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Interfacial stress is thought to have significant effects on electrical and oxygen transport properties in thin films of importance in solid oxide fuel cell applications. We investigate how in-plane biaxial stress modifies the electronic structure of La2/3Ca1/3MnO3 and La1/2Sr1/2MnO3 thin films prepared by pulsed laser deposition on three different substrates to vary the in-plane stress from tensile to compressive. The electronic structure was probed by X-ray absorption spectroscopy of the Mn L2,3-edge to characterize the interfacial disruption in this region in an element-specific, site-specific manner. The compressive or tensile interfacial strain modifies the relative concentrations of La and Sr in the interfacial region in order to achieve a better lattice match to the contact material. This atomic migration generates an interfacial region dominated by a compound with a single valency for the transition metal ion, resulting in a severe barrier to oxygen and electron transport through this region.

This paper investigates through-thickness propagation of compression waves induced by blast loads on the facesheet of a sandwich plate and how it is affected by the underlying material properties. A conventional sandwich design, which utilizes a closed cell foam core, is considered together with a modified design, which includes a thin polyurea interlayer between the outer (loaded side) facesheet and the foam core. The latter design is known to perform exceptionally well under impulse loads due to the significant stiffening of polyurea under high strain rates. This property reduces the amplitude and velocity of compression waves traveling into the foam core and prevents its sudden, excessive crushing. The problem was modeled with the explicit LS-Dyna finite element code. The results compare the short term behavior of the conventional and modified sandwich designs using a one-dimensional model for through-thickness wave propagation, and illustrate the long term effects on a multi-span sandwich plate subjec...

In this study, the behavior of conventional and modified sandwich plate designs subjected to blast loads is examined with the finite element method. The conventional sandwich design consists of thin outer (loaded side) and inner facesheets made of fibrous laminates, separated by a layer of structural foam core. In the modified designs, a thin ductile interlayer is inserted between the outer facesheet and the foam core. Two materials are selected for the interlayers; one is rate-independent, hyperelastic (polyurethane, PUR), and the other is rate and pressure-dependent, elastic—plastic (polyurea). A comparison is made between the two enhanced designs and the conventional design during an extended time period of 5.0 ms under an exponential pressure impulse lasting for 0.05 ms, and has a peak pressure of 100 MPa. Results show that utilizing PUR or polyurea to separate the outer facesheet and the foam core leads to a much reduced core compression, facesheet vibration, and overall deflection compared to the conventional design. Similar reductions are found in the kinetic energy and the stored and dissipated strain energy. This is attributed to the ability of the interlayers to store energy and shield the inner foam by exhibiting great stiffness under pressure. Although strain rates as high as 104 s—1 are produced by the blast pressure impulse in the sandwich plates, the strains in both the PUR and the polyurea interlayers are relatively small. This leads to generally similar responses for the two interlayer types, with the initially stiffer PUR providing a slightly better protection for the foam core.

Surfaces and interfaces in solids may behave differently from their bulk counterparts, particularly when the geometry is on the nanoscale. Our objective in this work is to assess the overall behavior of composites containing cylindrical inclusions with surface effects prevailing along the interfaces. In the formulation, we first decompose the loadings into three different deformation modes: the axisymmetric loadings, the transverse shear and the antiplane shear. For each deformation mode, we derive the energy potential incorporating the surface effects. Using a variational approach, we construct the Euler-Lagrange equation together with the natural transition (jump) conditions. The surface effects are represented by an interface of a membrane type, with in-plane moduli different from those of either phase. The overall elastic behavior of the composite is characterized by five constants. Four of them, except the transverse shear modulus, are derived in simple closed forms using an approach of neutral inclusion. For the transverse shear, we derive the value based on the generalized self-consistent method.

A novel procedure is proposed for evaluation of stress intensity factors of planar Mode III shear cracks perpendicular to a nearby interface between two isotropic elastic solids. Shear cracks traversing a flat layer bonded to two different elastic solids are also analyzed. The method is based on superposition of singular near tip stress and displacement fields generated by both the main crack and certain image cracks. Both the main and the image cracks are loaded by self-equilibrating shear tractions of different magnitude, such that matching parts of the said fields are made to satisfy traction and displacement continuity conditions at the interface. Selected comparisons with results obtained by different methods show good agreement. Applications of the method to other crack problems are discussed.

Sandwich plates used in marine structures are made of laminated face sheets bonded to a structural foam core. Low-velocity impact by a stiff indenter may cause local deflection of the face sheet and permanent deformation or crushing of an underlying volume of the foam core. Upon unloading, the face sheet tends to spring back, while the permanent strain in the core gives rise to residual stresses that may nucleate local interfacial cracks. Extension of such interfacial cracks by applied loads can compromise structural integrity. This article examines the protective effect of thin, ductile interlayers, inserted between the face sheet and the foam core, that absorb the face sheet deflection and thus prevent or reduce the extent of damage to the foam core. Finite element solutions are obtained for a stiff, incompressible, and very ductile polyurethane (PUR) interlayer, and also for a compliant and compressible elastomeric foam (EF) layer, in a sandwich plate made of quasi-isotropic AS4/3501-6 laminated face sheets and H100 PVC core. Loading is applied by a concentrated force acting on a rigid cylindrical indenter. Results show that the PUR interlayer better supports the impacted face sheet than does the foam core or the EF interlayer. The PUR layer also reduces the extent of permanent deformation of the foam core. At a given magnitude of applied load, the energy release rate for cracks extended by residual stresses at the interface between the foam core and either interlayer is much lower than that at the interface between the face sheet and the foam core in the conventional design.

