An analysis of the effects of matrix void growth on deformation and ductility in metal-ceramic composites

Deformation and failure of metal-matrix composites, by the nucleation and growth of voids within the ductile matrix, are studied numerically and experimentally. The matrix material is modelled as an elastic-viscoplastic ductile porous solid to characterize the evolution of damage from void formation. The material systems chosen for parametric analyses and for quantitative comparisons between numerical analyses and experiments are aluminum alloys discontinuously reinforced with SiC. The brittle reinforcement phase, in the form of spheres, particulates with sharp corners, or cylindrical whiskers, is modelled as elastic or rigid, with the interfaces between the ductile matrix and the brittle reinforcement assumed to be perfectly bonded. The overall constitutive response of the composite and the evolution of matrix failure are analyzed using finite element models within the context of axisymmetric and plane strain formulations. Detailed parametric analyses of the effects of (i) reinforcement shape, (ii) reinforcement volume fraction, (iii) mechanical properties of the matrix, (iv) nucleation strain and volume fraction of void-nucleating particles, and (v) reinforcement distribution on the overall deformation and ductility of the composite are discussed. The numerical predictions of yield strength, strain hardening exponent and ductility for the composites with different volume fractions of SiC particulates are also compared with experimental measurements.     

An experimental and numerical study of deformation in metal-ceramic composites

The deformation characteristics of ceramic whisker- and particulate-reinforced metal-matrix composites were studied experimentally and numerically with the objective of investigating the dependence of tensile properties on the matrix microstructure and on the size, shape, and distribution of the reinforcement phase. The model systems chosen for comparison with the numerical simulations included SiC whisker-reinforced 2124 aluminum alloys with well-characterized microstructures and 1100-o aluminum reinforced with different amounts of SiC particulates. The overall constitutive response of the composite and the evolution of stress and strain field quantities in the matrix of the composite were computed using finite element models within the context of axisymmetric and plane strain unit cell formulations. The results indicated that the development of significant triaxial stresses within the composite matrix, due to the constraint imposed by the reinforcements, provides an important contribution to strengthening. Systematic calculations of the alterations in matrix field quantities in response to controlled changes in reinforcement distribution give valuable insights into the effects of particle clustering on the tensile properties. The numerical results also deliver a mechanistic rationale for experimentally observed trends on: (i) the effects of reinforcement morphology and volume fraction on yield and strain hardening behavior of the composite, (ii) the pronounced influence of reinforcement clustering on the overall constitutive response, (iii) ductile failure by void growth within the composite matrix, (iv) the insensitivity of the yield strength of the composite to changes in matrix microstructure, and (v) the dependence of ductility on the microstructure of the matrix and on the morphology and distribution of the reinforcement. The predictions of the present analyses are compared and contrasted with current theories of elastic and plastic response in multi-phase materials in an attempt to develop an overall perspective on the mechanisms of composite strengthening and of matrix and interfacial failure.     

The effect of matrix microstructure on the tensile and fatigue behavior of SiC particle-reinforced 2080 Al matrix composites

The effect of matrix microstructure on the stress-controlled fatigue behavior of a 2080 Al alloy reinforced with 30 pct SiC particles was investigated. A thermomechanical heat treatment (T8) produced a fine and homogeneous distribution of S′ precipitates, while a thermal heat treatment (T6) resulted in coarser and inhomogeneously distributed S′ precipitates. The cyclic and monotonic strength, as well as the cyclic stress-strain response, were found to be significantly affected by the microstructure of the matrix. Because of the finer and more-closely spaced precipitates, the composite given the T8 treatment exhibited higher yield strengths than the T6 materials. Despite its lower yield strength, the T6 matrix composite exhibited higher fatigue resistance than the T8 matrix composite. The cyclic deformation behavior of the composites is compared to monotonic deformation behavior and is explained in terms of microstructural instabilities that cause cyclic hardening or softening. The effect of precipitate spacing and size has a significant effect on fatigue behavior and is discussed. The interactive role of matrix strength and SiC reinforcement on stress within “rogue” inclusions was quantified using a finite-element analysis (FEA) unit-cell model.     

