J. Eng. Mater. Technol. 1999;121(4):405. doi:10.1115/1.2812394.
Topics: Durability
Commentary by Dr. Valentin Fuster


J. Eng. Mater. Technol. 1999;121(4):406-412. doi:10.1115/1.2812395.

A geometrically nonlinear formulation for the behavior of composite delaminated beams of arbitrary stacking sequence, and with the effects of transverse shear deformation included, is presented. The formulation is based on a first-order shear deformation kinematic model, which incorporates the bending-stretching coupling effect and also assumes an arbitrary initial imperfection. The nonlinear differential equations are solved by Newton’s method using a finite-difference scheme. The growth of the delamination is also studied by applying the J-integral in order to derive a formula for the energy release rate, which includes transverse shear. Results are presented which illustrate the shear effect, especially with respect to the ratio of the in-plane extensional over shear modulus and with respect to the ratio of plate length over thickness. It is seen that transverse shear can affect largely the displacement profiles, rendering the structure more compliant, and can promote growth by increasing the energy release rate, but this latter effect is moderate and mainly noticable only at the later stages in the postbuckling regime.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 1999;121(4):413-421. doi:10.1115/1.2812396.

The purpose of this paper is to investigate the effect of material heterogeneity on damage evolution and subsequent crack propagation in bimaterial systems. Strain gradient theory analysis reveals that a higher stress triaxiality always occurs on the softer material side due to the material mismatch in yield capacity and the corresponding strain gradient along the interface. High stress triaxiality is a major condition which promotes ductile damage and facilitates crack growth. To investigate this link, numerical simulations of ductile interface crack growth are performed using a damage based constitutive model. Both the numerical and experimental results show that a crack may grow along the interface or deviate into the softer material, but never turn into the harder material. The theoretical and numerical analysis reveal three factors which strongly affect the direction of crack growth and the resistance capacity of the bimaterial system against fracture. These are the boundary conditions which determine the global kinematically admissible displacement field, the stress/strain gradient near the interface due to the material mismatch, and the distance from the crack tip to the interface.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 1999;121(4):422-429. doi:10.1115/1.2812397.

The mode I and II stress intensity factors in a fully anisotropic infinite strip with a single-edge or double-edge crack configuration are obtained from an approach based on the continuous dislocation technique. The elastic solution of a single dislocation in an anisotropic half plane is used in conjunction with an array of dislocations along the boundary of the infinite strip, which is supposed to be traction-free, to provide the solution of a single dislocation in an anisotropic infinite strip. The dislocation densities of the dislocation array are determined in such a way that the traction forces generated by the dislocation array cancel the residual tractions along the boundary due to the single dislocation in the half plane. The stress field of a single dislocation in the infinite strip is thus a superposition of that of the single dislocation and the dislocation array in the half plane. This solution is then applied to calculate the mixed mode I and II stress intensity factors for a single-edge and a double-edge crack in the anisotropic strip, by replacing the cracks with a series of dislocations and satisfying the crack surface traction-free conditions. To illustrate the results, typical material data for graphite/epoxy were used in a unidirectional construction with the fiber orientation, θ, measured from the load direction (perpendicular to the crack direction), varying between 0 and 90 degrees. It is found that the effect of anisotropy on the mode I stress intensity factor is significant between 30 and 60 degrees and depends strongly on the relative crack length, being larger for cracks of relative larger length. The mode mixity, defined such that it is zero for pure mode I and 90 degrees for pure mode II, is significant between 40 and 70 degrees, and is in general between zero and 20 degrees.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 1999;121(4):430-435. doi:10.1115/1.2812398.

An investigation into the growth behavior of interlayer and intralayer cracks in delaminated cross-ply laminates subjected to fatigue compression is presented. Experimental data indicate different fatigue growth patterns for the two cases. The effects of mode mixity and position of the delamination in the formation of the cracks are studied. A mode-dependent fatigue growth law is applied in order to predict the behavior of the intralayer and interlayer cracks. Successful correlation of the analytical and test data is conducted for the interlayer cracks. For the intralayer cracks, addition of contact effects and local geometrical parameters in the model are suggested.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 1999;121(4):436-444. doi:10.1115/1.2812399.

A model is developed herein for predicting the evolution of interface degradation, matrix cracking, and delamination at multiple sites in laminated continuous fiber composite plates subjected to monotonic and/or cyclic mechanical loading. Due to the complicated nature of the many cracks and their interactions, a multi-scale micro-meso-local-global methodology is deployed in order to model all damage modes. Interface degradation is first modeled analytically on the microscale, and the results are homogenized to produce a cohesive zone model that is capable of predicting interface fracture. Subsequently, matrix cracking in the plies is modeled analytically on the meso-scale, and this result is homogenized to produce ply level damage dependent constitutive equations. The evolution of delaminations is considered on the local scale, and this effect is modeled using a three dimensional finite element algorithm. Results of this analysis are homogenized to produce damage dependent laminate equations. Finally, global response of the damaged plate is modeled using a plate finite element algorithm. Evolution of all three modes of damage is predicted via interfacing all four scales into a single multi-scale algorithm that is computationally tenable for use on a desktop computer. Results obtained herein suggest that this model may be capable of accurately predicting complex damage patterns such as that observed at open holes in laminated plates.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 1999;121(4):445-452. doi:10.1115/1.2812400.

