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.

Thermal Simulation of an Arbitrary Residual Stress Field in a Fully or Partially Autofrettaged Thick-Walled Spherical Pressure Vessel

2008 ◽  
Author(s):  
M. Perl
Keyword(s):  
Residual Stress ◽  
Finite Element ◽  
Stress Field ◽  
Pressure Vessel ◽  
Stress Fields ◽  
Equivalent Temperature ◽  
Residual Stress Field ◽  
Element Analysis ◽  
Spherical Pressure ◽  
The Ideal

The equivalent thermal load was previously shown to be the only feasible method by which the residual stresses due to autofrettage and its redistribution, as a result of cracking, can be implemented in a finite element analysis, of a fully or partially autofrettaged thick-walled cylindrical pressure vessel. The present analysis involves developing a similar methodology for treating an autofrettaged thick-walled spherical pressure vessel. A general procedure for evaluating the equivalent temperature loading for simulating an arbitrary, analytical or numerical, spherosymmetric autofrettage residual stress field in a spherical pressure vessel is developed. Once presented, the algorithm is applied to two distinct cases. In the first case, an analytical expression for the equivalent thermal loading is obtained for the ideal autofrettage stress field in a spherical shell. In the second case, the algorithm is applied to the discrete numerical values of a realistic autofrettage residual stress field incorporating the Bauschinger effect. As a result, a discrete equivalent temperature field is obtained. Furthermore, a finite element analysis is performed for each of the above cases, applying the respective temperature field to the spherical vessel. The induced stress fields are evaluated for each case and then compared to the original stress. The finite element results prove that the proposed procedure yields equivalent temperature fields that in turn simulate very accurately the residual stress fields for both the ideal and the realistic autofrettage cases.

Thermal Simulation of an Arbitrary Residual Stress Field in a Fully or Partially Autofrettaged Thick-Walled Spherical Pressure Vessel

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
M. Perl
Keyword(s):  
Residual Stress ◽  
Temperature Field ◽  
Stress Field ◽  
Pressure Vessel ◽  
Fe Analysis ◽  
Stress Fields ◽  
Equivalent Temperature ◽  
Residual Stress Field ◽  
Spherical Pressure ◽  
The Ideal

The equivalent thermal load was previously shown to be the only feasible method by which the residual stresses due to autofrettage and its redistribution, as a result of cracking, can be implemented in a finite element (FE) analysis of a fully or partially autofrettaged thick-walled cylindrical pressure vessel. The present analysis involves developing a similar methodology for treating an autofrettaged thick-walled spherical pressure vessel. A general procedure for evaluating the equivalent temperature loading for simulating an arbitrary, analytical or numerical spherosymmetric autofrettage residual stress field in a spherical pressure vessel is developed. Once presented, the algorithm is applied to two distinct cases. In the first case, an analytical expression for the equivalent thermal loading is obtained for the ideal autofrettage stress field in a spherical shell. In the second case, the algorithm is applied to the discrete numerical values of a realistic autofrettage residual stress field incorporating the Bauschinger effect. As a result, a discrete equivalent temperature field is obtained. Furthermore, a FE analysis is performed for each of the above cases, applying the respective temperature field to the spherical vessel. The induced stress fields are evaluated for each case and then compared to the original stress. The FE results prove that the proposed procedure yields equivalent temperature fields that in turn simulate very accurately the residual stress fields for both the ideal and the realistic autofrettage cases.

3-D Stress Intensity Factors due to Autofrettage for an Inner Radial Lunular or Crescentic Crack in a Spherical Pressure Vessel

2015 ◽  
Author(s):  
M. Perl ◽  
M. Steiner ◽  
J. Perry
Keyword(s):  
Residual Stress ◽  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Stress Field ◽  
Pressure Vessel ◽  
Bauschinger Effect ◽  
Three Dimensional ◽  
Residual Stress Field ◽  
Spherical Pressure

Three dimensional Mode I Stress Intensity Factor (SIF) distributions along the front of an inner radial lunular or crescentic crack emanating from the bore of an autofrettaged spherical pressure vessel are evaluated. The 3-D analysis is performed using the finite element (FE) method employing singular elements along the crack front. A novel realistic autofrettage residual stress field incorporating the Bauschinger effect is applied to the vessel. The residual stress field is simulated in the FE analysis using an equivalent temperature field. SIFs for three vessel geometries (R0/Ri=1.1, 1.2, and 1.7), a wide range of crack depth to wall thickness ratios (a/t=0.01–0.8), various ellipticities (a/c=0.2–1.5), and three levels of autofrettage (e=50%, 75%, and 100%) are evaluated. In total, about two hundred and seventy different crack configurations are analyzed. A detailed study of the influence of the above parameters on the prevailing SIF is conducted. The results clearly indicate the possible favorable effect of autofrettage in considerably reducing the prevailing effective stress intensity factor i.e., delaying crack initiation, slowing crack growth rate, and thus, substantially prolonging the total fatigue life of the vessel. Furthermore, the results emphasize the importance of properly accounting for the Bauschinger effect including re-yielding, as well as the significance of the three dimensional analysis herein performed.

