Analytical Solution of Aluminum Alloy Plates with Holes Subjected to Cold Expansion with Reverse Yielding

2021 ◽  
Author(s):  
Abdel-Hakim Bouzid ◽  
Hacène Touahri ◽  
Khaled Benfriha
Keyword(s):  
Aluminum Alloy ◽  
Residual Stresses ◽  
Strain Hardening ◽  
Analytical Model ◽  
Material Behavior ◽  
Thick Wall ◽  
Plastic Behavior ◽  
Good Prediction ◽  
Fatigue Damage Accumulation ◽  
Reverse Yielding

Abstract The expansion induced by cold working is a common process that generates residual stresses. It is used when fatigue damage accumulation and life reduction of aluminum alloy perforated plates is an issue in the aeronautics industry. This process is an attractive solution to extend the fatigue lifetime of these structures. It aims at generating residual stresses and increases thereby the strength of hollow parts including aluminum alloy plates with holes commonly used in the manufacture of airplane fuselage. Unfortunately, the life predictions require a good prediction of the residual stresses and in particular when reverse yielding takes place. An analytical model to predict the residual stresses induced during the expansion process due to the cold strain hardening is developed. The proposed analytical model is based on an elasto-plastic behavior, with a power law material behavior and relies on the theory of autofrettaged thick wall cylinders in plane strain state to which reverse yielding is incorporated. The application of Hencky theory of plastic deformation is used in the analytical calculations of the stresses and strains. Finite-element numerical simulation is used to validate the developed analytical model by comparison of the radial, Hoop, longitudinal and equivalent stresses for both the loading and unloading phases. The obtained results show clearly that the level of residual stresses depends mainly on the interference and strain hardening while reverse yielding reduce the stresses near the hole.

Analytical and Numerical Modelling of Sheet Plate Cold Expanded Hole Subjected to Reverse Yielding

2019 ◽  
Author(s):  
Abdel-Hakim Bouzid ◽  
Hacène Touahri
Keyword(s):  
Aluminum Alloy ◽  
Residual Stresses ◽  
Strain Hardening ◽  
Analytical Model ◽  
Life Assessment ◽  
Thick Wall ◽  
Plastic Behavior ◽  
Alloy Plate ◽  
Proposed Model ◽  
Reverse Yielding

Abstract Predicting and mitigating the effect of expansion induced by cold working on damage fatigue accumulation and life assessment of aluminum alloy is a common process in the aeronautics industry, especially to extend the fatigue lifetime of their structures. This process aims at generating residual stresses and increases thereby the strength of hollow parts including aluminum alloy plate holes that are employed in manufacturing the airplane fuselage. An analytical model to predict the residual stresses induced during the expansion process due to the cold strain hardening is developed. The proposed model is based on an elasto-plastic behavior, with a power law material behaviour and relies on the theory of autofrettaged thick wall cylinders in plane strain state to which reverse yielding is incorporated. The application of Hencky theory of plastic deformation is used in the analytical calculations of the stresses and strains. Finite-element numerical simulation is used to validate the developed analytical model by comparison of the radial, Hoop, longitudinal and equivalent stresses for both the loading and unloading phases. The obtained results show clearly that the level of residual stresses depends mainly on the interference and strain hardening while reverse yielding reduce the stresses near the hole.

An Analytical Solution for Three-Dimensional Elliptical Elastic-Plastic Rolling Contact

2014 ◽  
Vol 658 ◽  
pp. 207-212
Author(s):  
Gabriel Popescu
Keyword(s):  
Residual Stresses ◽  
Yield Criterion ◽  
Tangential Force ◽  
Rolling Direction ◽  
Three Dimensional ◽  
Rolling Contact ◽  
Material Behavior ◽  
Hertzian Contact ◽  
Plastic Behavior ◽  
Elastic Plastic

An analytical three-dimensional elastic-plastic over-rolling solution is used to evaluate the plastic strains and residual stresses. Central to this plastic contact formulation is the incremental approach to deal with non-linear material behavior. The Prandtl-Reuss constitutive equations in conjunction with Huber-Mises-Hencky yield criterion and Ramberg-Osgood strain-hardening relationships are applied to describe the plastic behavior of common hardened bearing steel. The model was extended to include the tangential force in the rolling direction, assumed to be proportional to the hertzian contact pressure. Comparisons of three-dimensional pure rolling and rolling/sliding contact results were provided to elucidate the differences in residual stresses and residual profiles in case of kinematic and work-hardening materials.