This study is concerned with the treatment of the dynamic antiplane failure behavior of fiber reinforced composites involving matrix cracks and partially-debonded fibers. The matrix/fiber interphase was modeled as a thin interfacial layer with varying elastic modulus. The steady-state theoretical solution of this class of problems is formulated using a newly developed pseudo-incident wave method, thus reducing the original interaction problem into the solution of coupled single fiber/crack solutions. By using Fourier transform technique and solving the resulting singular integral equations, the dynamic stress intensity factor at the matrix crack was obtained analytically. Numerical examples were provided to show the effect of the location and material property of fibers, the size of debonded layer, and the frequency of the incident wave upon the dynamic stress intensity factors of the matrix crack.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 1999;121(4):453-459. doi:10.1115/1.2812401.

The effects of vanadium layer thickness (100, 200 and 400 μm) on the resistance-curve behavior of NiAl/V, microlaminates are examined in this paper. The fracture resistance of the NiAl microlaminates reinforced with 20 vol.% of vanadium layers is shown to increase with increasing vanadium layer thickness. The improved fracture toughness (from an NiAl matrix toughness of ̃6.6 MPam to a steady-state toughness of ̃15 MPam obtained from finite element analysis) is associated with crack bridging and the interactions of cracks with vanadium layers. The reinitiation of cracks in adjacent NiAl layers is modeled using finite element methods and the reinitiation is shown to occur as a result of strain concentrations at the interface between the adjacent NiAl layers and vanadium layers. The deviation of the reinitiated cracks from the pure mode I direction is shown to occur in the direction of maximum shear strain. Toughening due to crack bridging is also modeled using large-scale bridging models. The intrinsic toughness levels of the microlaminates are also inferred by extrapolating the large scale bridging models to arbitrarily large specimen widths. The extrapolations also show that the small-scale bridging intrinsic toughness increases with increasing vanadium layer thickness.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 1999;121(4):460-467. doi:10.1115/1.2812402.

This article concerns the mechanical response of random glass fiber strand swirl-mat/urethane matrix composite under static and cyclic loads as well as under elevated temperatures. The article presents an extensive amount of experimental data as well as predictions based upon a coupled damage/viscoelastic constitutive formulation generated specifically to model the behavior of the material at hand. Damage evolution relations are derived from an empirical relationship. This work extends previously published results.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 1999;121(4):468-475. doi:10.1115/1.2812403.

Fiber reinforced composites, due to their higher specific strength and specific stiffness, are replacing many metallic structures. Of these, thick composite laminates are of high interest in various, millitary, transportation and marine applications for their use in ballistic and shock protection. One such application is in Composite Armored Vehicle (CAV) integral armor comprising of thick section composite that serves as the primary load-bearing component. The current solution of the structural backing laminate utilizes an S2-glass/epoxy system processed using automated fiber placement method. While proven structurally suitable, this method is time consuming as well as expensive. This paper presents several alternative cost-effective manufacturing solutions for fabricating composite laminates of 20 mm (0.8 in.) nominal thickness (made of 45 layer, 2 × 2 twill weave S2-glass with 933 sizing/vinyl ester C-50 resin), consisted with them CAV application in focus. They include Vacuum Assisted Resin Transfer Molding (VARTM) and Vacuum Assisted Resin Infusion Modeling (VARIM) and their variations. The effectiveness of different affordable processing approaches adopted in fabricating the structural laminate is compared in terms of static and dynamic compression response of the laminations. Static studies have been conducted on thick composites using specimen based on Army Material Technology Laboratory’s (AMTL) recommendation for thick section composites, while dynamic response is studied on cubic specimen samples using a Split Hopkinson Pressure Bar (SHPB).

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 1999;121(4):476-482. doi:10.1115/1.2812404.

A numerical study was conducted to simulate and predict damage initiation and growth around the crack tip crack tip in particulate composite specimens made of hard particles embedded in a soft rubber-like matrix material. Therefore, damage evolution in the matrix material around crack tips was investigated. The progressive damage was modeled using a micro/macro-approach which combined two levels of analyses like the micro-level and the macro-level analyses. Damage description was undertaken at the microlevel using a simplified three-dimensional unit-cell model and an isotropic continuum damage theory. The numerical study examined both him and thick specimens with a short or long edge crack to understand the effects of specimen thickness and crack size on the damage initiation, growth, and saturation. Numerical results were compared with experimental data.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 1999;121(4):483-487. doi:10.1115/1.2812405.