Overall and local deflections of a single span of a continuous sandwich plate are evaluated under local contacts with a rigid indenter, at relative velocities of 10 and 20 m/s (20-40 knots), to simulate the effect of impacts that can be applied to ship sandwich structures by floating objects or moorings. Laminated carbon-vinyl ester face sheets and a H100 PVC foam core, possibly separated from the impacted face sheet by a stiff and ductile polyurethane (PUR) interlayer, comprise the sandwich plate. As in our previous study of the effect of quasi-static contacts (Suvorov, A.P. and Dvorak, G.J. (2005). Protection of Sandwich Plates from Low Velocity Impact, Journal of Composite Materials (to appear)), the focus is on the evaluation of contact forces and deflections of the face sheet and foam core interface, and on the membrane or in-plane strains in the face sheet at the contact point. These quantities are well-known potential sources of damage, causing core crushing, and face sheet delamination and/or penetration. As expected, the results show that the magnitudes of these quantities depend on both the distance of the contact point from the nearest support, and on the initial velocity of the indenter of a given mass. Both local face sheet deflections and core interface indentations are high if the impact point is within a distance from a support that is equal to 2-3 times the total sandwich plate thickness; significantly lower values are found at more distant contact points. These deflections are much reduced by replacing the foam core with an aluminum honeycomb in the supported region of the plate. However, this reinforcement elevates both the contact force and the in-plane strain in the face sheet. Therefore, thickening of the exposed face sheets should be considered around supports. Most of the kinetic energy is absorbed by the core, hence addition of the stiff and ductile PUR interlayer does not have as much effect on the results as it had in quasi-static contact.

The present paper deals with the cylindrical bending of sandwich plates consisting of an arbitrary number of orthotropic layers and resting on periodically spaced supports of finite length. A plane-strain analytical solution is developed based on series expansion of the plate displacements. This approach allows one to consider plates subjected to prescribed tractions or displacements on the top and bottom surfaces. In addition, nonuniform eigenstress distribution can be applied within each layer. A numerical solution is presented for two four-layer sandwich plates with different thin interlayers inserted between the orthotropic top face sheet and the foam core. Stress concentrations near supports are analyzed in detail.

Conventionally designed sandwich plates used in marine and ship structures consist of thin, laminated composite face sheets bonded to a relatively thick, compressible structural foam core layer. In service, the external face sheet often makes low velocity contact with floating objects or moorings that may cause reversible local deflection of the face sheet and permanent compression or crushing of the underlying foam, resulting in interface delaminations. Extension of such interfacial cracks under service loads may impair structural integrity. Modified designs that protect the foam core by inserting a ductile interlayer under the external face sheet, first proposed in our recent paper [Dvorak, G.J., Suvorov, A.P., in press. Protection of sandwich plates from low velocity impact. Journal of Composite Materials 38], are analyzed here in much greater detail and compared with their conventional counterparts. Two different interlayer materials are used, a stiff and incompressible polyurethane (PUR), and a compliant and compressible elastomeric foam (EF), together with the same face sheet and core materials. Response of the three different sandwich plate configurations of constant overall thickness is analyzed under uniformly applied load to a span of a continuous plate, and under forces imparted by two shapes of rigid indenters in a low velocity impact. The results show that the PUR interlayer reduces both overall and local deflections of the face sheet, and also the local compression of the foam core and the residual stresses left after unloading. The EF interlayer offers a much better protection against compression of the foam core, while magnifying both overall and local deflections. Both interlayers substantially reduce the strain energy release rates of interfacial cracks driven by residual stresses generated by foam core compression.

A finite element evaluation of local stresses in the adhesive and adherends is presented for a tongue-and-groove joint of a homogenized thick composite laminate to steel plate. The quasi-isotropic laminate is made of glass fabric/vinyl ester plies. Most results are obtained for elastic response of the Dexter-Hysol 9338 adhesive that was used in recent experiments (Compos Sci Technol 61 (2001) 1123–1142). A non-linearly viscoelastic adhesive is also considered, with illustrative properties taken from experiments on the FM-73 system. Both in-plane force resultants and out-of-plane moments are included in the applied loads. Scaling of the elastic results with regard to plate thickness shows that for given levels of overall stresses applied to the adherend plates, the stresses supported by the adhesive do not depend on plate thickness. Adhesive stress relaxation is shown to be relatively small, and occurring in a short time period.

A prestressing procedure for reduction of adhesive peel and shear stresses at the leading edge of a skin-flange assembly is analyzed for tensile and bending loads applied to the skin. Both an analytical solution based on the Green’s functions and a finite element solution are presented for specific examples, together with design diagrams. Substantial shear and peel stress reductions are obtained with the proposed procedure.

