J. Eng. Mater. Technol. 1994;116(3):255. doi:10.1115/1.2904282.
Commentary by Dr. Valentin Fuster


J. Eng. Mater. Technol. 1994;116(3):256-259. doi:10.1115/1.2904283.

A micromechanically based enrichment of the nonlocal operator by a term taking into account the directional dependence of crack interactions (Bažant, 1992) can be expected to improve the performance of the nonlocal model. The aim of this paper is to examine this new model in the context of a simple localization problem reducible to a one-dimensional description. Strain localization in an infinite layer under plain stress is studied using both the old and the new nonlocal formulations. The importance of renormalization of the averaging function in the proximity of a boundary is demonstrated and the differences between the localization sensitivity of the old and new model are pointed out.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 1994;116(3):260-267. doi:10.1115/1.2904284.

This paper consists of two parts: (a) a concise summary and discussion is given of the recent contributions of the author in the micromechanics of piezoelectric composites. The underlying theme here is the derivation of exact connections for the local fields and effective moduli of heterogeneous piezoelectric solids. Composites of arbitrary phase geometry as well as fibrous systems are considered. (b) New results are presented on the effective behavior of fibrous piezoelectric systems. Fibrous composites with transversely isotropic constituents and cylindrical microgeometry are considered. The exact connections of the author (Benveniste (1993), Proc. R. Soc., Series A, Vol. 441, pp. 59-81) are extended to include the most generally possible overall symmetry of the composite aggregate. The other category of the new findings concerns exact expressions for the effective thermal terms of fibrous systems which possess the same shear modulus GT .

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 1994;116(3):268-273. doi:10.1115/1.2904285.

Finite Element based micromechanical methods are used to study the influence of microscale phase arrangements on the overall and microscale thermomechanical properties of two advanced two-phase materials, duplex steels and unidirectional continuously reinforced metal matrix composites (MMCs). Both inclusion-matrix topologies and interwoven microgeometries are investigated for duplex steels, and the predicted macroscopic transverse elastoplastic responses are correlated with quantitative stereological descriptions of the microgeometries. For the MMCs, the emphasis is put on the influence of the fiber arrangement on the microscale residual stress states of the as-produced material and on their effects on damage mechanisms.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 1994;116(3):274-278. doi:10.1115/1.2904286.

A micromechanical model using simultaneously Green’s function techniques and interfacial operators is proposed in order to solve the elastic inhomogeneous coated inclusion problem. For a composite material made of a non dilute concentration of coated inclusions and a homogeneous matrix, the interactions between the reinforcements are solved by a self-consistent scheme. The theoretical results for a composite of hollow spheres of glass in a polyester matrix are in good agreement with experimental measurements of Huang and Gibson.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 1994;116(3):279-285. doi:10.1115/1.2904287.

An analytical solution for the extended stress field of the fundamental problem of interfacial Somigliana ring dislocation in fiber-matrix composites is obtained. The result of this work provides a powerful tool which can be used to address a class of three-dimensional defect problems encountered in heterogeneous materials, such as fiber-matrix debonding, fiber pull-out, broken fibers and others, as well as interaction among defects.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 1994;116(3):286-289. doi:10.1115/1.2904289.

Dynamic compressive damage evolution in solids, associated with brittle microcracking and ductile plastic flow, is modeled through plastic flow and tensile microcracking, which are induced by the deformation of preexisting microflaws at grain boundaries, slip bands, and microcavities. The micromechanical aspect of this model is discussed in terms of the dominance of microcracking or plastic flow, and possible transition from microcracking to plastic flow is investigated. The effect of lateral confinement on the dynamic damage evolution is investigated, emphasizing the brittle-ductile transition.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 1994;116(3):290-297. doi:10.1115/1.2904290.

The aim of this paper is to extend the classical Gurson (1977) analysis of a hollow rigid ideal-plastic sphere loaded axisymmetrically to an ellipsoidal volume containing a confocal oblate ellipsoidal cavity. An “expansion” velocity field satisfying conditions of homogeneous boundary strain rate is used to derive a two-field estimate of the overall yield criterion. The latter is shown to be reducible, with a few approximations, to a Gurson-like criterion depending on the “shape parameter” of the cavity. The accuracy of this estimate is assessed through comparison with some results derived from a numerical minimization procedure. An approximate evolution equation for the shape parameter is also presented; comparison with some finite element simulations suggests a slight modification of the theoretical formula leading to considerably enhanced agreement.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 1994;116(3):298-304. doi:10.1115/1.2904291.

