Plastic relaxation of the transformation strain energy of a misfitting spherical precipitate: Ideal plastic behavior

1980 ◽  
Vol 11 (11) ◽  
pp. 1837-1847 ◽  
Author(s):  
J. K. Lee ◽  
Y. Y. Earmme ◽  
H. I. Aaronson ◽  
K. C. Russell
Keyword(s):  
Strain Energy ◽  
Transformation Strain ◽  
Plastic Relaxation ◽  
Plastic Behavior ◽  
Ideal Plastic ◽  
Spherical Precipitate

scholarly journals Strain and interface energy of ellipsoidal inclusions subjected to volumetric eigenstrains: shape factors

2022 ◽  
Author(s):  
H. J. Böhm ◽  
G. A. Zickler ◽  
F. D. Fischer ◽  
J. Svoboda
Keyword(s):  
Elastic Strain ◽  
Strain Energy ◽  
Materials Science ◽  
Elastic Strain Energy ◽  
Transformation Strain ◽  
Interface Energy ◽  
Shape Factors ◽  
Computational Materials Science ◽  
The Matrix ◽  
Computational Materials

AbstractThermodynamic modeling of the development of non-spherical inclusions as precipitates in alloys is an important topic in computational materials science. The precipitates may have markedly different properties compared to the matrix. Both the elastic contrast and the misfit eigenstrain may yield a remarkable generation of elastic strain energy which immediately influences the kinetics of the developing precipitates. The relevant thermodynamic framework has been mostly based on spherical precipitates. However, the shapes of actual particles are often not spherical. The energetics of such precipitates can be met by adapting the spherical energy terms with shape factors. The well-established Eshelby framework is used to evaluate the elastic strain energy of inclusions with ellipsoidal shapes (described by the axes a, b, and c) that are subjected to a volumetric transformation strain. The outcome of the study is two shape factors, one for the elastic strain energy and the other for the interface energy. Both quantities are provided in the form of easy-to-use diagrams. Furthermore, threshold elastic contrasts yielding strain energy shape factors with the value 1.0 for any ellipsoidal shape are studied.

Failure of Porous Metals Based on Strain Energy Density Criterion

2020 ◽  
Vol 142 (4) ◽  
Author(s):  
A. Y. Elruby ◽  
Sam Nakhla
Keyword(s):  
Strain Energy ◽  
Elastic Response ◽  
Micromechanical Modeling ◽  
Plastic Behavior ◽  
Extensive Literature ◽  
Loading Capacity ◽  
Porous Metals ◽  
Elastoplastic Behavior ◽  
Damage Process ◽  
Extensive Literature Search

Abstract Porosity in metals is well known to influence the mechanical behavior, namely, the elastic response, the plastic behavior, and the material loading capacity. The main focus of the current work is to investigate the failure of porous metals. Extensive literature search was conducted to identify failure mechanisms associated with the increase of porosity for up to 15% by volume. Consequently, micromechanical modeling is utilized to investigate the damage process at microlengths. Finally, a complete macromechanical modeling approach is proposed for specimen-sized models. The approach utilizes the extended Ramberg–Osgood relationship for the elastoplastic behavior, while the failure is predicted using a strain energy-based failure criterion capturing the effect of porosity. The proposed approach is validated against several testing results for different metals at various porosity levels.

scholarly journals Validation of a New Quality Assessment Procedure for Ductile Irons Production Based on Strain Hardening Analysis

Metals ◽  
2019 ◽  
Vol 9 (8) ◽  
pp. 837 ◽  
Author(s):  
Angella ◽  
Zanardi
Keyword(s):  
Energy Density ◽  
Quality Assessment ◽  
Strain Hardening ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Plastic Behavior ◽  
Assessment Procedure ◽  
Flow Curves ◽  
Fundamental Assumption ◽  
Voce Equation

A mathematical procedure based on the analysis of tensile flow curves has been proposed to assess the microstructure quality of several ductile irons (DIs). The procedure consists of a first diagram for the assessment of the ideal microstructure of DIs, that is, the matrix where mobile dislocations move, and a second diagram for the assessment of the casting integrity because of potential metallurgical discontinuities and defects in DIs. Both diagrams are based on the dislocation-density-related constitutive Voce equation that is used for modeling the tensile plastic behavior of DIs. The procedure stands on the fundamental assumption that the strain hardening behavior of DIs is not affected by the nature and the density of the potential metallurgical discontinuities and defects, which are expected to affect only the elongations to fracture. However, this fundamental assumption is not obvious, and so its validity was evaluated through tensile testing Isothermed Ductile Irons (IDIs) 800, showing a wide scatter of elongations to rupture. The analysis of the strain hardening behaviors supported by strain energy density calculations of IDIs tensile tests proved that the fundamental assumption was valid and the quality assessment procedure could be applied to IDIs. A modified Voce equation was also introduced to improve the fitting of the experimental tensile flow curves and the strain energy density calculations.