A prestressing procedure is proposed for reduction of stress concentrations at the leading edges of adhesive bondlines in composite skin/flange assemblies. A finite-element analysis of a specific geometry of such an assembly is presented, which accounts for nonlinear viscoelastic deformation of the adhesive. Design diagrams based on elastic analysis are constructed for evaluation of prestress forces that reduce or completely eliminate adhesive stress concentrations caused by either tension stresses or bending applied to the skin.

Viscoelastic deformation caused in symmetric laminated plates by release of fiber prestress and by uniform thermomechanical loads is analyzed on the constituent, ply and overall laminate scales with the Transformation Field Analysis (TFA) method (G. J. Dvorak, Proc. R. Soc. Lond., 1992, A437, pp. 311–327). Fiber prestress is applied in individual plies prior to matrix cure and released after matrix consolidation. Linear or nonlinear viscoelastic constitutive relations are used to evaluate the inelastic deformation rates in terms of current constituent stress averages. The TFA method regards both thermal and inelastic strains as piecewise uniform eigenstrains acting in superposition with mechanical loads and fiber prestress release on an elastic laminate. Interactions between the eigenstrains at the three different size scales are described by certain influence functions derived from micromechanical analysis of the plies and laminates. Applications describe stress relaxation in two carbon/epoxy laminates after cooling from the curing temperature and release of optimized fiber prestress, that allows maximum tensile load application while keeping both interior and free-edge stresses within prescribed strength limits. Subsequent viscoelastic deformation under constant rate loading, and stress relaxation caused by a sustained application of an elevated temperature to a laminate without prestress are also analyzed. Results are presented in the form of initial failure maps that identify overall stress states which may or may not initiate a specific damage mode in the laminate.

Oxide-isolated GaAs nanowires (NWs) were obtained through a lithography-free method in which axial growth of NWs coated in aluminum oxide (Al2O3) is restarted using an annealing step. NWs are grown using the vapor-liquid-solid method and coated in nanometer thin oxide films using atomic layer deposition. Continued growth at the oxide-coated nanoparticle (NP) occurs after the thermally-induced fracture of the oxide during annealing. This oxide fracture is observed to depend on NP diameter, oxide thickness and annealing temperature. A thermal expansion mismatch model for stresses on the oxide shell is put forward to explain these results.

Evolution of distributed damage in heterogeneous solids is modeled using the transformation field analysis method (Proc. Roy. Soc. Lond. A (1992) 437, 311) and selected models of interface debonding in fibrous or particulate composites. In this approach, stress changes caused by local debonding under increasing overall loads are represented by residual stresses generated by damage-equivalent eigenstrains that act together with the applied mechanical loading program and physically based local transformation strains on an undamaged elastic aggregate. Interaction of the actual and equivalent eigenstrains with the mechanical loads at any state of damage is described by certain transformation influence functions; this provides explicit expressions for the local stress averages and the damage-induced enhancement of the overall compliance at any current damage state. Damage rates are then derived from a prescribed probability distribution of interface strength and local potential energy released by debonding. Numerical simulations of damage evolution in a glass/elastomer composite indicate which of these two conditions controls the process at different reinforcement densities and overall stress states. In general, the energy released by a single particle at a given overall stress decreases with increasing reinforcement density, and in proportion to particle size. Therefore, dense reinforcement by small-diameter particles or fibers should enhance resistance to inclusion debonding in composite systems.

An analytical procedure is described for evaluation of the effect of release of fiber prestress, applied prior to matrix consolidation, on stress distribution in individual plies and at free edges of laminated composite plates. Both thermal changes, piecewise uniform transformation strains in the plies and overall mechanical loads can be considered in the analysis. The thermal and transformation load contributions are decomposed into superpositions of certain uniform fields with mechanical loads. Release of fiber prestress is regarded as an equivalent uniaxial compression applied at the edges of each prestressed ply. Optimized distributions of fiber prestress are found in individual plies such that stresses in both laminate interior and at the free edges remain within allowable limits, while the applied mechanical load may change from zero to a certain maximum value. Specific results are found for cross-ply and quasi-isotropic symmetric S-glass/epoxy laminates under tension. They clearly demonstrate the substantial potential of fiber prestress in damage control and prevention in laminated composite structures.

A new approach is explored for the joining of thick, woven E-glass/vinyl-ester composite laminated plates to steel or other composite plates, with applications in naval ship structures. Adhesive is applied along through-thickness contoured interfaces, employing tongue-and-groove geometry. Both experimental and finite element modeling results are presented. They show that adhesively bonded tongue-and-groove joints between steel and composite plates loaded in monotonically increasing longitudinal tension are stronger than conventional strap joints even in relatively thin plates. In particular, a single 0.25 inch wide and 8 or 12 inch long steel tongue, bonded by the Dexter-Hysol 9339 adhesive to a groove in a 0.5 inch thick laminated plate, can support a 20,000 lbs tension force. This force is expected to increase in proportion to plate thickness. Simple design rules indicate that the adhesive bond can be made stronger than that of the tongues, so that failure is transferred from the adhesive to the adherends. High joint efficiency can be achieved for any thickness of the joined plates, (C) 2001 Elsevier Science Ltd. All rights reserved.

