Directional Coarsening of γ′ Phase Induced by Phase Transformation Stress

2005 ◽  
Vol 20 (9) ◽  
pp. 2314-2321 ◽  
Author(s):  
K. Zhao ◽  
Y.H. Ma ◽  
L.H. Lou ◽  
Z.Q. Hu
Keyword(s):  
Free Energy ◽  
Phase Transformation ◽  
Uniform Distribution ◽  
Strain Energy ◽  
Coherency Strain ◽  
Preferential Direction ◽  
Nickel Based Superalloy ◽  
Directional Coarsening ◽  
Energy Theory ◽  
Transformation Stress

It was found that directional coarsening was induced by phase transformation stress due to non-uniform distribution of μ phase in an experimental nickel-based superalloy. The mechanism based on the existing diffusion and coherency strain energy theory has been discussed. It was concluded that directional coarsening was the course of dissolving of γ′ portion with high free energy, diffusing and growing on the existed γ′ particles along a preferential direction.

scholarly journals Determination of the Critical Stress Associated with Dynamic Phase Transformation in Steels by Means of Free Energy Method

Metals ◽  
2018 ◽  
Vol 8 (5) ◽  
pp. 360 ◽  
Author(s):  
Clodualdo Aranas ◽  
Samuel Rodrigues ◽  
Ameth Fall ◽  
Mohammad Jahazi ◽  
John Jonas
Keyword(s):  
Free Energy ◽  
Phase Transformation ◽  
Energy Method ◽  
Critical Stress ◽  
Dynamic Phase

Prediction of Cylinder Flow Pressures in Mass-Flow Bins Using Minimum Strain Energy

1976 ◽  
Vol 98 (4) ◽  
pp. 1370-1374 ◽  
Author(s):  
A. G. McLean ◽  
P. C. Arnold
Keyword(s):  
Mass Flow ◽  
Strain Energy ◽  
Plane Flow ◽  
Geometry Design ◽  
Numerical Effort ◽  
Minimum Strain Energy ◽  
Flow Pressure ◽  
Energy Theory ◽  
Cylinder Flow ◽  
Complete Variation

Jenike, et al. [1] have presented a minimum strain energy theory to predict cylinder flow pressures in mass-flow bins. The complete variation of strain energy pressures is depicted by bounds requiring considerable numerical effort to develop for a specific cylinder geometry. Design charts are presented, but these are available for only two circular cylinder geometries. This paper summarizes and clarifies the minimum strain energy theory for predicting cylinder flow pressures. A single bound approximation which allows the magnitude of the peak flow pressure to be determined for both axisymmetric and plane flow cylinders is presented. This peak pressure may also be estimated by a single calculation of strain energy pressure. The usefulness and accuracy of these procedures are illustrated by reworking the example presented by Jenike, et al. [1].

Constitutive Modeling of Porous Shape Memory Alloys Using Gurson–Tvergaard–Needleman Model Under Isothermal Conditions

2020 ◽  
Vol 12 (04) ◽  
pp. 2050038
Author(s):  
Xiang Zhu ◽  
Liangliang Chu ◽  
Guansuo Dui
Keyword(s):  
Experimental Data ◽  
Phase Transformation ◽  
Shape Memory Alloys ◽  
Shape Memory ◽  
Strain Hardening ◽  
Constitutive Relationship ◽  
Model Parameters ◽  
Gtn Model ◽  
Critical Phase ◽  
Transformation Stress

Based on the Gurson–Tvergaard–Needleman (GTN) model, a constitutive relationship considering both the effects of strain hardening and hydrostatic stress for porous shape memory alloys (SMAs) is proposed. To capture the relationship between microscopic and mesoscopic behaviors, a representative volume element (RVE) containing an array of spherical voids is presented. In this paper, an approximate solution including strain hardening exponent [Formula: see text] is deduced by considering the porous SMA as a two phase composite with the SMA matrix and the second phase representing voids. The model parameters, [Formula: see text] and [Formula: see text], accounting for interactions between voids are investigated to take into account their influences on strain hardening, critical phase transformation stress and yield surface. In addition, the evolution equations of phase transformation are derived and then applied to the simulation of porous Ni–Ti SMAs with a porosity of 13%. Using the calibrated GTN model parameters, the critical phase transformation stress closer to experimental data is obtained. The predictions of stress–strain curve by the proposed constitutive model are found to be in excellent agreement with published experimental data and finite element results. The results prove that the model is capable of reproducing the features of porous SMAs such as superelasticity, tensile-compressive asymmetry and internal loops under uniaxial even combined loading conditions. A conclusion is drawn that the present constitutive relationship is powerful and useful for the analysis of porous SMAs.

On Energy Strength Theories for Geomaterials

2013 ◽  
Vol 353-356 ◽  
pp. 901-904
Author(s):  
Shou Yi Xue
Keyword(s):  
Energy Density ◽  
Shear Strain ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Volumetric Strain ◽  
Dissipated Energy ◽  
Energy Theory ◽  
Shear Strain Energy ◽  
Shear Energy ◽  
Strain Energy Density Theory

The composition of the energy in the process of material deformation and failure and the relationship between energy and strength were summarized; the features, essences and main problems of the energy release rate theory, the three-shear energy theory and the net shear strain energy density theory were illustrated. It is pointed out that the roles of distortion strain energy, volumetric strain energy and dissipated energy are not identical, especially distortion strain energy and volumetric strain energy must be separately processed. The three-shear energy theory and the net shear strain energy density theory can properly deal with the problems, and also well reflect the intermediate principal stress effect. The above research results can provide references for further discussions.

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