scholarly journals A Fully Implicit, Lower Bound, Multi-Axial Solution Strategy for Direct Ratchet Boundary Evaluation: Theoretical Development

2012 ◽  
Author(s):  
Alan Jappy ◽  
Donald Mackenzie ◽  
Haofeng Chen
Keyword(s):  
Lower Bound ◽  
Yield Strength ◽  
Stress Component ◽  
Direct Methods ◽  
Theoretical Development ◽  
Implicit Methods ◽  
Element Analysis ◽  
Elastic Plastic ◽  
Boundary Evaluation ◽  
Fully Implicit

Ensuring sufficient safety against ratchet is a fundamental requirement of pressure vessel design. Determining the ratchet boundary can however prove difficult when using a full elastic plastic finite element analysis and a number of direct methods have been proposed that overcome the difficulties associated with ratchet boundary evaluation. Here, a new approach based on fully implicit methods, similar to conventional elastic-plastic methods, is presented. The method utilizes a two-stage procedure. The first stage determines the cyclic stress state, which can include a varying residual stress component, by repeatedly converging on the solution for the different loads by superposition of elastic stress solutions using a modified elastic-plastic solution. The second stage calculates the constant loads which can be added to the steady cycle whilst ensuring the equivalent stresses remain below a modified yield strength. During stage 2 the modified yield strength used is updated throughout the analysis thus satisfying Melans Lower bound ratchet theorem. This is achieved through the same elastic plastic model as the first stage, using a modified radial return method. The methods that have been proposed here are shown to provide better agreement with upper bound ratchet method than the Hybrid method, however some limitations in this type of method have been identified and are discussed.

scholarly journals A Fully Implicit, Lower Bound, Multi-Axial Solution Strategy for Direct Ratchet Boundary Evaluation: Theoretical Development

2013 ◽  
Vol 135 (5) ◽  
Author(s):  
Alan Jappy ◽  
Donald Mackenzie ◽  
Haofeng Chen
Keyword(s):  
Finite Element ◽  
Lower Bound ◽  
Yield Strength ◽  
Stress Component ◽  
Direct Methods ◽  
Theoretical Development ◽  
Element Analysis ◽  
Elastic Plastic ◽  
Boundary Evaluation ◽  
Fully Implicit

Ensuring sufficient safety against ratchet is a fundamental requirement in pressure vessel design. Determining the ratchet boundary can prove difficult and computationally expensive when using a full elastic–plastic finite element analysis and a number of direct methods have been proposed that overcome the difficulties associated with ratchet boundary evaluation. Here, a new approach based on fully implicit finite element methods, similar to conventional elastic–plastic methods, is presented. The method utilizes a two-stage procedure. The first stage determines the cyclic stress state, which can include a varying residual stress component, by repeatedly converging on the solution for the different loads by superposition of elastic stress solutions using a modified elastic–plastic solution. The second stage calculates the constant loads which can be added to the steady cycle while ensuring the equivalent stresses remain below a modified yield strength. During stage 2 the modified yield strength is updated throughout the analysis, thus satisfying Melan's lower bound ratchet theorem. This is achieved utilizing the same elastic plastic model as the first stage, and a modified radial return method. The proposed methods are shown to provide better agreement with upper bound ratchet methods than other lower bound ratchet methods, however limitations in these are identified and discussed.

scholarly journals A Fully Implicit, Lower Bound, Multi-Axial Solution Strategy for Direct Ratchet Boundary Evaluation: Implementation and Comparison

2012 ◽  
Author(s):  
Alan Jappy ◽  
Donald Mackenzie ◽  
Haofeng Chen
Keyword(s):  
Finite Element ◽  
Lower Bound ◽  
Hybrid Method ◽  
Direct Methods ◽  
Benchmark Problems ◽  
Element Analysis ◽  
Elastic Plastic ◽  
Boundary Evaluation ◽  
Fully Implicit ◽  
Tangent Moduli