New joint designs are proposed for adhesive bonding of thick multilayered composite adherends. The objective is to reduce or eliminate the failure modes associated with delamination and tensile and/or shear failure of the surface plies that are often observed in lap joints, and provide for a better stress distribution in the adhesive. In contrast to lap-joint designs, which transfer in-plane tensile stresses and other loads from the adherends to doubler plates by out-of-plane shearing of the surface plies, the new joint configurations transfer most of the load by in-plane shear and normal stresses, through bonded inserts or interlocking interfaces which have the same thickness as the laminate adherends. Doublers will transfer a calculated percentage of the load. Finite-element evaluations of the internal stresses in laminates, joined in both the conventional lap method and the new manner, suggest that the proposed load-transfer mechanism may improve joint efficiency by substantially increasing the size of adhesively bonded areas, and by making the stresses in the adherends nearly uniform through the thickness of the laminate. Some of the designs allow for selected ratios of shear to normal stresses in the adhesive layers. The stress concentrations often found in conventional designs, in the adherend surface plies and the adhesive layer at the leading edges of the doublers, are substantially reduced.

It is well known that the dynamic compressive strength of ceramics is enhanced by confining compressive stress. The paper shows how a biaxial in-plane compressive stress can be induced in a ceramic layer by encapsulation in a fiber-prestressed composite laminate. Optimal prestress distribution in individual plies of the laminate is found, together with the resulting residual stresses. Large compressive stress, 600–1000 MPa can be supported in an alumina layer by aramid/epoxy or carbon/epoxy laminates of the same total thickness as the ceramic. Stress relaxation due to either temperature changes or matrix creep is found to be of minor significance. Examples present results for specific material systems and laminate layups.

Stresses and deformations caused by fiber pre-stress are analyzed in symmetric elastic laminates that are loaded by uniform in-plane tractions, temperature changes, and uniform eigenstrains induced by various physical processes in symmetrically located pairs of plies. The pre-stress is applied to all fibers of selected symmetric pairs of plies prior to matrix cure, and is released after cooling to room temperature. The effect of the pre-stress on residual stress distribution is illustrated by failure maps constructed in overall stress planes of ply strength branches, derived from the computed local stresses and the maximum stress criterion. Examples are presented for 9-ply (0/90) 2s and (0/±45/90/0) s S-glass/epoxy laminates, both in the stress-free state, and after −150°C cooling from the curing temperature, with different magnitudes of pre-stress applied either to all plies or to the 0° plies. Releasing the pre-stress is shown to be equivalent to applying a sustained compression in the axial direction of each ply. The ply strength branches and initial failure envelopes, therefore translate in the overall stress space in the direction and by the magnitude of the overall stresses that are equivalent to the applied pre-stress. In systems with compliant polymer matrices, fairly small fiber stress changes are needed to support large translations of the ply strength branches. The implication is that matrix damage can be retarded or avoided altogether by moderate pre-stress magnitudes that are within the operating capacity of existing filament-winding fiber or placement devices.

The effects of surface condition, moisture and temperature on the mechanical behavior of SiCf/SiC composites produced by Dupont Lanxide are described. Elastic moduli and tensile strengths have been established at temperatures between 25 and 1200°C. A degradation in properties is noted by thermal exposure alone, but the effect is altered by the presence of moisture in the test atmosphere. The influence of a surface coating on the observed behavior is described. Changes in microstructure accompanying environmental embrittlement are described. Implications for structural applications of these composites are discussed.

Contributions of solid mechanics research to the development of composite materials and structures are reviewed. The main topics include the tensile and compressive strength of fibrous composites; transformation and residual fields in composite and laminated microstructures; plasticity and viscoplasticity of composites during processing, under thermomechanical service loads, and in the presence of evolving fatigue damage; delamination, damage and fracture; and future research needs.

This is the sequel to the first part of this paper ( Dvorak et al., 1999 , Int. J. Solids Structures 36, 3917–3943) , concerned with modeling and analysis of laminated composite cylinder fabrication procedures, such as filament winding or fiber placement, which involve fiber pre-stress for waviness reduction as well as overall or local heating to and cooling from matrix curing temperatures. The fiber pre-stress applied in individual plies is shown to cause a self-stress in the respective plies, and relaxation stresses in the already completed plies and in the supporting mandrel. The final residual stress state is reached after mandrel removal. Influence functions that relate the ply stresses to the applied pre-stress forces are derived. Direct problems are solved for ply stresses caused by prescribed constant or linearly or parabolically changing pre-stress magnitudes in the layers. A superposition of the constant and parabolic distributions is shown to lead to nearly uniform stresses through the cylinder wall. The magnitudes depend on the radial stiffness of the mandrel that supports the structure during fabrication. Inverse problems are formulated as nonlinear optimizations and solved by quadratic programming. The goal is to determine fiber pre-stress distributions through the wall thickness such that the total stresses due to external hydrostatic pressure and fiber pre-stress are as uniform as possible through the wall thickness and confined by the ply strength magnitudes.