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.

A 3-D Model for Evaluating the Residual Stress Field Due to Swage Autofrettage

2008 ◽  
Vol 130 (4) ◽  
Author(s):  
J. Perry ◽  
M. Perl
Keyword(s):  
Residual Stress ◽  
Stress Field ◽  
Three Dimensional ◽  
Weight Ratio ◽  
Computer Code ◽  
Residual Stress Field ◽  
Three Dimensional Model ◽  
Equilibrium Equations ◽  
Von Mises ◽  
Experimental Findings

In order to maximize the performance of modern gun barrels in terms of strength-to-weight ratio and total fatigue life, favorable compressive residual stresses are introduced to the inner portion of the barrel, commonly by the autofrettage process. There are two major autofrettage processes for overstraining the tube: the hydrostatic and the swage. There are several theoretical solutions for hydrostatic autofrettage based on Lamé’s solution and the von Mises or Tresca yield criteria. The residual stress field due to hydraulic autofrettage is treated as an axisymmetric two-dimensional problem solved in terms of the radial displacement solely. Once the Bauschinger effect was included in these models they yield very realistic results. Unlike in the case of hydraulic autofrettage, swage autofrettage needs to be modeled by a three-dimensional model. The present analysis suggests a new 3-D axisymmetric model for solving the residual stress field due to swage autofrettage in terms of both the radial and the axial displacements. The axisymmetric equilibrium equations are approximated by finite differences and solved then by Gauss–Seidel method. Using the new computer code the stresses, the strains, the displacements, and the forces are determined. A full-scale instrumented swage autofrettage test was conducted and the numerical results were validated against the experimental findings. The calculated strains, the permanent bore enlargement, and the mandrel pushing force were found to be in very good agreement with the measured values.

A 3-D Model for Evaluating the Residual Stress Field Due to Swage Autofrettage

2006 ◽  
Author(s):  
J. Perry ◽  
M. Perl
Keyword(s):  
Residual Stress ◽  
Stress Field ◽  
Three Dimensional ◽  
Weight Ratio ◽  
Computer Code ◽  
Residual Stress Field ◽  
Three Dimensional Model ◽  
Equilibrium Equations ◽  
Von Mises ◽  
Experimental Findings

In order to maximize the performance of modern gun barrels in terms of strength-to-weight ratio and total fatigue life, favorable compressive residual stresses are introduced to the inner portion of the barrel, commonly by the autofrettage process. There are two major autofrettage processes for overstraining the tube: the hydrostatic, and the swage. There are several theoretical solutions for hydrostatic autofrettage, based on Lame´’s solution and the von Mises or Tresca yield criteria. The residual stress field due to hydraulic autofrettage is treated as an axisymetric, two-dimensional problem solved in terms of the radial displacement solely. Once the Bauschinger effect was included in these models they yield very realistic results. Unlike in the case of hydraulic autofrettage, swage autofrettage needs to be modeled by a three-dimensional model. The present analysis suggests a new 3-D axisymmetric model for solving the residual stress field due to swage autofrettage in terms of both the radial and the axial displacements. The axisymetric equilibrium equations are approximated by finite differences and solved then by Gauss-Seidel method. Using the new computer code the stresses, the strains, the displacements and the forces are determined. A full-scale instrumented swage autofrettage test was conducted and the numerical results were validated against the experimental findings. The calculated strains, the permanent bore enlargement, and the mandrel pushing force were found to be in very good agreement with the measured values.

