Kenneth M. Liechti

On the compressive failure of fiber reinforced composites

Abstract In this paper a combination of experimentation and analysis is used to identify and study the mechanisms that govern the failure of unidirectional fiber composites under compression. The experimental part includes experiments in which the compressive strength and the prevalent failure mechanisms of AS4/PEEK composite are established, tests for establishing the constitutive properties of the composite and its constituents, and an evaluation of the extent of misalignment of fibers in manufactured composites. The failure load of the composite was confirmed to be affected by geometric imperfections in the form of fiber waviness, and failure was found to lead to kink bands with distinct orientations and widths. Motivated by the experimental findings, the composite was idealized as a two-dimensional solid with alternating fiber and matrix layers, each having the measured properties of the two constituents. The compressive responses of microsections of finite width with imperfections of various spatial distributions were established numerically. The calculated responses are characterized by an initially stiff, stable regime terminated by a limit load instability which is associated with the strength of the composite. Following the limit load, the deformation localized into inclined bands with distinct widths. It has been verified that, as the localization process progresses, the fiber bending stresses at the ends of these bands grow to values comparable to those of the fiber strength. The sensitivity of the calculated response to the geometric characteristics of the imperfections was studied parametrically.

Cohesive zone modeling of crack nucleation at bimaterial corners

The prediction of crack nucleation from bimaterial corners that have the same corner angle (and therefore singularity) via stress intensity factors is fairly well established. The objective of this work was to examine crack nucleation from a range of corner angles and see if a more general crack nucleation criterion could be formulated. A series of experiments was conducted using an aluminum-epoxy bimaterial specimen loaded under 4-point bending. In addition to the usual measurements of load and an associated displacement, the displacements near the corner were measured using moire interferometry. Numerical analyses were first conducted assuming a rigid interface. However, the resulting displacements differed from the measured ones, especially near the corner and along the interface. The interface was then modeled as a separate constitutive entity by incorporating a cohesive zone model in the numerical analysis. Following calibration via an interface crack configuration (zero corner angle), the cohesive zone model yielded displacements that were in good agreement with the measured values for all the other corner angles that were considered. The predicted failure loads were also in good agreement with the experimental results. Thus the consistent nucleation criterion was that the area under the traction-separation curve and its maximum traction (the dominant cohesive zone model parameters) remain the same. The numerical solutions indicated that the plastic deformation in the epoxy was small and that failure was predominantly in opening mode. In addition, the critical vectorial crack opening displacement and mode-mix were independent of the corner angle. Finally, a simple design parameter was proposed for predicting the failure load of a bimaterial specimen with an arbitrary corner angle, based on the failure load of a bimaterial specimen with an interface crack.

Biaxial Loading Experiments for Determining Interfacial Fracture Toughness

The paper establishes the range of in-plane fracture mode mixtures and contact zone sizes that can be obtained from an edge-cracked bimaterial strip under biaxial applied displacements. The development of a suitable loading device for and the application of crack opening interferometry to interfacial crack initiation experiments is described. The crack initiation process under bond-normal loading is examined in detail for a glass/epoxy interface in order to establish a hybrid optical interference/finite element analysis technique for extracting mixed-mode fracture parameters.

Anomalous Moisture Diffusion in Viscoelastic Polymers: Modeling and Testing

It is now well known that Ficks Law is frequently inadequate for describing moisture diffusion in polymers or polymer composites. Non-Fickian or anomalous diffusion typically occurs when the rates of diffusion and viscoelastic relaxation in a polymer are comparable, and the ambient temperature is below the glass transition temperature (T g ) of the polymer, As a result, it is necessary to take into account the time-dependent response of a polymer, analogous to viscoelastic relaxation of mechanical properties, in constructing such a model. In this paper, a simple yet robust methodology is proposed that would allow characterization of non-Fickian diffusion coefficients from moisture weight gain data for a polymer below its T g . Subsequently, these diffusion coefficients are used for predicting moisture concentration profiles through the thickness of a polymer. Moisture weight gain data at different temperatures for an epoxy adhesive is employed to calibrate the model. Specimen thickness independence of the modeling parameters is established through comparison with test data. A finite element procedure that extends this methodology to more complex shapes and boundary conditions is also validated.

Asymmetric Shielding Mechanisms in the Mixed-Mode Fracture of a Glass/Epoxy Interface

An asymmetric increase in the apparent values of the interfacial fracture toughness with increasing mode II component of loading has been observed by several investigators. In this study, cracks were grown in a steady-state manner along the glass/epoxy interface in sandwich specimens in order to determine the mechanisms responsible for the shielding effect. Finite element analysis using a hydrostatic stress and strain rate dependent plasticity model for the epoxy and a cohesive zone model for the interface shows that plastic dissipation in the epoxy accounts for the asymmetric shielding seen in these experiments which cover a wide range of mode mix. Numerical predictions of normal crack-opening displacements yielded results that were consistent with measured values which were made as close as 0.3 μm from the crack tip.

