Analysis of the adhesively bonded three-point bending specimen for evaluation of adhesive shear behaviour

The adhesive shear stress-strain behaviour is an essential input for the design of structural adhesive joints. Relative to current standard tests, the main advantage of bonded beams is reducing spurious adhesive joint end effects on strength measurements. A beam model was developed in this work for the three-point bending test considering metal adherends, support effects and adhesive elastic-perfectly plastic stress-strain behaviour. Model predictions were in good agreement with finite element analyses for specimens with the thin bondlines typical of structural joints. The present results show that the adhesively bonded three-point bending test can be an interesting approach for the thin bondlines used in structural joints. Nevertheless, there are limitations on the range of measurable properties and data analysis requires models such as the one developed herein.     

Use of artificial neural networks for modelling rate dependent behaviour of adhesive materials

This research work highlights the use of artificial neural networks (ANN) for modelling the rate-dependent response of adhesive materials with the purpose of expanding the established method for modelling the response of adhesively bonded structures, and in particular single lap joints. The motivation for this work comes after a viscoplastic model developed in a previous research work failed to predict the response of single lap joints bonded with a rate dependent adhesive material. The viscoplastic model, however, was successful in replicating both bulk and shear properties of the used adhesive system. Predictions made using the rate-dependent von Mises material model proved to be successful in predicting the behaviour of single lap joints, but it could not model the shear data using the tensile data due to hydrostatic stress sensitivity in the adhesive itself. Accurate predictions of the rate-dependent behaviour using artificial neural networks are possible with the availability of stress and strain data sets from experiments. This is where the neural network constitutive model directly acquires the information on the material behaviour from experimental data sets. Material data defining both the tensile and shear response of the adhesive system was extracted from previous research work. An artificial neural network constitutive model was developed and then used to replicate experimental data and also to generate further data at other strain rates. The available model could be slightly modified and then used to investigate various geometrical parameters, such as overlap length, plate thickness and adhesive thickness on joint strength.     

Comparison of recent rubber-elasticity theories with biaxial stress-strain data: the slip-link theory of Edwards and Vilgis

The Edwards-Vilgis (EV) slip-link theory (1986) derives the elastic free energy of a rubber-like network model containing stable and sliding network junctions (crosslinks and slip-links) and predicts both low-strain softening and high-strain hardening. The four-parameter stress-strain relations calculated by the theory for geometrically different deformation modes up to high strains were tested experimentally using published biaxial stress-strain data on simple covalently crosslinked networks. For networks with low degrees of strain softening and low extensibilities, the experimental dependencies could be described rather well but, generally, a simultaneous satisfactory fit to uniaxial, pure shear and equibiaxial data was not obtained. Systematic experiment-theory deviations exceeding 10% were observed and some of the parameters had a tendency to assume values lying outside the reasonably expected range. The prediction of a pronounced maximum in the strain dependence of stress supported by slip-links seems to be a reason for the discrepancy. Also, modeling of the high-strain singularity in entropy is done in the EV theory using a rather simple approximation. As a result, the finite extensibility contribution to the stress of a slip-link-free network model becomes improbably high and significantly exceeds that following, at a given modulus and locking stretch, from the rigorously derived Langevin-statistics-based eight-chain-network elasticity theory of Arruda and Boyce.     

A new rheological constitutive equation for the network model of polymer melts

A new network model is suggested and a constitutive equation is developed on the basis of the assumed validity of Boltzmann's superposition principle for the shear stress. The predictions of the model concerning the relaxation behavior of polymer melts after steady shear or instantaneous deformation are compared to Lodge's theoretical results and to experimental data from the literature.     

A mathematical model for the prediction of damage in concrete

A mathematical model was developed to describe the compressive stress-strain behaviour of concrete, mortar and cement paste. The determination of a suitable stress-strain function was necessary to determine the energy dissipated in damage on loading. Previous research had shown that the envelope of the cyclic loading sequence used in assessing damage was the stress-strain curve obtained by monotonic loading. The amount of plastic strain on unloading was determined by constructing a pseudo-stress conventional strain curve. Comparison with experimental results indicated that the model for the prediction of the stress-strain curve provided good correlation. Similarly, predictions of change in initial elastic modulus and energy dissipated in damage were also in close agreement with the experimentally obtained values.     

Modeling the rheology of gelatin gels for finite deformations. Part 1. Elastic rheological model

The rheological behavior of gelatin gels is studied through a constitutive equation derived in the literature from the classical hyperelasticity theory by using a nonlinear strain energy density. Gelatin gels are assumed to be an elastic solid here, which at a given maturation time has a degree of physical cross-links composing a permanent elastic network. It is also studied in particular: (a) the validation of the elastic rheological model proposed here in relation to the prediction of two data sets pertaining to different experimental tests (shear and simple compression) by using fixed values of rheological parameters, (b) the increase of the stress-strain nonlinearity with increasing maturation time, at a given protein concentration, (c) the evolution of the stress-strain nonlinearity with increasing gelatin concentration. It is found that gelatin gels exhibit a strong nonlinear strain energy density, which is expressed through two shear modules related to nucleation and growing of junction zones.     

