On the Inversion of Residual Stresses From Surface Displacements

1989 ◽  
Vol 56 (3) ◽  
pp. 508-513 ◽  
Author(s):  
Zhanjun Gao ◽  
T. Mura
Keyword(s):  
Residual Stress ◽  
Stress Field ◽  
Integral Equations ◽  
Surface Displacement ◽  
Plastic Strains ◽  
Residual Stress Field ◽  
Residual Displacements ◽  
Plastic Damage ◽  
Surface Displacements ◽  
The Difference

When plastic damage regions are accumulated in a material, there exist residual displacements on the surface of the material after all the loadings are removed. The residual displacements are defined as the difference between before and after loading, and can be measured experimentally without destruction of the material. This paper addresses the problem of evaluating the residual stress field caused by the accumulation of the plastic damage regions in a subdomain of the material. The problem is formulated as a system of integral equations relating the surface displacements to the unknown plastic strains. The damage domain, which appears as the domain of integration of the integral equations, is also unknown. Determination of the shape of the damage domain, together with the plastic strains, is a very complicated nonlinear problem. In addition to the residual surface displacement data, it requires more information about the loading history or other restrictive assumptions. However, the residual stress field in the vicinity of the damage domain is obtained after the equivalent damage domain and the equivalent plastic strains are introduced. The problem is an inverse problem, which is substantially different from the conventional forward analysis of structural mechanics. Special attention is given to the uniqueness and stability of the solution.

Effects of Crack Introduction History on Fracture Initiation in Residually Stressed Components

2018 ◽  
Author(s):  
Molly A. Probert ◽  
Harry E. Coules ◽  
Christopher E. Truman
Keyword(s):  
Residual Stress ◽  
Stress Field ◽  
Plastic Material ◽  
Fracture Initiation ◽  
Residual Stress Field ◽  
Introduction History ◽  
Fracture Assessment ◽  
Novel Method ◽  
The Difference ◽  
Elastic Plastic Material

If a crack is introduced progressively into an elastic-plastic material containing a residual stress field, the incremental relaxation of the residual stress field causes the formation of a plastic wake along the crack boundaries. This leads to the reduction in the J parameter for a crack of a given size, compared to a crack with the same dimensions which has been introduced instantaneously, having the crack faces released simultaneously along the whole length, a 40% reduction is observed in the current analysis. This reduction in J is due to the dissipation of strain energy which is otherwise available for further crack extension, as in the instantaneously introduced crack. This is important for the current J-based fracture assessment common in the nuclear and petrochemical industries such as EDF Energy’s R6 and BS7910:2013 as they currently assume instantaneous insertion of cracks as this is inherently more conservative. Although many studies demonstrating this effect in FE are available, there is little experimental evidence for this phenomenon. Especially those including rigorous comparisons with specimens that have been ‘instantaneously’ cracked. This may be due to the difficulty inherent in manufacturing such a specimen as manufacturing processes rely on the incremental removal of material. The aim of this paper is to detail analysis of a novel method of crack introduction that aims to replicate the deformation behavior of an instantaneously introduced crack tip in a model that has had the nodes released in a progressive manner. This will allow specimens to be machined in a way that replicates ‘instantaneous’ cracking allowing for experimental techniques to be developed to display the difference between instantaneous and progressively introduced cracks.

A Numerical Model for Evaluating the Residual Stress Field in an Autofrettaged Spherical Pressure Vessel Incorporating the Bauschinger Effect

2007 ◽  
Author(s):  
M. Perl ◽  
J. Perry
Keyword(s):  
Differential Equation ◽  
Residual Stress ◽  
Stress Field ◽  
Pressure Vessel ◽  
Weight Ratio ◽  
Pressure Vessels ◽  
Flow Rule ◽  
Plastic Strains ◽  
Residual Stress Field ◽  
Spherical Pressure

Increased strength-to-weight ratio and extended fatigue life are the main objectives in the optimal design of modern pressure vessels. These two goals can mutually be achieved by creating a proper residual stress field in the vessel’s wall, by a process known as autofrettage. Although there are many studies that have investigated the autofrettage problem for cylindrical vessels, only few such studies exist for spherical ones. There are two principal autofrettage processes for pressure vessels: hydrostatic and swage autofrettage, but spherical vessels can only undergo the hydrostatic one. Because of the spherosymmetry of the problem, autofrettage in a spherical pressure vessel is treated as a two-dimensional problem and solved solely in terms of the radial displacement. The mathematical model is based on the idea of solving the elasto-plastic autofrettage problem using the form of the elastic solution. Substituting Hooke’s equations into the equilibrium equation and using the strain-displacement relations, yields a differential equation, which is a function of the plastic strains. The plastic strains are determined using the Prandtl-Reuss flow rule and the differential equation is solved by the explicit finite difference method. The previously developed 2-D computer program, for the evaluation of hydrostatic autofrettage in a thick-walled cylinder, is adapted to handle the problem of spherical autofrettage. The appropriate residual stresses are then evaluated using the new code. The presently obtained residual stress field is then compared to three existing solutions emphasizing the major role the material law plays in determining the autofrettage residual stress field.