In this paper, we briefly review some of the recent developments in the methodology of heterogenization. A connection between a group structure on the set (−1, 1) of real numbers t such that −1 < t < 1, and the elastostatics of a multilayered fiber perfectly bonded to an infinite matrix is pointed out. Also, universal formulae, pertaining to the solution of two circular elastic inclusions perfectly bonded to a matrix, of infinite extent, which is subjected to arbitrary loading, are discussed. As a novel illustration of the heterogenization procedure, we study here the case where the inclusions are elastically (i.e., “imperfectly”) embedded in the matrix. Several cases are presented and discussed.

Topics: Fibers
Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 1994;116(3):305-309. doi:10.1115/1.2904292.

The double-inclusion model consists of an ellipsoidal inclusion of arbitrary elasticity, containing another ellipsoidal heterogeneity of arbitrary elasticity, size, and orientation, which are embedded in an infinitely extended homogeneous domain of yet another arbitrary elasticity. Average field quantities for the double inclusion are obtained analytically, and used to estimate the overall moduli of two-phase composites. The technique includes the self-consistent and other related methods as special cases. Furthermore, exact bounds for the overall moduli are obtained on the basis of the double-inclusion model. The double-inclusion model has been generalized (Nemat-Nasser and Hori, 1993) to a multi-inclusion model, where, again, all the average field quantities are estimated analytically. The application of the multiinclusion model includes a composite containing inclusions with multi-layer coatings.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 1994;116(3):310-318. doi:10.1115/1.2904293.

A micromechanical framework is presented to predict effective (overall) elasto-(visco-)plastic behavior of two-phase particle-reinforced metal matrix composites (PRMMC). In particular, the inclusion phase (particle) is assumed to be elastic and the matrix material is elasto-(visco-)plastic. Emanating from Ju and Chen’s (1994a,b) work on effective elastic properties of composites containing many randomly dispersed inhomogeneities, effective elastoplastic deformations and responses of PRMMC are estimated by means of the “effective yield criterion” derived micromechanically by considering effects due to elastic particles embedded in the elastoplastic matrix. The matrix material is elastic or plastic, depending on local stress and deformation, and obeys general plastic flow rule and hardening law. Arbitrary (general) loadings and unloadings are permitted in our framework through the elastic predictor-plastic corrector two-step operator splitting methodology. The proposed combined micromechanical and computational approach allows us to estimate overall elastoplastic responses of PRMMCs by accounting for the microstructural information (such as the spatial distribution and micro-geometry of particles), elastic properties of constituent phases, and the plastic behavior of the matrix-only materials. Comparison between our theoretical predictions and experimental data on uniaxial elastoplastic tests for PRMMCs is also presented to illustrate the capability of the proposed framework. A straightforward extension to accommodate viscoplastic matrix material is also presented to further enhance the applicability of the proposed method.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 1994;116(3):319-324. doi:10.1115/1.2904294.

The paper discusses experimental observations and some related theoretical results associated with the mechanical response of two Ti3 Al matrix composites, subjected to transverse loading. Both composites contain continuous unidirectional fibers; however, there are considerable differences in the composition of the two interfaces. The Ti3 Al/SCS-6 system contains brittle reaction products around the fibers that degrade the strength of the composite. The second composite consists of a Ti3 Al matrix reinforced by sapphire fibers that are strongly bonded to the matrix. Experimental observations indicate that the damage mechanisms in the two composites are substantially different. Utilizing elastic analyses of the local stress field, an attempt was made to explain the dependence of the observed damage mechanisms on the residual field and the properties of the interface.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 1994;116(3):325-330. doi:10.1115/1.2904295.

Utilizing statistical methods known from linear elasticity it is shown how effective 3rd (and higher) order elastic constants (TOEC) of micro-heterogeneous media can be calculated. Emphasis is put on the self consistent scheme. The ensemble average of the fluctuating TOEC yields a 0th approximation to the rigorous selfconsistent moduli. A first approximation is also given in closed form. The insight that the well-established statistical methods of the linear theory, which uses Green functions, are applicable also to nonlinear problems is considered as the main result of this paper.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 1994;116(3):331-336. doi:10.1115/1.2904296.

For ceramic composites, continuum damage mechanics models are built, which include information coming from both the “micro” and “macro” scales. These models are constitutive relations which, when included in a structural analysis code, are able to predict the damage state of the studied structure at any time and at any point until final fracture.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 1994;116(3):337-347. doi:10.1115/1.2904297.