Analysis of Residual Stresses in the Transition Zone of Tube-to-Tubesheet Joints

2019 ◽  
Vol 141 (4) ◽  
Author(s):  
Abdel-Hakim Bouzid ◽  
Mohammad Pourreza
Keyword(s):  
Residual Stresses ◽  
Transition Zone ◽  
Analytical Model ◽  
Plastic Material ◽  
Plastic Region ◽  
Material Behavior ◽  
Maximum Expansion ◽  
Perfectly Plastic ◽  
Major Interest ◽  
Comparison Of The Results

The rigorous stress analysis of tube-to-tubesheet joints requires a particular attention to the transition zone of the expanded tube because of its impact on joint integrity. This zone is the weakest part of the joint due to the presence of high tensile residual stresses produced during the expansion process, which coupled to in-service loadings and harsh corrosive fluids results in joint failure. In fact, it is often subjected to stress corrosion cracking caused by intergranular attack leading to plant shutdown. Therefore, the evaluation of the residual stresses in this zone is of major interest during the design phase and its accurate assessment is necessary to achieve a reliable joint in service. In this study, an analytical model to evaluate the residual axial and hoop stresses in the transition zone of hydraulically expanded tubes based on an elastic perfectly plastic material behavior has been developed. The model is capable of predicting the stress state when maximum expansion pressure is applied and after its release. Three main regions are identified in the transition zone: the fully plastic region, the partially plastic region, and the elastic region. Therefore, various theories have been applied to analyze the stresses and deformations neglecting the elastoplastic region because of simplicity. The validation of analytical model is conducted by comparison of the results with those of 3D finite element models of two typical joints of different geometries and mechanical properties. The effect strain hardening and reverse yielding of the expansion zone are also investigated.

Loading and Unloading of Thick-Walled Cylindrical Pressure Vessels of Strain-Hardening Material

1994 ◽  
Vol 116 (2) ◽  
pp. 105-109 ◽  
Author(s):  
A. Loghman ◽  
M. A. Wahab
Keyword(s):  
Residual Stresses ◽  
Strain Hardening ◽  
Yield Criterion ◽  
Strain Curve ◽  
Pressure Vessels ◽  
Critical Conditions ◽  
Hardening Material ◽  
Wide Range ◽  
Reverse Yielding ◽  
Von Mises

A thick-walled closed-end cylinder of isotropic, homogeneous and strain-hardening material is considered in this study. Loading is assumed to consist of a temperature gradient as well as an internal pressure. Unloading is completely elastic without considering a Bauschinger effect. A generalized plane strain case in which the material obeys Von Mises yield criterion is studied. Using the yield criterion, critical conditions for a wide range of loading combinations and thickness ratios are investigated. After the critical condition is established, load is increased beyond the critical values and calculations are made for plastic stresses and strains and progress of plastic zone using an incremental theory of plasticity. Residual stresses are obtained as the cylinder is unloaded from a 25 and 50-percent overstrained condition. Reverse yielding is not considered while the residual stresses at the onset of reverse yielding are calculated. Loading function is assumed to follow the stress-strain curve of SUS 304 at a constant temperature of 400°C, which is selected from the experimental work of earlier researchers.

Laser shock processing with two different laser sources on 2050‐T8 aluminum alloy

2011 ◽  
Vol 2 (1) ◽  
pp. 87-100 ◽  
Author(s):  
Patrice Peyre ◽  
Neila Hfaiedh ◽  
Hongbin Song ◽  
Vincent Ji ◽  
Vincent Vignal ◽  
...  
Keyword(s):  
Aluminum Alloy ◽  
Residual Stresses ◽  
Work Hardening ◽  
Material Behavior ◽  
Al Alloy ◽  
Numerical Comparison ◽  
Laser Shock ◽  
Content Type ◽  
Surface Deformations ◽  
Laser Sources