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.     

Micromechanical modeling of reinforcement fracture in particle-reinforced metal-matrix composites

Finite element analyses of the effect of particle fracture on the tensile response of particle-reinforced metal-matrix composites are carried out. The analyses are based on two-dimensional plane strain and axisymmetric unit cell models. The reinforcement is characterized as an isotropic elastic solid and the ductile matrix as an isotropically hardening viscoplastic solid. The reinforcement and matrix properties are taken to be those of an Al-3.5 wt pet Cu alloy reinforced with SiC particles. An initial crack, perpendicular to the tensile axis, is assumed to be present in the particles. Both stationary and quasi-statically growing cracks are analyzed. Resistance to crack growth in its initial plane and along the particle-matrix interface is modeled using a cohesive surface constitutive relation that allows for decohesion. Variations of crack size, shape, spatial distribution, and volume fraction of the particles and of the material and cohesive properties are explored. Conditions governing the onset of cracking within the particle, the evolution of field quantities as the crack advances within the particle to the particle-matrix interface, and the dependence of overall tensile stress-strain response during continued crack advance are analyzed. Formerly Graduate Research Assistants, Brown University     

Reinforcement shape effects on the fracture behavior and ductility of particulate-reinforced 6061-Al matrix composites

Particle shape effects on the fracture and ductility of a spherical and an angular particulate-reinforced 6061-Al composite containing 20 pct vol Al₂O₃ were studied using scanning electron microscopy (SEM) fractography and modeled using the finite element method (FEM). The spherical particulate composite exhibited a slightly lower yield strength and work hardening rate but a considerably higher ductility than the angular counterpart. The SEM fractographic examination showed that during tensile deformation, the spherical composite failed through void nucleation and linking in the matrix near the reinforcement/matrix interface, whereas the angular composite failed through particle fracture and matrix ligament rupture. The FEM results indicate that the distinction between the failure modes for these two composites can be attributed to the differences in the development of internal stresses and strains within the composites due to particle shape.     

Mechanical behavior of Al−Li/SiC composites: Part III. Micromechanical modeling

A micromechanical model is developed to compute the stress-strain curve of particle-reinforced metal-matrix composites under monotonic and cyclic deformation. The composite was modeled as a three-dimensional array of hexagonal prisms, each containing an intact or fractured reinforcement. The average stresses acting on the intact and damaged cells—as well as on the ceramic particles —were computed from the finite-element analysis of axisymmetric cylindrical cells, and the overall composite response was then calculated through an isostrain approach. The model was validated against the experimental results, reported in Parts I and II of this article, for an 8090 Al alloy reinforced with 15 vol pct SiC particles,^[1,2] where the matrix and reinforcement properties were obtained from mechanical tests on the unreinforced alloy and from quantitative microscopy analyses of the fraction of broken reinforcements in the composite. The critical mechanisms which controlled the deformation and damage processes in the composite during monotonic and cyclic deformation are discussed in light of the model results.     

Mechanical behavior of Al-Li/SiC composites: Part III. Micromechanical modeling

A micromechanical model is developed to compute the stress-strain curve of particle-reinforced metal-matrix composites under monotonic and cyclic deformation. The composite was modeled as a three-dimensional array of hexagonal prisms, each containing an intact or fractured reinforcement. The average stresses acting on the intact and damaged cells — as well as on the ceramic particles — were computed from the finite-element analysis of axisymmetric cylindrical cells, and the overall composite response was then calculated through an isostrain approach. The model was validated against the experimental results, reported in Parts I and II of this article, for an 8090 Al alloy reinforced with 15 vol pct SiC particles,^[1,2] where the matrix and reinforcement properties were obtained from mechanical tests on the unreinforced alloy and from quantitative microscopy analyses of the fraction of broken reinforcements in the composite. The critical mechanisms which controlled the deformation and damage processes in the composite during monotonic and cyclic deformation are discussed in light of the model results.     

