1,721,024 research outputs found
Dynamic characterization of a solid with microcracking zones
No full textUltrasound waves are a powerful tool to evaluate material properties and to characterize microstructures like distributions of microcracks in solids. For example most ceramics contain microcracks, as a result of the way they are manufactured. Ceramics that contain localized residual stresses are known to be capable of microcracking. The residual stresses arise in ceramics as a result of phase transformations, thermal expansion anisotropy in single-phase materials and thermal expansion or elastic mismatch in multiphase materials. Regions of low toughness, such as grain boundaries, would also be expected to be attractive sites for such cracks. Microcracks can form spontaneously during the fabrication process if the grain or particle size is above a critical value. Ceramics containing microcracks after fabrication have been associated with good thermal shock resistance but such materials are expected to have low strengths, as the microcracks are likely failure origins. Therefore, the analysis of microcracking influence on the dynamic response of a solid to propagating waves is important for the material characterization.
In the present study, the time-harmonic response of an elastic solid with a microcracked region is analysed. The region is permeated by a random distribution of aligned penny-shaped cracks and the solid is uncracked outside this region. Crack faces are supposed to be traction free. The problem is formulated in terms of the mean values of displacement, strain and stress fields and a nonlocal effective constitutive relation is adopted for the cracked region, assuming a dilute concentration of cracks. Longitudinal waves propagating along the direction normal to the crack surfaces are considered. In the case of waves with half-wavelength greater than the crack diameter, explicit expressions are given for the attenuation and phase velocity of the mean wave in the cracked region, and for the amplitudes of the reflected and transmitted waves in the uncracked parts of the solid
PRIN - Programma di Ricerca Scientifica di Rilevante Interesse Nazionale (Protocollo 2005085158)
No full textDiagnostica e salvaguardia di opere in calcestruzzo armato per le infrastrutture con degrado ambiental
Dynamic response of a solid with a cracked slab region
No full textThe time-harmonic response of an elastic solid with a cracked slab region is analysed. The slab region is permeated by a random distribution of aligned penny-shaped cracks and the solid is uncracked outside this region. Longitudinal waves propagating along the direction normal to the crack surfaces are considered. In the case of waves with half-wavelength greater than the crack diameter, explicit expressions are given for the attenuation and phase velocity of the mean wave in the cracked region, and for the amplitudes of the reflected and transmitted waves in the uncracked parts of the solid. Numerical examples show the influence of the cracked-slab thickness and of the crack density on the overall dynamic response of the medium
Green's function for incremental nonlinear elasticity: shear bands and boundary integral formulation
No full textAn elastic, incompressible, infinite body is considered subject to plane and homogeneous deformation. At a certain value of the loading, when the material is still in the elliptic range, an incremental concentrated line load is considered acting at an arbitrary location in the body and extending orthogonally to the plane of deformation. This plane strain problem is solved, so that a Green’s function for incremental, nonlinear elastic deformation is obtained. This is used in two different ways: to quantify the decay rate of self-equilibrated loads in a homogeneously stretched elastic solid; and to give a boundary element formulation for incremental deformations superimposed upon a given homogeneous strain. The former result provides a perturbative approach to shear bands, which are shown to develop in the elliptic range, induced by self-equilibrated perturbations. The latter result lays the foundations for a rigorous approach to boundary element techniques in finite strain elasticity
A perturbative approach to material instabilities in anisotropic solids
No full textThe dynamic behaviour of pre-stressed, elastic orthotropic and incompressible materials is considered in the time-harmonic regime. Depending on the level of pre-stress and anisotropy, wave patterns are shown to emerge, with focussing of signals in the direction of shear bands. Varying the direction of the dynamic perturbation excites different wave patterns, which tend to degenerate to families of plane waves parallel to the shear bands, when the elliptic boundary is approached
Perturbations and boundary integral equations for pre-stressed elastic materials
No full textThe behaviour of pre-stressed, elastic, orthotropic and incompressible materials is analysed in both the static and dynamic regimes. Perturbations caused by dipoles, either static or pulsating, are considered to investigate material instabilities arising near the boundary of ellipticity loss. The perturbation approach is capable of revealing aspects which may remain undetected using methods for material instabilities based on weak discontinuity surfaces. In the static case, for instance, the approach reveals shear band formation for a Mooney-Rivlin material, a circumstance not detected by the conventional approach. In the dynamic case, the perturbative approach provides a basis for the analysis of propagation of disturbances near the boundary of loss of ellipticity. Depending on the level of pre-stress and anisotropy, wave patterns are shown to emerge, with focussing of signals in the direction of shear bands. Varying the direction of the dynamic perturbation excites different wave patterns, which tend to degenerate to families of plane waves parallel to the shear bands, when the elliptic boundary is approached.
At the base of the perturbation approach are infinite-body Green’s functions for incremental displacements and in-plane hydrostatic stress obtained by the authors for small isochoric and plane deformation superimposed upon a nonlinear elastic and homogeneous strain. The same functions are employed to develop a boundary element technique for the solution of boundary value incremental problems. In this technique, “static” and “dynamic” contributions are uncoupled in the Green function for incremental tractions: the dynamic contributions are regular whereas the static terms are strongly singular and are solved in closed-form expressions, particularly useful for numerical calculations. The formulation is used to examine the influence of pre-stress on the vibrational response of elastic structures
Time-harmonic Green's function and boundary integral formulation for incremental nonlinear elasticity: dynamics of wave patterns and shear bands
No full textSuperimposed dynamic, time-harmonic incremental deformations are considered in an elastic, orthotropic and incompressible, infinite body, subject to plane, homogeneous - but otherwise arbitrary - deformation. The dynamic, infinite body Green's function is found and, in addition, new boundary integral equations are obtained for incremental in-plane hydrostatic stress and displacements. These findings open the way to integral methods in incremental, dynamic elasticity. Moreover, the Green's function is employed as a dynamic perturbation to analyze interaction between wave propagation and shear band formation. Depending on anisotropy and pre-stress level, peculiar wave patterns emerge with focussing and shadowing effects of signals, which may remain undetected by the usual criteria based on analysis of weak discontinuity surfaces
On decay effects in nonlinear elasticity
No full textAn elastic, incompressible, infinite body is considered subject to biaxial, finite and homogeneous deformation. At a certain value of the loading, when the material is still in the elliptic range, a small concentrated line load is considered acting in a point of the body and extending orthogonally to the plane of deformation. This plane strain problem is solved and, using superposition of incremental solutions, two equal and opposite line loads are considered in a region of a continuum. The solution of this problem allows us to quantify the decay rate of self-equilibrated loads in finite elasticity. In particular, it is shown that the decay rate depends crucially, say, the distance of the current state from the boundary of the elliptic regime. When this boundary is approached, the solution blows up and, at the elliptic boundary, decay does not occur
Wave propagation in elastic media with cracks. Part I: transient nonlinear response of a single crack
No full textThe transient dynamic response of a single crack to an incident wave in an infinite elastic medium is studied. Nonlinearity in the response due to contact between crack faces during the motion is taken into account. A regularization of the hypersingular stress integral equation is presented where the hypersingular integrals are isolated and transformed into regular line integrals along the crack edge. This is made possible by giving a suitable form to the infinite-body elastodynamic Green tensor. In the case of a penny-shaped crack excited by a normally incident longitudinal wave, explicit formulae are given for a one-dimensional formulation requiring a discretization only along the crack radius. Numerical examples showing the crack response to low-frequency and high-frequency incident waves are presented
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