This is the first of a two-part paper concerned with both structural and fabrication process design of a closed-end laminated composite cylinder intended for service in deep sea environment. The cylinder is made of many different orthotropic layers and is loaded by uniform, axisymmetric surface tractions. In addition, piecewise uniform eigenstrains and residual stresses may be caused in the layers during fabrication, by fiber prestress for waviness reduction and by piecewise uniform changes in temperature. The overall goal is to assure efficient use of the composite structure under a prescribed hydrostatic pressure, and to select fiber prestress distribution such that the total stresses in the plies do not exceed certain strength magnitudes. Mechanical and residual stresses in the layers are evaluated with mechanical and transformation influence functions. For the proportional loading applied by a hydrostatic pressure, a procedure is outlined for design of several layups such that the cylinder wall experiences an isotropic in-plane strain and, therefore, all layers support the same compressive normal stresses, regardless of fiber orientation. The results are applied in design and analysis stress fields in a specific structure. Fabrication process design is discussed in the second part of the paper ( Srinivas et al., 1999 , Int. J. Solids Structures, 36, 3945–3976) .

This is a brief survey of some recently developed micromechanical modeling methods and certain results concerning the overall thermomechanical response and average local fields in both elastic and inelastic composite materials with extensions to laminated plates.

Micromechanical modeling is employed to evaluate the stresses and strains in Sigma/ Timetal 2IS liminates under the isothermal fatigue conditions described in Part I [1], The effects of temperature and time variations on the constitutive response of the matrix and fiber are considered. Loading is limited to uniform in-plane stresses and to uniform changes in temperature. The local fields and macroscopic response of the plies are estimated with the finite-element method in conjunction with the transformation field analysis method, which utilizes overall elastic properties and transformation influence coefficients derived from the Mori-Tanaka model. Fiber debonding and sliding are modeled by modifying certain fiber elastic moduli. The results show that the inelastic deformation of the titanium matrix, assisted by extensive fiber debonding in the off-axis plies, promotes stress transfer to the fibers in the 0° plies. Under repeated loads, the fiber strain increase gradually at a certain rate, which depends o...

Experimental results are reported on the effect of static and cyclic loading (at 0.1 and 0.001 Hz) on the inelastic response of and damage development in (0)4, (0190), and (0/ ±45/90), SiC/Ti (Sigma/Timetal 21S) laminates, and the Timetal 21S matrix, at 650°C and 21°C. At the elevated temperature, viscoplastic deformation of the matrix can be observed even at relatively low applied stresses. At both temperatures, reduction of unloading elastic moduli of the laminates, which indicates onset of damage by interface decohesion, also starts after hailing to relatively low stresses. The cyclic loading rate has a significant effect on the number of cycles to failure, but not on the endurance limit of the (0/90), and (0/ ±45/90), laminates loaded by constant-amplitude tension at 650°C. In the (0)4 laminate, higher endurance limits were detected at 0.1 Hz than at 0.001 Hz However, regardless of loading rate and layup, the total strain at failure under both static and cyclic loading at 650°C was measured at 1 ±0.1%...

This work examines the mechanical behavior of a 2D woven, 0–90 SiC fiber-reinforced SiC matrix composite. Tensile experiments show that the short-term behavior is largely independent of test temperature below 1000 °C. Microscopic examination reveals that the extent of fiber pull-out and the integrity of the remaining material are also independent of temperature in this range. Conversely, at 1200 °C, the material retains much of its low-temperature stiffness and proportional limit, while the strength increases substantially. Micrographs of these specimens reveal little individual fiber pull-out and a higher density of matrix microcracks. Room-temperature tensile data show that the mechanical behavior is rate-dependent; higher strain rates lead to a lower Young's Modulus, higher proportional limit and higher ultimate strength. In-plane shear experiments demonstrate that the unreinforced matrix strength is approximately 10% of the composite tensile strength.

A device has been developed for hot‐gripping cylindrical specimens subjected to biaxial (tension/torsion) loading. By supporting the specimen very near the hot zone, the influence of thermal stresses on ultimate or yield strength as well as endurance limit can be minimized. This design thus increases the reliability of high‐temperature biaxial mechanical properties data for materials, such as ceramics or other brittle composites, which are sensitive to thermal stresses. Features of this apparatus include high‐temperature dimensional stability via in situ load pin adjustability and adaptability to various specimen and furnace geometries.

A thick-walled composite cylinder consisting of many different cylindrically orthotropic layers is loaded by uniform, axisymmetric surface tractions and by piecewise uniform eigenstrains in the layers. A theoretical framework is established for evaluation of internal stress fields. An optimization procedure is implemented to find eigenstrain distributions that adjust the stresses in the layers to selected levels, while allowing the application of certain ranges of fiber prestrain magnitude to reduce fiber waviness. A particular fabrication process that utilizes fiber prestress as a source of the layer eigenstrains is analyzed, and a distribution of the fiber prestress forces is found that produces a desired distribution of both hoop and axial stresses in the cylinder wall. Both mandrel stiffness and the chosen prestress magnitude in the first layer influence the distribution. It is shown that application of a high fiber prestress that is constant through the wall thickness can be harmful as it may generate very high hoop stress gradients.

