On stress-state dependent plasticity modeling: Significance of the hydrostatic stress, the third invariant of stress deviator and the non-associated flow rule

It has been shown that the plastic response of many materials, including some metallic alloys, depends on the stress state. In this paper, we describe a plasticity model for isotropic materials, which is a function of the hydrostatic stress as well as the second and third invariants of the stress deviator, and present its finite element implementation, including integration of the constitutive equations using the backward Euler method and formulation of the consistent tangent moduli. Special attention is paid for the adoption of the non-associated flow rule. As an application, this model is calibrated and verified for a 5083 aluminum alloy. Furthermore, the Gurson-Tvergaard-Needleman porous plasticity model, which is widely used to simulate the void growth process of ductile fracture, is extended to include the effects of hydrostatic stress and the third invariant of stress deviator on the matrix material.     

Analysis of single-fiber pull-out from composites by using stress birefringence

During a fiber pull-out test, it is desirable to analyze the stress profiles along the embedded fiber directly within the same time scale as the normal pull-out tests. In the present study, the axial tensile stress profiles of the fiber in a model composite are measured during the single-fiber pull-out tests by using stress birefringence of the fiber. It is concluded from the analysis of the measured stress profiles that an effective radius of matrix, i.e. a radius defining the region of the matrix where the major deformation takes place, is not constant but is an increasing function of the interfacial shear stress. By incorporating the variable values of the effective radius of matrix into the shear-lag model, the axial tensile and the interfacial shear stress profiles are calculated. To accurately estimate the interfacial shear strength, the stress distribution along the embedded fiber and the variability of the effective radius of matrix should be taken into account instead of calculating the interfacial shear strength simply from the pull-out stress and the embedded length.     

Interfacial crack problem in layered soft ferromagnetic materials in uniform magnetic field

The magnetoelastic plane strain problem of an interfacial Griffith crack between two dissimilar soft ferromagnetic elastic materials subjected to a uniform magnetostatic field is considered within the framework of linear magnetoelasticity. By making use of the Fourier integral transform technique, the mixed boundary problem is then reduced to a pair of singular integral equations of the second kind. Solutions of the singular integral equations are obtained numerically by means of a Jacobi polynomial expansion method. Effects of the magnetic field, the combinations of the magnetic properties of materials and the geometric parameters on the magnetoelastic stress intensity factors in the vicinity of crack tip are shown graphically.     

Impact response of an interface crack in a hybrid piezoelectric laminate

Summary  In a hybrid laminate containing an interfacial crack between piezoelectric and orthotropic layers, the dynamic field intensity factors and energy release rates are obtained for electro-mechanical impact loading. The analysis is performed within the framework of linear piezoelectricity. By using integral transform techniques, the problem is reduced to the solution of a Fredholm integral equation of the second kind, which is obtained from one pair of dual integral equations. Numerical results for the dynamic stress intensity factor show the influence of the geometry and electric field. Received 29 June 2001; accepted for publication 3 December 2001     

Endolaryngeal contact pressures

In this work, we present a new method for in vivo endolaryngeal contactpressure measurement with a miniature pressure transducer. Using this methodology, contact pressures can be measured during videoendoscopy at different locations between the artyenoids and also at various locations along the membranous vocal folds. Twenty adults with organic and functional voice disorders and two vocally healthy adults participated as subjects. Endolaryngeal contact pressure measures were made during a series of phonatory tasks varying pitch, loudness, and phonatory onset and offset. Measures were also made during nonphonatory tasks, including throat clearing, coughing, Valsalva maneuvres, and gagging. The most remarkable findings were: (1) interarytenoid contact pressures were considerably greater than intraglottal contact pressures; (2) interarytenoid contact pressures were greater for lower than higher pitches; (3) both interarytenoid and intraglottal contact pressures were remarkably large during hard glottal attack; and (4) overall, the largest endolaryngeal pressures were recorded between the arytenoids, during a thoracic fixation maneuver and during gag reflex.This work was supported in part by Deutsche Forschungsgemeinschaft (He 2869/1-1), by a grant from the “Verein zur Förderung hör-, sprach- und stimmgestörter Patienten an der FU Berlin e.V.” (nonprofit organization), Berlin, Germany, and by Grant No. K08 DC00139 from the National Institute on Deafness and Other Communication Disorders.     

An asymptotic approach to crack initiation in fretting fatigue of complete contacts

The stress state near the corner of a complete contact subject to fretting action is studied using an asymptotic analysis. The spatial distribution of stress, together with the generalised stress intensity factor defining the severity of the stress state are found, and the implications for experimental determination of crack initiation conditions discussed.     

Development of cross-hatch grid morphology and its effect on ordering growth of quantum dots

We investigate the development of cross-hatch grid surface morphology in growing mismatched layers and its effect on ordering growth of quantum dots (QDs). For a 60° dislocation (MD), the effective part in strain relaxation is the part with the Burgers vector parallel to the film/substrate interface within its component; so the surface stress over a MD is asymmetric. When the strained layer is relatively thin, the surface morphology is cross-hatch grid with asymmetric ridges and valleys. When the strained layer is relatively thick, the ridges become nearly symmetrical, and the dislocations and the ridges inclined-aligned. In the following growth of InAs, QDs prefer to nucleate on top of the ridges. By selecting ultra-thin In_0.15Ga_0.85As layer (50 nm) and controlling the QDs layer at just formed QDs, we obtained ordered InAs QDs.     

Superelements for the finite element solution of two-dimensional elliptic problems with boundary singularities

A novel singular superelement (SSE) formulation has been developed to overcome the loss of accuracy encountered when applying the standard finite element schemes to two-dimensional elliptic problems possessing a singularity on the boundary arising from an abrupt change of boundary conditions or a reentrant corner. The SSE consists of an inner region over which the known analytic form of the solution in the vicinity of the singular point is utilized, and a transition region in which blending functions are used to provide a smooth transition to the usual linear or quadratic isoparametric elements used over the remainder of the domain. Solution of the finite element equations yield directly the coefficients of the asymptotic series, known as the flux/stress intensity factors in linear heat transfer or elasticity theories, respectively. Numerical examples using the SSE for the Laplace equation and for computing the stress intensity factors in the linear theory of elasticity are given, demonstrating that accurate results can be attained for a moderate computational effort.     

Reflectance difference spectroscopy during CdTe/ZnTe interface formation

We have investigated the first stages of epitaxial growth of CdTe on ZnTe and ZnTe on CdTe with reflectance difference (RD) spectroscopy. Spectroscopic RD data show strong optical anisotropy responses at the critical points of the bulk dielectric function at the E₀, E₁ and E₁+Δ₁ interband transitions of ZnTe and CdTe, respectively, which indicate that anisotropic in-plane strain occurs during epitaxial growth. Kinetic RD data taken at the E₁ transition of the respective material exhibit with an accuracy of 1 ML the onset of the formation of misfit dislocations for these material systems.     

Computing bounds to mixed-mode stress intensity factors in elasticity

A bounding procedure combined with an effective error bound method for linear functionals of the displacements and a simple two points displacement extrapolation method is presented to compute the lower and upper bounds to the stress intensity factors in elastic fracture problems. First, the displacements of two nodes (or node pairs) on the crack edges are used to construct the linear extrapolation to obtain the stress intensity factors at the crack tip, so that stress intensity factors are explicitly expressed as linear functionals of the displacements. Then, a posteriori bounding method is utilized to compute the bounds to the stress intensity factors. Finally, the bounding procedure is verified by a mixed-mode homogenous elastic fracture problem and a bimaterial interface crack problem.