Elastic wave propagation and stop-band generation in strongly damaged solids

In this work, we study the propagation of elastic waves in elongated solids with an array of equallyspaced deep transverse cracks, focusing in particular on the determination of stop-bands. We consider solids with different types of boundary conditions and different lengths, and we show that the eigenfrequencies associated with non-localized modes lie within the pass-bands of the corresponding infinite periodic system, provided that the solids are long enough. In the stop-bands, instead, eigenfrequencies relative to localized modes may be found. Furthermore, we use an asymptotic reduced model, whereby the cracked solid is approximated by a beam with elastic connections. This model allows to derive the dynamic properties of damaged solids through analytical methods. By comparing the theoretical dispersion curves yielded by the asymptotic reduced model with the numerical outcomes obtained from finite element computations, we observe that the asymptotic reduced model provides a better fit to the numerical data as the slenderness ratio increases. Finally, we illustrate how the limits of the stop-bands vary with the depth of the cracks

Elastic wave propagation and stop-band generation in strongly damaged solids

In this work, we study the propagation of elastic waves in elongated solids with an array of equallyspaced deep transverse cracks, focusing in particular on the determination of stop-bands. We consider solids with different types of boundary conditions and different lengths, and we show that the eigenfrequencies associated with non-localized modes lie within the pass-bands of the corresponding infinite periodic system, provided that the solids are long enough. In the stop-bands, instead, eigenfrequencies relative to localized modes may be found. Furthermore, we use an asymptotic reduced model, whereby the cracked solid is approximated by a beam with elastic connections. This model allows to derive the dynamic properties of damaged solids through analytical methods. By comparing the theoretical dispersion curves yielded by the asymptotic reduced model with the numerical outcomes obtained from finite element computations, we observe that the asymptotic reduced model provides a better fit to the numerical data as the slenderness ratio increases. Finally, we illustrate how the limits of the stop-bands vary with the depth of the cracks

Dislocation dynamics: from microscopic models to macroscopic crystal plasticity

In this paper we study the connection between four models describing dislocation dynamics: a generalized 2D Frenkel-Kontorova model at the atomic level, the Peierls-Nabarro model, the discrete dislocation dynamics and a macroscopic model with dislocation densities. We show how each model can be deduced from the previous one at a smaller scale

Measurement of the muon flux from 400 GeV/c protons interacting in a thick molybdenum/tungsten target

The SHiP experiment is proposed to search for very weakly interacting particles beyond the Standard Model which are produced in a 400 GeV/c proton beam dump at the CERN SPS. About 1011 muons per spill will be produced in the dump. To design the experiment such that the muon-induced background is minimized, a precise knowledge of the muon spectrum is required. To validate the muon flux generated by our Pythia and GEANT4 based Monte Carlo simulation (FairShip), we have measured the muon flux emanating from a SHiP-like target at the SPS. This target, consisting of 13 interaction lengths of slabs of molybdenum and tungsten, followed by a 2.4 m iron hadron absorber was placed in the H4 400 GeV/c proton beam line. To identify muons and to measure the momentum spectrum, a spectrometer instrumented with drift tubes and a muon tagger were used. During a 3-week period a dataset for analysis corresponding to (3.27±0.07) × 1011 protons on target was recorded. This amounts to approximatively 1% of a SHiP spill

Track reconstruction and matching between emulsion and silicon pixel detectors for the SHiP-charm experiment

In July 2018 an optimization run for the proposed charm cross section measurement for SHiP was performed at the CERN SPS. A heavy, moving target instrumented with nuclear emulsion films followed by a silicon pixel tracker was installed in front of the Goliath magnet at the H4 proton beam-line. Behind the magnet, scintillating-fibre, drift-tube and RPC detectors were placed. The purpose of this run was to validate the measurement's feasibility, to develop the required analysis tools and fine-tune the detector layout. In this paper, we present the track reconstruction in the pixel tracker and the track matching with the moving emulsion detector. The pixel detector performed as expected and it is shown that, after proper alignment, a vertex matching rate of 87% is achieved

Dynamic response of a growing inclusion in a discrete system

AbstractThe propagation of a semi-infinite line defect, contained in an infinite square-cell lattice is considered. The defect is composed of particles lighter than those in the ambient lattice and it is assumed this defect propagates with constant speed. Dispersion properties of the lattice are related to waves generated by the propagating defect. In order to determine these properties, the Wiener–Hopf technique is applied. Additional features, related to localisation along the defect are also identified. Analysis of the dispersion relations for this lattice, from the kernel function inside the Wiener–Hopf equation, is carried out. The solution of the Wiener–Hopf equation is presented for the case when an external load is applied corresponding to an energy flux at infinity

Analytical model of thermal striping for a micro-cracked solid

AbstractUsing the formal asymptotic approximation of the Mode I stress intensity factor for an edge crack in a thermoelastic half plane containing several small voids obtained in [Nieves, M.J., Movchan, A.B., and Jones, I.S., 2011. Asymptotic study of a thermoelastic problem in a semi-infinite body containing a surface-breaking crack and small perforations. QJMAM 64 (3), 349–369] we investigate the effect of micro-cracks on this stress intensity factor. In numerical examples, we show how the behaviour of the stress intensity factor as a function of crack depth is affected by micro-cracks of different orientations occurring in the half space