Thermal residual and mechanical stresses generated by hot isostatic pressing, cooling and subsequent mechanical loading of SCS6/Ni3Al and SCS6/Ti3Al composites with uncoated and carbon-coated fibres have been simulated by micromechanical modelling. The solutions were found in a periodic hexagonal array model of the microstructure with the finite element method. The intermetallic matrices were assumed to be elastic-plastic, with temperature-dependent properties. The fibre and coating were assumed to be elastic. Local stress fields and overall response were found for several processing sequences. The results suggest that plastic deformation of the matrix during cooling from fabrication temperatures reduces residual stresses. The Ni3Al matrix system yields more easily than the Ti3Al system. HIP programmes that promote such yielding are proposed and analysed in both systems. Compliant and expansive fibre coatings tend to reduce the thermal stresses, but may also enhance the interface stresses in the matrix under overall mechanical loads.

Several types of bonds may exist at the juncture between adjacent phases in contact. On the microscale of many composite materials, most desired is a perfect bond along a sharp spatial boundary S of vanishing thickness. It guarantees that both traction and displacement vectors remain continuous on S. Contact between phase surfaces may also involve presence of one or more interphases, thin bonded layers of additional homogeneous phases introduced, for example, as coatings on particles or fibers, or as products of an interfacial chemical reaction. During composites manufacture and/or loading, an interface is expected to transmit certain tractions between adjacent constituents. When the resolved tensile and/or shear stress reaches a high magnitude, the interface may become imperfect by allowing partial or complete decohesion, a displacement jump, possibly accompanied by a distribution of ‘adhesive’ tractions. In an opposite situation, a high compressive stress may cause radial cracking in one of the phases in contact, or in the surrounding matrix. While magnitudes of interface tractions determine material propensity to distributed damage, the work required by either decohesion or radial cracking must be provided by release of potential energy, which is proportional to phase volume Chap. 5. Therefore, small inhomogeneities are less likely sources of damage than large ones.

SUMMARY Fatigue failure of metal matrix composite laminates is often preceded by a substantial loss of stiffness associated with cyclic plastic straining and subsequent low-cycle fatigue crack growth in the matrix. Experimental observations suggest that two principal crack patterns are involved; these are related here to the deformation modes predicted by the bimodal plasticity theory of fibrous composites. The relation is utilized in modelling the damage process such that matrix crack growth is regarded as a shakedown mechanism leading to a saturation damage state. For a given program of variable cyclic loading, evaluation of the saturation state is formulated as a non-linear optimization problem, where the total damage in a laminate is minimized subject to non-linear constraints derived from the ply yield criterion, hardening rule, and physically motivated bounds on the damage parameters. Effective elastic stiffness reduction and local stress redistribution predicted by the optimization procedure are co...

In its original form, the Mori-Tanaka method estimates constant overall properties of statistically homogeneous composite materials subjected to uniform overall stresses, strain or temperature changes, from averages of local fields in the phases. To permit applications involving large overall stress and/or temperature gradients, and functionally graded materials with a variable reinforcement density, the method has been extended to linearly variable overall and local fields by Zuiker and Dvorak (Composites Engineering, Vol. 4, 19–35, 1994) as a first step toward application of the method to statistically inhomogeneous materials with variable reinforcement density. Here, the effective properties are examined in detail. Non-zero components of the stiffness matrix are shown to satisfy invariance requirements and to vary with reinforcement volume fraction and size of the representative volume. It is shown that the linear and constant field approaches provide different estimates of overall properties for small representative volumes, but nearly identical estimates for large volumes.

The transformation field analysis is a general method for solving inelastic deformation and other incremental problems in heterogeneous media with many interacting inhomogeneities. The various unit cell models, or the corrected inelastic self-consistent or Mori-Tanaka fomulations, the so-called Eshelby method, and the Eshelby tensor itself are all seen as special cases of this more general approach. The method easily accommodates any uniform overall loading path, inelastic constitutive equation and micromechanical model. The model geometries are incorporated through the mechanical transformation influence functions or concentration factor tensors which are derived from elastic solutions for the chosen model and phase elastic moduli. Thus, there is no need to solve inelastic boundary value or inclusion problems, indeed such solutions are typically associated with erroneous procedures that violate (62); this was discussed by Dvorak (1992). In comparison with the finite element method in unit cell model solutions, the present method is more efficient for cruder mesches. Moreover, there is no need to implement inelastic constitutive equations into a finite element program. An addition to the examples shown herein, the method can be applied to many other problems, such as those arising in active materials with eigenstrains induced by components made of shape memory alloys or other actuators. Progress has also been made in applications to electroelastic composites, and to problems involving damage development in multiphase solids. Finally, there is no conceptural obstacle to extending the approach beyond the analysis of representative volumes of composite materials, to arbitrarily loaded structures.

This paper examines several aspects of numerical implementation of the transformation field analysis (TFA) method in applications to inelastic composite materials. In its general form, the method can accommodate any uniform overall loading path, inelastic constitutive equations, and micromechanical model. The response of a selected model to thermomechanical loads and local inelastic or transformation strains is found through mechanical transformation influence functions, which reflect the chosen microgeometry and the elastic response of the phases. Application of the transformation field analysis to elastic-plastic fibrous composites considers a unit cell model and incremental plasticity constitutive equations. For moderate mesh subdivisions of the unit cell, TFA proved to be more efficient than the finite-element method.

