Q. D. Yang

Mixed-mode fracture analyses of plastically-deforming adhesive joints

A mode-dependent embedded-process-zone (EPZ) model has been developed and used to simulate the mixed-mode fracture of plastically deforming adhesive joints. Mode-I and mode-II fracture parameters obtained from previous work have been combined with a mixed-mode failure criterion to provide quantitative predictions of the deformation and fracture of mixed-mode geometries. These numerical calculations have been shown to provide excellent quantitative predictions for two geometries that undergo large-scale plastic deformation: asymmetric T-peel specimens and single lap-shear joints. Details of the deformed shapes, loads, displacements and crack propagation have all been captured reasonably well by the calculations.

Numerical simulations of adhesively-bonded beams failing with extensive plastic deformation

Abstract An embedded-process-zone (EPZ) model was used to study the coupling between fracture of the interface and plastic deformation of the adherends in an adhesively-bonded joint. In this model, it was assumed that the primary role of the adhesive layer is to provide a traction-separation law for the interface. A series of experiments were performed in which thin, adhesively-bonded, symmetrical, double-cantilever beams made of an aluminum alloy were split by inserting different sizes of wedges along the interface. The parameters for the interfacial traction-separation law were determined by comparing the results of these experiments with numerical simulations using the EPZ model. It was found that once these parameters had been established for one thickness of specimen, the EPZ model could be used without further modification to predict the effect of the wedges on specimens made with different thicknesses of aluminum. These predictions showed excellent agreement with experimental observations. A subsequent series of tests involved monitoring the load, displacement and deformed shapes of a series of T-peel specimens made with the same combination of adhesives and adherends. Without changing any of the parameters determined from the wedge tests, the EPZ model gave excellent quantitative predictions for the results of these T-peel tests.

In Quest of Virtual Tests for Structural Composites

The difficult challenge of simulating diffuse and complex fracture patterns in tough structural composites is at last beginning to yield to conceptual and computational advances in fracture modeling. Contributing successes include the refinement of cohesive models of fracture and the formulation of hybrid stress-strain and traction-displacement models that combine continuum (spatially averaged) and discrete damage representations in a single calculation. Emerging hierarchical formulations add the potential of tracing the damage mechanisms down through all scales to the atomic. As the models near the fidelity required for their use as virtual experiments, opportunities arise for reducing the number of costly tests needed to certify safety and extending the design space to include material configurations that are too complex to certify by purely empirical methods.

Elastic-plastic mode-II fracture of adhesive joints

Abstract A numerical study of the elastic–plastic mode-II fracture of adhesive joints is presented in this paper. A traction–separation law was used to simulate the mode-II interfacial fracture of adhesively bonded end-notched flexure (ENF) specimens loaded in three-point bending, with extensive plastic deformation accompanying failure. The fracture parameters for the traction–separation law were determined by comparing the numerical and experimental results for one particular geometry. These parameters were then used without further modification to simulate the fracture of other ENF specimens with different geometries. It was found that the numerical predictions for the loads and deformation were in excellent agreement with the corresponding experimental results.

Free vibrations of piezoelectric cylindrical shells filled with compressible fluid

Abstract Three displacement functions are introduced to represent each mechanical displacement according to the three-dimensional theory. After expanding these functions and the electric potential with orthogonal series, the free vibration equation of piezoelectric cylindrical shells satisfying SS3 edge conditions can be obtained. The equation was solved by utilizing Bessel functions with complex arguments. The effects of compressible fluid on shells are considered and some new phenomena which are exclusive for piezoelectric cylindrical shells are reported. Results of empty infinite piezoelectric cylindrical shells are compared to those presented in relative references. Some lowest frequencies that were missed by Paul and Venkatesan [Paul, H. S. and Venkatesan, M. (1987). Vibrations of hollow circular cylinder of piezoelectric ceramics. Journal of the Acoustic Society of America82, 852–856] were discovered.

Analysis of the symmetrical 90°-peel test with extensive plastic deformation

Abstract A numerical 2-D study of the symmetrical 90°-peel test (a similar geometry to the T-peel test) in which extensive plastic deformation occurs in the adherends is presented in this paper. A traction-separation relation is used to simulate failure of the interface, and the conditions for both crack initiation and steady-state crack growth are investigated. The numerical predictions for the steady-state peel force are compared with those based on elementary beam theory. It is shown that two competing effects dominate the mechanics of the peel test to such an extent that the results of beam-bending analyses cannot be used to predict the peel force. At one extreme range of parameters, delamination is driven by shear rather than by bending, resulting in a lower peel force than would be predicted by beam-bending analyses. At the other extreme, where delamination is bending-dominated, the constraint induced by the interfacial tractions cause an increase in the peel force. The numerical results are compared with the results of experiments in which adhesively-bonded specimens are tested in the symmetrical 90°-peel configuration. Excellent agreement between the numerical and experimental results validates the numerical approach.