On the flow behavior of constrained ductile phases

Effects of the matrix/reinforcement interface and the mechanical properties and size of the ductile reinforcement on the flow behavior of the constrained ductile reinforcement have been evaluated using a tensile test on a single Nb lamina imbedded in MoSi₂ matrix. It was found that work of rupture of the ductile reinforcement increased with size of the ductile reinforcement and with decreasing fracture energy of the matrix/reinforcement interface. It was also found that the work of rupture normalized by size and yield strength of the reinforcement was dependent on the interfacial properties and size of the reinforcement. Based on the observation, an analytical model is developed which gives insight into the influence on the stress-displacement curve of yield strength, work hardening, fracture energy of matrix/reinforcement interface, and size of the reinforcement. A characteristic decohesion length, which is a function of size of the reinforcement, has been identified by the model and related to the measured decohesion length. The results allow the extrapolation of the work of rupture measured from the large size of constrained ductile phases to the small size of the ductile phases. As the reinforcements used in composites are usually smaller in size than those tested in such tensile tests, the extrapolation of the work of rupture allows the contribution of ductile reinforcements to the toughness of a brittle matrix composite to be calculated.     

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.     

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.     

Structure and room-temperature deformation of alumina fiber-reinforced aluminum

Plastic deformation under uniaxial longitudinal tension and compression is investigated for pure aluminum reinforced with a high volume fraction of parallel alumina fibers. The matrix substructure is also examined in transmission electron microscopy. The aim is to study thein situ room-temperature mechanical behavior, particularly the work-hardening rate, of pure aluminum when reinforced with a high volume fraction of chemically inert ceramic reinforcement. The matrix substructure prior to deformation, composed of cells about2 μm in diameter, is similar to that of highly deformed unreinforced aluminum. Measured compressive composite elastic moduli agree with rule of mixture predictions; however, no elastic regime is found during tensile loading. As tensile deformation proceeds above a strain around 0.05 pct, a constant rate of work hardening is reached, in which the matrix contribution is negligible within experimental error. Upon unloading from tensile straining, Bauschinger yielding begins before the composite reaches zero load, as predicted by the rule of mixtures. The matrix substructure after load reversal retains a2- μm cell size but with greater irregularity in the dislocation configurations. Using the rule of mixtures,in situ stress-strain curves are derived for the reinforced aluminum matrix and described by a modified Voce law. Formerly with the Department of Materials Science and Engineering, Massachusetts Institute of Technology     

Ductile reinforcement toughening of γ-TiAl: Effects of debonding and ductility

The effects of reinforcement debonding and work hardening on ductile reinforcement toughening of γ-TiAl have been examined. Debonding has been varied by either the development of a brittle reaction product layer or by depositing a thin oxide coating between the reinforement and matrix. The role of work hardening has been explored by comparing a Nb reinforcement that exhibits high work hardening with a solution hardened TiNb alloy that exhibits negligible work hardening. It is demonstrated that a high work rupture is encouraged by extensive debonding when the reinforcement exhibits high work hardening. Conversely, debonding is not beneficial when the reinforcement exhibits low intrinsic ductility due to an absence of work hardening.     

Strain Rate Effect on Material Behavior of TRIP‐Steel/Zirconia Honeycomb Structures

A pure TRIP‐steel alloy and a novel zirconia reinforced TRIP‐steel matrix composite were implemented in a 2D square‐celled honeycomb structure fabricated by a paste extrusion method, respectively. In terms of a series of compression tests in out‐of‐plane loading direction the buckling and the pronounced strain hardening behavior of the honeycomb structures are described with regard to different material compositions and varied nominal strain rates. Both the compressive flow behavior and the microstructure evolution in the crushed zones are controlled by the rate of formation of strain‐induced martensite and the ceramic particle/steel matrix interactions. The insertion of magnesia partially‐stabilized zirconia (Mg‐PSZ) particles in the austenitic steel matrix cause an increased yield strength and higher compression stresses up to certain deformations degrees. The limited ductility of the composite materials is a consequence of the rearrangement and fracture of zirconia particles initiating cracks and shear bands during deformation. Consistently, the visible strain rate effects on the mechanical responses of the honeycomb structures are similar to AISI 304L austenitic stainless steel specimens in the form of compact rods. However, at high local strain rates generated in drop weight impact tests a micro‐inertia factor support the failure behavior of the cellular structures.     

