David A. Dillard

A theoretical and numerical study of a thin clamped circular film under an external load in the presence of a tensile residual stress

Tensile residual stress in a plate or membrane clamped at the perimeter can be measured by either applying a uniform hydrostatic pressure or a central load via a cylindrical punch (with several different loading configurations). Analytical constitutive relations are derived here based on an average membrane stress approximation and are compared to finite element analysis results. The thickness and flexural rigidity of the film are not confined to a small range but will span a wide spectrum. The elastic responses of the blistering films are shown to be linear when the film is thick, relatively rigid, or subjected to a large residual stress, and cubic when the film is thin, flexible, or under a small residual stress. The linear-to-cubic transition is formulated.

Two- and three-dimensional geometrical nonlinear finite elements for analysis of adhesive joints

Abstract Special two- and three-dimensional adhesive elements have been developed for stress and displacement analyses in adhesively bonded joints. Both the 2-D and 3-D elements are used to model the whole adhesive system: adherends and adhesive layer. In the 2-D elements, adherends are represented by Bernoulli beam elements with axial deformation and the adhesive layer by plane stress or plane strain elements. The nodes of the plane stress–strain elements that lie in the adherend–adhesive interface are rigidly linked with the nodes of the beam elements, resulting in the offset nodes which coincide with the midplanes of the adherends. The 3-D elements consist of shell elements that represent the adherends and solid brick elements to model the adhesive. This technique results in smaller models with faster convergence than conventional 3-D finite element models. The resulting mesh can represent arbitrary beam- or plate-like geometries, which are a large part of adhesive joint designs. This model can include debonds as well as cracks within the adhesive, therefore it can be used for durability analysis of adhesive joints. Since large displacements are often observed in adhesively bonded joints, geometric nonlinearity is modeled. 2-D and 3-D stress analyses of single lap joints are presented. Important 3-D effects can be appreciated. A stress analysis of a crack patch geometry is presented.

Viscoelastic Stress Analysis of Constrained Proton Exchange Membranes Under Humidity Cycling

Many premature failures in proton exchange membrane (PEM)fuel cells are attributed to crossover of the reactant gas from microcracks in the membranes. The formation of these microcracks is believed to result from chemical and/or mechanical degradation of the constrained membrane during fuel cell operation. By characterizing the through-membrane leakage, we report failures resulting from crack formation in several PEMs mounted in 50 cm 2 fuel cell fixtures and mechanically stressed as the environment was cycled between wet and dry conditions in the absence of chemical potential. The humidity cycling tests also show that the failure from crossover leaks is delayed if membranes are subjected to smaller humidity swings. To understand the mechanical response of PEMs constrained by bipolar plates and subjected to changing humidity levels, we use Nafion® NR-111 as a model membrane and conduct numerical stress analyses to simulate the humidity cycling test. We also report the measurement of material properties required for the stress analysis-water content, coefficient of hygral expansion, and creep compliance. From the creep test results, we have found that the principle of time-temperature-humidity superposition can be applied to Nafion® NR-111 to construct a creep compliance master curve by shifting individual compliance curves with respect to temperature and water content. The stress prediction obtained using the commercial finite element program ABAQVS® agrees well with the stress measurement of Nafion® NR-111 from both tensile and relaxation tests for strains up to 8%. The stress analysis used to model the humidity cycling test shows that the membrane can develop significant residual tensile stress after humidity cycling. The result shows that the larger the humidity swing and/or the faster the hydration/dehydration rate, the higher the residual tensile stress. This result is confirmed experimentally as PEM failure is significantly delayed by decreasing the magnitude of the relative humidity cycle. Based on the current study, we also discuss potential improvements for material characterization, material state diagnostics, and a stress model for PEMs.

