%,Cf增强作用明显优于SiCf;纤维类型相同时,具有炭涂层的纤维增强效果更显著,5%Cf/C-MoSi2复合材料的强度最高,达到了364.7MPa,比纯MoSi2的强度提高了30%;扫描电镜分析表明,无炭涂层的SiCf与MoSi2基体间存在着明显的裂缝,炭涂层改变了纤维与基体的界面结合;有涂层纤维的断裂机制为首先脱粘然后拔出.     

Dynamic Deformation Behavior of Zr-Based Amorphous Alloy Matrix Composites Reinforced with STS304 or Tantalum Fibers

The Zr-based amorphous alloy matrix composites reinforced with stainless steel (STS) or tantalum (Ta) continuous fibers were fabricated without pores or defects by liquid pressing process, and their dynamic deformation behaviors were investigated. Dynamic compressive tests were conducted by a split Hopkinson pressure bar, and then the test data were analyzed in relation to the microstructures and the deformation modes. In the STS-fiber?Creinforced composite, the STS fibers could interrupt the propagation of cracks initiated in the matrix and promoted the continuous deformation without fracture according to the strain-hardening effect of the fibers themselves. The Ta-fiber?Creinforced composite showed the higher yield strength than the STS-fiber?Creinforced composite, but the cracks were not interrupted properly by the Ta fibers according to the lower ductility and strain hardening of the Ta fibers. Both the Ta and STS fibers favorably affected the strength and ductility of the composites by interrupting the propagation of cracks formed in the amorphous matrix, by dispersing the stress applied to the matrix, and by promoting deformation mechanisms such as fiber buckling. The STS-fiber?Creinforced composite showed the higher compressive strength and ductility than the Ta-fiber?Creinforced composite because the STS fibers were higher in the resistance to deformation and fracture than the tantalum fibers.     

Fibre uniformity and cavitation during the consolidation of metal-matrix composite via fibre-mat and matrix-foil diffusion bonding

Fibre uniformity is important for ensuring overall mechanical properties of a composite. The conditions for achieving uniform fibre distribution in solid-state consolidated composites are quantitatively analysed. It is shown that the uniformity is influenced by initial fibre spacing, fibre packing and foil thickness before consolidation and matrix flow during consolidation. A graphical technique is presented to determine optimum pre-consolidation arrangement of fibres and foils for a given volume fraction. Residual cavities in partially bonded composites are observed in both hexagonally and rectangularly packed fibre arrays. Foil bending is mainly the cause for the cavities found in the former case, whereas in the rectangular array an ear defect is observed after an intermediate stage of bonding and is believed to be responsible for the voids which form during matrix flow in this case. The initiation of the ear defect is determined by matrix volume incompressibility and quantitatively analysed with respect to different conditions of the flow constraint imposed during consolidation. These predictions are compared favourably with experimental results.