A. Barroso

Singularity analysis of anisotropic multimaterial corners

Singular stress states induced at the tip of linear elastic multimaterial corners are characterized in terms of the order of stress singularities and angular variation of stresses and displacements. Linear elastic materials of an arbitrary nature are considered, namely anisotropic, orthotropic, transversely isotropic, isotropic, etc. Thus, in terms of Stroh formalism of anisotropic elasticity, the scope of the present work includes mathematically non-degenerate and degenerate materials. Multimaterial corners composed of materials of different nature are typically present at any metal-composite, or composite-composite adhesive joint. Several works are available in the literature dealing with a singularity analysis of multimaterial corners but involving (in the vast majority) only materials of the same nature (e.g., either isotropic or orthotropic). Although many different corner configurations have been studied in literature, with almost any kind of boundary conditions, there is an obvious lack of a general procedure for the singularity characterization of multimaterial corners without any limitation in the nature of the materials. With the procedure developed here, and implemented in a computer code, multimaterial corners, with no limitation in the nature of the materials and any homogeneous orthogonal boundary conditions, could be analyzed. As a particular case, stress singularity orders in corners involving extraordinary degenerate materials are, to the authors’ knowledge, presented for the first time. The present work is based on an original idea by Ting (1997) in which an efficient procedure for a singularity analysis of anisotropic non-degenerate multimaterial corners is introduced by means of the use of a transfer matrix.

Notched-Butt Test for the Determination of Adhesion Strength at Bimaterial Interfaces

For the experimental determination of adhesion strength between materials it is desirable to have a uniform stress distribution within the interface of the specimen. The common butt-test with a flat interface between two adhering materials produces stress singularities at the edges of the specimen but shows uniform stress distribution along the interface within the material. To avoid a premature failure at the edge due to the presence of the singular stress field, a notch can be machined at the interface within one of the materials. For isotropic materials, the notch geometry depends on the Dundurs parameters of the bimaterial system. This notch produces a certain local material angle and eliminates stress singularities at the specimen edges. Analytical and finite-element calculations provide the notch geometry appropriate for uniform stress distribution along the whole interface. The applicability of the test is proven by the determination of adhesion strength between polycarbonate and thermoplastic polyurethane.

Evaluation of the stiffnesses of the Achilles tendon and soleus from the apparent stiffness of the triceps surae

The triceps surae plays an important role in the performance of many sports. Although the apparent average mechanical properties of the triceps surae may be a satisfactory parameter for estimating the training level of an athlete, a knowledge of the mechanical properties of the individual constituents of the triceps surae (in particular the Achilles tendon and soleus) permits a more detailed and in-depth control of the effects of training from more physically based parameters. The objective of this work is therefore the estimation of the individual viscoelastic properties (stiffness and viscosity) of soleus and Achilles tendon from the apparent properties of the triceps surae obtained by free vibration techniques. Different procedures have been developed and discussed, showing a high degree of robustness in the predictions. The results obtained for a non-oriented set of subjects present a high level of variability, depending on the training conditions and anthropometric features, although the corresponding average values compare well with data previously reported in the literature, particularly those associated with the tendon stiffness.

A critical study on the experimental determination of stiffness and viscosity of the human triceps surae by free vibration methods

Muscles and tendons play an important role in human performance. Their mechanical behaviour can be described by analytical/numerical models including springs and dampers. Free vibration techniques are a widely used approach to the in vivo determination of stiffness and viscosity of muscle–tendon complexes involved in sport movements. By considering the data reported in the literature, it appears that the visco-elastic properties of the triceps surae muscle–tendon complexes are independent of the modality in which free vibration is induced as well as they do not depend on the composition of the population of subjects submitted to the experiments. This research will critically discuss this important aspect focussing in particular on two studies documented in the literature. For this purpose, two equipments will be developed to reproduce literature experiments under the assumption that the oscillating part of the body behaves as a single-degree-of-freedom system: The governing degree of freedom is associated with the vertical displacement of the lower leg or with the rotation of the foot around the ankle articulation. Unlike literature, measurements are now conducted on the same population of subjects in order to draw more general conclusions on the real equivalence of results and validity of the mechanical properties determined experimentally. Free vibration tests are accurately simulated by analytical models describing the response of each vibrating system. It is found that if the two measurement protocols are applied to the same population of individuals as it is done in this study, values of visco-elastic properties of muscle–tendon complexes extracted from experimental data are significantly different, the differences presenting a convincing consistency. This result is in contrast with the literature and confirms the need to evaluate results of free vibration techniques by taking homogeneous bases of comparison.

