Derivation of Polycrystal Creep Properties From the Creep Data of Single Crystals

1977 ◽  
Vol 44 (1) ◽  
pp. 73-78 ◽  
Author(s):  
T. H. Lin ◽  
C. L. Yu ◽  
G. J. Weng
Keyword(s):  
Single Crystals ◽  
Creep Deformation ◽  
Tensile Loading ◽  
Present Theory ◽  
Sole Source ◽  
Stress And Strain ◽  
Creep Data ◽  
Stress Strain ◽  
Macroscopic Stress ◽  
Additional Constant

A method developed for calculating the polycrystal stress-strain-time relation from the creep data of single crystals is shown. Slip is considered to be the sole source of creep deformation. This method satisfies, throughout the aggregate, both the condition of equilibrium and that of continuity of displacement as well as the creep characteristics of single crystals. A very large three-dimensional region is assumed to be filled with innumerable identical cubic blocks, each of which consists of 64 cube-shaped crystals of different orientations. This region is assumed to be embedded in an infinite elastic isotropic medium. This infinite medium is subject to a uniform loading. The average stress and strain of a cubic block at the center of the region is taken to represent the macroscopic stress and strain of the polycrystal. This method is self-consistent and considers the heterogeneous interaction effect of the creep deformation of all slid crystals. The macroscopic stress-strain-time relations of the polycrystal were calculated for three tensile loadings, one radial loading, and two nonradial loadings of combined tension and torsion. The numerical results given by the present theory agree well with those predicted by the so-called “Mechanical Equation of State.” The creep strain components calculated by the present theory for the case of a constant tensile loading followed by an additional constant tensile loading are found to be considerably higher than those predicted by von Mises and Tresca’s theories. These results agree well qualitatively with experimental results.

Material Response and Continuum Relations; or From Microscales to Macroscales

1984 ◽  
Vol 106 (4) ◽  
pp. 286-289 ◽  
Author(s):  
D. C. Drucker
Keyword(s):  
Plastic Deformation ◽  
Shear Stress ◽  
Aluminum Alloys ◽  
Single Crystals ◽  
Continuum Mechanics ◽  
Stress Strain ◽  
Material Response ◽  
Macroscopic Behavior ◽  
Macroscopic Stress ◽  
Structural Metals

Brief qualitative assessments are presented of a few approaches to macroscopic stress-strain relations for structural metals, alloys, and composites and some remarks are made about fracture. Ignoring the scale and applying continuum mechanics to the microstructure lies at one extreme, the dislocation scale treatment of single crystals and simple polycrystals at another. When, as for structural aluminum alloys, the shear stress required for continuing plastic deformation is so much higher than for the constituent single crystals, it seems unlikely that the latter approach is able to exhibit the salient features of macroscopic behavior.

scholarly journals Infarcted Left Ventricles Have Stiffer Material Properties and Lower Stiffness Variation: Three-Dimensional Echo-Based Modeling to Quantify In Vivo Ventricle Material Properties

2015 ◽  
Vol 137 (8) ◽  
Author(s):  
Longling Fan ◽  
Jing Yao ◽  
Chun Yang ◽  
Dalin Tang ◽  
Di Xu
Keyword(s):  
Wall Thickness ◽  
Material Properties ◽  
Strain Curve ◽  
Stress And Strain ◽  
Stress Strain ◽  
Material Stiffness ◽  
The Mean ◽  
Lv Volume ◽  
Parameter Values

Methods to quantify ventricle material properties noninvasively using in vivo data are of great important in clinical applications. An ultrasound echo-based computational modeling approach was proposed to quantify left ventricle (LV) material properties, curvature, and stress/strain conditions and find differences between normal LV and LV with infarct. Echo image data were acquired from five patients with myocardial infarction (I-Group) and five healthy volunteers as control (H-Group). Finite element models were constructed to obtain ventricle stress and strain conditions. Material stiffening and softening were used to model ventricle active contraction and relaxation. Systolic and diastolic material parameter values were obtained by adjusting the models to match echo volume data. Young's modulus (YM) value was obtained for each material stress–strain curve for easy comparison. LV wall thickness, circumferential and longitudinal curvatures (C- and L-curvature), material parameter values, and stress/strain values were recorded for analysis. Using the mean value of H-Group as the base value, at end-diastole, I-Group mean YM value for the fiber direction stress–strain curve was 54% stiffer than that of H-Group (136.24 kPa versus 88.68 kPa). At end-systole, the mean YM values from the two groups were similar (175.84 kPa versus 200.2 kPa). More interestingly, H-Group end-systole mean YM was 126% higher that its end-diastole value, while I-Group end-systole mean YM was only 29% higher that its end-diastole value. This indicated that H-Group had much greater systole–diastole material stiffness variations. At beginning-of-ejection (BE), LV ejection fraction (LVEF) showed positive correlation with C-curvature, stress, and strain, and negative correlation with LV volume, respectively. At beginning-of-filling (BF), LVEF showed positive correlation with C-curvature and strain, but negative correlation with stress and LV volume, respectively. Using averaged values of two groups at BE, I-Group stress, strain, and wall thickness were 32%, 29%, and 18% lower (thinner), respectively, compared to those of H-Group. L-curvature from I-Group was 61% higher than that from H-Group. Difference in C-curvature between the two groups was not statistically significant. Our results indicated that our modeling approach has the potential to determine in vivo ventricle material properties, which in turn could lead to methods to infer presence of infarct from LV contractibility and material stiffness variations. Quantitative differences in LV volume, curvatures, stress, strain, and wall thickness between the two groups were provided.

scholarly journals Microscopic Stress and Strain Evolved in a Twinning-Induced Plasticity Fe-Mn-C Steel

2014 ◽  
Vol 996 ◽  
pp. 135-140
Author(s):  
Shigeru Suzuki ◽  
Shigeo Sato ◽  
Koji Hotta ◽  
Eui Pyo Kwon ◽  
Shun Fujieda ◽  
...  
Keyword(s):  
Strain Distribution ◽  
Crystal Orientation ◽  
Fem Simulation ◽  
Tensile Loading ◽  
Stress And Strain ◽  
X Ray Diffraction ◽  
Principal Stresses ◽  
Orientation Data ◽  
Tensile Direction ◽  
X Ray

White X-ray diffraction with micro-beam synchrotron radiation was used to analyze microscopic stress evolved in coarse grains of a twinning-induced plasticity Fe-Mn-C steel under tensile loading. In addition, electron backscatter diffraction (EBSD) was used to determine the crystal orientation of grains in the polycrystalline Fe-Mn-C steel. Based on these orientation data, the stress and strain distribution in the microstructure of the steel under tensile loading was estimated using FEM simulation where the elastic anisotropy or the crystal orientation dependence of the elasticity was taken into account. The FEM simulation showed that the strain distribution in the microstructure depends on the crystal orientation of each grain. The stress analysis by the white X-ray diffraction indicated that the direction of the maximum principal stresses at measured points in the steel under tensile loading are mostly oriented toward the tensile direction. This is qualitatively consistent with the results of by the FEM simulation, although absolute values of the principal stresses may contain the effect of heterogeneous plastic deformation on the stress distribution.

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