Fracture Mechanics Tests in Adhesively Bonded Joints: A Literature Review

Fracture mechanics characterization tests for adhesive joints are analyzed and reviewed in order to understand their advantages and disadvantages. Data reduction techniques for analytical methods are summarized to understand the improvements implemented in each test. Numerical approaches are also used complementing tests information. Both linear and non-linear methods to obtain the fracture energy release rate are presented. Pure mode I and mode II tests are described. Simple mixed-mode tests, varying only the specimen geometry, with limited mode-mixity are also presented. Performing a wider mode-mixity range requires sophisticated apparatus that are studied in detail. There is no general agreement about the test suitability for mixed-mode fracture assessment of adhesive joints. A universal test that can easily be performed and give accurate results is essential to optimize the expensive testing at the design stage.

Structure–property relationships of void-free phenolic–epoxy matrix materials

Abstract The structure–property relationships of phenolic–epoxy networks have been investigated by several methods. Network densities have been explored by measuring the moduli in the rubbery regions and these experimental values were compared with those predicted from stoichiometry. The T g s decreased, and toughness increased, as the phenolic Novolac content in the network was increased. Both results could be correlated to the decrease in network densities along this series. Analysis of the cooperativity of the networks suggests a crossover in properties from two competing factors, network density and intermolecular forces (hydrogen bonding). Measured fracture toughness values exceed those of typical untoughened epoxy networks and far exceed existing commercial phenolic networks. In addition, an increase in Novolac content improves the flame retardance rather dramatically. Thus, by controlling the Novolac content to reach an appropriate phenol to epoxy ratio, a void-free system with both favorable mechanical properties and flame retardance can be achieved.

The effect of the T-stress on crack path selection in adhesively bonded joints

This paper investigates the effect of the T-stress on crack path selection in adhesively bonded joints. Fleck et al. (Int. J. Solids Structures 27 (1991) 1683) concluded that, similar to the situation in homogeneous solid media, the directional stability of cracks in adhesive bonds is also significantly influenced by the magnitude of the T-stress. Cracks tend to be directionally stable when the T-stress is negative (compressive) and directionally unstable when the T-stress is positive (tensile). This T-stress dependence of crack path selection in adhesively bonded joints is demonstrated experimentally in this study using double cantilever beam (DCB) specimens with various levels of the T-stress. The technique reported to vary the T-stress involves a mechanical stretching procedure of the specimens and is able to continuously alter the T-stress level over a fairly wide range. Using the finite element analysis (FEA) method, the T-stress for DCB specimens is calculated and comparison is made with the analytical solution obtained by Fleck et al. (Int. J. Solids Structures 27 (1991) 1683) for the bi-material sandwich geometry with semi-infinite adherends. The FEA results show that the T-stress increases as the thickness of the adherends decreases, indicating a mild effect of adherend thickness on the directional stability of cracks. This prediction is verified in this paper using DCB specimens with different thickness adherends.

The cracked lap shear specimen revisited—a closed form solution

This paper revisits the cracked lap shear specimen and reports a closed form solution to determine three fracture parameters, the energy release rate, the fracture mode mixity, and the fracture efficiency parameter. The solution is based on a beam-column approach pioneered by Goland and Reissner. Because of the geometrically nonlinear nature of this specimen, it is found that the fracture parameters are functions of five independent nondimensional parameters. The closed form solution reported in this paper provides a simple and useful tool to design the cracked lap shear specimen and to understand the behavior of this test geometry. The results in this paper suggest that to design a specimen with an energy release rate less dependent on the crack length, the adherend thickness should be small compared to the specimen length, and the thicker or stiffer adherend should be used as the strap. For a specimen of unequal adherend thickness, using the thicker adherend as the strap would significantly reduce the likelihood of yielding in the adherend. Compared with the finite element analyses found in the literature, the closed form solution shows good agreement in energy release rates, but less satisfactory agreement in fracture mode mixities. Finally, the closed form solution is used to give a reasonable explanation of anomalous debond behavior in a series of fatigue experiment using the cracked lap shear specimen.