The intrinsic toughness and adhesion mechanisms of a glass/epoxy interface

Glass/epoxy interfaces of sandwich specimens were fractured under steady-state conditions over a wide range of in-plane mode-mix. The plastic dissipation was calculated via finite element analysis and subtracted from the steady-state fracture toughness to obtain the intrinsic toughness of the interface. Mechanisms which contribute to the intrinsic toughness were found to include the thermodynamic work of adhesion, local inelastic deformations and polymer chain pull-out, but their combined energy was only approximately 15% of the intrinsic toughness. Angular dependent x-ray photoelectron spectroscopy of the glass surfaces after fracture revealed epoxy adsorbed to a depth of approximately 3 nm. Cleavage of epoxy strands was found to be the most significant mechanism contributing approximately 40% to the intrinsic toughness of the interface.

Multiaxial Nonlinear Viscoelastic Characterization and Modeling of a Structural Adhesive

Many polymeric materials, including structural adhesives, exhibit a nonlinear viscoelastic response. The nonlinear free volume approach is based on the Doolittle concept that the free volume controls the mobility of polymer molecules and, thus, the inherent time scale of the material. It then follows that factors such as temperature and moisture, which change the free volume, will influence the time scale. Furthermore, stress-induced dilatation will also affect the free volume and, hence, the time scale. However, during this investigation dilatational effects alone were found to be insufficient in describing the response of near pure shear tests performed on a bisphenol A epoxy with an amido amine hardener. Thus, the free volume approach presented here has been modified to include distortional effects in the inherent time scale of the material. In addition to predicting the global response under a variety of multiaxial stress states, the modified free volume theory also accurately predicts the local displacement fields, including those associated with a localized region, as determined from geometric moire measurements at various stages of deformation.

A Distortion-Modified Free Volume Theory for Nonlinear Viscoelastic Behavior

Many polymeric materials, including structural adhesives, exhibit anonlinear viscoelastic response. The nonlinear theory of Knauss and Emri(Polym. Engrg. Sci.27, 1987, 87–100) is based on the Doolittle conceptthat the ‘free volume’ controls the mobility of polymer molecules and,thus, the inherent time scale of the material. It then follows thatfactors such as temperature and moisture, which change the free volume,will influence the time scale. Furthermore, stress-induced dilatationwill also affect the free volume and, hence, the time scale. However,during this investigation, dilatational effects alone were found to beinsufficient for describing the response of near pure shear tests of abisphenol A epoxy with amido amine hardener. Thus, the free volumeapproach presented here has been modified to include distortionaleffects in the inherent time scale of the material. The same was foundto be true for a urethane adhesive.The small strain viscoelastic responses of the two materials havebeen determined from master curves of uniaxial and bulk creep testing atvarious temperatures. The nonlinear free volume model, modified toinclude distortional effects in the reduced time, was incorporated inthe ABAQUS finite element code via a user-defined material subroutine.For the epoxy, validation of the modified theory (a strain-basedformulation of free volume) has been achieved through good agreementbetween the computational and experimental results of butterfly-shapedArcan specimens subjected to loadings ranging from near pure shear toshear with various amounts of superposed tension and compression. Inaddition to predicting the response under a variety of multiaxial stressstates, the modified free volume theory also accurately predicts theformation and growth of shear banding, or regions of highly localizeddeformation, which have been found to occur upon continued loading ofthe epoxy. The urethane did not appear to exhibit any localizeddeformation over the range of temperatures at which it was tested.As a result, a stress-based modified free volume approach was requiredto model its multiaxial and temperature-dependent behavior. Althoughfree volume was the unifying parameter for the two materials, the needfor a stress-based and strain-based formulation of the free volume forthe urethane and epoxy, respectively, could not be reconciled at thistime.

On the large deformation and localization behavior of an epoxy resin under multiaxial stress states

Abstract The paper describes a series of experiments that were conducted in order to examine the response of a cross linked epoxy resin. A variety of stress states were considered by conducting experiments under uniaxial tension, plane strain compression, simple shear and combinations of tension or compression and shear (biaxial). Strain rate effects were considered in the simple shear experiments and displacement measurements using geometric moire were made in order to follow the onset and propagation of shear bands under simple shear and compression on shear. Some birefringence measurements were also made. Localization in the form of shear bands occurred under the tensile, simple shear and the biaxial stress states but not under plane strain compression. The shear bands in simple shear and compression and shear grew quickly along the specimen gage length and then broadened, and detailed strain distributions were determined as a function of load level. The birefringence became constant in regions where shear banding had occurred. The onset of shear banding was delayed by higher strain rates and compressive stresses but was promoted by tensile stresses. The lack of a limit load in the plane strain compression response indicates that the epoxy considered here does not strain soften and that the response obtained is the true material one.

Interfacial adhesion between graphene and silicon dioxide by density functional theory with van der Waals corrections

Interfacial adhesion between graphene and a SiO2 substrate is studied by density functional theory (DFT) with dispersion corrections. The results demonstrate the van der Waals (vdW) interaction as the predominant mechanism at the graphene/SiO2 interface. It is found that the interaction strength is strongly influenced by changes of the SiO2 surface structures due to surface reactions with water. The adhesion energy is reduced when the reconstructed SiO2 surface is hydroxylated, and further reduced when covered by a monolayer of adsorbed water molecules. Moreover, it is noted that vdW forces are required to accurately model the graphene/SiO2 interface with DFT and that the adhesion energy is underestimated by empirical force fields commonly used in atomistic simulations.