Seismic Behavior of Concrete Columns Reinforced by Steel-FRP Composite Bars

Steel-fiber-reinforced polymer (FRP) composite bars (SFCBs) are a novel reinforcement for concrete structures. Because of the FRP’s linear elastic characteristic and high ultimate strength, they can achieve a stable postyield stiffness even after the inner steel bar has yielded, which subsequently enables a performance-based seismic design to easily be implemented. In this study, lateral cyclic loading tests of concrete columns reinforced either by SFCBs or by ordinary steel bars were conducted with axial compression ratios of 0.12. The main variable parameters were the FRP type (basalt or carbon FRP) and the steel/FRP ratio of the SFCBs. The test results showed the following: (1)?compared with ordinary RC columns, SFCB-reinforced concrete columns had a stable postyield stiffness after the SFCB’s inner steel bar yielded; (2)?because of the postyield stiffness of the SFCB, the SFCB-reinforced concrete columns exhibited less column-base curvature demand than ordinary RC columns for a given column cap lateral deformation. Thus, reduced unloading residual deformation (i.e., higher postearthquake reparability) of SFCB columns could be achieved; (3)?the outer FRP type of SFCB had a direct influence on the performance of SFCB-reinforced concrete columns, and concrete columns reinforced with steel-basalt FRP (BFRP) composite bars exhibited better ductility (i.e., a longer effective length of postyield stiffness) and a smaller unloading residual deformation under the same unloading displacement when compared with steel-carbon FRP (CFRP) composite bar columns; (4)?the degradation of the unloading stiffness by an ordinary RC column based on the Takeda (TK) model was only suitable at a certain lateral displacement. In evaluating the reparability of important structures at the small plastic deformation stage, the TK model estimated a much smaller residual displacement, which is unsafe for important structures.     

Experimental Investigation of Cyclic Behavior of Concrete-Filled Fiber Reinforced Polymer Tubes

Concrete-filled fiber reinforced polymer (FRP) tubes (CFFT) have in the last decade been used as girders, beam columns, and piles. The focus of research, however, has been exclusively on their monotonic behavior, with little or no attention to the implications of using CFFT in seismic regions. A total of six CFFT specimens were tested as simple span beam columns under constant axial loading and quasi-static reverse lateral loading in four point flexure. Three of the tubes were made using centrifuge (spin) casting with 12.7?mm thickness with the majority of the fibers in the longitudinal direction, whereas the other three were filament wound with 5?mm thickness and ±55° fiber orientation. One specimen for each type of tube had no internal reinforcement, whereas the other two incorporated approximately 1.7 and 2.5% steel reinforcement ratios, respectively. The two types of tubes represented two different failure modes; a brittle compression failure for the thick tubes with the majority of the fibers in the longitudinal direction, and a ductile tension failure for the thin tubes with off-axis fibers. The study showed that CFFT can be designed with ductility behavior comparable to reinforced concrete members. Significant ductility can stem from the fiber architecture and interlaminar shear in the FRP tube. Moderate amounts of internal steel reinforcement in the range of 1–2% may further improve the cyclic behavior of CFFT.     