Failure Process and Stress-Strain Curve of Plane Strain Rock Specimen with Initially Random Material Imperfections

2007 ◽  
Vol 353-358 ◽  
pp. 1133-1136 ◽  
Author(s):  
X.B. Wang
Keyword(s):  
Rock Specimen ◽  
Failure Process ◽  
Shear Bands ◽  
Strain Curve ◽  
Peak Stress ◽  
Plastic Behavior ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Initial Imperfections ◽  
Ideal Plastic

The failure process of heterogeneous rock specimen with initially random material imperfections in uniaxial plane strain compression and the macroscopically mechanical response are numerically modeled by using FLAC (Fast Lagrangian Analysis of Continua). A FISH function is generated to prescribe the initial imperfections within the heterogeneous specimen by using Matlab. The imperfection is weaker than the intact rock. Beyond the failure of the imperfection, it undergoes ideal plastic behavior, while intact rock exhibits linear strain-softening behavior and then ideal plastic behavior once failure occurs. The specimen with smooth ends is loaded at a constant strain rate and is divided into 3200 elements. The maximum numbers of the initial imperfections in five schemes are 100, 300, 500, 700 and 900. The effects of the number of the imperfections on the fracture process, the final fracture pattern and the complete stress-strain curve are investigated. Prior to the peak stress, some imperfections extend in the axial direction and then a part of them coalesce to form inclined shear bands. Beyond the peak stress, shear bands progressively intersect the specimen; in the process the number of the yielded elements approximately remains a constant. With an increase of the number of the initial imperfections, the spacing of shear fractures decreases, the peak stress and corresponding axial strain decrease; the post-peak branch of stress-strain curve becomes steeper; much more elements fail in tension; the number of the yielded elements in tension in the vicinity of the two lateral edges of the specimen remarkably increases.

The wustite-spinel interface

1987 ◽  
Vol 45 ◽  
pp. 268-269
Author(s):  
S.R. Summerfelt ◽  
C.B. Carter
Keyword(s):  
Solid State ◽  
Solid State Reaction ◽  
Strain Energy ◽  
Matrix Material ◽  
Lattice Misfit ◽  
Solid State Reactions ◽  
Oxygen Sublattice ◽  
Large Particles ◽  
Small Lattice ◽  
Coherent Interfaces

The wustite-spinel interface can be viewed as a model interface because the wustite and spinel can share a common f.c.c. oxygen sublattice such that only the cations distribution changes on crossing the interface. In this study, the interface has been formed by a solid state reaction involving either external or internal oxidation. In systems with very small lattice misfit, very large particles (>lμm) with coherent interfaces have been observed. Previously, the wustite-spinel interface had been observed to facet on {111} planes for MgFe2C4 and along {100} planes for MgAl2C4 and MgCr2O4, the spinel then grows preferentially in the <001> direction. Reasons for these experimental observations have been discussed by Henriksen and Kingery by considering the strain energy. The point-defect chemistry of such solid state reactions has been examined by Schmalzried. Although MgO has been the principal matrix material examined, others such as NiO have also been studied.

Delamination in the scoring and folding of paperboard

TAPPI Journal ◽  
2012 ◽  
Vol 11 (1) ◽  
pp. 61-66 ◽  
Author(s):  
DOEUNG D. CHOI ◽  
SERGIY A. LAVRYKOV ◽  
BANDARU V. RAMARAO
Keyword(s):  
Finite Element ◽  
Plane Deformation ◽  
Strain Analysis ◽  
Local Strain ◽  
Uniaxial Stress ◽  
Material Model ◽  
Element Model ◽  
Plastic Behavior ◽  
Stress Strain ◽  
Strain Fields

Delamination between layers occurs during the creasing and subsequent folding of paperboard. Delamination is necessary to provide some stiffness properties, but excessive or uncontrolled delamination can weaken the fold, and therefore needs to be controlled. An understanding of the mechanics of delamination is predicated upon the availability of reliable and properly calibrated simulation tools to predict experimental observations. This paper describes a finite element simulation of paper mechanics applied to the scoring and folding of multi-ply carton board. Our goal was to provide an understanding of the mechanics of these operations and the proper models of elastic and plastic behavior of the material that enable us to simulate the deformation and delamination behavior. Our material model accounted for plasticity and sheet anisotropy in the in-plane and z-direction (ZD) dimensions. We used different ZD stress-strain curves during loading and unloading. Material parameters for in-plane deformation were obtained by fitting uniaxial stress-strain data to Ramberg-Osgood plasticity models and the ZD deformation was modeled using a modified power law. Two-dimensional strain fields resulting from loading board typical of a scoring operation were calculated. The strain field was symmetric in the initial stages, but increasing deformation led to asymmetry and heterogeneity. These regions were precursors to delamination and failure. Delamination of the layers occurred in regions of significant shear strain and resulted primarily from the development of large plastic strains. The model predictions were confirmed by experimental observation of the local strain fields using visual microscopy and linear image strain analysis. The finite element model predicted sheet delamination matching the patterns and effects that were observed in experiments.

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