scholarly journals Review of “Analytical solution for residual stress and strain preserved in anisotropic inclusion entrapped in isotropic host” by Zhong et al.

2020 ◽  
Author(s):  
Anonymous
Keyword(s):  
Residual Stress ◽  
Analytical Solution ◽  
Stress And Strain ◽  
Anisotropic Inclusion

scholarly journals Analytical solution for residual stress and strain preserved in anisotropic inclusion entrapped in isotropic host

2020 ◽  
Author(s):  
Xin Zhong ◽  
Marcin Dabrowski ◽  
Bjørn Jamtveit
Keyword(s):  
Residual Stress ◽  
Aspect Ratio ◽  
Analytical Solution ◽  
Strain State ◽  
Spherical Inclusion ◽  
Raman Shift ◽  
Stress And Strain ◽  
Anisotropic Inclusion ◽  
Inclusion Shape ◽  
Diamond Inclusions

Abstract. Raman elastic thermobarometry has recently been applied in many petrological studies to recover the pressure-temperature (P-T) conditions of mineral inclusion entrapment. Existing modelling methods in petrology either adopt an assumption of a spherical, isotropic inclusion embedded in an isotropic, infinite host, or use numerical techniques such as finite element method to simulate the residual stress and strain state preserved in the non-spherical anisotropic inclusion. Here, we use the Eshelby solution to develop an analytical framework for calculating the residual stress and strain state of an elastically anisotropic, ellipsoidal inclusion in an infinite, isotropic host. The analytical solution is applicable to any class of inclusion symmetry and an arbitrary inclusion aspect ratio. Explicit expressions are derived for some symmetry classes including e.g. tetragonal, hexagonal and trigonal. The effect of changing the aspect ratio on residual stress is investigated including quartz, zircon, rutile, apatite and diamond inclusions in garnet host. Quartz is demonstrated to be the least affected, while rutile is the most affected. For prolate quartz inclusion (c-axis longer than a-axis), the effect of varying the aspect ratio on Raman shift is demonstrated to be insignificant. When c/a = 5, only ca. 0.3 cm−1 wavenumber variation is induced as compared to the spherical inclusion shape. For oblate quartz inclusions, the effect is more significant, when c/a = 0.5 ca. 0.8 cm−1 wavenumber variation for the 464 cm−1 band is induced compared to the reference spherical inclusion case. We also show that it is possible to fit an effective ellipsoid to obtain a proxy for the averaged residual stress/strain within faceted inclusion. The difference between the volumetrically averaged stress of a faceted inclusion and the analytically calculated stress from the best-fitted effective ellipsoid is calculated to obtain the root mean square deviation (RMSD) for quartz, zircon, rutile, apatite and diamond inclusions in garnet host. Based on the results of 500 randomly generated (a wide range of aspect ratio and random crystallographic orientation) faceted inclusion, we show that the volumetrically averaged stress serves as an excellent stress measure and the associated RMSD is less than 2 %, except for diamond with a systematically higher RMSD (ca. 8 %). This expands the applicability of the analytical solution for any arbitrary inclusion shape in practical Raman measurements.

scholarly journals Analytical solution for residual stress and strain preserved in anisotropic inclusion entrapped in an isotropic host

Solid Earth ◽  
2021 ◽  
Vol 12 (4) ◽  
pp. 817-833
Author(s):  
Xin Zhong ◽  
Marcin Dabrowski ◽  
Bjørn Jamtveit
Keyword(s):  
Residual Stress ◽  
Aspect Ratio ◽  
Analytical Solution ◽  
Strain State ◽  
Spherical Inclusion ◽  
Raman Shift ◽  
Stress And Strain ◽  
Wide Range ◽  
Inclusion Shape ◽  
Diamond Inclusions

