Showing papers in "Journal of The Mechanics and Physics of Solids in 1992"

The relation between crack growth resistance and fracture process parameters in elastic-plastic solids

Abstract: CKA~K growth initiation and subsequent resistance is computed for an elastic-plastic solid with an idealized traction separation law specified on the crack plane to characterize the fracture process. The solid is specified by its Young’s modulus, E, Poisson’s ratio, v, initial tensile yield stress, (or, and strain hardening exponent, N. The primary parameters specifying the traction-separation law of the fracture process are the work of separation per unit area, To. and the peak traction, 6. Highly refined calculations have been carried out for resistance curves. K,(Arr), for plane strain, mode I growth in small-scale yielding as dependent on the parameters characterizing the elastic-plastic properties of the solid and its fracture process. With K,, = [El-,/( I ~ v’)] ’ 2 as the intensity needed to advance the crack in the absence ofplasticity, K,J& is presented in terms of its dependence on the two most important parameters, d/nr and N, with special emphasis on initiation toughness and steady-state toughness, Three applications of the results are made : to predict toughnesss when the fracture process is void growth and coalescence, to predict the role of plasticity on interface toughness for similar materials bonded together, and to illuminate the role of plasticity in enhancing toughness in dual-phase solids. The regime of applicability of the present model to ductile fracture due to void growth and coalescence, wherein multiple voids interact within the fracture process zone, is complementary to the regime of applicability of models describing the interaction between a single void and the crack tip. The two mechanism regimes are delineated and the consequence of a transition between them is discussed.

Dislocation nucleation from a crack tip : an analysis based on the Peierls concept

Abstract: Dislocation nucleation from a stressed crack tip is analyzed based on the Peierls concept. A periodic relation between shear stress and atomic shear displacement is assumed to hold along the most highly stressed slip plane emanating from a crack tip. This allows some small slip displacement to occur near the tip in response to small applied loading and, with increase in loading, the incipient dislocation configuration becomes unstable and leads to a fully formed dislocation which is driven away from the crack. An exact solution for the loading at that nucleation instability is developed via the J -integral for the case when the crack and slip planes coincide, and an approximate solution is given when they do not. Solutions are also given for emission of dissociated dislocations, especially partial dislocation pairs in fcc crystals. The level of applied stress intensity factors required for dislocation nucleation is shown to be proportional to √γ us , where γ us , the unstable stacking energy, is a new solid state parameter identified by the analysis. It is the maximum energy encountered in the block-like sliding along a slip plane, in the Burgers vector direction, of one half of a crystal relative to the other. Approximate estimates of γ us are summarized and the results are used to evaluate brittle vs ductile response in fcc and bcc metals in terms of the competition between dislocation nucleation and Griffith cleavage at a crack tip. The predictions seem compatible with known behavior and also show that in many cases solids which are predicted to first cleave under pure mode I loading should instead first emit dislocations when that loading includes very small amounts of mode II and III shear. The analysis in this paper also reveals a feature of the near-tip slip distribution corresponding to the saddle point energy configuration for cracks that are loaded below the nucleation threshold, as is of interest for thermal activation.

Fracture mechanics for piezoelectric ceramics

Abstract: We Study cracks either in piezoelectrics, or on interfaces between piezoelectrics and other materials such as metal electrodes or polymer matrices. The projected applications include ferroelectric actuators operating statically or cyclically, over the major portion of the samples, in the linear regime of the constitutive curve, but the elevated field around defects causes the materials to undergo hysteresis locally. The fracture mechanics viewpoint is adopted—that is, except for a region localized at the crack tip, the materials are taken to be linearly piezoelectric. The problem thus breaks into two subproblems: (i) determining the macroscopic field regarding the crack tip as a physically structureless point, and (ii) considering the hysteresis and other irreversible processes near the crack tip at a relevant microscopic level. The first Subproblem, which prompts a phenomenological fracture theory, receives a thorough investigation in this paper. Griffith's energy accounting is extended to include energy change due to both deformation and polarization. Four modes of square root singularities are identified at the tip of a crack in a homogeneous piezoelectric. A new type of singularity is discovered around interface crack tips. Specifically, the singularities in general form two pairs: r1/2±ieand r1/2±ie, where e. and k are real numbers depending on the constitutive constants. Also solved is a class of boundary value problems involving many cracks on the interface between half-spaces. Fracture mechanics are established for ferroelectric ceramics under smallscale hysteresis conditions, which facilitates the experimental study of fracture resistance and fatigue crack growth under combined mechanical and electrical loading. Both poled and unpoled fcrroelectrie ceramics are discussed.