The study of the effective thermomechanical response of active fibrous composites with shape memory alloy (SMA) fibers is the subject of this work. A 3-D constitutive response for the SMA fibers is formulated first. To model thermomechanical loading path dependence, an incremental approach is used assuming that within each stress and temperature increment the volume fraction of the martensitic phase remains constant in the SMA fibers. The Mori-Tanaka averaging scheme is then used to give an estimate of the instantaneous effective thermomechanical properties in terms of the thermomechanical properties of the two phases and martensitic volume fraction. A unit cell model for a periodic active composite with cubic and hexagonal arrangement of fibers is also developed to study the effective properties using finite element analysis. It is found that since the fibers and not the matrix undergo the martensitic phase transformation that induces eigenstrains, the Mori-Tanaka averaging scheme accurately models the thermomechanical response of the composite, relative to the finite element analysis, for different loading paths. Specific results are reported for the composite pseudoelastic and shape memory effect for an elastomeric matrix continuous SMA fiber composite.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 1994;116(3):348-358. doi:10.1115/1.2904298.

The growth and collapse of isolated voids in power-law viscous matrix materials are investigated. The study is restricted to axisymmetric remote stressing and to voids which are initially spheroidal with the axis of symmetry of the voids coincident with the axis of symmetry of the remote loading. Particular attention is given to the evolution of initially spherical voids, but the effect of initial void shape on subsequent void evolution is also investigated. For linearly viscous matrix materials, the voids evolve through spheroidal shapes and the work of Budiansky et al. (1982) provides the desired information about the history of void shape and volume. For nonlinear matrix materials, the void evolution is idealized as proceeding through a sequence of spheroidal shapes, and the rate of deformation for a given instant is evaluated using a Ritz procedure developed by Lee and Mear (1992). The results of the study demonstrate that the history of void volume and void shape is influenced significantly by the material nonlinearity, the remote stress state and the initial void aspect ratio.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 1994;116(3):359-366. doi:10.1115/1.2904299.

Based upon the Mori-Tanaka method, the constitutive equations of power-law materials and the failure criteria of multiple cracks materials are investigated. The piecewise linear incremental approach is also employed to analyze the effective stress and strain of the power-law materials. Results are presented for the case of pure shear where the matrix is a power-law material with rigid or void inhomogeneities. For the multiple cracked materials, the Griffith fracture criterion is applied to determine the critical volume fraction which causes the catastrophic failure of a material. The failure criteria of penny shaped, flat ellipsoidal, and slit-like cracked materials are examined and it is found that the volume fraction of cracks and critical applied stress are in linear relation.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 1994;116(3):367-377. doi:10.1115/1.2904300.

Stress fields in a continuous fiber composite with a variable interphase subjected to thermomechanical loadings are studied by using a four concentric circular cylinders model. An exact closed form solution is obtained for the stress field in the interphase in a series form using Frobenius method in a certain case. Numerical results are presented for FP fiber/Al 6061 composite with interphase, and carbon fiber/Al 6061 composite with interphase. It is found that the variableness of the thermoelastic constants in the interphase has significant effects on the stress distributions in the interphase. Therefore, this will, in turn, affect the initiation of cracks in the interphase.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 1994;116(3):378-383. doi:10.1115/1.2904301.

In this paper, a nonlocal theory based upon crystalline plasticity is used in case of a dislocation cell structure induced during plastic straining and represented by a two-phase material. By describing convective dislocation motion (which appears to be a basic feature of hardening) and storage mechanisms, under some simplifying assumptions, numerical simulations exhibit significant effects on the intragranular heterogeneization, as well as on global results like the Bauschinger effect.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 1994;116(3):384-391. doi:10.1115/1.2904302.

We study the effective moduli and damage formation in out-of-plane elasticity (i.e., two-dimensional conductivity) of matrix-inclusion composite materials with either randomly or periodically distributed inclusions (fibers). In this paper, we focus our attention on composites with isotropic phases, both of which have elastic-brittle response in damage. The elastic-brittle behavior is modeled with the help of a fine mesh finite-difference system, whereby damage evolution is simulated by sequentially removing/breaking bonds in this lattice in accordance with the state of stress/strain concentrations. The composite systems are specified by two parameters: stiffness ratio and strength ratio of both phases. In particular, we investigate the following aspects: basic classification of effective constitutive responses, geometric patterns of damage, varying degrees of randomness of the inclusions’ arrangements, and mesh resolutions of continuum phases.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 1994;116(3):392-397. doi:10.1115/1.2904303.

In this paper a constitutive-model based on micromechanics is given to predict the time dependent ductile behavior of ice under compressive load. It is presumed creep and microcracking are the two dominant mechanisms in the ductile range. The proposed model is formulated on the idea that shear slip along the basal plane is the cause of the permanent deformation of ice, and that microcracking is caused by the local stress due to the mismatch strain. A single crystal is modeled as an inclusion constrained in a polycrystalline matrix with random orientation of the basal plane. Eshelby’s solution is used to estimate the local stress due to the mismatch strain. Maximum tensile stress criterion is adopted to predict microcracking and then crack density is predicted as a function of time. The stress-strain relation of the polycrystalline ice is calculated on the basis of single crystal property in which effect of internal structural changes is incorporated as the reduction of constraint of the surrounding matrix with increasing microcracking. The model predictions for constant load and constant strain rate tests are shown to demonstrate the validity of the model. The constitutive model is implemented in finite element analysis code and a small-scale indentation test is simulated as an example.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 1994;116(3):398-402. doi:10.1115/1.2904304.