Failure models for composite joints: An approach based on singular stress states

In the present chapter, the failure prediction of composite joints is addressed in the framework of failure induced by the presence of singular stress states at the multi-material corners appearing at the end of the overlap region. A comprehensive description of the singular stress characterization at multi-material corners of composite materials is presented. The asymptotic stress field is defined by the stress singularities (characteristic exponents), the characteristic angular shape functions, and the generalized stress intensity factors (GSIFs). The singular stress field at these multi-material corners is used to predict failure initiation, using a fracture mechanics approach in which the GSIFs are compared with their allowable values, namely the generalized fracture toughness values. An experimental procedure based on the Brazilian disk specimen is proposed to determine the generalized fracture toughness of the corner, and a failure envelope and a failure criterion are proposed based on the singular parameters of the corner. Experimental tests on double-lap joints are in good agreement with the proposed failure envelope. Finally, and to facilitate the application of this proposal to real design processes, a parametric analysis was carried out to calculate the GSIFs in a wide range of geometrical and mechanical combinations of the single- and double-lap joint configurations. The results have been presented in a graphical form, allowing the GSIFs to be calculated by means of a simple structural analysis of the joint.

Failure initiation criterion in bonded joints with composites based on singularity parameters and practical procedure for design purposes

Composite to metal adhesively bonded joints generates critical points where geometry and material properties change abruptly. These points (multimaterial corners) are potential locations for failure initiation. There exist proposals predicting the initiation of failure at these multimaterial corners using a Fracture Mechanics approach, in which the Generalized Stress Intensity Factors (GSIFs) at the multimaterial corner control the failure initiation. The calculation of these GSIFs at anisotropic multimaterial corners involves not-straightforward calculations of the stress singularities and characteristic angular functions, numerical modeling of the joint and a careful postprocessing of the results. In this study a parametric Finite Element Analysis has been carried out allowing the generation of plots to calculate the GSIFs for unit values of the axial force, shear force and bending moment at one end of the overlap length. These results allow calculating the GSIFs at the multimaterial corners by a simple beam analysis of the joint, the use of these plots and the application of the superposition principle, for their use in the prediction of failure initiation by means of the singular parameters of the joint. Additionally, experiments have been carried out to propose an explicit failure criterion based on GSIF and Generalized Fracture Toughness values which fit very well with double-lap joint test results.

Fatigue crack initiation and damage characterization in Brazilian test specimens for adhesive joints

The present study is focused on the fatigue failure initiation at bimaterial corners by means of a configuration based on the Brazilian disc specimens. These specimens were previously used for the generalized fracture toughness determination and prediction of failure in adhesive joints, carried out under static compressive loading. Under static loading, local yielding effects might affect the asymptotic two-dimensional linear elastic stress representation under consideration. Fatigue loading avoids this fact due to the lower load levels used. The present tests were performed using load control; video microscopy and still cameras were used for monitoring initiation and crack growth. The fatigue tests were halted periodically and images of the corner were taken where fatigue damage was anticipated. Damage initiation and subsequent crack growth were observed in some specimens, especially in those which presented brittle failure under static and fatigue tests. These analyses allowed the characterization of damage initiation for a typical bimaterial corner that can be found in composite to aluminium adhesive lap joints.