Relaxed Configurations and Elastic Range in Elasto-Plastic Models

1989 ◽  
pp. 245-255
Author(s):  
Sanda Cleja-Tigoiu ◽  
Eugen Soós
Keyword(s):  
Elastic Range

scholarly journals Influence of Cold Rotary Swaging on Microstructure and Uniaxial Mechanical Behavior in Alloy 718

2021 ◽  
Author(s):  
Alexander Klumpp ◽  
Alexander Kauffmann ◽  
Sascha Seils ◽  
Stefan Dietrich ◽  
Volker Schulze
Keyword(s):  
Mechanical Behavior ◽  
Electron Backscatter Diffraction ◽  
Moderate Increase ◽  
Alloy 718 ◽  
Pronounced Increase ◽  
Rotary Swaging ◽  
Elastic Range ◽  
Nickel Based Superalloy ◽  
Tempering Treatment ◽  
Tension And Compression

AbstractIn this study, the influence of cold rotary swaging on microstructure and mechanical properties of the precipitation-strengthened nickel-based superalloy 718 (Alloy 718) was investigated. The initial stages of work-hardening were characterized by means of microhardness, electron backscatter diffraction (EBSD), and X-ray diffraction (XRD) analyses. Furthermore, attention was devoted to the mechanical behavior at ambient and elevated temperature (550 °C) in uniaxial tension and compression. Rotary swaging to different true strains of maximum $$\varphi = 0.91$$ φ = 0.91 caused a moderate increase of microhardness and enhanced markedly the load-bearing capacity in tension, giving rise to yield strength beyond 2000 MPa. The mechanical strength $$R_{p0.2}$$ R p 0.2 in tension subsequent to rotary swaging perfectly correlates with increasing dislocation density $$\rho $$ ρ estimated from XRD in the form of a Taylor-like relationship $$R_{p0.2} \propto \sqrt{\rho }$$ R p 0.2 ∝ ρ . In compression, transient stress–strain evolution without the occurrence of a clear elastic range and distinct yield phenomenon was observed. Restoration of the elastic range, accompanied by a pronounced increase of microhardness, was obtained by a post-swaging tempering treatment at 600 °C.

scholarly journals Eigenproblem Versus the Load-Carrying Capacity of Hybrid Thin-Walled Columns with Open Cross-Sections in the Elastic Range

Materials ◽  
2021 ◽  
Vol 14 (13) ◽  
pp. 3468
Author(s):  
Zbigniew Kolakowski ◽  
Andrzej Teter
Keyword(s):  
Cross Sections ◽  
Carrying Capacity ◽  
Ultimate Load ◽  
Equilibrium Path ◽  
Load Carrying Capacity ◽  
Nonlinear Buckling ◽  
Elastic Range ◽  
Load Carrying ◽  
Thin Walled ◽  
Ultimate Load Carrying Capacity

The phenomena that occur during compression of hybrid thin-walled columns with open cross-sections in the elastic range are discussed. Nonlinear buckling problems were solved within Koiter’s approximation theory. A multimodal approach was assumed to investigate an effect of symmetrical and anti-symmetrical buckling modes on the ultimate load-carrying capacity. Detailed simulations were carried out for freely supported columns with a C-section and a top-hat type section of medium lengths. The columns under analysis were made of two layers of isotropic materials characterized by various mechanical properties. The results attained were verified with the finite element method (FEM). The boundary conditions applied in the FEM allowed us to confirm the eigensolutions obtained within Koiter’s theory with very high accuracy. Nonlinear solutions comply within these two approaches for low and medium overloads. To trace the correctness of the solutions, the Riks algorithm, which allows for investigating unsteady paths, was used in the FEM. The results for the ultimate load-carrying capacity obtained within the FEM are higher than those attained with Koiter’s approximation method, but the leap takes place on the identical equilibrium path as the one determined from Koiter’s theory.

scholarly journals Internal stress created by plastic flow in mild steel, and stress-strain curves for the atomic lattice of higher carbon steels

1944 ◽  
Vol 182 (991) ◽  
pp. 404-414 ◽  
Keyword(s):  
Mild Steel ◽  
Internal Stress ◽  
Plastic Flow ◽  
Carbon Steels ◽  
External Stress ◽  
Stress Strain ◽  
Atomic Lattice ◽  
X Ray ◽  
Elastic Range ◽  
Residual Strains