Crystallographic texture evolution in bulk deformation processing of FCC metals

Abstract: A Taylor-type polycrystalline model, together with a new fully-implicit time-integration scheme has been developed and implemented in a finite element program to simulate the evolution of crystallographic texture during bulk deformation processing of face centered cubic metals deforming by crystallographic slip. The constitutive equations include a new equation for the evolution of slip system deformation resistance which leads to macroscopic strain hardening behavior that is in good accord with experiments performed on OFHC copper. The good predictive capabilities of the constitutive equations and the time-integration procedure for simulating the stress-strain behavior and the evolution of texture under both homogeneous and non-homogeneous deformation conditions are demonstrated by comparing numerical simulations against experimental measurements in simple shear and a simple plane-strain forging experiment on copper.

Family of crack-tip fields characterized by a triaxiality parameter—II. Fracture applications

Abstract: C entral to the J-based fracture mechanics approach is the concept of J-dominance whereby J alone sets the stress level as well as the size scale of the zone of high stresses and strains. In Part I the idea of a J Q annulus was developed. Within the annulus, the plane strain plastic near-tip fields are members of a family of solutions parameterized by Q when distances are normalized by J σ 0 , where σ0is the yield stress, J and Q have distinct roles: J sets the size scale over which large stresses and strains develop while Q scales the near-tip stress distribution and the stress triaxiality achieved ahead of the crack. Specifically, negative (positive) Q values mean that the hydrostatic stress is reduced (increased) by Qσ0 from the Q = 0 plane strain reference state. Therefore Q provides a quantitative measure of crack-tip constraint, a term widely used in the literature concerning geometry and size effects on a material's resistance to fracture. These developments are discussed further in this paper. It is shown that the J Q approach considerably extends the range of applicability of fracture mechanics for shallow-crack geometries loaded in tension and bending, and deep-crack geometries loaded in tension. The J Q theory provides a framework to organize toughness data as a function of constraint and to utilize such data in engineering applications. Two methods for estimating Q at fully yielded conditions and an interpolation scheme are discussed. The effects of crack size and specimen type on fracture toughness are addressed.

Composite materials with poisson's ratios close to — 1

Abstract: A family of two-dimensional, two-phase, composite materials with hexagonal symmetry is found with Poisson's ratios arbitrarily close to — 1. Letting k∗, k1,k2 and μ∗,μ1,μ2 denote the bulk and shear moduli of one such composite, stiff inclusion phase and compliant matrix phase, respectively, it is rigorously established that when k1 = K2r and μ1 = μ2r there exists a constant c depending only on k2, μ2 and the geometry such that k∗/μ∗

Delamination R-curve phenomena due to damage

Abstract: Resistance to delamination in composites can be enhanced by a variety of bridging mechanisms. The bridging zone size is usually several times the lamina thickness, so it is questionable to think of delamination resistance as a material property independent of specimen size and geometry. When measured with slender beams, the plateau resistance is found to be independent of the beam thickness. However, the steady-state bridging zone size increases with the beam thickness. Further implications of the large-scale bridging are studied using a family of steady-state, mixed-mode delamination beams, in conjunction with an idealized damage response. The complete solution is obtained for the model, which allows the R-curves to be constructed for given model parameters. The significance of the steady-state cracking, which is crucial in understanding delamination R-curves, is elucidated by contrasting double-cantilever beams loaded by moments and by wedge forces. As an inverse process, it is recommended that R-curves be used as an experimental probe to study localized damage response, such as polymer craze and interface separation.