The addition of the low-cost mineral filler kaolin to high-density polyethylene (HDPE) creates a composite with both improved stiffness and toughness properties. This study focuses on two aspects of the toughness of these composites: the fracture toughness increment produced by work at the fracture surface and the directionality induced by the injection molding fabrication process. The Essential Work of Fracture (EWF) method gives results which show that a higher volume fraction of kaolin produces more surface work, consistent with earlier work using Compact Tension (CT) tests. The EWF method also demonstrates that a lower volume fraction can produce a higher overall plastic work and apparent toughness. A heat treatment that removes the orientation of the matrix but not that of the particles was applied to study the effect of matrix crystallinity. The results indicate that the matrix supramolecular structure (crystallinity and skin-core effect) is responsible for the directionality of toughness, and that a heat treatment can be used to produce high toughness behavior in both major directions.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 1999;121(4):488-493. doi:10.1115/1.2812406.

A novel technique is presented for the fabrication and fracture testing of large-scale polymeric based Functionality Graded Materials (FGMs). The technique generates a continuously inhomogeneous property variation by taking advantage of the susceptibility of a polyethylene carbon monoxide copolymer (ECO) to ultraviolet irradiation. The resulting FGMs exhibit a varying Young’s modulus, usually in a linear fashion, from approximately 160 MPa to 250 MPa over 150 mm wide specimens. The fracture behaviour of the FGM is experimentally investigated through the use of single edge notch fracture tests on both homogeneously irradiated and functionally graded ECO. Two approaches are used to evaluate fracture parameters: The first, a hybrid numerical-experimental method, is based on far field measurements only. The second uses digital image correlation to obtain near tip measurements. The energy release rates of uniformly irradiated ECO and of several FGMs are measured and compared. It was seen that the FGM showed a built-in fracture resistance behavior implying that it requires increased driving force to sustain crack growth.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 1999;121(4):494-502. doi:10.1115/1.2812407.

The crushing response of polycarbonate circular cell honeycomb to inplane uniaxial loading under displacement control is analyzed through a combination of experiment and numerical simulation. The experiments, which correspond to two different uniaxial loading conditions, are performed using honeycomb material which has a nearly periodic microstructure. In the initial part of the response, the specimens deform in a uniform fashion. Next, a nonlinear phase characterized by progressive localization of deformation is observed. The progressive localization causes the walls of each cell to contact. These experimental results are simulated through numerical analysis using the finite element method. The reasons for the orthotropic response of the honeycombs are discussed.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 1999;121(4):503-513. doi:10.1115/1.2812408.

Experimental findings are presented which demonstrate the coupled transport, mechanical and morphological changes in porous battery materials when they are cycled electrochemically. These materials, comprised of a mixture of powdered nickel and nickel fiber, act as substrates in nickel-metal hydride (NiMH) cells, and function as porous, conductive containment for positive-plate active material. They can offer substantial weight and cost savings over more traditional sintered or foam materials, provided they can be designed to produce good conductivity over many (>500) electrochemical cycles. This study represents an expansion of previous work by the authors, which had established some key differences in the behavior of substrate materials for a small number of cells. Here, these difference are validated with a greater variety and number of electrochemical/material experiments, along with a parallel study on morphological changes. In the second paper in this series (Cheng et al., 1999b), transport and mechanics models are presented to explain the observed differences, using microstructural models based on observations in this study.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 1999;121(4):514-523. doi:10.1115/1.2812409.

Models are presented for the evolution of transport and mechanical properties of nickel-metal hydride (NiMH) battery substrates. In the first paper in this series (Wang et al., 1999), conductive losses and enhancement of mechanical properties in these materials were quantified experimentally. These were qualitatively shown to be related to observed morphological changes in the substrate materials. Here, an evolution hypothesis for changes in these structures is presented, along with a simplified approximation of the real material microstructure (porous fiber/powder nickel network) with a tractable simulation geometry (porous fiber networks). Transport and mechanics models are then compared with experimental results, with stochastically-arranged fibers approximated as conductive beams connected by elastic torsion springs. Both quantitative and qualitative agreement are found with the models. Limitations of the approaches proposed are also discussed, along with the consequences of the simplifications of geometry for analysis.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 1999;121(4):524-529. doi:10.1115/1.2812410.

Much research has been conducted to understand the damage tolerance behavior of polymer matrix composites, but there are so many parameters involved that the development of a generic model is rather difficult. The present paper proposes an information system, which can overcome such difficulty. In this system, a list of possible parameters is generated and used as input. The output contains compression strength after impact, dent depth and damage area as well as pertinent reference information. The information system is constituted in a relational database environment and tools from expert system technology are incorporated. Case examples are included to demonstrate the practical use of the software for both data retrieval and similarity studies.

Commentary by Dr. Valentin Fuster

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