Latent Elastic Strain Energy Due to the Residual Stresses in a Plastically Deformed Polycrystal

1967 ◽  
Vol 34 (3) ◽  
pp. 606-611 ◽  
Author(s):  
T. H. Lin ◽  
Marvin Ito
Keyword(s):  
Residual Stress ◽  
Residual Stresses ◽  
Elastic Strain ◽  
Strain Energy ◽  
Elastic Strain Energy ◽  
Residual Stress Field ◽  
Latent Energy ◽  
Energy Part ◽  
Crystallographic Slip ◽  
Work Done

A part of the work done on a plastically deformed metal reappears in the form of heat and the remaining part remains latent in the metal, known as latent energy. Part of this latent energy is the elastic strain energy of the residual stresses of the plastically deformed metal. In this paper, this strain energy in a polycrystal is calculated from the crystallographic slip properties of single crystals. The polycrystalline aggregate is composed of differently oriented cube-shaped crystals, each with one slip plane on which there are three slip directions. Neglecting the inhomogeneity and anisotropy of elastic constants, the polycrystal is taken to be elastically homogeneous and isotropic. The analogy between plastic strain gradient and body force in an infinite elastic medium is used to calculate the residual stress field. The residual stress calculation satisfies the condition of continuity, the equilibrium condition, and the single crystal stress-strain relationship throughout the aggregate. The variation of the latent elastic strain energy with the aggregate stress is shown. A similar method may be used to calculate the latent elastic strain energy of f.c.c. and b.c.c. polycrystals.

scholarly journals Effect of Carbide Precipitation on the Evolution of Residual Stress during Tempering

Metals ◽  
2019 ◽  
Vol 9 (6) ◽  
pp. 709 ◽  
Author(s):  
Wenhong Ding ◽  
Yazheng Liu ◽  
Jianxin Xie ◽  
Li Sun ◽  
Tianwu Liu ◽  
...  
Keyword(s):  
Residual Stress ◽  
Elastic Strain ◽  
Strain Energy ◽  
Elastic Strain Energy ◽  
Hardness Test ◽  
Carbide Precipitation ◽  
Material Surface ◽  
Low Carbon ◽  
Alloy Carbide ◽  
Isothermal Tempering

The evolution of microstructure and residual stress during the tempering of 700 L low-carbon micro-alloyed steel was studied using a crack compliance method for measuring residual stress. Additionally, a non-isothermal tempering dilatation test, Vickers micro-hardness test, and transmission electron microscopy were used. The evolution of residual stress during tempering consists of two stages. The first stage coincided with cementite precipitation. Under the initial residual stress, the transformation plasticity due to cementite precipitation leads to partial relaxation of the micro-stress evoked by the austenite-to-ferrite transformation during quenching. It also caused the material surface and the core to exhibit different residual stress evolution trends. After tempering at 300 ∘ C for 30 min, the residual stress was reduced from 487 MPa to 200 MPa; however, the elastic strain energy remained unchanged. The second stage coincided with alloy carbide precipitation and Mn partitioning, but the precipitation of the alloy carbide only reduced the elastic strain energy by 8.7%. Thus, the change in activation energy was the main reason for the relaxation of residual stress at this stage. After tempering at 600 ∘ C for 30 min, the residual stress was reduced to 174 MPa, the elastic strain energy was reduced by 72.72%, and the residual stress was controlled.

scholarly journals Residual stresses in thermite welded rails: significance of additional forging

2020 ◽  
Vol 64 (7) ◽  
pp. 1195-1212
Author(s):  
B. Lennart Josefson ◽  
R. Bisschop ◽  
M. Messaadi ◽  
J. Hantusch
Keyword(s):  
Residual Stress ◽  
Stress Field ◽  
Residual Stresses ◽  
Weld Metal ◽  
Welding Process ◽  
Surface Zone ◽  
Fe Model ◽  
Uneven Surface ◽  
Residual Stress Field ◽  
High Dynamic

Abstract The aluminothermic welding (ATW) process is the most commonly used welding process for welding rails (track) in the field. The large amount of weld metal added in the ATW process may result in a wide uneven surface zone on the rail head, which may, in rare cases, lead to irregularities in wear and plastic deformation due to high dynamic wheel-rail forces as wheels pass. The present paper studies the introduction of additional forging to the ATW process, intended to reduce the width of the zone affected by the heat input, while not creating a more detrimental residual stress field. Simulations using a novel thermo-mechanical FE model of the ATW process show that addition of a forging pressure leads to a somewhat smaller width of the zone affected by heat. This is also found in a metallurgical examination, showing that this zone (weld metal and heat-affected zone) is fully pearlitic. Only marginal differences are found in the residual stress field when additional forging is applied. In both cases, large tensile residual stresses are found in the rail web at the weld. Additional forging may increase the risk of hot cracking due to an increase in plastic strains within the welded area.

Do muscles function as adaptable locomotor springs?