A simple model for non-linear stress relaxation

A simple model for the prediction of non-linear stress relaxation following the cessation of steady shear flow is proposed. The model allows the calculation of the shear and first normal stress difference components of the stress. The mathematical flexibility of the model is reduced to a minimum with the result that no adjustable parameters are employed and only linear dynamic deformation data are required to calculate the non-linear behaviour. Verification of the model was carried out with data available for two viscoelastic fluids and good agreement between the predictions and the experimental results was obtained for the range of shear rates examined (0.167 ? γ ? 16.7 sec^?1).     

Molecular modelling of the elastic behaviour of poly(ethylene terephthalate) network chains

The Monte-Carlo (MC) method developed to model the elastomeric stress-strain behaviour of polyethylene (PE) and poly(dimethyl siloxane) (PDMS) networks and the stress-optical behaviour of PE networks is now applied to the stress-strain behaviour of poly(ethylene terephthalate) (PET) networks. In keeping with the previous results for PE and PDMS networks, increases in the proportions of fully extended chains with macroscopic deformation are found to give rise to steady decreases in the rates of Helmholtz energy changes, causing reductions in moduli at moderate macroscopic deformations. There is no need to invoke a transition from affine to phantom chain behaviour as deformation increases.By using rotational-isomeric-state (RIS) models of the network chains and the MC method, stress-strain behaviour can be related to chemical structure. In this respect, the greater conformational flexibility of the PET chain leads to lower network moduli and smaller deviations from Gaussian network behaviour than for PE networks. In addition, the stiff, aromatic section of the PET repeat unit structure is seen to endow particular characteristics on the end-to-end distribution functions of PET chains. These characteristics are taken fully into account in evaluating the elastomeric properties of the PET networks. Subsequent publications will apply the present results to interpreting the measured stress-strain and the stress-optical properties of entangled PET melts.     

Experimental and Numerical Analysis of the Viscous Fingering Instability of Shear‐Thinning Fluids

Miscible flow displacements in a rectilinear Hele‐Shaw cell of Newtonian as well as rheologically well‐characterized shear‐thinning fluids are examined through experimental measurements and numerical modelling. Water is used as a displacing fluid while the displaced fluid consists of either a reference Newtonian glycerol solution or shear‐thinning solutions of Alcoflood? polymers of different molecular weights. The experimental measurements revealed that the shear‐thinning behaviour of the non‐Newtonian solutions resulted in more complex instability patterns and new finger structures not previously observed in the case of Newtonian displacements are identified and characterized. An analysis of the effects of the rheological behaviour of the shear‐thinning fluids on instability characteristics such as the finger width and finger tip velocity is presented. Numerical simulations using a pseudo‐spectral method are conducted and allowed to compare the predictions of the mathematical model based on an effective Darcy's law with the experimental measurements.     

Elasticity of real networks: Comparison of molecular theory with experiments

Predictions of the theory of elasticity of real networks are compared with results of experiments. The shape of the stress-strain curve for networks in the dry and swollen states and over wide ranges of strain, both in tension and compression, agrees with results of calculations based on the theory. The theory is also in close agreement with results of multiaxial stress-strain experiments and with the predictions of the degree of crosslinking obtained from measurements of the modulus. The theory may additionally be applied to the analysis of birefringence. The assumption of the linear additivity of the elastic and mixing free energies in a swollen network leads to results which are in agreement with experimental findings on different crosslinked systems.     

Experimental evaluation and theoretical prediction of elastic properties and failure of C/C-SiC composite

The paper presents experimental characterization and theoretical predictions of elastic and failure properties of continuous carbon fiber reinforced silicon carbide (C/C-SiC) composite fabricated by Liquid Silicon Infiltration (LSI). Its mechanical properties were determined under uniaxial tensile, compression, and pure shear loads in two sets of principal coordinate systems, 0°–90° and ±45°, respectively. The properties measured in the 0°–90° coordinate system were employed as the input data to predict their counterparts in the ±45° coordinate system. Through coordinate transformations of stress and strain tensors, the elastic constants and stress-strain behaviors were predicted and found to be in good agreement with the experimental results. In the same way, three different failure criteria, maximum stress, Tsai-Wu, and maximum strain, have been selected for the evaluation of the failure of C/C-SiC as a type of genuinely orthotropic material. Based on the comparisons with experimental results, supported by necessary practical justifications, the Tsai-Wu criterion was found to offer a reasonable prediction of the strengths, which can be assisted by the maximum stress criterion to obtain an indicative prediction of the respective failure modes.     

Comparison of the Shear Stress-strain Behaviour of some Structural Adhesives

The shear stress-strain behaviour of structural adhesives provides important data for the designer. Shear modulus, strength, and elastic and plastic strain to failure have been determined using a torsional butt joint technique which is relatively quick to perform and is believed to be very accurate. A range of structural adhesives have been compared, which has highlighted some important differences in their behaviour. Increasing the bond line thickness of an adhesive lowers the plastic strain to failure.     

