Elastic-plastic Stress Analysis Research Articles

Three-dimensional elastic–plastic stress analysis of wheel–rail cyclic rolling contact using finite element method

The rail is subjected to cyclic stress and plastic deformation, excessive accumulation of which can promote rail degradation. A finite element (FE) model of three-dimensional (3D) cyclic rolling contact (CRC) with the implementation of an improved cyclic plasticity constitutive material model is developed to analyze the 3D elastic–plastic stress. Comparisons of the FE simulation results of 2D repeated moving pressure (RMP), 3D RMP, and 3D CRC models are conducted to elucidate the differences. The evolution and distribution patterns of the elastic–plastic mechanical behavior of wheel–rail contact with the number of cycles are also investigated. The FE results show that the 2D RMP model is conservative in predictions, and the results derived from the 3D RMP and 3D CRC models are comparable, while opposite results are available for some essential components. The 3D CRC model is a necessary choice especially for fatigue life prediction study. Due to the partial slip and cyclic rolling, the stresses and strains near the rail surface layer are significant and continuously accumulate. The residual equivalent plastic strain and the ratchetting strain increase with the increase of the tangential traction and the axle load, which will accelerate rail damage.

Investigation on effect of neutron irradiation on welding residual stresses in core shroud of pressurized water reactor

This paper presents the results of investigating the change in welding residual stresses of the core shroud, which is one of subcomponents in reactor vessel internals, performing finite element analysis. First, the welding residual stresses of the core shroud were calculated by applying the heat conduction based lumped pass technique and finite element elastic-plastic stress analysis. Second, the temperature distribution of the core shroud during the normal operation was calculated by performing finite element temperature analysis considering gamma heating. Third, through the finite element viscoelastic-plastic stress analysis using the calculated temperature distribution and setting the calculated residual stresses as the initial stress state, the variation of the welding residual stresses was derived according to repeating the normal operation. In the viscoelastic-plastic stress analysis, the effects of neutron irradiation on mechanical properties during the cyclic normal operations were considered by using the previously developed user subroutines for the irradiation agings such as irradiation hardening/embrittlement, irradiation-induced creep, and void swelling. Finally, the effect of neutron irradiation on the welding residual stresses was analysed for each irradiation aging. As a result, it is found that as the normal operation is repeated, the welding residual stresses decrease and show insignificant magnitudes after the 10th refueling cycle. In addition, the irradiation-induced creep/void swelling has significant mitigation effect on the residual stresses whereas the irradiation hardening/embrittlement has no effect on those.

Elastic-Plastic Stress Analysis of Steel Fiber Reinforced Composite Plates Under Axial Load

Composite materials, obtained by combining two or more materials; It is defined as a new type of material with high strength, high rigidity and lightness. Composite plates are structural elements that are used in machines and structures under different loads, consist of at least two types of materials and can be produced in various constructions. In this study, elastic-plastic stress analysis of polymer matrix continuous fiber reinforced composite plate under axial load was solved with Airy Stress Function proposed as a 5th order non-uniform polynomial to solve the elasticity problem. Polyethylene matrix composite reinforced with steel fibers was taken as the plate material and the material was accepted as ideal elastic-plastic. Tsai-Hill Yield Criterion was used for the plastic solution. According to the results of the analysis, as the fiber angle increased in the composite plate, the plastic stress limit decreased, the increase in the fiber angle decreased the plastic stress limit, and the decrease in the plastic stress limit caused the residual stresses to increase.

Elastic-Plastic stress analysis in the pole fixation of an electric generator

Hydroelectric power plants are currently the most efficient large scale electric energy producers. Therefore, there are many opportunities for construction of new hydroelectric power plants throughout the world, which makes the study and design of improved electric power generators a priority. The core equipment of an electric power plant is the electric power generator, which can deliver hundreds of MW of electric power, while withstanding high levels of mechanical and thermal stresses under high rotation speeds. Therefore, the design of the electric generator, especially the rotor component, must ensure structural integrity, safety of operation, and an extended lifetime of 30–40 years. To achieve the safe and reliable operation of the generator, one of its components that must be designed after a detailed and comprehensive stress analysis is the rotor pole fixation. When the hydroelectric generator operates under high stress conditions, due to frequent start-stop cycles, structural elements such as the rotor poles fixations could operate beyond their endurance limit and could be exposed to the risk of failure. This paper presents an elastic–plastic finite element analysis of the mechanical response of the pole fixation, part of an assembly with three hammerheads of a hydroelectric generator rotor, under various loading conditions. The elastic–plastic stress analysis leads to a safe design at much higher operational loads compared to a linear elastic analysis and may be further used to study the effect of crack appearance in the plastic zone, preventing a catastrophic failure of the generator.