Yielding of metal powder bonded by isolated contacts

Abstract: A macroscopic constitutive law is developed for the plastic yielding of a random aggregate of perfectly plastic spherical metal particles. The particles are bonded perfectly by isolated contacts and deformation occurs by plastic yielding of material at and near these contacts. The configuration is treated as isotropic and homogeneous as far as particle size and properties are concerned. The results are considered valid for aggregates with densities ranging from about 60% to around 90% of the theoretical fully dense level. The yield surface is obtained from the plastic dissipation at necks between particles given an imposed macroscopically uniform strain rate. The contact yield surface resulting from this analysis is sensitive to pressure as well as to deviatoric stress. The plastic strain rate direction is outwardly normal to the yield surface. Densification takes place when pressure is present, but a notable feature is a vertex on the yield surface at the points of pure positive and negative pressure. Consequently, plastic flow in the presence of pure pressure is nonunique, and deviatoric components may be superposed on densification.

New variational principles in plasticity and their application to composite materials

Abstract: I n this paper , a variational method for bounding the effective properties of nonlinear composites with isotropic phases, proposed recently by ponte castaneda (J. Mech. Phys. Solids 39, 45, 1991), is given full variational principle status. Two dual versions of the new variational principle are presented and their equivalence to each other, and to the classical variational principles, is demonstrated. The variational principles are used to determine bounds and estimates for the effective energy functions of nonlinear composites with prescribed volume fractions in the context of the deformation theory of plasticity. The classical bounds of Voigt and Reuss for completely anisotropic composites are recovered from the new variational principles and are given alternative, simpler forms. Also, use of a novel identity allows the determination of simpler forms for nonlinear Hashin-Shtrikman bounds, and estimates, for isotropic, particle-reinforced composites, as well as for transversely isotropic, fiber-reinforced composites. Additionally, third-order bounds of the Beran type are determined for the first time for nonlinear composites. The question of the optimality of these bounds is discussed briefly.

Theory of stress transfer in a 0°—90°—0° cross-ply laminate containing a parallel array of transverse cracks

Abstract: Two new analytical methods have been developed that can predict the stress transfer between the 0 and 90° plies in a 0°—90°—0° cross-ply laminate containing transverse cracks. Account is taken of thermal residual stresses arising from a mismatch in thermal expansion coefficients of the 0 and 90° plies. The first method is based on a 2-D model which assumes that generalised plane strain conditions prevail. The theoretical approach retains all relevant stress and displacement components, and satisfies exactly the equilibrium equations, the interface conditions, and other boundary conditions involving stresses. The stress—strain—temperature relations are satisfied either exactly or in an average sense. The 2-D representation can be used to predict the stress and displacement fields for a laminate containing parallel transverse cracks. In this paper the solutions are used to estimate the dependence of the longitudinal values of Young's modulus, Poisson's ratio, and thermal expansion coefficient on the density of transverse cracks. The second analytical method extends the 2-D model so that it can apply to 3-D problems which arise, for example, when edge effects or orthogonal cracking are to be taken into account. For the special case of very large laminate widths the 2- and 3-D models predict results which are very close to each other for both glass fibre/epoxy and carbon fibre/epoxy laminates. It is shown how the 3-D model can be used to predict the transverse Young's modulus and thermal expansion coefficient. Theoretical predictions of the dependence of Poisson's ratio on transverse crack density indicate that experimental measurements can be sensitive to the strain measurement technique used, and to specimen width when using a transverse extensometer. Theoretical predictions, for glass fibre/epoxy and carbon fibre/epoxy laminates, of the dependence of Young's modulus and Poisson's ratio on the crack density are compared with some experimental results.

The elastic moduli of a sheet containing circular holes

Abstract: W e apply computer simulation techniques to obtain the clastic moduli of a matrix containing circular holes. As the area fraction of holes increases, the Young's modulus of the composite decreases from E0 until it eventually vanishes at the percolation threshold. We study three distinct geometries: (a) periodically centered circular holes on a honeycomb lattice, (b) periodically centered circular holes on a triangular lattice, and (c) randomly centered circular holes. All three cases have the same dilute limit that can be calculated exactly. By examining the narrow necks between adjacent circles, we have calculated the critical behavior for the regular cases and obtain critical exponents of 1 2 or 3 2 , depending on the local breakdown mode at the necks. For (c) we compare our results with an effective-medium theory, which predicts that the Poisson's ratio tends to 1 3 as the percolation threshold is approached, independent of its value in the pure system. Our results are also compared with recent experimental results. Based on this work, we propose that the relative Young's modulus E E 0 of a two-dimensional sheet containing circular holes, overlapping or not, is the same for ail materials, independent of the Poisson's ratio v0, for any prescribed geometry.