2002 ◽  
Vol 205 (15) ◽  
pp. 2211-2216 ◽  
Author(s):  
Stan L. Lindstedt ◽  
Trude E. Reich ◽  
Paul Keim ◽  
Paul C. LaStayo
Keyword(s):  
Skeletal Muscle ◽  
Elastic Strain ◽  
Strain Energy ◽  
Elastic Strain Energy ◽  
Normal Animal ◽  
Eccentric Contractions ◽  
Normal Muscle ◽  
Energetic Costs ◽  
Locomotor Muscles ◽  
Power Outputs

SUMMARYDuring normal animal movements, the forces produced by the locomotor muscles may be greater than, equal to or less than the forces acting on those muscles, the consequences of which significantly affect both the maximum force produced and the energy consumed by the muscles. Lengthening (eccentric)contractions result in the greatest muscle forces at the lowest relative energetic costs. Eccentric contractions play a key role in storing elastic strain energy which, when recovered in subsequent contractions, has been shown to result in enhanced force, work or power outputs. We present data that support the concept that this ability of muscle to store and recover elastic strain energy is an adaptable property of skeletal muscle. Further, we speculate that a crucial element in that muscle spring may be the protein titin. It too seems to adapt to muscle use, and its stiffness seems to be`tuned' to the frequency of normal muscle use.

Buckling of Multiple-Bay Ring-Reinforced Cylindrical Shells Subject to Hydrostatic Pressure

1953 ◽  
Vol 20 (4) ◽  
pp. 469-474
Author(s):  
W. A. Nash
Keyword(s):  
Cylindrical Shell ◽  
Hydrostatic Pressure ◽  
Strain Energy ◽  
Elastic Strain Energy ◽  
Middle Surface ◽  
Elastic Buckling ◽  
Elastic Instability ◽  
Total Potential ◽  
External Forces ◽  
Work Done

Abstract An analytical solution is presented for the problem of the elastic instability of a multiple-bay ring-reinforced cylindrical shell subject to hydrostatic pressure applied in both the radial and axial directions. The method used is that of minimization of the total potential. Expressions for the elastic strain energy in the shell and also in the rings are written in terms of displacement components of a point in the middle surface of the shell. Expressions for the work done by the external forces acting on the cylinder likewise are written in terms of these displacement components. A displacement configuration for the buckled shell is introduced which is in agreement with experimental evidence, in contrast to the arbitrary patterns assumed by previous investigators. The total potential is expressed in terms of these displacement components and is then minimized. As a result of this minimization a set of linear homogeneous equations is obtained. In order that a nontrivial solution to this system of equations exists, it is necessary that the determinant of the coefficients vanish. This condition determines the critical pressure at which elastic buckling of the cylindrical shell will occur.

The Elastostatic Axisymmetric Problem of a Cracked Sphere Embedded in a Dissimilar Matrix

1980 ◽  
Vol 47 (3) ◽  
pp. 545-550 ◽  
Author(s):  
R. Kant ◽  
D. B. Bogy
Keyword(s):  
Elastic Strain ◽  
Strain Energy ◽  
Elastic Strain Energy ◽  
Companion Paper ◽  
Infinite Medium ◽  
Applied Mechanics ◽  
Axisymmetric Solution ◽  
Material Parameters ◽  
The Difference ◽  
Elastostatic Problem

The axisymmetric elastostatic problem of a cracked sphere embedded in a dissimilar matrix is solved by using the solution for a spherical cavity in an infinite medium together with the axisymmetric solution for a cracked sphere given in the companion paper in this issue of the Journal of Applied Mechanics, Pages 538-544. Numerical results are presented for (a) interface stress for various composites (b) dependence of the stress-intensity factor on the material parameters and ratios of crack to sphere radii, (c) the difference in the elastic strain energy for a cracked and uncracked composite.

Weld Residual Stress in Large Diameter Nuclear Nozzles

2011 ◽  
Author(s):  
Tao Zhang ◽  
F. W. Brust ◽  
Gery Wilkowski
Keyword(s):  
Residual Stress ◽  
Residual Stresses ◽  
Nuclear Power ◽  
Kinematic Hardening ◽  
Large Diameter ◽  
Thick Wall ◽  
Isotropic Hardening ◽  
Residual Stress Field ◽  
Mixed Hardening ◽  
Weld Residual Stress

Weld residual stresses in nuclear power plant can lead to cracking concerns caused by stress corrosion. These are large diameter thick wall pipe and nozzles. Many factors can lead to the development of the weld residual stresses and the distributions of the stress through the wall thickness can vary markedly. Hence, understanding the residual stress distribution is important to evaluate the reliability of pipe and nozzle joints with welds. This paper represents an examination of the weld residual stress distributions which occur in various different size nozzles. The detailed weld residual stress predictions for these nozzles are summarized. Many such weld residual stress solutions have been developed by the authors in the last five years. These distributions will be categorized and organized in this paper and general trends for the causes of the distributions will be established. The residual stress field can therefore feed into a crack growth analysis. The solutions are made using several different constitutive models such as kinematic hardening, isotropic hardening, and mixed hardening model. Necessary fabrication procedures such as repair, overlay and post weld heat treatment are also considered. Some general discussions and comments will conclude the paper.

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