Abstract. Raman elastic thermobarometry has recently been applied in many petrological studies to recover the pressure and temperature (P–T) conditions of mineral inclusion entrapment. Existing modelling methods in petrology either adopt an assumption of a spherical, isotropic inclusion embedded in an isotropic, infinite host or use numerical techniques such as the finite-element method to simulate the residual stress and strain state preserved in the non-spherical anisotropic inclusions. Here, we use the Eshelby solution to develop an analytical framework for calculating the residual stress and strain state of an elastically anisotropic, ellipsoidal inclusion in an infinite, isotropic host. The analytical solution is applicable to any class of inclusion symmetry and an arbitrary inclusion aspect ratio. Explicit expressions are derived for some symmetry classes, including tetragonal, hexagonal, and trigonal. The effect of changing the aspect ratio on residual stress is investigated, including quartz, zircon, rutile, apatite, and diamond inclusions in garnet host. Quartz is demonstrated to be the least affected, while rutile is the most affected. For prolate quartz inclusion (c axis longer than a axis), the effect of varying the aspect ratio on Raman shift is demonstrated to be insignificant. When c/a=5, only ca. 0.3 cm−1 wavenumber variation is induced as compared to the spherical inclusion shape. For oblate quartz inclusions, the effect is more significant, when c/a=0.5, ca. 0.8 cm−1 wavenumber variation for the 464 cm−1 band is induced compared to the reference spherical inclusion case. We also show that it is possible to fit an effective ellipsoid to obtain a proxy for the averaged residual stress or strain within a faceted inclusion. The difference between the volumetrically averaged stress of a faceted inclusion and the analytically calculated stress from the best-fitted effective ellipsoid is calculated to obtain the root-mean-square deviation (RMSD) for quartz, zircon, rutile, apatite, and diamond inclusions in garnet host. Based on the results of 500 randomly generated (a wide range of aspect ratio and random crystallographic orientation) faceted inclusions, we show that the volumetrically averaged stress serves as an excellent stress measure and the associated RMSD is less than 2 %, except for diamond, which has a systematically higher RMSD (ca. 8 %). This expands the applicability of the analytical solution for any arbitrary inclusion shape in practical Raman measurements.

Endochronic Analysis of Cyclic Elastoplastic Strain Fields in a Notched Plate

1983 ◽  
Vol 50 (4a) ◽  
pp. 789-794 ◽  
Author(s):  
K. C. Valanis ◽  
J. Fan
Keyword(s):  
Residual Stress ◽  
Numerical Scheme ◽  
External Loading ◽  
Stress And Strain ◽  
Elastoplastic Strain ◽  
Residual Stress Field ◽  
Progressive Change ◽  
Strain Fields ◽  
Cyclic Tension ◽  
Cyclic Elastoplastic Strain

In this paper we present an analytical cum-numerical scheme, based on endochronic plasticity and the finite element formalism. The scheme is used to calculate the stress and elastoplastic strain fields in a plate loaded cyclically in its own plane along its outer edges and bearing two symmetrically disposed edge notches. One most important result that stands out is that while the external loading conditions are symmetric and periodic, the histories of stress and strain at the notch tip are neither symmetric nor periodic in character. In cyclic tension ratcheting phenomena at the tip of the notches prevail and a progressive change of the residual stress field at the notch line is shown to occur.

scholarly journals X-Ray Residual Stress and Strain-Induced Transformation of Retained Austenite in TRIP-Aided Dual-Phase Steels.

1995 ◽  
Vol 61 (581) ◽  
pp. 80-86 ◽  
Author(s):  
Koh-Ichi Sugimoto ◽  
Mitsuyuki Kobayashi ◽  
Hidehiro Matsushima ◽  
Shun-ichi Hashimoto
Keyword(s):  
Residual Stress ◽  
Retained Austenite ◽  
Stress And Strain ◽  
Dual Phase ◽  
Dual Phase Steels ◽  
X Ray

Effect of process parameters on stress and strain of hybrid deposition and micro-rolling

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Xushan Zhao ◽  
Yuanxun Wang ◽  
Guilan Wang ◽  
Runsheng Li ◽  
Haiou Zhang
Keyword(s):  
Residual Stress ◽  
Plastic Strain ◽  
Three Dimensional ◽  
Substantial Effect ◽  
Weld Bead ◽  
Stress And Strain ◽  
Residual Tensile Stress ◽  
Content Type ◽  
Orthogonal Optimization ◽  
Selection Of

Purpose This paper aims to summarize the influence law of hybrid deposited and micro-rolling (HDMR) technology on the shaping strain and residual stress. And the rolling parameters combination was further optimized to guide the actual production. Design/methodology/approach This paper proposed a three-dimensional coupled thermo-mechanical model of the HDMR process. The validated model is used to investigate the influences of rolling parameters on stress and plastic strain (the distance between the energy source and roller [De–r], the rolling compression [cr] and the friction coefficient [fr]). The orthogonal optimization of three factors and three levels was carried out. The influence of rolling parameters on the plastic strain and residual stress is analyzed. Findings The simulation results show that HDMR technology can effectively increase the shaping strain of the weld bead and reduce the residual tensile stress on the weld bead surface. Furthermore, the influence of rolling parameters on stress and strain is obtained by orthogonal analysis, and the corresponding optimal combination is proposed. Also, the rolling temperature significantly affects the residual stress, and the rolling reduction has a substantial effect on the plastic deformation. Research limitations/implications Owing to the choice of research methods, this paper failed to study microstructure evolution. Originality/value This paper provides a reference principle for the optimal selection of rolling parameters in HDMR.

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