Uniform fields and universal relations in piezoelectric composites

Abstract: 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.

Non-Schmid yield behavior in single crystals

Abstract: A parently , certain single crystals do not obey Schmid's law for slip on individual systems. For example, many intermetallic compounds such as Ni 3Al with the LI 2 structure display yield behaviors that are called “anomalous” in the sense that the critical resolved shear stress on the primary slip system at yield is a function of the orientation of the loading axis and the sense of load. To accommodate such non-Schmid behaviors, a generalization of Schmid's law is proposed where stress components other than the Schmid stress also enter the criterion. The general effects of “cross slip” in FCC single crystals as well as the detailed shield behavior of Ni 3Al are well described. Finally, we demonstrate that non-Schmid effects can make it more difficult to activate many slip systems simultaneously.

The constitutive law of nonlinear viscous and porous materials

Abstract: This Paper examines with the help of micromechanics the overall behaviour of nonlinear viscous materials containing voids. In complement to variational bounds derived here and to several models proposed in the recent literature we derive a simple model which meets exactly a closed-form solution of a hollow sphere under hydrostatic tension. More generally we consider the problem of a hollow sphere under hydrostatic tension when the constitutive material of the sphere is already porous. The solution is used in a self-consistent scheme and a differential scheme to derive a constitutive law for a porous material containing different populations of micro-voids with distributed sizes. These schemes predict a higher damage effect for the same porosity than the models based on a single size of voids. All the models considered in this paper make use of a strain-rate potential and most of them assume a simple “quadratic” form for it.

Measurement of interface strength by a laser spallation technique

Abstract: A laser spallation experiment has been developed to measure the strength of planar interfaces between a substrate and a thin coating (in the thickness range of 0.3–3 μm). In this technique a laser pulse of a high enough energy and a pre-determined duration is converted into a pressure pulse of a critical amplitude and width that is sent through the substrate toward the free surface with the coating. The reflected tensile wave from the free surface of the coating pries-off the coating. The critical stress amplitude that accomplishes the removal of the coating is determined from a computer simulation of the process. The simulation itself is verified by means of a piezo-electric crystal probe that is capable of mapping out the profile of the stress pulse generated by the laser pulse. Interface strength values ranging from 3.7 to 10.5 GPa were determined for the Si/SiC system. For the interfaces between pyrolytic graphite and SiC coatings an average strength of 7.2 GPA was measured, while the corresponding interface strength between a Pitch-55 type ribbon with a fiber-like morphology and SiC coatings was found to be 0.23 GPa. Intrinsic strengths of SiC coatings and Si crystal were also determined using this technique. These were, on the average, 8.6 GPa for Si crystals and 11.9 GPa for a SiC coating. Furthermore, the potential of the laser technique to determine the interface toughness was also demonstrated, provided well-characterizable flaws can be planted on the interface.

Cavitation in elastic and elastic-plastic solids

Abstract: I n this study, we examine the phenomenon of cavitation under non-symmetric loading. We seek all points in (τ 1 , τ 2 , τ 3 )-stress space, such that, when the local principal true stress components (τ 1 , τ 2 , τ 3 ) at a particle reach a point on that set, cavitation ensues. This set can be described by a surface (τ 1 , τ 2 , τ 3 ) = 0 in stress space, which we refer to as a cavitation surface , and corresponds to a cavitation criterion that arises naturally from the analysis. By considering a particular subclass of the set of all kinematically admissible deformation fields, we determine an approximate analytical expression for by using the principle of virtual work. We explicitly determine and discuss the cavitation surface for a neo-Hookean material. We then consider the special case of axisymmetric cavitation corresponding to a stress state (τ 1 , τ 2 , τ 3 ), and illustrate our results for a neo-Hookean material and for a piccewisc power-law clastic-plastic material of the deformation theory . If cavitation occurs before yielding, we find that a good approximate criterion for cavitation is that it occurs when the mean stress τ m = (τ 1 + 2τ 2 )/3 reaches a critical value, even if τ 1 ≠ τ 2 ; however, if cavitation is preceded by yielding, we find that this is not a good approximation. The accuracy of our approximate analytical results is assessed by comparing them with finite element results and the results of other researchers. The utility of the cavitation surface is illustrated by applying the cavitation criterion = 0 to two experimental settings.