Ensuring sufficient safety against ratcheting is a fundamental requirement of pressure vessel design. However, determining the ratchet boundary using a full elastic plastic finite element analysis can be problematic and a number of direct methods have been proposed to overcome difficulties associated with ratchet boundary evaluation. This paper proposes a new approach, similar to the previously proposed Hybrid method but based on fully implicit elastic-plastic solution strategies. This method utilizes superimposed elastic stresses and modified radial return integration to converge on the residual state throughout, resulting in one Finite Element model suitable for solving the cyclic stresses (stage 1) and performing the augmented limit analysis to determine the ratchet boundary (stage 2). The modified radial return methods for both stages of the analysis are presented, with the corresponding stress update algorithm and resulting consistent tangent moduli. Comparisons with other direct methods for selected benchmark problems are presented. It is shown that the proposed method consistently evaluates a lower bound estimate of the ratchet boundary, which has not been demonstrated for the Hybrid method and is yet to be clearly shown for the UMY and LDYM methods. Limitations in the description of plastic strains and compatibility during the ratchet analysis are identified as being a cause for the differences between the proposed methods and other current upper bound methods.

scholarly journals A Fully Implicit, Lower Bound, Multi-Axial Solution Strategy for Direct Ratchet Boundary Evaluation: Implementation and Comparison

2013 ◽  
Vol 136 (1) ◽  
Author(s):  
Alan Jappy ◽  
Donald Mackenzie ◽  
Haofeng Chen
Keyword(s):  
Finite Element ◽  
Lower Bound ◽  
Direct Methods ◽  
Element Model ◽  
Benchmark Problems ◽  
Element Analysis ◽  
Elastic Plastic ◽  
Boundary Evaluation ◽  
Fully Implicit ◽  
Tangent Moduli

Ensuring sufficient safety against ratcheting is a fundamental requirement in pressure vessel design. However, determining the ratchet boundary using a full elastic-plastic finite element analysis can be problematic and a number of direct methods have been proposed to overcome difficulties associated with ratchet boundary evaluation. This paper proposes a new lower bound ratchet analysis approach, similar to the previously proposed hybrid method but based on fully implicit elastic-plastic solution strategies. The method utilizes superimposed elastic stresses and modified radial return integration to converge on the residual state throughout, resulting in one finite element model suitable for solving the cyclic stresses (stage 1) and performing the augmented limit analysis to determine the ratchet boundary (stage 2). The modified radial return methods for both stages of the analysis are presented, with the corresponding stress update algorithm and resulting consistent tangent moduli. Comparisons with other direct methods for selected benchmark problems are presented. It is shown that the proposed method evaluates a consistent lower bound estimate of the ratchet boundary, which has not previously been clearly demonstrated for other lower bound approaches. Limitations in the description of plastic strains and compatibility during the ratchet analysis are identified as being a cause for the differences between the proposed methods and current upper bound methods.

Three-Dimensional Finite Element Analysis of Elastic-Plastic Crack Problems

1981 ◽  
Vol 103 (3) ◽  
pp. 214-218 ◽  
Author(s):  
B. V. Kiefer ◽  
P. D. Hilton
Keyword(s):  
Finite Element ◽  
Normal Stress ◽  
Crack Front ◽  
Stress Component ◽  
Three Dimensional ◽  
Specimen Thickness ◽  
Element Analysis ◽  
Finite Element Program ◽  
Elastic Plastic ◽  
Crack Problems

A three-dimensional, elastic-plastic finite element program is developed and applied to analyze the stress field in a plate containing a through crack. The center cracked plate is subjected to uniform tensile loading which results in mode I opening of the crack surfaces. Transverse variations of the opening tensile stress component and of the effective stress (von Mises) in the vicinity of the crack front are presented. They clearly demonstrate the three-dimensional nature of this problem with distributions that depend on specimen thickness. For thinner plates, the plastic deformation concentrates near the plate surfaces while the normal stress is largest in the plate interior. In thicker plates the deformation and normal stress fields are more uniform in the plate interior near the crack front, but they develop a rapid boundary layer-type variation in the vicinity of the plate surfaces.