In its original form, the Mori-Tanaka method estimates constant overall properties of statistically homogeneous composite materials subjected to uniform overall stresses, strain or temperature changes, from averages of local fields in the phases. To permit applications involving large overall stress and/or temperature gradients, and functionally graded materials with a variable reinforcement density, the method is extended here to linearly variable overall and local fields. This is done for representative volumes of statistically homogeneous solids with constant overall properties, as a first step toward application of the method to statistically inhomogeneous materials with variable reinforcement density. It is shown that the linear and constant field approaches provide different estimates of overall properties for small representative volumes, but nearly identical estimates for large volumes.

Some recent theoretical and experimental results on modeling of the inelastic behavior of composite materials are reviewed. The transformation field analysis method (G. J. Dvorak, Proc. R. Soc. London, Series A437, 1992, pp. 311–327) is a general procedure for evaluation of local fields and overall response in representative volumes of multiphase materials subjected to external thermomechanical loads and transformations in the phases. Applications are presented for systems with elastic-plastic and viscoelastic constituents. The Kroner-Budiansky-Wu and the Hill self-consistent models are corrected to conform with the generalized Levin formula. Recent experimental measurements of yield surfaces and plastic strains on thin-walled boron-aluminum composite tubes are interpreted with several micromechanical models. The comparisons show that unit cell models can provide reasonably accurate predictions of the observed plastic strains, while models relying on normality of the plastic strain increment vector to a single overall yield surface may not capture the essential features of the inelastic deformation process.

This paper presents a finite strain formulation of a plasticity theory of fibrous composite materials. An additive decomposition is adopted to describe the kinematics of large deformations; a lattice is defined by the current fiber direction. Elastic and plastic constitutive relations are developed from the proposition that distortions take place relative to the fiber direction. A numerical method is proposed for integrating the constitutive equations. Finally, an illustrative example of the formulation indicates that when axial loads along the fiber direction are comparable to the instantaneous shear stiffness, the finite deformation formulation is needed even with small strains.

Simple, explicit formulae are derived for estimates of the effective elastic moduli of several multiphase composite materials with the Mori-Tanaka method. Specific results are given for composites reinforced by aligned or randomly oriented, transversely isotropic fibers or platelets, and for fibrous systems reinforced by aligned, cylindrically orthotropic fibers.

Binary piezoelectric composites with unidirectional fibers are considered. The phase boundaries are cylindrical but otherwise the microgeometry is totally arbitrary. The constituents are transversely isotropic. The existence of uniform fields which can be generated by the application of certain mechanical and electrical boundary conditions in such composites is established. The results are used to derive universal relations for the pointwise fields as well as for the effective piezoelectric constants of such composites.

An analytical procedure for prediction of fracture strength in unidirectionally reinforced, notched metal matrix composite (MMC) plates is described. As in Parts I–III [Engng Fracture Mech.34, 87–104 (1989); 34, 105–123 (1989); 37, 1207–1232 (1990)], the objective is to evaluate the tension stress in a small volume of material ahead of the notch tip, while the composite plate is loaded in simple tension. In the composite systems considered in this study, fracture is typically preceded by formation of long, discrete plastic shear zones aligned in the fiber direction. The length of such zones is evaluated here by the crack interaction scheme proposed recently by Benveniste et al. [Int. J. Solids Structures25, 1279–1293 (1989)] and a Dugdale-type condition imposed at the end of the plastic zone. Then, the local tension stress ahead of the notch is found by superposition of a ligament stress and the stress induced by the shear tractions in the plastic zone. Comparison with numerous fracture strength measurements on notched B/Al and FP/Al plates confirms that the onset of fracture is associated with a critical magnitude of the local stress in a small volume of the composite material. The present procedure provides closed-form expressions for evaluation of the local stresses, and for fracture strength predictions in unidirectional MMC plates.

A new method is proposed for evaluation of local fields and overall properties of composite materials subjected to incremental thermomechanical loads and to transformation strains in the phases. The composite aggregate may consist of many perfectly bonded inelastic phases of arbitrary geometry and elastic material symmetry. In principle, any inviscid or time-dependent inelastic constitutive relation that complies with the additive decomposition of total strains can be admitted in the analysis. The governing system of equations is derived from the representation of local stress and strain fields by novel transformation influence functions and concentration factor tensors, as discussed in the preceding paper by G. J. Dvorak and Y. Benveniste. The concentration factors depend on local and overall thermoelastic moduli, and can be evaluated with a selected micromechanical model. Applications to elastic-plastic, viscoelastic, and viscoplastic systems are discussed. The new approach is contrasted with some presently accepted procedures based on the self-consistent and Mori—Tanaka approximations, which are shown to violate exact relations between local and overall inelastic strains.