PurposeThe purpose of this paper is to conduct a comparative study of the surface modifications induced by two different lasers on a 2050‐T8 aluminum alloy, with a specific consideration of residual stress and work‐hardening levels.Design/methodology/approachTwo lasers have been used for Laser shock peening (LSP) treatment in water‐confined regime: a Continuum Powerlite Plus laser, operating at 0.532 mm with 9 ns laser pulses, and near 1.5mm spot diameters; a new generation Gaia‐R Thales laser delivering 10 J‐10 ns impacts, with 4‐6mm homogeneous laser spots at 1.06 mm. Surface deformation, work‐hardening levels and residual stresses were analyzed for both LSP conditions. Residual stresses were compared with numerical simulations using a 3D finite element (FE) model, starting with the validation of surface deformations induced by a single laser impact.FindingsSimilar surface deformations and work‐hardening levels, but relatively lower residual stresses were obtained with the new large 4‐6 mm impact configuration. This was attributed to a reduced number of local cyclic loadings (2) compared with the small impact configuration (4). Additionally, more anisotropic stresses were obtained with small impacts. FE simulations using Johnson‐Cook's material' behavior were shown to simulate accurately surface deformations, but to overestimate maximum stress levels.Research limitations/implicationsThis work should provide LSP workers a better understanding of the possible benefits from the different LSP configurations currently co‐existing: using small (<2 mm) impacts at high‐cadency rates or large ones (>4‐5 mm). Moreover, experimental results and simulated data had never been presented on 2050‐T8 Al alloy.Originality/valueAn experimental (and numerical) comparison using two distinct laser sources for LSP, has never been presented before. This preliminary work should help LSP workers to choose adequate sources.

Theoretical Analysis of Hydraulically Expanded Tube-to-Tubesheet Joints With Linear Strain Hardening Material Behavior

2009 ◽  
Vol 131 (6) ◽  
Author(s):  
Nor Eddine Laghzale ◽  
Abdel-Hakim Bouzid
Keyword(s):  
Strain Hardening ◽  
Material Behavior ◽  
Plastic Behavior ◽  
Element Analysis ◽  
Hardening Material ◽  
Perfectly Plastic ◽  
Expansion Pressure ◽  
Proper Material ◽  
Elastic Perfectly Plastic ◽  
Design Calculations

The mechanism of failure of tube-to-tubesheet joints is related to the level of stresses produced in the tube expansion and transition zones during the expansion process. Maintaining a lower bound limit of the initial residual contact pressure over the lifetime of the expanded joint is a key solution to a leak free joint. An accurate model that estimates these stresses can be a useful tool to the design engineer to select the proper material geometry combination in conjunction with the required expansion pressure. Most existing design calculations are based on an elastic perfectly plastic behavior of the expansion joint materials. The proposed model is based on a strain hardening with a bilinear material behavior of the tube and the tubesheet. The interaction of these two components is simulated during the whole process of the application of the expansion pressure. The effects of the gap and the material strain hardening are to be emphasized. The model results are validated and confronted against the more accurate numerical finite element analysis models. Additional comparisons have been made to existing methods.

An Analytical Solution of Hydraulically Expanded Tube-to-Tubesheet Joints With Linear Strain Hardening Material Behaviour

2008 ◽  
Author(s):  
Nor Eddine Laghzale ◽  
Abdel-Hakim Bouzid
Keyword(s):  
Strain Hardening ◽  
Material Behavior ◽  
Plastic Behavior ◽  
Hardening Material ◽  
Whole Process ◽  
Perfectly Plastic ◽  
Expansion Pressure ◽  
Proper Material ◽  
Elastic Perfectly Plastic ◽  
Design Calculations

The mechanism of failure of tube-to-tubesheet joints is related to the level of stresses produced in the tube expansion and transition zones during the expansion process. Maintaining a lower bound limit of the initial residual contact pressure over the lifetime of the expanded joint is a key solution to a leak free joint. An accurate model that estimates these stresses can be a useful tool to the design engineer to select the proper material geometry combination in conjunction with the required expansion pressure. Most existing design calculations are based on an elastic perfectly plastic behavior of the expansion joint materials. The proposed model is based on a strain hardening with a bilinear material behavior of the tube and the tubesheet. The interaction of these two components is simulated during the whole process of the application of the expansion pressure. The effects of the gap and the material strain hardening will be emphasized. The model results are validated and confronted against the more accurate numerical FEA models. Additional comparisons have been made to existing methods.

