Torsional impact of transversely isotropic solid with functionally graded shear moduli and a penny-shaped crack

The torsional impact response of a penny-shaped crack in an unbounded transversely isotropic solid is considered. The shear moduli are assumed to be functionally graded such that the mathematics is tractable. Laplace transform and Hankel transform are used to reduce the problem to solving a Fredholm integral equation. The crack tip stress fields are obtained. Investigated are the influence of material nonhomogeneity and orthotropy on the dynamic stress intensity factor. The peak value of the dynamic stress intensity factor can be suppressed by increasing the shear moduli's gradient and/or increasing the shear modulus in a direction perpendicular to the crack surface.

The instability analysis of saturated soil under shear load

A theoretical description of shear instability is presented in a system of equations. It is shown that two types of instability may exist. One of them is dominated by pore pressure softening while the other by strain softening. A criterion combining pore pressure softening, strain hardening, and volume strain coefficient is obtained and practical implications are discussed.

A New Version of Smoothed Point Method to Simulate Linear Elastic Wave Propagation

By using the kernel function of the smoothed particle hydrodynamics (SPH) and modification of statistical volumes of the boundary points and their kernel functions, a new version of smoothed point method is established for simulating elastic waves in solid. With the simplicity of SPH kept, the method is easy to handle stress boundary conditions, especially for the transmitting boundary condition. A result improving by de-convolution is also proposed to achieve high accuracy under a relatively large smooth length. A numerical example is given and compared favorably with the analytical solution.

Dynamic stress intensity factor of a functionally graded material under antiplane shear loading

The dynamic response of a finite crack in an unbounded Functionally Graded Material (FGM) subjected to an antiplane shear loading is studied in this paper. The variation of the shear modulus of the functionally graded material is modeled by a quadratic increase along the direction perpendicular to the crack surface. The dynamic stress intensity factor is extracted from the asymptotic expansion of the stresses around the crack tip in the Laplace transform plane and obtained in the time domain by a numerical Laplace inversion technique. The influence of graded material property on the dynamic intensity factor is investigated. It is observed that the magnitude of dynamic stress intensity factor for a finite crack in such a functionally graded material is less than in the homogeneous material with a property identical to that of the FGM crack plane.

The Size-Dependent Elastic Properties of Nanofilms with Surface Effects

Size-dependent elastic constants are investigated theoretically with reference to a nanoscale single-crystal thin film. A three-dimensional _3D_ model is presented with the relaxation on the surface of the nanofilm taken into consideration. The constitutive relation of the 3D model is derived by using the energy approach, and analytical expressions for the four nonzero elastic constants of the nanofilm are obtained. The size effects of the four elastic constants are then discussed, and the dependence of these elastic constants on the surface relaxation and the ambiguity in the definition of the thickness of the nanofilm are also analyzed. In addition, the elastic moduli of the nanofilm in two kinds of plane problem are obtained and discussed in the case of a special boundary condition.

Behavior of Multiple Shear Bands in Zr-Based Bulk Metallic Glass

The deformation behavior of Zr41.2Ti13.8Cu12.5Ni10Be22.5 bulk metallic glass was studied by in situ scanning electron microscopy (SEM) quasi-static uniaxial compression tests at room temperature. Multiple shear bands were observed with a large plasticity. Microscopic examination demonstrates that slipping, branching and intersecting of multiple shear bands are the main mechanisms for enhancing the plasticity of this metallic glass. Additionally, nano/micro-scale voids and cracks at the intersecting sites of shear bands and preferential etching of shear bands were observed as well. These observations demonstrated that the formation of shear bands in bulk metallic glasses is resulted mainly from local free volume coalescence.

Size effects in the constrained deformation of metallic foams

The constrained deformation of an aluminium alloy foam sandwiched between steel substrates has been investigated. The sandwich plates are subjected to through-thickness shear and normal loading, and it is found that the face sheets constrain the foam against plastic deformation and result in a size effect: the yield strength increases with diminishing thickness of foam layer. The strain distribution across the foam core has been measured by a visual strain mapping technique, and a boundary layer of reduced straining was observed adjacent to the face sheets. The deformation response of the aluminium foam layer was modelled by the elastic-plastic finite element analysis of regular and irregular two dimensional honeycombs, bonded to rigid face sheets; in the simulations, the rotation of the boundary nodes of the cell-wall beam elements was set to zero to simulate full constraint from the rigid face sheets. It is found that the regular honeycomb under-estimates the size effect whereas the irregular honeycomb provides a faithful representation of both the observed size effect and the observed strain profile through the foam layer. Additionally, a compressible version of the Fleck-Hutchinson strain gradient theory was used to predict the size effect; by identifying the cell edge length as the relevant microstructural length scale the strain gradient model is able to reproduce the observed strain profiles across the layer and the thickness dependence of strength. © 2002 Elsevier Science Ltd. All rights reserved.

