scholarly journals Plane-strain waves in nonlinear elastic solids with softening

Wave Motion ◽  
2019 ◽  
Vol 89 ◽  
pp. 65-78 ◽  
Author(s):  
Harold Berjamin ◽  
Bruno Lombard ◽  
Guillaume Chiavassa ◽  
Nicolas Favrie
Keyword(s):  
Plane Strain ◽  
Elastic Solids ◽  
Strain Waves ◽  
Nonlinear Elastic

scholarly journals Dislocations and inclusions in prestressed metals

2013 ◽  
Vol 469 (2154) ◽  
pp. 20120752 ◽  
Author(s):  
Luca Argani ◽  
Davide Bigoni ◽  
Gennady Mishuris
Keyword(s):  
Shear Band ◽  
Constitutive Model ◽  
Plane Strain ◽  
Deformation Theory ◽  
Shear Band Formation ◽  
Dislocation Dipole ◽  
Elastic Solids ◽  
Band Formation ◽  
Ductile Metals ◽  
Nonlinear Elastic

The effect of prestress on dislocation (and inclusion) fields in nonlinear elastic solids is analysed by extending previous solutions by Eshelby and Willis. Using a plane-strain constitutive model (for incompressible incremental nonlinear elasticity) to describe the behaviour of ductile metals ( J 2 -deformation theory of plasticity), we show that when the level of prestress is high enough that shear band formation is approached, strongly localized strain patterns emerge, when a dislocation dipole is emitted by a source. These may explain cascade activation of dislocation clustering along slip band directions.

Synthesis and elastic and mechanical properties of Cr2GeC

2008 ◽  
Vol 23 (8) ◽  
pp. 2157-2165 ◽  
Author(s):  
Shahram Amini ◽  
Aiguo Zhou ◽  
Surojit Gupta ◽  
Andrew DeVillier ◽  
Peter Finkel ◽  
...  
Keyword(s):  
Mechanical Energy ◽  
Kink Band ◽  
Max Phase ◽  
Elastic Solids ◽  
Max Phases ◽  
Kink Bands ◽  
Young’S Moduli ◽  
Microscale Model ◽  
Energy Dissipated ◽  
Nonlinear Elastic

Herein we report on the synthesis and characterization of Cr2GeC, a member of the so-called Mn+1AXn (MAX) phase family of layered machinable carbides and nitrides. Polycrystalline samples were synthesized by hot pressing pure Cr, Ge, and C powders at 1350 °C at ∼45 MPa for 6 h. No peaks other than those associated with Cr2GeC and Cr2O3, in the form of eskolaite, were observed in the x-ray diffraction spectra. The samples were readily machinable and fully dense. The steady-state Vickers hardness was 2.5 ± 0.1 GPa. The Young’s moduli measured in compression and by ultrasound were 200 ± 10 and 245 ± 3 GPa, respectively; the shear modulus and Poisson’s ratio deduced from the ultrasound results were 80 GPa and 0.29, respectively. The ultimate compressive strength for a ∼20 μm grain size sample was 770 ± 30 MPa. Samples compressively loaded from 300 to ∼570 MPa exhibited nonlinear, fully reversible, reproducible, closed hysteretic loops that dissipated ∼20% of the mechanical energy, a characteristic of the MAX phases, in particular, and kinking nonlinear elastic solids, in general. The energy dissipated is presumably due to the formation and annihilation of incipient kink bands. The critical resolved shear stress of the basal plane dislocations—estimated from our microscale model—is ∼22 MPa. The incipient kink band and reversible dislocation densities, at the maximum stress of 568 MPa, are estimated to be 1.2 × 10−2 μm−3 and 1.0 × 1010 cm−2, respectively.

Thermal Stresses in Plane Strain of Porous Elastic Solids

Meccanica ◽  
2004 ◽  
Vol 39 (2) ◽  
pp. 125-138 ◽  
Author(s):  
D. Ieşan ◽  
L. Nappa
Keyword(s):  
Plane Strain ◽  
Thermal Stresses ◽  
Elastic Solids

Direct observation of nonlinear acoustoelastic hysteresis in kinking nonlinear elastic solids

2009 ◽  
Vol 94 (24) ◽  
pp. 241904 ◽  
Author(s):  
P. Finkel ◽  
A. G. Zhou ◽  
S. Basu ◽  
O. Yeheskel ◽  
M. W. Barsoum
Keyword(s):  
Direct Observation ◽  
Elastic Solids ◽  
Nonlinear Elastic ◽  
Kinking Nonlinear Elastic Solids

Magnetic Fields Generated by a Mechanical Singularity in a Magnetized Elastic Half Plane

1989 ◽  
Vol 56 (1) ◽  
pp. 89-95 ◽  
Author(s):  
Chau-Shioung Yeh
Keyword(s):  
Fourier Transform ◽  
Magnetic Fields ◽  
Exact Solutions ◽  
Closed Form ◽  
Plane Strain ◽  
Half Plane ◽  
Elastic Solids ◽  
Soft Ferromagnetic ◽  
Single Force ◽  
The Fourier Transform

The induced magnetic fields generated by a line mechanical singularity in a magnetized elastic half plane are investigated in this paper. One version of linear theory for soft ferromagnetic elastic solids which has been developed by Pao and Yeh (1973) is adopted to analyze the plane strain problem undertaken. By applying the Fourier transform technique, the exact solutions for the generated magnetic inductions due to various mechanical singularities such as a single force, a dipole, and single couple are obtained in a closed form. The distributions of the generated inductions on the surface are shown with figures.

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