A New Constitutively Accurate Lower Bound Direct Shakedown Method

2013 ◽  
Author(s):  
Alan Jappy ◽  
Donald Mackenzie ◽  
Haofeng Chen
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Lower Bound ◽  
Yield Surface ◽  
Direct Methods ◽  
Accurate Description ◽  
Element Analysis ◽  
Surface Plasticity ◽  
Fundamental Requirement ◽  
Linear Matching Method

Ensuring sufficient safety against shakedown or ratchet is a fundamental requirement of pressure vessel design. Determining the shakedown or ratchet boundary can however prove difficult when using a full elastic plastic finite element analysis and a number of direct methods have been proposed that overcome the difficulties associated with shakedown or ratchet boundary evaluation. Here a new direct lower bound shakedown method, which can be extended to a ratchet method, is proposed. The method maintains a constitutively accurate description of the assumed material response through the use of non-smooth multi yield surface plasticity models. The proposed shakedown method can consider arbitrary load cases and may be solved in a single analysis step in a standard finite element analysis with a user-programed non-smooth multi yield surface plasticity model. It is demonstrated that by maintaining a constitutively accurate description of the plastic strains the method is able to calculate strict lower bound shakedown boundaries. The resulting boundary is shown to give excellent agreement with the upper and lower bound linear matching method.

Elastic-Shakedown Analysis of Axisymmetric Nozzles

2003 ◽  
Vol 125 (4) ◽  
pp. 365-370 ◽  
Author(s):  
Martin Muscat ◽  
Donald Mackenzie
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Lower Bound ◽  
Pressure Vessel ◽  
Element Analysis ◽  
Shakedown Analysis ◽  
Elastic Plastic ◽  
Section Viii ◽  
Elastic Shakedown ◽  
Division 2

An investigation of the shakedown behavior of axisymmetric nozzles under internal pressure is presented. The analysis is based on elastic-plastic finite element analysis and Melan’s lower bound shakedown theorem. Calculated shakedown pressures are compared with values from the literature and with the ASME Boiler and Pressure Vessel Code Section VIII Division 2 primary plus secondary stress limits. Results obtained by the lower bound method are also verified by cyclic elastic-plastic finite element analysis.

Representing the Effect of Crystallographic Texture on the Anisotropic Performance Behavior of Rolled Aluminum Plate

1999 ◽  
Vol 122 (1) ◽  
pp. 10-17 ◽  
Author(s):  
M. P. Miller ◽  
N. R. Barton
Keyword(s):  
Finite Element ◽  
Lower Bound ◽  
Yield Strength ◽  
Upper Bound ◽  
Crystallographic Texture ◽  
Rolling Direction ◽  
Rolled Plate ◽  
Elastic Plastic ◽  
Polycrystal Plasticity ◽  
Rolled Aluminum

Rolled aluminum alloys are known to be anisotropic due to their processing histories. This paper focuses on measuring and modeling monotonic and cyclic strength anisotropies as well as the associated anisotropy of the elastic/elastic-plastic transition of a commercially-available rolled plate product. Monotonic tension tests were conducted on specimens in the rolling plane of 25.4 mm thick AA 7075-T6 plate taken at various angles to the rolling direction (RD). Fully-reversed tension/compression cyclic experiments were also conducted. As expected, we found significant anisotropy in the back-extrapolated yield strength. We also found that the character of the elastic/elastic-plastic transition (knee of the curve) to be dependent on the orientation of the loading axis. The tests performed in RD and TD (transverse direction) had relatively sharp transitions compared to the test data from other orientations. We found the cyclic response of the material to reflect the monotonic anisotropy. The material response reached cyclic stability in 10 cycles or less with very little cyclic hardening or softening observed. For this reason, we focused our modeling effort on predicting the monotonic response. Reckoning that the primary source of anisotropy in the rolled plate is the processing-induced crystallographic texture, we employed the experimentally-measured texture of the undeformed plate material in continuum slip polycrystal plasticity model simulations of the monotonic experiments. Three types of simulations were conducted, upper and lower bound analyses and a finite element calculation that associates an element with each crystal in the aggregate. We found that all three analyses predicted anisotropy of the back-extrapolated yield strength and post-yield behavior with varying degrees of success in correlating the experimental data. In general, the upper and lower bound models predicted larger and smaller differences in the back-extrapolated yield strength, respectively, than was observed in the data. The finite element results resembled those of the upper bound when initially cubic elements were employed. We found that by employing an element shape that was more consistent with typical rolling microstructure, we were able to improve the finite element prediction significantly. The anisotropy of the elastic/elastic-plastic transition predicted by each model was also different in character. The lower bound predicted sharper transitions than the upper bound model, capturing the shape of the knee for the RD and TD data but failing to capture the other orientations. In contrast, the upper bound model predicted relatively long transitions for all orientations. As with the upper bound, the FEM calculation predicted gentle transitions with less transition anisotropy predicted than that of the upper bound. [S0094-4289(00)00201-2]