Calculation of frozen wall thickness considering the non-uniform distribution of the strength properties

The static design of artificial ground freezing during the construction of mine shafts includes the strength analysis of the frozen wall (FW). The existing formulas for FW strength calculation do not take into account the non-uniform distribution of strength properties in the volume of frozen soils. The non-uniform distribution of the properties is caused, first of all, by the non-uniform temperature distribution inside the FW. This article shows the significance of this factor in analyzing the FW thickness. The elastic-plastic stress analysis was carried out under the assumption of an infinite height of the thick-walled cylinder consisting of frozen soil. An integral function was obtained to calculate the FW thickness by strength given the arbitrary radial non-uniformity of the cohesion in the frozen soil volume. Also, an approximate formula is proposed for calculating the FW thickness in the case of a piecewise linear cohesion function of the radial coordinate.

A modification on 3S criterion and simplified elastic-plastic ratcheting analysis in ASME VIII-2

Ratcheting is a common and important failure mode in pressure vessels. ASME VIII-2 2019 edition provides two kinds of ratcheting assessment methods——the elastic stress ratcheting assessment (paragraph 5.5.6) applied to the design by elastic stress analysis and the elastic-plastic ratcheting assessment (paragraph 5.5.7) applied to the design by elastic-plastic stress analysis. This paper focuses on the elastic stress ratcheting assessment, which includes again two methods——the elastic ratcheting analysis (paragraph 5.5.6.1), i.e. the 3S criterion, and the thermal stress ratcheting assessment (paragraph 5.5.6.3). This article reviews the development history of 3S criterion and discusses its applicable scope. The study found that the 3S criterion is not a complete elastic ratcheting assessment criterion, when the primary membrane stress range exceeds two-thirds of the cyclic yield stress, i.e. (2/3)Sy, the ratcheting assessment based on 3S criterion is unsafe for some situations. When the general primary membrane stress Pm and the local primary membrane stress PL, which allowable limit exceeds (2/3)Sy, are applied simultaneously, there is still the possibility of ratcheting failure in the structure even if the 3S criterion is met. As an extension of the 3S criterion, a complete and safe criterion on three-dimensional elastic ratcheting assessment is proposed in this paper. In order to avoid the inconvenience of partition assessment, a simplified thermal stress ratcheting assessment method based on double checking surfaces is proposed. It is a simple and conservative assessment method. Finally, elastic ratcheting analysis, thermal stress ratcheting assessment and simplified elastic-plastic analysis in ASME VIII-2 are integrated, a universal elastic stress ratcheting assessment is proposed.

A method for calculating low-temperature stress-strain curves of austenitic stainless steels

Low-temperature stress-strain curves of austenitic stainless steels are essential for cryogenic pressure vessels’ elastic-plastic stress analysis. But, the method that how to get the low-temperature stress-strain curves is still missing in the current pressure vessel standards. To resolve this problem, related work is carried out based on 351 sets of tensile data of 15 austenitic stainless steels. Similar characteristics of low-temperature stress-strain curves in the phase composition, martensitic transformation and curve shape are found. Thus, the same low-temperature material model can be adopted for different austenitic stainless steels. Furthermore, the empirical relations between low-temperature material model parameters and mechanical properties (Rp0.2, Rm and A) are founded. Finally, a calculating method for low-temperature stress-stain curves of austenitic stainless steels is proposed based on the empirical relations and low-temperature material model. Compared with experimental curves, the calculated stress-strain curves show similar shape characteristics and is also of uniqueness and conservation. This is of important significance to the light-weight design of cryogenic pressure vessels.