Environmental aging effects on the durability of electrically conductive adhesive joints

Abstract The mechanical behavior of electrically conductive adhesive (ECA) joints exposed to elevated temperature and relative humidity conditions has been investigated, and failure mechanisms of conductive adhesive joints have been determined. Three silver-filled, epoxy-based model adhesive systems have been studied in conjunction with printed circuit board (PCB) substrates with metallizations of Au/Ni/Cu and Cu. Double cantilever beam (DCB) tests have been adopted to investigate the effects of environmental aging on ECA joints. This study reveals that conductive adhesives as well as substrate metallizations both play important roles in the durability of conductive adhesive joints. The rate of water attack on the interface of conductive adhesive joints with Cu-plated PCB substrates is faster than for those with Au/Ni/Cu metallization. A possible explanation of this phenomenon is based on considerations of surface free energy and interfacial free energy. Following drying of the aged conductive adhesive joints, the fracture energy recovered to some extent. This recovery in the fracture energy could be attributed to the reversible effect of plasticization of the bulk adhesives, as well as the regaining of bond strength between the adhesive and the substrate during drying at 150°C. XPS analysis of DCB failure surfaces suggested that diffusion of Cu to the Au surface might have occurred on the Au/Ni/Cu-plated PCB substrates during aging. Copper oxide was detected on the substrate surface upon exposure of the conductive adhesive joints to the hot/wet environment.

Residual Stress Development in Adhesive Joints Subjected to Thermal Cycling

Abstract The effect of thermal cycling on the state of residual stress in thermoviscoelastic polymeric materials bonded to stiff elastic substrates was investigated using numerical techniques, including finite element methods. The work explored the relationship between a cyclic temperature environment, temperature-dependent viscoelastic behavior of polymers, and thermal stresses induced in a bimaterial system. Due to the complexity of developing a closed-form solution for a system with time- and temperature-dependent material properties, and time-varying temperature and coupled boundary conditions, numerical techniques were used to acquire approximate solutions. The results indicate that residual stresses in an elastic-viscoelastic bimaterial system incrementally shift over time when subjected to thermal cycling. Potentially damaging tensile axial and peel stresses develop over time as a result of viscoelastic response to thermal stresses induced in the polymeric layer. The applied strain energy release r...

Environmental aging of high-performance polymeric composites: Effects on durability

Abstract The effect of sub-Tg environmental aging on the durability of two high-performance polymeric composites has been investigated. The material systems under study were a thermoplastic-toughened cyanate ester resin (Fiberite 954-2) and a semicrystalline thermoplastic resin (Fiberite ITX), and their respective carbonfiber composites, IM8/954-2 and IM8/ITX. Specimens were aged for periods of up to 9 months in environmental chambers at 150 °C and in one of three different gas environments: nitrogen, a reduced air pressure of 13·8 kPa (2psi air) or atmospheric ambient air (14·7psi air). The glass transition temperatures, Tg, of the two resin systems were monitored as a function of aging time and environment. The changes in Tg showed effects of both physical aging and chemical degradation; the latter appeared to be sensitive to the oxygen concentration in the aging environment. Flexure tests were performed on 8-ply unidirectional (90 °) IM8/954-2 and IM8/ITX composites, aged up to 6 months in the three gas environments at 150 °C. The samples showed a 30–40% loss in the bending strength after aging. These strength reductions were sensitive to the oxygen concentrations in the aging environment. Stress/strain tests were also conducted on the same composites to measure the ultimate properties of the materials before and after aging in the three different environments at 150 °C. The results showed a decrease of 40–60% in the ultimate strain to failure with aging. The modulus of both composite systems on the other hand increased by up to 20 % after aging for 6 months, possibly as a consequence of the physical aging phenomena. In both systems greatest reduction in ‘useful’ mechanical properties occurred in the ambient air environment, while the least reduction occurred in nitrogen. Weight loss in the plain resin and composite samples was monitored as a function of aging time and environment. Typically, all of the samples showed 1–2 % weight loss after 9 months of aging at 150 °C, and the composite samples lost much more weight (on a polymer basis) than unreinforced resin specimens over the same aging period. The weight loss data as well as all the above-mentioned observations were indicative of an oxidation process in the composites.