Effect of Defect on Elastic/Plastic and Creep Behavior of Bone: A Finite Element Study

2007 ◽  
Author(s):  
A. Ajdari ◽  
P. K. Canavan ◽  
H. Nayeb-Hashemi ◽  
G. Warner
Keyword(s):  
Mechanical Properties ◽  
Finite Element ◽  
Trabecular Bone ◽  
Fatigue Loading ◽  
Dimensional Structure ◽  
Plastic Behavior ◽  
Element Analysis ◽  
Elastic Plastic ◽  
Local Bone ◽  
Osteoporotic Vertebral Fractures

Three-dimensional structure of trabecular bone can be modeled by 2D or 3D Voronoi structure. The effect of missing cell walls on the mechanical properties of 2D honeycombs is a first step towards understanding the effect of local bone resorption due to osteoporosis. In patients with osteoporosis, bone mass is lost first by thinning and then by resorption of the trabeculae [1]. Furthermore, creep response is important to analyze in cellular solids when the temperature is high relative to the melting temperature. For trabecular bone, as body temperature (38 °C) is close to the denaturation temperature of collagen (52 °C), trabecular bone creeps [1]. Over the half of the osteoporotic vertebral fractures that occur in the elderly, are the result of the creep and fatigue loading associated with the activities of daily living [2]. The objective of this work is to understand the effect of missing walls and filled cells on elastic-plastic behavior of both regular hexagonal and non-periodic Voronoi structures using finite element analysis. The results show that the missing walls have a significant effect on overall elastic properties of the cellular structure. For both regular hexagonal and Voronoi materials, the yield strength of the structure decreased by more than 60% by introducing 10% missing walls. In contrast, the results indicate that filled cells have much less effect on the mechanical properties of both regular hexagonal and Voronoi materials.

Stress and Fatigue Life Modeling of Cannon Breech Closures Including Effects of Material Strength and Residual Stress

2000 ◽  
Vol 123 (1) ◽  
pp. 150-154
Author(s):  
John H. Underwood ◽  
Michael J. Glennon
Keyword(s):  
Residual Stress ◽  
Finite Element ◽  
Fatigue Life ◽  
Yield Strength ◽  
Residual Stresses ◽  
Solid Mechanics ◽  
Element Model ◽  
Pressure Vessels ◽  
Material Strength ◽  
Element Analysis

Laboratory fatigue life results are summarized from several test series of high-strength steel cannon breech closure assemblies pressurized by rapid application of hydraulic oil. The tests were performed to determine safe fatigue lives of high-pressure components at the breech end of the cannon and breech assembly. Careful reanalysis of the fatigue life tests provides data for stress and fatigue life models for breech components, over the following ranges of key parameters: 380–745 MPa cyclic internal pressure; 100–160 mm bore diameter cannon pressure vessels; 1040–1170 MPa yield strength A723 steel; no residual stress, shot peen residual stress, overload residual stress. Modeling of applied and residual stresses at the location of the fatigue failure site is performed by elastic-plastic finite element analysis using ABAQUS and by solid mechanics analysis. Shot peen and overload residual stresses are modeled by superposing typical or calculated residual stress distributions on the applied stresses. Overload residual stresses are obtained directly from the finite element model of the breech, with the breech overload applied to the model in the same way as with actual components. Modeling of the fatigue life of the components is based on the fatigue intensity factor concept of Underwood and Parker, a fracture mechanics description of life that accounts for residual stresses, material yield strength and initial defect size. The fatigue life model describes six test conditions in a stress versus life plot with an R2 correlation of 0.94, and shows significantly lower correlation when known variations in yield strength, stress concentration factor, or residual stress are not included in the model input, thus demonstrating the model sensitivity to these variables.

Sign in / Sign up

Export Citation Format

Share Document