Numerical Simulation of Residual Stresses Due to Cladding Process

2007 ◽  
Author(s):  
Dieter Siegele ◽  
Marcus Brand
Keyword(s):  
Numerical Simulation ◽  
Residual Stress ◽  
Finite Element ◽  
Stress Field ◽  
Residual Stresses ◽  
Base Metal ◽  
Base Material ◽  
Pressure Vessels ◽  
Measured Temperature ◽  
Residual Stress Field

The inner surface of reactor pressure vessels is protected against corrosion by an austenitic cladding. Generally, the cladding is welded on the ferritic base metal with two layers to avoid sub-clad cracks and to improve the microstructure of the cladding material. On the other hand, due to the cladding process and the difference of the thermal expansion coefficient of the austenitic cladding and the ferritic base material residual stresses act in the component. This residual stress field is important for assessing crack postulates in the cladding or subclad flaws in the base metal. For the determination of the residual stress field, plates of RPV steel were cladded and heat treated representative to the RPV relevant conditions. During the cladding process the temperature and distortion were measured as basis for the validation of the finite element simulations. The numerical simulation was performed with the finite element code SYSWELD. The heat source of the model was calibrated on the measured temperature profile. In the analysis, the temperature dependent material properties as well as the transformation behavior of the ferritic base metal were taken into account. The calculated residual stresses show tensile stresses in the cladding followed by compressive stresses in the base metal that are in agreement with measurements with X-ray diffraction technique.

The Favorable Effect of Autofrettage on Uniform Arrays of 3-D Unequal-Depth Cracks in a Thick-Walled Cylindrical Pressure Vessel

2003 ◽  
Author(s):  
M. Perl ◽  
B. Ostraich
Keyword(s):  
Residual Stress ◽  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Stress Field ◽  
Pressure Vessel ◽  
Crack Depth ◽  
Favorable Effect ◽  
Residual Stress Field ◽  
Cylindrical Pressure Vessel

The favorable effect of autofrettage on the mode I stress intensity factor (SIF) distributions along the fronts of radial, semi-elliptical surface cracks pertaining to large uniform arrays of unequal-depth cracks emanating at the bore of a pressurized thick-walled cylinder is studied. The analysis is based on the, previously proposed, “two-crack-depth level model”. SIF values are evaluated by the finite element method (FE) using the ANSYS 6.1 code. In the FE model singular elements are employed along the crack front and an equivalent temperature load simulates the autofrettage residual stress field. The distribution of KIN = KIP + KIA, the combined stress intensity factor due to pressurization and full autofrettage, for numerous uneven array configurations bearing n = n1 + n2 = 8 to 128 cracks, a wide range of crack depth to wall thickness ratios, a1/t = 0.01 to 0.4, and various crack ellipticities, a1/c1 = 0.3 to 1.5, are evaluated for a cylinder of radii ratio Ro/Ri = 2. The accuracy of the evaluated SIFs is increased using an improved displacement extrapolation. The results clearly indicate the favorable effect of the residual stress field on the fracture endurance and the fatigue life of autofrettaged cylindrical pressure vessel bearing uniform arrays of 3-D unequal-depth cracks emanating from its inner bore. This favorable effect is governed by Ψ = σo/p — the ratio of the vessel’s material yield stress to its internal pressure. The higher ψ is the more effective autofrettage becomes. The “interaction range” for the various configurations of uneven crack arrays is evaluated. The range of influence between adjacent cracks on the maximal combined SIF, KNmax, is found to be dependent on the density of the array, as reflected in the inter-crack aspect-ratio, as well as on the cracks’ ellipticity.

Full Thermal Simulation of an Arbitrary, Plane Axisymmetric Residual Stress Field

2019 ◽  
Vol 142 (1) ◽  
Author(s):  
Anthony P. Parker
Keyword(s):  
Residual Stress ◽  
Stress Field ◽  
Pressure Vessels ◽  
Thermal Simulation ◽  
Residual Stress Field ◽  
Subsequent Determination ◽  
Arbitrary Plane ◽  
Stress Profiles ◽  
Hoop Stresses

Abstract In this paper, numerical formulations are presented; these permit full thermal simulation of an arbitrary plane axisymmetric residual stress field encompassing hoop, radial, and axial stresses. Earlier formulations were based upon the determination of a temperature profile within the tube that could only replicate radial and hoop stresses; in general, axial stresses were incorrect. This new thermal simulation provides all three stresses and is achieved by incorporating orthotropic coefficients of thermal expansion that themselves vary with radius. Results are generally highly accurate. Crucial near-bore hoop and axial stresses can be replicated within 1%. Near-bore behavior is discussed in detail. These formulations will permit subsequent determination of stress intensity factors (SIF) for arbitrarily orientated cracks within pressure vessels in the presence of pre-existing residual stresses. Note that these thermal solutions mimic known, residual stress profiles; they do not predict residual stress profiles.

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