The effect of uniform thermal changes and mechanical loads on the inelastic response is described for certain two-phase materials of arbitrary phase geometry, and for two-phase fibrous systems of any geometry in the transverse plane. Auxiliary uniform strain fields are derived by superposition of the actual thermal field with a field caused by specific uniform overall stresses or strains. For many actual composite systems, the uniform fields are shown to be isotropic and thus capable of causing only elastic strains in a plastically incompressible matrix. This property permits an exact replacement of the actual thermomechanical loading path with a modified mechanical path. The modified path is utilized in derivation of many closed-form expressions for evaluation of the translation vectors for centers of overall yield and relaxation surfaces, instantaneous inelastic moduli, and plastic strains during thermomechanical deformation of the composite materials.

The dimensional stability of metal matrix composite laminates under thermal fluctuations and thermomechanical load cycles is examined. The system considered as a model material is a Gr/Al (±ϕ) s laminate. The analysis is performed by the finite-element method while the underlying constitutive equations of unidirectional composites are provided by the periodic-hexagonal-array (PHA) micromechanical model. A computationally more efficient and equally accurate method based on fiber-dominated analysis of unidirectional composites by the self-consistent method is also presented. The results show that laminates of the model system with ϕ=12° are dimensionally stable in the elastic range when subjected to pure temperature changes. Plastic deformation of the matrix causes permanent dimensional changes, which can be reduced by heat treatment of the composite. Under thermomechanical loads, (±ϕ) s laminates are not in general dimensionally stable. Dimensional stability of the laminate was enhanced by plastic deformation of the matrix for in-phase thermal and mechanical load cycles and reduced for out-of-phase cycles.

This two-part paper presents a closed-form procedure for evaluation of estimates of local thermomechanical stress fields in two-phase fibrous composites and laminates. The first part is concerned with a unidirectional elastic laminate subjected to uniform mechanical loads and to uniform changes in temperature. Both phases are assumed to be elastic, with temperature-dependent moduli and expansion coefficients; the solution reflects the influence of thermomechanical interactions. Exact solutions are not possible for any real system, because the local geometry is not known in detail. Instead, estimates of the fields are found from a modified Mori-Tanaka approximation. Examples are presented for two SiC/TiAlNb composites. Local stresses of interest are found after cooling from fabrication to room temperature. The presence of local yielding, and the influence of coupling terms on the local stress magnitudes are examined. Extension of the results to laminated plates is presented in Part II (Dvorak, G.J., Chen, T. & Teply, J., Composites Science and Technology, 43 (1992) 359–368, this issue).

The results of Part I of this work are extended to laminated plates. It is assumed that the plates are, at most, macroscopically orthotropic, and that they are subjected to a uniform change in temperature and to in-plane mechanical loads. Average stresses and microstress fields are evaluated in each layer of the plate. Failure envelopes based on critical magnitudes of interface and axial matrix stresses are constructed for one of the SiC/TiAlNb systems of Part I.

General connections are established between the mechanical and thermal responses of composite materials with debonded or imperfectly bonded interfaces, and with internal cracks or cavities. In particular, such results are found for multiphase composites or polycrystals in which normal and/or shear displacement jumps may exist at interfaces or cracks, consistent with complete debonding or with the presence of a nonlinearly elastic interphase layer. In two-phase systems with isotropic phases and sliding interfaces, we also recover exact connections between the mechanical and thermal stress or strain fields in the phases.

Simple mechanical models of unidirectional metal matrix composites are used to analyze elastoplastic deformation and shakedown in the matrix under cyclic composite loads. Both axial and off-axis loadings of a lamina are considered. It is shown that the fatigue limits of as-fabricated boron-aluminum, beryllium-aluminum, tungsten-copper, and other composites generally coincide with the composite shakedown limits because the matrix yield stresses and fatigue limits are equal. In heat-treated composites, the matrix yield stress is usually much higher than the fatigue limit, and matrix fatigue failure can take place in the shakedown state. The residual microstresses caused by heat treatment are estimated, and their influence on fatigue is discussed. A method for improvement of the fatigue resistance of heat-treated composites is discussed. The theoretical predictions of fatigue limits are verified by an extensive comparison with available experiments, and a very good agreement is obtained. It is concluded that, in principle, the composite fatigue failure can be avoided if each of the constituents is stressed within its particular fatigue limits during a cyclic loading program of the composite.

Micromechanical modeling is employed to evaluate the stresses and strains in laminated composite plates reinforced by elastic fibers in a thermo-viscoplastic matrix. Loading is limited to uniform in-plane stresses and to uniform changes in temperature. The local fields and macroscopic response of the plies are estimated with the transformation field analysis method that utilizes overall elastic properties and transformation influence coefficients derived from the Mori-Tanaka model. Fiber debonding and sliding are modeled by modifying certain fiber elastic moduli. This methodology, incorporated in a finite element scheme, is applied in simulations of hot isostatic pressing and subsequent loading of a (0/′45/90) s Sigma/TIMETAL 21S laminate. Axial tension/tension stress cycles are applied at constant temperature and in-phase cyclic temperature changes. The results show that the inelastic deformation of the matrix, assisted by extensive fiber debonding in the off-axis plies, promotes stress transfer to the fibers in the 0° plies. Under repeated loads, the fiber stress increases gradually at a certain rate and the laminate fails when the fiber ultimate strength is exceeded.