Elasto-Plastic Contact Stress Analysis of Hardened Elements under Repeated Contact Loading

An elastic-plastic contact stress analysis is presented to study cyclic plastic deformation of surface hardened rolling elements under repeated contacts. The rolling contact is simulated by a Hertz contact loading moving across an elastic-plastic half-space. An exponential model with hardness varying with depth is employed for the surface hardened components, and the Chaboche nonlinear hardening rule is used to model cyclic plastic behavior of contact elements. Numerical results show that the hardened layer can effectively reduce the plastic deformation near contact surface. The contact elements with sufficient surface hardness may reach elastic shakedown state under repeatedly rolling contact. As the hardened layer reaches a certain depth, e.g. two times of half contact length, however, the effects of case depth on plastic strain and residual stress become negligible after hundred contact cycles.

A unified analytical solution for elastic–plastic stress analysis of a cylindrical cavity in Mohr–Coulomb materials under biaxial in situ stresses

This paper presents a unified analytical solution for elastoplastic stress analysis around a cylindrical cavity under biaxial in situ stresses during both loading and unloading. The two-dimensional solution is obtained by assuming that the connected plastic zone is statically determinate and using the complex variable theory in the elastic analysis. It is shown that the biaxial state of initial stresses applies significant influences on the stress distribution around the inner cavity. Under biaxial far-field stresses, the asymptotic conformal mapping function predicts that the outer boundary of the statically determinate plastic zone is in oval shape in Mohr–Coulomb materials. The major axis of the elastic–plastic interface lies in the direction of the greatest far-field compression pressure during loading, whereas it is along the perpendicular direction during unloading. The loading and unloading solutions are validated by comparing with the results of numerical simulation and other analytical solutions. In the assumed states, the new solution provides an accurate analytical method to capture the biaxial in situ stress effect in the prediction of the plastic failure zone and calculations of the static stress field and the elastic displacement field around a cylindrical cavity within an infinite medium.

Inverse analysis of residual stress in orthogonal cutting

An inverse analysis is proposed to obtain the orthogonal cutting process parameters for desirable residual stresses for the first time. The residual stress has substantial influence on fatigue life, corrosion resistance, part distortion, and crack propagation. Hence, having a desired residual stress can help to control the abovementioned concerns. The proposed model uses an analytical model to predict the residual stress directly. The residual stress is induced by severe thermo-mechanical loading. The heat generated during the machining process is obtained using an imaginary heat source model. An elastic-plastic stress analysis approach is used to predict the residual stress by incorporating a hybrid function as a limiting case for very large and very small plastic strain range. Next, an iterative gradient search is used to adaptively approach the specific residual stress by the optimization of the process parameters. The inverse analysis identifies the cutting process parameters such as depth of cut and cutting speed and predicts the optimal solution for the residual stress. Experimental measurements validated the effectiveness of the proposed model since the maximum calculated error is less than 4.5% between the predicted residual stress and experimental measurements.

Assessment of DBA-L Pressure Vessel Design Method by a Cylindrical Vessel with Hemispherical Ends

Stress categorization is an essential procedure in Design by Analysis (DBA) pressure vessel design methods based on elastic analysis in ASME and EN code. It was difficult to implement especially around structural discontinuities. A new elastic analysis, DBA-L, was proposed recently to avoid stress categorization. A model of the cylindrical pressure vessel with spherical end is used to check the validity of this method by comparing with other design methods based on stress categorization procedures and elastic-plastic stress analysis from ASME and EN code. The results indicate that the DBA-L is an economic and explicit method, and can be used an alternative method to stress categorization.

Failure Modes of American Petroleum Institute 12F Tanks With a Rectangular Cleanout and Stepped Shell Design

The design and fabrication of shop-welded and prefabricated relatively small tanks, when compared to field-welded tanks, used in the upstream segment of the oil and gas industry is governed by the American Petroleum Institute specification 12F (API 12F). This study explores the changing designs of API 12F tanks to include a new rectangular cleanout design with reinforcement as shell extension internally of cleanout frame and a stepped shell design. This study also investigated the introduction of two additional tank sizes in addition to existing eleven tank sizes in the current 12th edition of API 12F. The adequacy of the new design changes and proposed tank designs were verified by elastic stress analysis with nonlinear geometry, elastic–plastic stress analysis with nonlinear geometry, and elastic buckling analysis to verify their ability to operate at a design internal pressure of 16 oz/in2 (6.9 kPa) and maximum pressure during emergency venting of 24 oz/in2 (10.3 kPa). A vacuum pressure of 1.5 oz/in2 (0.43 kPa) was also investigated using the elastic buckling analysis. The stress levels and uplift of the tanks are reported in this report to provide insights into the behavior of proposed API 12F tanks exposed to higher internal pressure and vacuum pressure.