The Beneficial Contribution of Realistic Autofrettage to the Load-Carrying Capacity of Thick-Walled Spherical Pressure Vessels

2010 ◽  
Vol 132 (1) ◽  
Author(s):  
M. Perl ◽  
J. Perry
Keyword(s):  
Differential Equation ◽  
Residual Stress ◽  
Stress Field ◽  
Weight Ratio ◽  
Pressure Vessels ◽  
Flow Rule ◽  
Plastic Strains ◽  
Residual Stress Field ◽  
Explicit Finite Difference ◽  
Spherical Pressure

Increased strength-to-weight ratio and extended fatigue life are the main objectives in the optimal design of modern pressure vessels. These two goals can mutually be achieved by creating a proper residual stress field in the vessel’s wall by a process known as autofrettage. Although there are many studies that have investigated the autofrettage problem for cylindrical vessels, only a few of such studies exist for spherical ones. Because of the spherosymmetry of the problem, autofrettage in a spherical pressure vessel is treated as a one-dimensional problem and solved solely in terms of the radial displacement. The mathematical model is based on the idea of solving the elastoplastic autofrettage problem using the form of the elastic solution. Substituting Hooke’s equations into the equilibrium equation and using the strain-displacement relations yield a differential equation, which is a function of the plastic strains. The plastic strains are determined using the Prandtl–Reuss flow rule and the differential equation is solved by the explicit finite difference method. The existing 2D computer program, for the evaluation of hydrostatic autofrettage in a thick-walled cylinder, is adapted to handle the problem of spherical autofrettage. The presently obtained residual stress field is then validated against three existing solutions emphasizing the major role the material law plays in determining the autofrettage residual stress field. The new code is applied to a series of spherical pressure vessels yielding two major conclusions. First, the process of autofrettage increases considerably the maximum safe pressure that can be applied to the vessel. This beneficial effect can also be used to reduce the vessel’s weight rather than to increase the allowable internal pressure. Second, the specific maximum safe pressure increases as the vessel becomes thinner. The present results clearly indicate that autofrettaging of spherical pressure vessels can be very advantageous in various applications.

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.

A mechanism study on characteristic curve of residual stress field in Ti–6Al–4V induced by wet peening treatment

2015 ◽  
Vol 86 ◽  
pp. 761-764 ◽  
Author(s):  
Kang Li ◽  
Xue-song Fu ◽  
Rui-dong Li ◽  
Wen-long Zhou ◽  
Zhi-qiang Li
Keyword(s):  
Residual Stress ◽  
Stress Field ◽  
Characteristic Curve ◽  
Mechanism Study ◽  
Residual Stress Field

Dynamic evolution of welding residual stress field under noncontact electromagnetic force

2010 ◽  
Vol 107 (5) ◽  
pp. 054904
Author(s):  
Da Xu ◽  
Xuesong Liu ◽  
Ping Wang ◽  
Jianguo Yang ◽  
Wei Xu ◽  
...  
Keyword(s):  
Residual Stress ◽  
Stress Field ◽  
Electromagnetic Force ◽  
Welding Residual Stress ◽  
Dynamic Evolution ◽  
Residual Stress Field

Analysis of Thermal Stresses and Residual Stress Changes in Railroad Wheels Caused by Severe Drag Braking

1977 ◽  
Vol 99 (1) ◽  
pp. 18-23 ◽  
Author(s):  
M. R. Johnson ◽  
R. E. Welch ◽  
K. S. Yeung
Keyword(s):  
Residual Stress ◽  
Stress Field ◽  
Yield Point ◽  
Thermal Stresses ◽  
Material Behavior ◽  
Nonlinear Material ◽  
Residual Stress Field ◽  
Thermal Stress Field ◽  
Stress Changes ◽  
Railroad Wheels

A finite-element computer program, which takes into consideration nonlinear material behavior after the yield point has been exceeded, has been used to analyze the thermal stresses in railroad freight car wheels subjected to severe drag brake heating. The analysis has been used with typical wheel material properties and wheel configurations to determine the thermal stress field and the extent of regions in the wheel where the yield point is exceeded. The resulting changes in the residual stress field after the wheel has cooled to ambient temperature have also been calculated. It is shown that severe drag braking can lead to the development of residual circumferential tensile stresses in the rim and radial compressive stresses in the plate near both the hub and rim fillets.

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