In previous work, stress-strain curves for the atomic lattice of certain metals have been obtained from X-ray diffraction measurements of the lattice dimensions of test specimens under tension or compression, and it has been shown that when the external yield stress is exceeded, there is a systematic departure from Hooke’s Law. It is pointed out in the present paper that this departure indicates that the external applied stress above the yield is no longer balanced primarily by simple displacement of the atoms but also by a new type of secondary internal stress brought about by the process of plastic flow; and that this secondary stress, being of a permanent nature, can be measured by the residual lattice strains exhibited by the lattice after removal of the external stress. These residual strains are measured in various directions to the stress direction for mild steel subjected to tension, and it is shown that the lattice after tension exhibits a longitudinal compression and a transverse expansion in the ratio of 2:1, which means that the density of the material is thereby kept constant. Comparisons of X-ray and mechanical measurements further show that the hysteresis loop exhibited by the external stress-strain curve of mild steel after overstrain can disappear and the linear elastic relation be recovered without any corresponding change in the internal stress, which is therefore a more fundamental physical property. It is also shown that when the elastic range is extended by overstrain in tension, there is no symmetrical increase in the elastic range in subsequent compression, thus confirming the existence and direction of the secondary internal stress. Finally, the lattice stress-strain curves are also obtained for a 0.4 % C steel (partially pearlitic) and a 0.8 % C steel (pearlitic), and by comparison with the results on pure iron and 0.1 % C steel (annealed) it is shown that the maximum residual internal strain developed by the lattice increases markedly with the fineness to which the crystallites can be broken down by the plastic deformation.

Local vs. Global Ratcheting in Cracked Structures

2014 ◽  
Author(s):  
R. Adibi-Asl ◽  
Wolf Reinhardt
Keyword(s):  
Cyclic Loading ◽  
Component Structure ◽  
Elastic Range ◽  
Cracked Structures ◽  
Elastic Shakedown ◽  
Plastic Shakedown ◽  
Time Invariant ◽  
Global And Local ◽  
Mean Time ◽  
Cracked Structure

The classical approaches in shakedown analysis are based on the assumption that the stresses are eventually within the elastic range of the material everywhere in a component (elastic shakedown). Therefore, these approaches are not very useful to predict the ratcheting limit (ratchet limit) of a cracked component/structure in which the magnitude of stress locally exceeds the elastic range at any load, although in reality the configuration will certainly permit plastic shakedown. The Non-Cyclic Method (NCM) has been proposed recently to determine both the elastic and the plastic ratchet boundary of a component or structure under cyclic loading by generalizing the static shakedown theorem (Melan’s theorem). The proposed method is based on decomposing the loading into mean (time invariant) and fully reversed components. When a cracked structure is subjected to cyclic loading, the crack and its vicinity behave differently (local) than the rest of the structure (global). The crack may propagate during the application of cyclic loading. This will affect both local and global behavior of the cracked structure. This paper investigates global and local ratcheting of the cracked structures using the NCM and fracture mechanic parameters.

05.36: An efficient approach to limiting the elastic range in advanced analysis of steel structures via RPHM

ce/papers ◽  
2017 ◽  
Vol 1 (2-3) ◽  
pp. 1353-1362
Author(s):  
Ígor José Mendes Lemes ◽  
Rafael Cesário Barros ◽  
Everton André Pimentel Batelo ◽  
Ricardo Azoubel da Mota Silveira
Keyword(s):  
Steel Structures ◽  
Efficient Approach ◽  
Elastic Range ◽  
Advanced Analysis

Design of Long Rectangular Elasto-Plastic Plates

1961 ◽  
Vol 5 (04) ◽  
pp. 16-33
Author(s):  
Thein Wah
Keyword(s):  
Strengthening Effect ◽  
Rectangular Plates ◽  
Uniform Pressure ◽  
Analysis And Design ◽  
Elastic Range ◽  
Salient Features

In a previous paper3 a theory was derived for the analysis of rectangular plates loaded with a uniform pressure and beyond the elastic range of the material. The theory took into account the strengthening effect of membrane tensions in the plane of the plate, the effects of edge displacements and of initial deflections and locked-in moments which might exist in the plate. In the present paper the salient features of the theory are put in the form of charts and tables for convenience in analysis and design.

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