Search results for "Strain theory"
showing 10 items of 22 documents
Fabric attractors in general triclinic flow systems and their application to high strain shear zones: A dynamical system approach
2007
High strain zones may deform by flow with a triclinic symmetry. This paper describes triclinic flow in a reference frame where Instantaneous Stretching Axes (ISA) are fixed. The operation of triclinic flow is described in two ways: first in terms of flow and the nature of flow eigenvectors and in the second part of the paper in terms of finite strain. In monoclinic flow, at least one of the eigenvectors of the flow coincides with one of the ISA and one or two of the eigenvectors act as attractors of foliation or lineation elements. In triclinic flow some flow eigenvectors are undefined since the two largest eigenvalues (controlling the flow) are imaginary. Imaginary eigenvalues are particul…
Investigation of thick sheet AHSS springback in combined bending under tension
2012
In this paper, we investigate the springback behavior of several advanced high-strength sheet steels (TRIP, Dual-Phase, ferrite-bainite) with thicknesses up to 4 mm. Samples were tested by means of the bending-under-tension (BUT) test. The BUT has been extensively applied, in the literature, to relatively thin (1 mm and thinner) sheet metals for automotive applications; the applicability of several guidelines from the literature was investigated in this work in the context of thick advanced high strength steel (AHSS) sheets and using a sample width of 12 mm. The monotonic decrease of springback as back force increased was confirmed for this category of sheet steels, and a general trend for …
Modeling of anisotropic grain growth in minerals
2001
The role of surface energy anisotropy during grain growth is investigated using both physical experiments on octachloropropane and numerical experiments using the Elle microstructural modelling system. In particular the effects of anisotropy on growth rates, grain shapes and lattice preferred orientations are analysed. Anisotropic growth in thin polycrystalline sheets of octachloropropane is found to systematically remove certain c-axis orientations from the sample, without obviously modifying the grain shapes. By comparison with equivalent numerical experiments, we can explain these observations with a simple boundary layer model that treats each side of each grain boundary as an independe…
Strain state analysis of InGaN/GaN - sources of error and optimized imaging conditions.
2006
Transmission electron microscopy investigation of the chemical composition of In x Ga 1-x N/GaN layers by strain state analysis can lead to substantial artefacts. We evaluated simulated images in dependence of specimen thickness, specimen orientation and objective lens defocus. We observed that the measurement is in agreement with the true strain profile for certain conditions only. An analysis of error sources revealed that artefacts are mainly caused by a combination of delocalization and the composition dependence of the phases of the beams contributing to the image formation. The delocalization effect is minimized for interference of the undiffracted beam with one of the 000 ± 2 beams. …
Calculation of the elastic–plastic strain energy density under cyclic and random loading
2001
Abstract The paper presents a method of identification and calculation of the components of strain energy density under cyclic and random loading causing elastic–plastic strain in the material. The method consists in integration of the history of the strain instantaneous power.
NON-LINEAR MECHANICAL, ELECTRICAL AND THERMAL PHENOMENA IN PIEZOELECTRIC CRYSTALS
2003
Mechanical, electrical and thermal phenomena occurring in piezoelectric crystals were examined by non-linear approximation. For this purpose, use was made of the thermodynamic function of state, which describes an anisotropic body. Considered was the Gibbs function. The calculations included strain tensor εij = f(σkl , En, T), induction vector Dm = f(σkl , En, T) and entropy S = f(σkl , En, T) as function of stress σkl , field strength En and temperature difference T. The equations obtained apply to anisotropic piezoelectric bodies provided that the “forces” σkl , En, T acting on the crystal are known. Механічні, електричні та термічні явища у п’єзоелектричних кристалах вивчаються у неліній…
Quantification and visualization of finite strain in 3D viscous numerical models of folding and overthrusting
2020
Abstract Finite strain analysis and three-dimensional (3D) numerical modeling are important methods to understand the deformation history of rocks. Here, we analyze finite strain in 3D numerical simulations of power-law viscous folding and overthrusting. Simulations with different and laterally varying detachment geometries cause a lateral transition from folding (for thicker detachments) to overthrusting. We compute the 3D finite strain tensor, the principal strain values and their orientations. We compute the Nadai strain, e S , and the Lode’s ratio, ν , representing the strain symmetry (constriction or flattening). We apply Hsu diagrams to visualize strain distribution in e S - ν space, …
Volume strain, strain type and flow path in a narrow shear zone
1998
This study explores the state of finite strain and changes in the mean kinematic vorticity number, grain size, whole-rock chemistry and mineralogy across an upper amphibolite-facies shear zone in a metadiorite, northern Malawi, east-central Africa. P–T conditions during shear-zone formation and deformation were approximately 700–750 °C and 5–7 kbar and are slightly less than P–T conditions for the regional peak of metamorphism. The major rock-forming minerals, plagioclase, hornblende, biotite, and quartz, were deformed by crystal-plastic processes accompanied by, except for hornblende, dynamic recrystallization. The modal abundance of all four major rock-forming minerals shows no systematic…
Solution-mass-transfer deformation adjacent to the Glarus Thrust, with implications for the tectonic evolution of the Alpine wedge in eastern Switzer…
2001
Abstract We have studied aspects of absolute finite strain of sandstones and the deformation history above and below the Glarus Thrust in eastern Switzerland. The dominant deformation mechanism is solution mass transfer (SMT), which resulted in the formation of a semi-penetrative cleavage. Our analysis indicates that the Verrucano and Melser sandstones, which lie above the thrust, were deformed coaxially, with pronounced contraction in a subvertical Z direction and minor extension in a subhorizontal X direction, trending at ∼200°. Most of the contraction in Z was balanced by mass-loss volume strains, averaging ∼36%. Below the Glarus Thrust, sandstones of the North Helvetic flysch have small…
A nonlocal strain gradient plasticity theory for finite deformations
2009
Abstract Strain gradient plasticity for finite deformations is addressed within the framework of nonlocal continuum thermodynamics, featured by the concepts of (nonlocality) energy residual and globally simple material. The plastic strain gradient is assumed to be physically meaningful in the domain of particle isoclinic configurations (with the director vector triad constant both in space and time), whereas the objective notion of corotational gradient makes it possible to compute the plastic strain gradient in any domain of particle intermediate configurations. A phenomenological elastic–plastic constitutive model is presented, with mixed kinematic/isotropic hardening laws in the form of …