Experimental tests of entanglement models of rubber elasticity: 1. Uniaxial extension-compression

The predictions of several entanglement models of rubber elasticity for the uniaxial stress-strain response of crosslinked polymer networks are examined. It is found that the Gaylord tube model and the Flory constrained junction fluctuation model both agree well with the experimental data.     

The Shear Stress-Strain Behaviour of Low-modulus Structural Adhesives

The shear stress-strain behaviour of two low-modulus structural adhesives has been measured using the butt-torsion test. The Nadai correction for non-linear shear behaviour is explained as it is necessary to understand how this correction can be applied to butt joints. The results for one adhesive were accurately used to predict the strength of a lap joint, and it was shown that the strength of such a joint can approach that of a conventional, modern, structural epoxy. Structural adhesives are usually reckoned to be those with a high strength (50 MPa and upwards) and (these days), a strain to failure of at least 10% in tension, and which usually have a tensile modulus of 2 GPa or so. However, adhesives which are significantly less stiff, less strong, but much more ductile are entering the 'structural' arena. In order to evaluate their effectiveness and use in design, it is necessary to be able to measure accurately their stress-strain behaviour. Two such materials are 3M 9245 Structural Bonding Tape (SBT) and 3M 7838 B/A.     

Polyaxial Stress-Strain Relations in ATJS Graphite

Theoretical considerations are applied to Jortner's experimental data in order to develop a simple analytical stress-strain relation for ATJS graphite under arbitrary loading conditions. Since the relation proposed correlates well with the entire range of proportional loading encompassed by his data, it is reasonable to expect that the theoretical predictions of strains for stresses that are inaccessible in the laboratory will also be accurate. It is anticipated that, with minor changes hi the values of the theoretical parameters, the stress-strain law will also apply to other transversely isotropic graphites.     

A phenomenological energy-based model to characterize stress-softening effect in elastomers

A phenomenological energy-based model for stress-softening of isotropic, incompressible hyperelastic rubberlike materials is derived here. In this model, the microstructural damage is characterized by an exponential softening function that depends on the current magnitude of the strain-energy function and its maximum previous value in a deformation of the virgin material. Theoretical models are presented for uniaxial, equibiaxial and pure shear deformations by using Gaussian and non-Gaussian material molecular network models. The accuracy of the resulting constitutive equations is demonstrated on uniaxial, equibiaxial and pure shear experimental data provided in the literature. Comparisons between the energy-based model and the strain intensity based phenomenological model described in [Elías-Zúñiga A, Beatty MF. ZAMP 2002;53:794-814. [1]] show that the model developed here is slightly superior in following experimental data.     

A new fluid model for particles settling in a viscoplastic fluid

The study of the settling behaviour of particles in viscoplastic fluids is closely related to the study of rheology. In this paper, a thorough examination of the flow behaviour of viscoplastic fluids, in the form of aqueous polyacrylamide solutions, has been presented. The results of this study suggest that the experimental fluids exhibit time-dependent flow characteristics, where the apparent viscosity of the solutions depends highly on their shear history. This time dependency has been attributed towards the processes of destruction and rejuvenation in the ‘structural network’ of the fluids (due to the presence of hydrogen bonding between polyacrylamide and water molecules), as they are subjected to changing rates of shear. A new fluid model was thus developed to capture this flow behaviour. This model, termed as ‘semi-viscoplastic’, features temporary yield stress characteristics that tend to dissipate once the structural network of the fluid is destroyed due to the application of shear. The time dependency of the fluid viscous parameters becomes apparent in the settling sphere experiment, where it has been demonstrated that a sphere that is following the flow path of another sphere tends to attain a fall velocity that is significantly higher than the preceding sphere. Based on this finding, a new generalised correlation has been developed, through which predictions of the fall velocity of spherical particles settling through viscoplastic fluids, of various shear history, can be made.     

Failure Assessment on a Strip Biaxial Tension Specimen for a HTPB-Based Propellant Material

This paper indicates the possibility of assessing the failure of a strip biaxial tension specimen from the non-linear stress-strain behaviour of a uniaxial tension specimen which is useful for characterizing the propellant material. In order to examine the adequacy of the analytical and finite element methods, test data existing on a HTPB-based propellant material is used. Failure predictions on a strip biaxial tension specimen are found to be in reasonably good agreement with test results.     

Characterization of nonideal networks by stress-strain measurements at large extensions

It is shown how a characterization of unfilled, amorphous rubber networks can be evaluated from uniaxial stress-strain measurement data. Beside the cross-linking density, the relative scission probability during the curing procedure is evaluated, which determines the amount of dangling free chain ends and the number of trapped entanglements. These values are found from the C₂ term of the Mooney-Rivlin equation by using the predictions of a tube model. A necessary requirement for applying stress-strain measurements at large extensions is the consideration of the finite extensibility component of the reduced stress. It is taken into account by using a numerical procedure, which derives from a series expansion of the inverse Langevin approximation. The experimental results found at natural rubber networks cross-linked with thiuram (TMTD) and peroxid (DCP) show that network defects cannot be neglected in the DCP networks. They are assumed to be connected to the worse tensil strength properties compared to the TMTD networks. © 1993 John Wiley & Sons, Inc.