Failure modes of API 12D tanks with a semicircular-topped rectangular cleanout and stepped shell design

The American Petroleum Institute Specification 12D (API 12D) provides the oil and gas industry with ten tank designs with nominal capacities ranging from 500 bbl (79.5 m3) to 10,000 bbl (1590 m3). These tanks serve as a temporary product storage medium at the upstream segment of the industry, and are mass-produced to accommodate the demand. The structural performance of these ten 12D tanks is assessed in this study to verify that safe operation is maintained under various loading conditions. This study investigates the behavior and performance of the API 12D tank designs with a new rectangular cleanout with a semicircular top that is surrounded by a reinforcement pad. Various loading patterns were modeled in a finite element analysis approach including internal pressure, vacuum, hydrostatic pressure, and wind load. An elastic stress analysis, an elastic-plastic stress analysis, and an elastic buckling analysis were used in this work to compare the behavior of the tank designs against the failure criteria specified for each type of analyses. The stress level, plastic strain, buckling load, and tank uplift are reported for each of the ten API 12D tank designs and possible shell thickness variations are provided as insight into the performance expected with the new cleanout detail.

Electrochemical Corrosion Finite Element Analysis and Burst Pressure Prediction of Externally Corroded Underground Gas Transmission Pipelines

An integrative numerical simulation approach for pipeline integrity analysis is presented in this work, combining a corrosion model, which is the main focus of this paper, with a complementary structural nonlinear stress analysis, using the finite element method (FEM). Potential distributions in the trapped water existing beneath pipeline coating disbondments are modeled in conjunction with reaction kinetics on the corroding exposed steel surface using a moving boundary mesh. Temperature dependencies (25 °C and 50 °C) of reaction kinetics do not greatly affect final corrosion defect geometries after 3-yr simulation periods. Conversely, cathodic protection (CP) levels and pH dependencies within the near-neutral pH range (6.7–8.5) strongly govern depth profiles caused by corrosion, reaching a maximum of ∼3 mm into the pipeline wall. A 0.25 V amplification of CP potential combined with a 0.5 mm widening in disbondment opening size reduces defect penetration by almost 30%. Resulting corrosion defect geometries are used for stress examinations and burst pressure evaluations. Furthermore, nonlinear elastic–plastic stress analysis is carried out using shell elements in order to predict the burst pressure of corroded pipes. Corrosion is modeled by reducing the stiffness of a damaged element that has the dimensions of the defect. The predicted burst pressures are in good agreement with those obtained using an experimental-based formula.

A new pressure vessel design by analysis method avoiding stress categorization

Stress categorization in the design by analysis (DBA) procedure for protection against plastic collapse in pressure vessel has been problematic during application. For example, it is difficult to determine the proportion of primary and secondary stress at the gross structural discontinuities. This paper proposes a new method to avoid the stress categorization by extending the current elastic stress analysis method in ASME Code based on lower bound limit load theory. The proposed method assumes a stress distribution along the stress classification line (SCL) in the form of limit stress state for a beam under membrane and bending load, rather than a linear stress distribution. The effectiveness of proposed method is verified by comparing with the elastic stress analysis, Limit-Load Analysis, Elastic-Plastic stress Analysis of the ASME Code for axisymmetric pressure vessels. The results concluded that the new method is effective easy to use.

Two-parameter J-A concept in connection with crack-tip constraint

The paper presents theoretical and numerical aspects of the two-parameter J-A approach in elastic-plastic fracture mechanics in connection with crack-tip constraint. This approach is based on the three-term asymptotic expansion for the stress field near the tip of mode I crack in an elastic-plastic solid. It is shown that the parameter A can be introduced in fracture criterion as a constraint parameter. The constraint parameter A and the J-integral for various configurations of standard specimens and the hardening exponent is computed by means of three-dimensional elastic-plastic stress analyses employing finite element method. The magnitude of the constraint parameter A decreases (higher constraint) with the increase of relative specimen thickness. The unified JC-A master curve is constructed for different geometry and thickness of specimens. The two-parameter J-A fracture criterion allows estimating whether elastic approach is conservative or non-conservative. Relationship between the crack-tip constraint parameters A, A2, Q and S¯p of elastic-plastic fracture mechanics is investigated.