The paper presents the application of a boundary element scheme to the study of the behavior of a penny-shaped matrix crack which occurs at an isolated fiber which is frictionally constrained. An incremental technique is used to examine the progression of self similar extension of the matrix crack due to the axial straining of the composite region. The extension of the crack occurs at the attainment of the critical stress intensity factor in the crack opening mode. Iterative techniques are used to determine the extent to crack enlargement and the occurrence of slip and locked regions in the factional fiber-matrix interface. The studies illustrate the role of fiber-matrix interface friction on the development of stable cracks in such frictionally constrained zones. The methodologies are applied to typical isolated fiber configurations of interest to fragmentation tests.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 1994;116(3):403-407. doi:10.1115/1.2904305.

The paper reports an analysis and modeling of the damage behavior of two-dimensional woven SiC/SiC composites. The damage mechanics analysis originally developed by Ladeveze and coworkers for polymeric and C/C composites are adopted and extended for ceramic matrix composites. The experimental findings of the coauthors reported in a companion paper provides the data for analytical modeling. The damage model assumes quasi-isotropic elastic behavior of the undamaged SiC/ SiC composites as well as orthotropic damage development (e.g., matrix microcracking, interfacial debonding, and fiber fracture). The model utilize two damage variables which are determined from experimental data; and the constitutive relation takes into account the difference in damage development between tension and compression in the principal material directions. The validity of the theory is demonstrated by the prediction of damage evolution of a SiC/SiC specimen under four-point bend test based upon the experimental data of tension and compression tests. A finite element method coupled with damage is adopted for the flexural analysis. The predictions agree quite well with experimental results.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 1994;116(3):408-413. doi:10.1115/1.2904306.

Relaxation of misfit strains at interfaces between two different materials by dislocation punching is studied analytically by focusing on two types of interfaces: planar and nonplanar. As an example of planar type interface, the case of metal coating/ ceramic substrate system is studied while ceramic filler/metal matrix composite system is examined as an example of a nonplanar interface. Based on the present analytical model, the condition for dislocation punching for each interface is established. Validity of the dislocation punching model is verified by comparing the analytical results with limited experimental results, resulting in a good agreement.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 1994;116(3):414-420. doi:10.1115/1.2904307.

The energy approach recently proposed by Qiu and Weng (1992) is introduced to estimate the equivalent stress of the ductile matrix in Tohgo and Chou’s (1991) incremental damage theory for particulate-reinforced composites containing hard particles. In such a composite debonding of the particle-matrix interface is a significant damage process, as the damaged particles have a weakening effect while the intact particles have a reinforcing effect. In Tohgo-Chou’s theory, which describes the elastic-plastic behavior and the damage behavior of particulate-reinforced composites, it was assumed that the debonding damage is controlled by the stress of the particle and the statistical behavior of the particle-matrix interfacial strength, and that the debonded (damaged) particles are regarded as voids, resulting in an increased void concentration with deformation. On the other hand, Qiu-Weng’s energy approach provides a reasonable equivalent stress of the matrix in the porous material and particulate-reinforced composite even under a high triaxiality. The incremental damage theory developed here enables one to calculate the overall stress-strain response and damage evolution of the composite under high triaxial tension. The stress-strain relations for porous material obtained by the present incremental theory are completely consistent with that obtained by Qiu and Weng. The influence of the debonding damage on the stress-strain response is demonstrated for particulate-reinforced composites.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 1994;116(3):421-427. doi:10.1115/1.2904308.

In this paper, a micromechanical analysis is performed on a single ply continuous fiber SiC/Ti-15V-3Al-3Sn-3Cr (Ti-15-3) metal matrix composite to study the complex interactions between the composite microstructural components and the surrounding environment at high temperatures. Finite elements are incorporated to model oxygen diffusing into the free suface of a representative volume element (RVE) during cool down from the processing temperature. The resulting residual stress distribution is investigated assuming thermoelastic material models for the matrix, oxide layer, and fiber. Results indicate that the oxidized surface layer is prone to cracking upon subsequent mechanical loading, and this effect is strongly temperature dependent.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 1994;116(3):428-437. doi:10.1115/1.2904309.

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.

Commentary by Dr. Valentin Fuster


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