Thermally and mechanically induced residual strains in Al-SiC composites

Neutron diffraction experiments were conducted on 15vol.% whisker and 20vol.% particulate reinforced aluminum/silicon carbide composites subjected to a rapid quench followed by various deformation histories. Corresponding numerical simulations were carried out using an axisymmetric unit cell model, with a phenomenological, isotropic hardening descriotion of matrix plasticity. Thermal expansion and the temperature dependence of material properties were accounted for. For the whisker reinforced matrix, quantitative agreement was generally found between the measured and calculated residual elastic strains. For the particulate reinforced matrix, the calculations tended to overestimate the magnitude of the residual strains parallel to the deformation axis, but very good agreement was obtained transverse to the deformation axis. For the silicon carbide reinforcement, both whisker and particulate, the variation of predicted residual elastic strains along the deformation axis was qualitatively consistent with the measurements, although quantitative agreement was often lacking. Measured and predicted residual strains perpendicular to the deformation axis for the silicon carbide typically were not in agreement. Parametric studies were carried out to ascertain the dependence of calculated flow strengths and residual strains on cell and reinforcement aspect ratio, and on reinforcement spacing and shape.     

Mechanical behavior of Al-Li/SiC composites: Part II. Cyclic deformation

The deformation and failure mechanisms under cyclic deformation in an 8090 Al-Li alloy reinforced with 15 vol pct SiC particles were studied and compared to those of the unreinforced alloy. The materials were tested under fully reversed cyclic deformation in the peak-aged and naturally aged conditions to obtain the cyclic response and the cyclic stress-strain curve. The peak-aged materials remained stable or showed slight cyclic softening, and the deformation mechanisms were not modified by the presence of the ceramic reinforcements: dislocations were trapped by the S′ precipitates and the stable response was produced by the mobile dislocations shuttling between the precipitates to accommodate the plastic strain without further hardening. The naturally aged materials exhibited cyclic hardening until failure, which was attributed to the interactions among dislocations. Strain localization and slip-band formation were observed in the naturally aged alloy at high cyclic strain amplitudes, whereas the corresponding composite presented homogeneous deformation. Fracture was initiated by grain-boundary delamination in the unreinforced materials, while progressive reinforcement fracture under cyclic deformation was the main damage mechanism in the composites. The influence of these deformation and damage processes in low-cycle fatigue life is discussed.     

Reinforcement of structural materials by Long Strong Fibres

Materials which flow at low stresses such as soft metals or plastics, can be strengthened by incorporation of stronger fibres. The mechanical principles governing this reinforcement are presented in a fashion applicable to discontinuous fibres and to matrices which have flow stresses dependent upon the strain rate. The strengths attainable by composites containing discontinuous fibres are discussed. Compliant matrices of small breaking strain,e.g. cement or plaster, are reinforced with fibres in order to prevent a single crack leading to rupture of the composite. The rules governing the density of cracks, the stress-strain curve of the composite and the cracking strain of the matrix within the composite are discussed and applied. Finally the relationship between fibre reinforcement and dispersion hardening is commented upon and the ways in which fibres interfere with dislocation motion and rearrangement discussed.     

Ductile-reinforcement toughening in γ-TiAl intermetallic-matrix composites: Effects on fracture toughness and fatigue-crack propagation resistance

The influence of the type, volume fraction, thickness and orientation of ductile phase reinforcements on the room temperature fatigue and fracture resistance of γ-TiAl intermetallic alloys is investigated. Large improvements in toughness compared to monolithic γ-TiAl are observed in both the TiNb- and Nb-reinforced composites under monotonic loading. Toughness increases with increasing ductile phase content, reinforcement thickness and strength; orientation effects are minimal. Crack-growth behavior is characterized by steep resistance curves primarily due to crack trapping/renucleation and extensive crack bridging by the ductile-phase particles. In contrast, under cyclic loading the influence of ductile phases on fatigue resistance is strongly dependent upon reinforcement orientation. Compared to monolithic γ-TiAl, improvements in fatigue-crack growth resistance are observed in TiNb-reinforced composites only in the face (C-L) orientation; crack-growth rates for the edge (C-R) orientation are actually faster in the composite. In comparison, Nb-particle reinforcements offer less toughening under monotonic loading but enhance the fatigue properties compared to TiNb reinforcements under cyclic loading.