Analytical Evaluation of Residual Stresses in the Transition Zone of Expanded Tube-to-Tubesheet Joints

2018 ◽  
Author(s):  
Abdel-Hakim Bouzid ◽  
Mohammad Pourreza
Keyword(s):  
Residual Stresses ◽  
Transition Zone ◽  
Analytical Model ◽  
Plastic Material ◽  
Plastic Region ◽  
Material Behavior ◽  
Expansion Process ◽  
Maximum Expansion ◽  
Perfectly Plastic ◽  
Comparison Of The Results

The rigorous analysis of tube-to-tubesheet joints requires a particular attention to the transition zone of the expanded tube because of its impact on joint integrity. This transition zone is the weakest part of the joint due to the presence of high tensile residual stresses produced during the expansion process which coupled to other in-service loadings and harsh corrosive fluids results in joint failure. In fact, this zone is often subjected to stress corrosion cracking caused by intergranular attack leading to plant shutdown. Therefore, the evaluation of the residual stresses in the transition zone is of major concern during the design phase and its accurate assessment is necessary in order to achieve a reliable joint in service. In this study, a new analytical model to evaluate the residual axial and hoop stresses in the transition zone of hydraulically expanded tubes based on an elastic perfectly plastic material behavior has been developed. The model is capable of predicting the stress state under the maximum expansion pressure and after the expansion process has been completed. Three main regions are identified in the transition zone: the fully plastic region, the partially plastic region and the elastic region. Therefore, various theories have been applied to analyze the stresses and deformations neglecting the partial plastic region because of simplicity. The validation of analytical model is conducted by comparison of the results with the ones of 3D finite element models representing typical geometry and mechanical properties. The effect of reverse yielding of the expansion zone is also investigated.

Effects of Strain Hardening and Initial Yield Strength on Machining-Induced Residual Stresses

2007 ◽  
Vol 129 (4) ◽  
pp. 567-579 ◽  
Author(s):  
Mohamed N.A. Nasr ◽  
E.-G. Ng ◽  
M. A. Elbestawi
Keyword(s):  
Finite Element ◽  
Yield Strength ◽  
Residual Stresses ◽  
Strain Hardening ◽  
Plastic Behavior ◽  
Workpiece Material ◽  
Initial Yield ◽  
Wide Range ◽  
Steel Aisi ◽  
Aisi H13 Tool Steel

Finite element analysis was used in the current study to examine the effects of strain hardening and initial yield strength of workpiece material on machining-induced residual stresses (RS). An arbitrary–Lagrangian–Eulerian finite element model was built to simulate orthogonal dry cutting with continuous chip formation, then a pure Lagrangian analysis was used to predict the induced RS. The current work was validated by comparing the predicted RS profiles in four workpiece materials to their corresponding experimental profiles obtained under similar cutting conditions. These materials were AISI H13 tool steel, AISI 316L stainless steel, AISI 52100 hardened steel, and AISI 4340 steel. The Johnson–Cook (J–C) constitutive equation was used to model the plastic behavior of the workpiece material. Different values were assigned to the J-C parameters representing the studied properties. Three values were assigned to each of the initial yield strength (A) and strain hardening coefficient (B), and two values were assigned to the strain hardening exponent (n). Therefore, the full test matrix had 18 different materials, covering a wide range of commercial steels. The yield strength and strain hardening properties had opposite effects on RS, where higher A and lower B or n decreased the tendency for surface tensile RS. Because of the opposite effects of A and (B and n), maximum surface tensile RS was induced in the material with minimum A and maximum B and n values. A physical explanation was provided for the effects of A, B, and n on cutting temperatures, strains, and stresses, which was subsequently used to explain their effects on RS. Finally, the current results were used to predict the type of surface RS in different workpiece materials based on their A, B, and n values.

Effect of diamond burnishing parameters on the state of the processed surface layer of billets made of high-strength "30ХГСН2А-ВД" steel

2020 ◽  
pp. 82-86
Author(s):  
A.N. Shvetsov ◽  
D.L. Skuratov
Keyword(s):  
Surface Layer ◽  
Residual Stresses ◽  
Strain Hardening ◽  
Processing Speed ◽  
Synthetic Diamond ◽  
High Strength ◽  
The State ◽  
Diamond Burnishing

The influence of the burnishing force, tool radius, processing speed and feed on the distribution of circumferential and axial residual strses, microhardness and the depth of strain hardening in the surface layer when pr ssing of "30ХГСН2А-ВД" steel with synthetic diamond "ACB-1" is considered. Empirical dependencies determining these parameters are given. Keywords diamond burnishing, strain hardening depth, circumferential residual stresses, axial residual stresses, microhardness. [email protected], [email protected]

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