Extremum principles for elastic heterogenous media with imperfect interfaces and their application to bounding of effective moduli

Abstract: T he E lasticity extremum principles of minimum potential and minimum complementary energies are extended to the case of heterogenous media with imperfect interface conditions. The extended principles are applied to construct bounds for the effective elastic moduli of two-phase materials and polycrystalline aggregates with imperfect interfaces.

Axisymmetric deformation of power-law solids containing a dilute concentration of aligned spheroidal voids

Abstract: T he macroscopic response of an incompressible power-law matrix containing a dispersion of aligned, spheroidal voids is investigated. Attention is restricted to dilute concentrations of voids and to axisymmetric deformation of the solid. The essential step in the analysis is the solution of a kernel problem for an isolated void, and this solution is obtained accurately and efficiently using a Ritz procedure developed for this purpose. Results for macroscopic strain-rates are presented for void shapes ranging from penny-shaped cracks to infinitely long circular cylinders and for a wide range of triaxialities and matrix hardening exponents. These results are used to assess the role of void shape on the overall response of porous solids.

Effect of fiber inclination on crack bridging stress in brittle fiber reinforced brittle matrix composites

Abstract: The mechanical behavior of brittle matrix composites is strongly affected by the bridging of cracks by fibers. In random fiber composites, fibers can lie at an angle to the crack plane. Under such conditions, the bridging stress for a certain crack opening is governed by various micromechanisms including fiber debonding, fiber bending and rupture as well as matrix spalling. While fiber debonding has been widely investigated, the coupled fiber bending/matrix spalling mechanism has received little attention. In this paper, the fiber bending/matrix spalling mechanism is analyzed by treating the fiber as a beam bent on an elastic foundation with variable stiffness and the possibility of spalling. The foundation stiffness and spalling criterion are derived from a finite element analysis. The bridging stress due to bending alone as well as the total bridging stress are then obtained for the case with brittle fibers. Through this analysis, the effect of various microstructural parameters (such as fiber and matrix moduli, matrix spalling strain and fiber/matrix interfacial friction) on the behavior of random fiber composites can be studied. Prediction of maximum bridging stress for inclined fibers based on the present model is shown to be in good agreement with experimental results.

Pressure-shear impact investigation of strain rate history effects in oxygen-free high-conductivity copper

Abstract: A combined experimental and computational investigation of the behavior of oxygen-free high-conductivity copper under very high shear rates is presented. Pressure-shear plate impact is used for conducting constant strain rate tests and strain rate change texts in which the specimen is strained at shear rates up to 106s−1 for 1μs and then strained at substatially lower shear rates for another microsecond. The specimen is sandwiched between two hard elastic plates to impose conditions of simple shear at very high strain rates and constant hydrostatic pressure. Marked increases in flow stresses are observed at strain rates of 105s−1 and higher. Flow stresses decrease gradually after a sharp drop in strain rate in all strain rate change tests. Homogeneous equiaxed dislocation cells are found as the predominant substructure in the deformed specimens. Theoretical analyses of the nonlinear wave propagation within the specimen are carried out using a general internal variable formulation in which the hardening rate depends on the rate of deformation. The governing system of hyperbolic partial differential equations is solved using a finite-difference scheme; computational results are compared with the experimental results. Both small- and finite-deformation formulations are considered. Only the internal variable model which incorporates a strong rate sensitivity of strain hardening is successful in describing the observed response to the change in strain rate. The enhanced rate sensitivity at high strain rates is concluded to be related primarily to the rate sensitivity of strain hardening, not the rate sensitivity of the flow stress at constant dislocation structure. The generation and evolution of dislocation cells appears to be the dominant micromechanical process during the high- rate deformation of pure metals.

