Numerical plane stress elastic–perfectly plastic crack analysis under Tresca yield condition with comparison to Dugdale plastic strip model

A number of plane stress numerical analyses of the mode I elastoplastic fracture mechanics problem have been performed in the past using the Huber–Mises yield criterion. This study employs instead the Tresca yield condition using an incremental theory of plasticity for a stationary crack. A commercial finite element program is used to solve the opening mode of fracture problem (mode I) for a square plate containing a central crack under generalized plane stress loading conditions. A biaxial uniform tensile traction is applied to the edges of a thin plate composed of a linear elastic non-work hardening material under small strain assumptions. The finite element results are compared with the analytical predictions of the Dugdale plastic strip model for a crack in an infinite plate subject to a biaxial uniform load at infinity.     

Crack propagation in an orthotropic medium with coupled elastodynamic properties

In this paper the Mode-I elastodynamic problem of a crack propagating in an orthotropic medium is studied under the condition that the matrix of elastodynamic coefficients has repeated eigenvalues. It is shown that the crack is constrained in an elastodynamic state which is defined through a compulsory condition coupling its velocity with the elastic parameters of the orthotropic medium. The dynamic stress and displacement components ahead of the crack tip as well as the energy release rate are explicitly obtained.     

Mixed-mode I/II fields around a crack with a cohesive zone ahead of the crack tip

Considering a cohesive zone ahead of the crack tip, the linear elastic crack problem under Mode I, Mode II or mixed-mode conditions is formulated in an elliptic coordinate system, so that the cohesive surfaces are conveniently represented by straight line segments. It is shown that the displacement and stress fields around the crack tip and the cohesive zone, expressed in terms of elliptic coordinates, have a simple mathematical form, which does not contain a stress singularity at the crack tip due to the existence of the cohesive zone.     

Effect of material nonhomogeneities on the HRR dominance

This work studies the asymptotic stress and displacement fields near the tip of a stationary crack in an elastic–plastic nonhomogeneous material with the emphasis on the effect of material nonhomogeneities on the dominance of the crack tip field. While the HRR singular field still prevails near the crack tip if the material properties are continuous and piecewise continuously differentiable, a simple asymptotic analysis shows that the size of the HRR dominance zone decreases with increasing magnitude of material property gradients. The HRR field dominates at points that satisfy |α⁻¹ ∂α/∂x_δ|1/r, |α⁻¹ ∂²α/(∂x_δ ∂x_γ)|1/r², |n⁻¹ ∂n/∂x_δ|1/[r|ln(r/A)|] and |n⁻¹ ∂²n/(∂x_δ ∂x_γ)|1/[r²|ln(r/A)|], in addition to other general requirements for asymptotic solutions, where α is a material property in the Ramberg–Osgood model, n is the strain hardening exponent, r is the distance from the crack tip, x_δ are Cartesian coordinates, and A is a length parameter. For linear hardening materials, the crack tip field dominates at points that satisfy |E_tan⁻¹ ∂E_tan/∂x_δ|1/r, |E_tan⁻¹ ∂²E_tan/(∂x_δ ∂x_γ)|1/r², |E⁻¹ ∂E/∂x_δ|1/r, and |E⁻¹ ∂²E/(∂x_δ ∂x_γ)|1/r², where E_tan is the tangent modulus and E is Young’s modulus.     

Influence of long-chain branches in polyethylenes on linear viscoelastic flow properties in shear

 This contribution presents a survey on the influence of long-chain branching on the linear viscoelastic properties zero shear-rate viscosity and steady-state recoverable compliance of polyethylene melts. The materials chosen are linear and slightly long-chain branched metallocene-catalyzed polyethylenes of narrow molecular mass distribution as well as linear and highly long-chain branched polyethylenes of broad molecular mass distribution. The linear viscoelastic flow properties are determined in shear creep and recovery experiments by means of a magnetic bearing torsional creep apparatus. The analysis of the molecular structure of the polyethylenes is performed by a coupled size exclusion chromatography and multi-angle laser light scattering device. Polyethylenes with a slight degree of long-chain branching exhibit a surprisingly high zero shear-rate viscosity in comparison to linear polyethylenes whereas the highly branched polyethylenes have a much lower viscosity compared to linear samples. Slightly branched polyethylenes have got a higher steady-state compliance in comparison to linear products of similar polydispersity, whereas the highly branched polyethylenes of broad molecular mass distribution exhibit a surprisingly low elasticity in comparison to linear polyethylenes of broad molecular mass distribution. In addition sparse levels of long-chain branching cause a different time dependence in comparison to linear polyethylenes. The experimental findings are interpreted by comparison with rheological results from literature on model branched polymers of different molecular topography and chemical composition. Received: 12 July 2001 Accepted: 30 October 2001     

From crack deflection to lattice vibrations—macro to atomistic examination of dynamic cleavage fracture

A set of cleavage experiments with strip-shaped single-crystal silicon specimens subjected to three-point bending is reported. The experiments enabled examination of the relationships between the dynamic energy release rate, the velocity, the orientation-dependent cleavage energy, and the cleavage plane of propagation.Dynamic crack propagation experiments show that when a [0 0 1] silicon single crystal is fractured under three-point bending at ‘parallel’ velocity (directly measured at the bottom surface of the specimen) of up to , it prefers to cleave along the vertical (1 1 0) plane, while when the specimen is fractured under the same conditions but at a velocity higher than , it cleaves along the inclined (1 1 1) plane. At intermediate velocities, the crack will deflect from the (1 1 0) plane to the (1 1 1) plane. Crack velocity was determined by the initial notch length. The local (calculated) velocity of deflection between the cleavage planes ranges from , for a crack propagating on the (1 1 0) plane in the direction, to about , for a crack on the (1 1 0) plane, but in the [0 0 1] direction.It is suggested that the cause of the deflection phenomenon is the anisotropic, velocity-dependent cleavage energy, resulted phonon radiation caused by anisotropic, velocity-dependent lattice vibrations. We have studied the effect of material properties and propose selection criteria to explain the deflection phenomenon: the crack will deflect to the plane of least-energy, for which G−Γ_i(V)=max, or to the plane with maximum crack tip velocity, V_i(Γ)=max.     