Slip, stick, and reverse slip characteristics during dynamic fibre pullout

Inertial effects in the mechanism of fibre pullout (or push-in) are examined, with emphasis on how the rate of propagation of stress waves along the fibre, and thence the pullout dynamics, are governed by friction and the propagation of companion waves excited in the matrix. With a simple shear lag model (assuming zero debond energy at the fibre/matrix interface), the effect of uniform frictional coupling between the fibre and the matrix is accounted for in a straightforward way. Analytical solutions are derived when the pullout load increases linearly in time. The process zone of activated material is generally divided into two or three domains along the axis of the fibre. Within these domains, slip in the sense implied by the load, slip in the opposite sense (reverse slip), and stick may be observed. The attainable combinations define three regimes of behavior, which are realized for different material parameter values. The elastodynamic problem is also solved more accurately using a plane stress finite element method, with friction represented by an interfacial cohesive zone. The predictions of the shear lag theory are broadly confirmed.

Spatially Averaged Local Strains in Textile Composites Via the Binary Model Formulation

A previously published computational model of textile composites known as the Binary Model is generalized to allow systematic study of the effects of mesh refinement. Calculations using different meshing orders show that predictions of local strains are mesh independent when the strains are averaged over gauge volumes whose dimensions are greater than or equal to approximately half the width dimensions of a single tow. Strains averaged over such gauges are favored for use in failure criteria for predicting various mechanisms of failure in a textile composite, including transverse cracking within tows, kink band failure in compression, tensile tow rupture, and shear failure. For the highest order representations (infinitely dense meshes), the generalized formulation of the Binary Model necessarily approaches conventional finite element meshing strategies for textile composites in its predictions. However, the work reported here implies that usefully accurate predictions of spatially averaged strains can be obtained even at the lowest level of mesh refinement. This preserves great simplicity in the model set-up and rapid computation for relatively large features of structural components. Calculations for some textile structures provide insight into the strength or relative absence of textile effects in local strains for different loading configurations.@DOI: 10.1115/1.1605117#

Failure in the junction region of T-stiffeners: 3D-braided vs. 2D tape laminate stiffeners

Abstract Strain distributions and failure mechanisms are compared for a three-dimensionally (3D) braided T-stiffener (preform designed and supplied by 3TEX Inc.) and a conventional two-dimensional (2D) tape laminate T-stiffener, bonded onto a tape laminate skin. The strain distributions in a pull-off test are measured by laser speckle interferometry and calculated by computational simulations. With good agreement between experiment and theory, substantial differences are found between the two classes of stiffener. The tape laminate stiffeners exhibit large strain concentrations across the noodle region and in the adjacent radii, which correlate well with observed first cracking events. The 3D-braided stiffeners show relatively uniform strain distributions throughout the flanges, the web, and the flange/web junction region. Strain concentrations are modest at the corner of the junction and absent along the interface between the flanges and the skin. Failure in the 3D-braided stiffeners does not occur within the junction region, but by a sequence of cracking events, first next to the junction region and then at the end of one flange. The pull-off load at the first failure event is substantially higher for the 3D-braided stiffener than the tape laminate stiffener, which is attributed mainly to the relative absence of strain concentrations in the former. In predicting strain distributions, account is taken of the details of the 3D architecture of the 3D-braided stiffeners as specified by the supplier (3TEX Inc.) by using the Binary Model of textile composites, whose formulation has been described previously. Comparison of the predicted and measured spatial distributions of strain constitutes a critical test of the Binary Model. It is found to perform well in this case.

A three dimensional augmented finite element for modeling arbitrary cracking in solids

This paper presents a new three dimensional (3D) augmented finite element method (A-FEM) that can account for arbitrary crack initiation and propagation in 3D solids without the need of additional DoF or phantom nodes. The method permits the derivation of explicit, fully condensed elemental equilibrium equations which are of mathematical exactness in the piece-wise linear sense. The method has been implemented with a 4-node tetrahedron element and a simple local tracking algorithm has been employed for calculating and recording the evolving planar or non-planar crack surface. It has been demonstrated through ample numerical examples that the new 3D A-FEM can provide significantly improved numerical accuracy and efficiency when dealing with crack propagation problems in 3D solids with planar or non-planar crack surfaces.