Shear localization and recrystallization in dynamic deformation of 8090 Al-Li alloy

The microstructural evolution in localized shear deformation was investigated in an 8090 Al-Li alloy by split Hopkinson pressure bar (strain rate of approximately 10(3) s(-1)) at ambient temperature and 77 K. The alloy was tested in the peak-, over-, under-, and natural-aged conditions, that provide a wide range of microstructural parameters and mechanical properties. Two types of localized shear bands were distinguished by optical microscopy: the deformed shear band and the white-etching shear band. They form at different stages of deformation during localization. There are critical strains for the occurrence of deformed and white-etching localized shear deformation, at the imposed strain rate. Observations by transmission electron microscopy reveal that the white-etching bands contain fine equiaxed grains; it is proposed that they are the result of recrystallization occurring during localization. The deformed-type bands are observed after testing at 77 K in all heat treatment conditions, but they are not as well defined as those developed at ambient temperature. Cracking often occurs along the localized shear at ambient temperature. The decrement in temperature is favorable for the nucleation, growth and coalescence of the microcracks along the shear bands, inducing fracture.

A constitutive model for transversely isotropic foams, and its application to the indentation of balsa wood

An elastic-plastic constitutive model for transversely isotropic compressible solids (foams) has been developed. A quadratic yield surface with four parameters and one hardening function is proposed. Associated plastic flow is assumed and the yield surface evolves in a self-similar manner calibrated by the uniaxial compressive (or tensile) response of the cellular solid in the axial direction. All material constants in the model (elastic and plastic) can be determined from a combination of a total of four uniaxial and shear tests. The model is used to predict the indentation response of balsa wood to a conical indenter. For the three cone angles considered in this study, very good agreement is found between the experimental measurements and the finite element (FE) predictions of the transversely isotropic cellular solid model. On the other hand, an isotropic foam model is shown to be inadequate to capture the indentation response. © 2005 Elsevier Ltd. All rights reserved.

On the Evolution of Simple Shear in Saturated Soils

Development of shear bands in saturated soils is a multi-stage process based on the theoretical and numerical investigations in this paper. The soil is initially in homogenous shear strain state, and the instability can be characterized by a dimensionless number D. The inhomogenous distribution of shear strains appears when D>1, and the shear band will initiate and develop gradually. Numerical solutions show that only single shear band that is finally formed in the central region of the specimen even several disturbances (distributed along the specimen) appear in the beginning.

Prediction of structural dynamic plastic shear failure by Johnson's damage number

It is proved that Johnson's damage number is the sole similarity parameter for dynamic plastic shear failure of structures loaded impulsively, therefore, dynamic plastic shear failure can be understood when damage number reaches a critical value. It is suggested that the damage number be generally used to predict the dynamic plastic shear failure of structures under various kinds of dynamic loads (impulsive loading, rectangular pressure pulse, exponential pressure pulse, etc.,). One of the advantages for using the damage number to predict such kind of failure is that it is conveniently used for dissimilar material modeling.

Revelation of a Functional Dependence of the Sum of Two Uniaxial Strengths/Hardness on Elastic Work/Total Work of Indentation

Dimensional and finite element analyses were used to analyze the relationship between the mechanical properties and instrumented indentation response of materials. Results revealed the existence of a functional dependence of (engineering yield strength sigma(E,y) + engineering tensile strength sigma(E,b))/Oliver & Pharr hardness on the ratio of reversible elastic work to total work obtained from an indentation test. The relationship links up the Oliver & Pharr hardness with the material strengths, although the Oliver & Pharr hardness may deviate from the true hardness when sinking in or piling up occurs. The functional relationship can further be used to estimate the SUM sigma(E,y) + sigma(E,b) according to the data of an instrumented indentation test. The sigma(E,y) + sigma(E,b) value better reflects the strength of a material compared to the hardness value alone. The method was shown to be effective when applied to aluminum alloys. The relationship can further be used to estimate the fatigue limits, which are usually obtained from macroscopic fatigue tests in different modes.

Onset of Adiabatic Shear Instability in Strain Gradient Dependent Metal Matrix Composites

In this paper, effect of strain gradient on adiabatic shear instability in particle reinforced metal matrix composites is investigated by making use of the strain gradient dependent constitutive equation developed by Dai et al. [9] and the linear perturbation analysis presented by Bai [10]. The results have shown that the onset of adiabatic shear instability in metal matrix composites reinforced with small particles is more prone to occur than in the composites reinforced with large particles. This means that the strain gradient provides a strong deriving force for onset of adiabatic shear instability in metal matrix composites.