Multi-residue analysis of drugs of abuse in wastewater and surface water by solid-phase extraction and liquid chromatography-positive electrospray ionisation tandem mass spectrometry

A new-multi residue method was developed for the environmental monitoring of 65 stimulants, opiod and morphine derivatives, benzodiazepines, antidepressants, dissociative anaesthetics, drug precursors, human urine indicators and their metabolites in wastewater and surface water. The proposed analytical methodology offers rapid analysis for a large number of compounds, with low limits of quantification and utilises only one solid-phase extraction-ultra performance liquid chromatography-positive electrospray ionisation tandem mass spectrometry (SPE-LC-MS/MS) method, thus overcoming the drawbacks of previously published procedures. The method employed solid phase extraction with the usage of Oasis MCX sorbent and subsequent ultra performance liquid chromatography-positive electrospray ionisation tandem mass spectrometry. The usage of a 1.7 μm particle size column (1 mm×150 mm) resulted in very low flow rates (0.04 mLmin(-1)), and as a consequence gave good sensitivity, low mobile phase consumption and short retention times for all compounds (from 2.9 to 23.1 min). High SPE recoveries (>60%) were obtained for the majority of compounds. The mean correlation coefficients of the calibration curves were typically higher than 0.997 and showed good linearity in the range 0-1000 μgL(-1). The method limits of detection ranged from 0.1 ngL(-1) for compounds including cocaine, benzoylecgonine, norbenzoylecgonine and 2-oxo-3-hydroxy-LSD to 100 ngL(-1) for caffeine. Method quantification limits ranged from 0.5 to 154.2 ngL(-1). Intra- and inter-day repeatabilities were on average less than 10%. The method accuracy range was within -33.1 to 30.1%. The new multi-residue method was used to analyse drugs of abuse in wastewater and river water in the UK environment. Of the targeted 65 compounds, 46 analytes were detected at levels above the method quantification limit (MQL) in wastewater treatment plant (WWTP) influent, 43 in WWTP effluent and 36 compounds in river water.     

Pseudo global energy released locally by crack extension involving multiscale reliability

The energy release rate criterion, being mono scale by definition, is incompatible with the failure behavior of solids that are inherently dual, if not, multiscale. Time span of reliability is scale sensitive and can be addressed with consistency only by use of transitional functions that are designed to transform a function from one scale to another. A pseudo transitional energy release rate G^∗ is defined to address the cross-scaling properties of energy release rate. The reliability of such a function is found to fall quickly when the scale range deviates from that of micro-macro. In general, the time span of reliability based on G^* shortens considerably within the nano-micro and pico-nano scale ranges, resulting in fast turnover of system usability. Prediction accuracy tends to be scale range specific. Stress or strain based criteria are also mono scale. They may be adequate for some situations at the macroscopic scale, but can be ambiguous for multiscale problems. These situations are analyzed by application of the principle of least variance in conjunction with the R-integrals.Accelerated test data for the equivalent of 20 years’ fatigue crack growth in 2024-T3 aluminum panels were analyzed using the mutliscale reliability model. A time span plateau within the micro-macro range is from 8 to 17 years. This corresponds to the reliable portion of prediction, while the terminal 3 years are regarded as unreliable. A similar time span plateau were also found from 4 to 6 years within the nano-micro scale range. And an even smaller plateau hovering around 1.2 years were found for the pico-nano scale range. Time span of reliable prediction narrows with down sized scale range. The overlapping ends of the scale ranges are rendered unreliable as anticipated. These regions can be suppressed by the addition of meso scale ranges. Reference can be made to past discussions related to multiscaling and mesomechanics.     

Research on nonlinear constitutive relationship of permanent deformation in asphalt pavements

To predict correctly the rut depths in asphalt pavements, a new nonlinear viscoelastic-elastoplastic constitutive model of permanent deformation in asphalt pavements is presented. The model combines a generalized Maxwell model with an elastoplastic one. Then from the creep theory, the linear and nonlinear constitutive equations of the generalized Maxwell model are obtained. From the nonlinear finite element method for the rutting of the asphalt pavement, the rut depths of 4 asphalt-aggregate mixtures are obtained. And the results are compared with the ones from the finite element method by SHRP and the experiments by SWK/UN. The results in this paper are better than the ones by SHRP, and agree with the ones of the experiment by SWK/UN. This shows that the nonlinear viscoelastic-elastoplastic constitutive model, which is presented in this paper for the rutting of the asphalt pavement, is effective. The properties, such as nonlinear elasticity, plasticity, viscoelasticity and nonlinear viscoelasticity, which affect the rutting of an asphalt pavement, can be shown in the model. And the characteristics of the permanent deformation of the asphalt pavement can be presented entirely in the model.     

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.