Non-associated plastic flow in single crystals

Abstract: P lastic flow by shears on well-defined crystallographic planes is associated, most often, with the Schmid yield criterion which is expressed in terms of the resolved shear stress on those planes in the direction of the shears. In this case, for time-independent (low-temperature) flow, the yield function for each slip system is also the potential for the shear and. therefore, flow is said to be associated with that function (i.e. normality). Qin and Bassani (1992. J. Mech. Phys. Solids40, 813) propose a yield criterion to accommodate various non-Schmid behaviors. In this paper it is shown that this criterion leads to a nonassociated flow rule (i.e. non-normality). Time-independent constitutive relations are derived for single crystals undergoing non-associative plastic flow. The tension-compression asymmetry predicted for initial yield persists in strain hardening as well. Strain localization in the form of shear bands is investigated for both a single-slip and a symmetric double slip model. It is shown that non-Schmid effects increase the tendency for localization.

Properties of an adiabatic shear-band process zone

Abstract: The formation of adiabatie shear bands is examined with an approximate analytic model. The shear band is viewed as a propagating feature with a well-defined front. The shear band is further partitioned into a shear-band process zone within which most of the adiabatic heating and shear stress relaxation occurs, followed by a quasi-steady zone within which little dissipation occurs. Although a one-dimensional analysis of the shear-band dynamics is initially pursued, the analysis is then used to calculate properties of the inherently two-dimensional shear-band process zone. The length and width of the process zone are calculated along with the shear displacement. The model is further used to calculate the energy dissipation within the shear-band process zone and the concept of a shear-band toughness is introduced. The flow field within the vicinity of the process zone is also examined. Calculated properties of the shear-band process zone compared well with available experimental data.

Transition from micro-mechanics to computationally efficient phenomenology: Carbon black filled rubbers incorporating mullins' effect

Abstract: In this work a previously proposed micro-mechanical continuum damage model for carbon black filled rubbers exhibiting Mullins' effect is developed into a phenomenological model. The resulting model gives nearly the same agreement with experimental data as the fully micro-mechanical model but, more importantly, it is computationally efficient, unlike the fully micro-mechanical model. The derivation of the model follows from a few key observations about the fully micro-mechanical model along with a systematic application of the principle of maximum dissipation. Comparisons with experimental data are presented, and finite-element solutions to boundary value problems are shown.

The structure of the linear anisotropic elastic symmetries

Abstract: An insightful, structurally appealing and potentially utilitarian formulation of the anisotropic form of the linear Hooke's law due to Lord Kelvin was independently rediscovered by R ychlewski (1984, Prikl. Mat. Mekh. 48, 303) and M ehrabadi and C owin (1990, Q. J. Mech. appl. Math. 43, 14). The eigenvectors of the three-dimensional fourth-rank anisotropic elasticity tensor, considered as a second-rank tensor in six-dimensional space, are called eigentensors when projected back into three-dimensional space. The maximum number of eigentensors for any elastic symmetry is therefore six. The concept of an eigentensor was introduced by K elvin (1856, Phil. Trans. R. Soc. 166, 481) who called eigentensors “the principal types of stress or of strain”. Kelvin determined the eigentensors for many elastic symmetries and gave a concise summary of his results in the 9th edition of the Encyclopaedia Britannica (1878). The eigentensors for a linear isotropic elastic material are familiar. They are the deviatoric second-rank tensor and a tensor proportional to the unit tensor, the spherical, hydrostatic or dilatational part of the tensor. M ehrabadi and C owin (1990, Q. J. Mech. appl. Math. 43, 14) give explicit forms of the eigentensors for all of the linear elastic symmetries except monoclinic and triclinic symmetry. We discuss two approaches for the determination of eigentensors and illustrate these approaches by partially determining the eigentensors for monoclinic symmetry. With the nature of the eigentensors for monoclinic symmetry known, a rather complete table of the structural properties of all linear elastic symmetries can be constructed. The purpose of this communication is to give the most specifically detailed presentation of the eigenvalues and eigentensors of the Kelvin formulation to date.