Elastoplastic stress analysis of tunnel considering different principal stress directions

Based on the unified strength theory, the elastic-plastic stress analysis is carried out under the premise that the first principal stress in two cases of radial stress and circumferential stress, and the formula of the radius of the surrounding rock and the plastic zone is derived. Tunnel surrounding rock has three states which including the elastic state, the elastoplastic state that the maximum principal stress is the radial stress and the elastoplastic state that the maximum principal stress is the circumferential stress. When the elastic-plastic analysis was carried out on the tunnel, the state of the surrounding rock should be judged and the correct formula is chosen to calculate. Analysis results show that the intermediate principal stress is benefit to the rock to give full play to the strength of the potential, so as to improve the stability of surrounding rock of the tunnel and the smaller intermediate principal stress coefficient, the higher sensitivity of the surrounding rock stability to the intermediate stress. When the inside pressure is less than the second critical stress and increasing the hole pressure is beneficial to improving the stability of surrounding rock, while the hole pressure is greater than the second critical stress, the stability of surrounding rock will reduce with the increase of the hole pressure.

Effect of spray-cooling rate on the die-life of an HPDC die

The effect of spray-cooling on heat-checking revealed that a water-based release agent has a stronger effect in the crack extension stage than an oil-based release agent has. On the basis of the mode II mechanism of fracture mechanics explaining the crack initiation and propagation of heat-checking, the influence of the intensity of the cooling-spray was investigated through a casting-solidification simulation and an FEM elastic-plastic stress analysis. The surface strain analysis of the die for a flat shape part revealed that the initiated crack widens with repeated thermal expansion and contraction. The water-based release agent shows larger strain-amplitude at the die surface than the oil-based release agent shows, and thus is liable to cause heat-checking.

Development of Al/Cu Dissimilar Joint by New Friction Welding Method

Aluminum alloy / pure copper joint has been tried to produce by the conventional welding method. However, some combination of the joints could not show high joint efficiency. The reason for this is considered to the formation of the intermetallic compound and involvement of the metal flake of joint specimens. A2017 aluminum alloy/Cu joint was examined by the new friction welding technology which has the intermediate material for friction between joint specimens. Furthermore, thermal elastic-plastic stress analysis was conducted for searching the optimum welding condition. The results are as follows. (1) 60% joint efficiency larger than that in the conventional process was obtained. (2) Intermetallic compound and involvement of the metal flake are not recognized by a micro inspection such as SEM. (3) Increase of oxygen content is recognized in Al side near the interface, however, it occurred during upset stage because oxygen content does not increase in Cu side. (4) The precise position of welding interface could be determined from the change of oxygen content near interface. (5) For producing sound joint of this combination of the materials, it is important that both materials are plastically deformed by maintaining strength balance between Al and Cu near the interface.

Elastic-Plastic Thermal and Residual Stress Analysis of Adhesively Bonded Single Lap Joint

In this work, an elastic-plastic thermal and residual stress analysis were performed for adhesively bonded single lap joint. For this purpose, thermoplastic composite adherents were bonded to each other with epoxy adhesive. Thermoplastic composite material was reinforced by steel-fibres, unidirectionally. Finite element method (FEM) was preferred to obtain thermal elastic and elastic-plastic stress distributions on single lap joint. Accordingly, modelling and solution processes were achieved using ANSYS software. So as to determine effects of uniform temperature loadings on thermal and residual stresses, different values of it were loaded on the joint, uniformly. Briefly, both thermal and residual thermal stresses were calculated under uniform temperature loading which was selected from 40 °C to 80 °C. According to obtained results different thermal expansion coefficients of composite adherents and adhesive layer caused thermal and residual stresses on adhesively bonded single lap joint due to applied uniform temperature loadings. Thermal stress values for x and y-directions are very different from each other owing to orthotropic material properties of thermoplastic composite. The magnitudes of elastic analyses results are higher than elastic-plastic analysis results. Contrary to elastic analysis results, elastic-plastic analysis results were nonlinear. Thermal and residual stresses are increased by increasing uniform temperature values, so the highest values were calculated when 80 °C. The plastic yielding was firstly come into being for 50 °C loading and it is expanded related to raising thermal loadings as nonlinear.