The structure of the near-tip field during transient elastodynamic crack growth

Abstract: T he process of dynamic crack growth in a nominally elastic malerial under conditions of plane strain or plane stress is considered. Of particular concern is the influence of the transient nature of the process on the stress field in the immediate vicinity of the crack tip during nonsteady growth. Asymptotically, the crack tip stress field is square root singular at the crack tip, with the angular variation of the singular field depending weakly on the instantaneous crack tip speed and with the instantaneous stress intensity factor being a scalar multiplier of the singular field. However, for a material particle at a small distance from the moving crack, the local stress field depends not only on instantaneous values of crack speed and stress intensity factor, but also on the past history of these lime-dependent quantities. A representation of the crack tip field is obtained in the form of an expansion about the crack up in powers of radial coordinate, with the coefficients depending on the time rates of change of crack tip speed and stress intensity factor. This representation is used to interpret some experimental observations, with the conclusion that the higher-order expansion provides an accurate description of crack tip fields under fairly severe transient conditions. In addition, some estimates are made of the practical limits of using a stress intensity factor field alone to characterize the local fields.

Effect of crack meandering on dynamic, ductile fracture

Abstract: Dynamic crack growth is analyzed numerically for a plane strain edge cracked specimen subject to impulsive tensile loading at one end. An elastic—viscoplastic constitutive relation for a porous plastic solid is used to model ductile fracture by the nucleation and subsequent growth of voids to coalescence. Two populations of second-phase particles are represented: large inclusions with low strength, which result in large voids near the crack tip at an early stage, and small second-phase particles, which require large strains before cavities nucleate. Adiabatic heating due to plastic dissipation and the resulting thermal softening are accounted for in the analyses. Various two-dimensional distributions of the larger inclusions in front of the crack tip are considered, while the small second-phase particles are taken to be uniformly distributed. It is found that in most cases cracks grow in a zig-zag manner, dependent on the distribution of larger inclusions. Predictions for the dynamic crack growth behavior and for the time variation of crack tip characterizing parameters are obtained for each case analyzed. The computed crack growth paths and speeds are entirely based on the ductile failure predictions of the material model, so that the present study is free from ad hoc assumptions regarding appropriate dynamic crack growth criteria.

Interfacial crack-tip field in anisotropic elastic solids

Abstract: For interfacial cracks in anisotropic elastic solids, controversies exist in that several different definitions for the crack-tip field have been proposed in the literature. In this paper, we first devise a novel and convenient scheme for constructing the interfacial crack fields and then carry out a mismatch analysis for understanding the oscillatory structure of the crack-tip stress singularity. It is hoped that the mismatch analysis can shed some light on the controversial issues from a different perspective. Among different definitions for the stress intensity factors, it is found that the solution proposed by Wu [Int. J. Solids Struct. 27, 455 (1991)] , which conforms to a general definition suggested by Rice [J. appl. Mech. 55, 98 (1988)] , is consistent with the analysis of local interface mismatch near the crack tip. Critical quantities governing the oscillation and mismatch are numerically evaluated for a number of materials including two fiber-reinforced composites and a group of crystals of cubic symmetry.

Relationships between the effective properties of transversely isotropic piezoelectric composites

Abstract: We consider two-phase fibre-reinforced piezoelectric composites of arbitrary transverse phase geometry wherein both the constitutents and the composite exhibit transverse isotropy. Such a material is described by a total of 10 overall elastic moduli, piezoelectric constants and permittivities. It is shown that five universal relationships which are independent of geometry at given volume fractions connect six of these effective physical constants. The result is a generalization of the relations found by Hill [J. Mech. Phys. Solids 12, 199 (1964)] for the purely elastic case. An additional relationship between three of the other constants is also known to exist.

Mechanical behavior of a continuous fiber reinforced aluminum matrix composite subjected to transverse and thermal loading

Abstract: The transverse properties of an aluminum alloy metal matrix composite reinforced by continuous alumina fibers were investigated. The composite is subjected to both mechanical and cyclic thermal loading. The results of an experimental program indicate that the shakedown concept of structural mechanics provides a means of describing the material behavior. When the loading conditions are within the shakedown region, the material finally responds in an elastic manner after initial plastic response, and for loading conditions outside the shakedown region, the material exhibits a rapid incremental plastic strain accumulation. The failure strain varies by an order of magnitude according to the operating conditions. Hence, for high mechanical and low thermal loading, the failure strains is small; for low mechanical and high thermal loading, the failure strain is large.

A model for fully formed shear bands

Abstract: An asymptotic analysis of the morphology of a fully formed shear band is given for a simple flow law in a perfectly plastic material. Scaling laws are given for the maximum strain rate and the width of the band.