Elastic-plastic Finite Element Analysis Research Articles

A finite crack growth energy release rate for elastic-plastic fracture

The concept of energy release rate proposed by Griffith originally used for elastic brittle material was extended for ductile material by Irwin and Orowan using the sum of the surface energy and the work of plastic dissipation as fracture resistance. This fracture resistance, however, depends on the load type and specimen geometry, which hinders its wide application. In contrast, in this paper, a finite crack growth energy release rate is proposed by assuming a finite crack growth, which is conveniently applicable to finite element analysis. The effect of the plastic dissipation on the crack growth is considered in the driving force. Elastic-plastic finite element analysis is used to apply the present energy release rate. Compared to the experiment results, it is shown that for a fixed finite crack growth, a constant critical energy release rate can well predict the stable crack growths and residual strengths of sheets with single and various collinear cracks subjected to different types of loads. The present finite crack growth energy release rate is conceptually simple, has a solid physical foundation, and would be appealing for ductile crack growth analysis.

Numerical Investigation of Residual Stress Formation Mechanisms in Flash-Butt Welded Rail

For the construction of long and continuous railway lines as well as the replacement of defected rails, rails are joined using flash-butt welding. Under various localized temperatures and thermo-mechanical stresses, a residual stress can develop in the flash-butt welded joint. The residual stress can affect the performance and reliability of the welded rail, particularly in terms of progressive structural damage caused by repeated wheel load. In the present work, the mechanisms of residual stress formation in a flash-butt welded rail and the influence of upsetting force (including its temperature range and magnitude) were investigated using the thermal elastic–plastic finite element analysis. The formation mechanisms of residual stress involved the changes in thermal expansion coefficient, strain, and elastic modulus of the welded joint with respect to temperature. The calculated cooling temperatures and residual stresses in the flash-butt welded joint were in good agreement with the measured results. Compressive residual stresses were observed around the rail head and the rail foot (i.e., approximately −648 MPa at the rail head and −495 MPa at the rail foot), while tensile residual stresses were observed at the rail web (i.e., approximately 165 MPa). It was observed that the investigated compressive upsetting force predominantly induced plastic deformation within the welded joint, resulting in minimal alteration of stress. Consequently, the investigated ranges of upsetting temperature and upsetting forces had an insignificant impact on the formation of residual stress.

Effects of angles and shapes of a corner crack on the driving force at a set-in nozzle-cylinder in a PWR pressure vessel

Corner cracks are one of the common forms of flaws in the reactor pressure vessels (RPVs) of nuclear power plants (NPPs). Accurate evaluation of the driving force of such corner cracks is essential and critical for the efficient design and integrity assessment of the RPVs. In this study, the combined effect of the depth, length and angle of a given corner crack under the service loading was analyzed using elastic–plastic finite element analysis (EPFEA). Based on the consideration of the distribution profiles of stress intensity factor (SIF) and J integral as the crack growth along corner crack front, the crack growth stability with various crack shapes and angles was analyzed. Finite element analysis (FEA) results showed that the crack growth driving force is affected by the shape and angle of the initial crack. It is also found that the sliding mode (mode II) crack or tearing mode (mode III) crack should be taken into account in the structural integrity analysis of RPVs.

Analysing the effect of defects on stress concentration and fatigue life of L-PBF AlSi10Mg alloy using finite element modelling

Additive manufacturing (AM) is a developing manufacturing technology, which provides excellent attributes compared to other manufacturing techniques. However, one of the critical challenges is the presence of defects that hinder the mechanical properties of the parts, particularly the fatigue life. Experimental understanding of fatigue is a cumbersome process. Therefore, numerical prediction based on specified conditions (such as porosity and applied load) can be an alternative to experimental analysis at the design stage of AM parts. In this study, elastic–plastic finite element analysis (FEA) is performed to obtain the stress distribution around pores, and their resultant effect on fatigue life for L-PBF (laser powder bed fusion) produced AlSi10Mg alloy samples. The stress field is calculated for both single and multiple pore models, where stress concentration is evaluated as a function of the pore’s location and its size. It is found that both pore location and size affect the stress field; however, location effects dominate over pore size. For the same remote applied stress level, the stress concentration around the pore increases with an increase in pore size, and the local maximum stress occurs near the pores that are closest to the surface. The current study also evaluates the relative effect of porosity fraction, average pore size, and location. It is found that the magnitude and sensitivity of stress concentration are hierarchically controlled by porosity location, pore size, and porosity density. A multi-scale finite element (FE) model is proposed based on inherent porosity data measured using Computed Tomography (CT) to predict overall fatigue life. The fatigue cycles are calculated using the rainflow counting algorithm in FE Safe using the stress–strain data obtained from the proposed FEA model. Using the proposed model, it is possible to generate S–N curves for any loading condition for a given porosity condition (porosity density and average pore size). The S–N curve results obtained from the FE model are compared to the experimental observations. The predicted fatigue life shows approximately 5% error with experimental results at high stress loading conditions. However, the proposed model overpredicts the fatigue life at low stress loading by almost 30%.

Reinforcement of cracked aluminum plates using polymeric composite patches embedded with prestressed SMA wires

Many studies have been performed on composite patches as reinforcement of cracked metal sheets. However, in most previous research, composite patches without prestressing have been used to repair cracks. In the present study, a novel method for repairing cracked aluminum sheets is proposed by using polymer composite patches with embedded prestressed Nitinol shape memory alloy (Ni-Ti SMA) wires. Elastic-plastic finite element analysis of an aluminum plate, with a central crack in the pure mode I and the mixed-mode I/II fracture, repaired with SMA wires reinforced composite patch (SMA-CP) was performed. The peel stress on the adhesive layer between the composite patch and the aluminum plate was calculated to evaluate the performance and efficiency of the repair. The effect of the prestress of the embedded Ni-Ti SMA wires on the efficiency of the composite patch was examined. The results show that embedding prestressed SMA wires in the composite patch reduces the stiffness ratio of the patch. Also, the value of the J-integral and the size of the plastic area compared to the patch without SMA wires were decreased.

Study on the relationship between the root welding residual stress and the root-failure fatigue strength of Plug Welded specimens

It is difficult to examine the relation between the root notch welding residual stress (WRS) and the root-failure fatigue strength because of the difficulty in the direct root WRS measurement. The root WRS can be calculated by thermal elastic-plastic finite element analysis (TEPFEA), but its accuracy has not been fully verified yet. In this study, root-failure fatigue tests, in which direct root WRS measurement can be performed, are carried out. Plug welded (PW) specimens with backing plates are used in those tests, and the root WRS in as-welded (AW) and stress-relieved (SR = PWHT) specimens are measured using X-ray diffraction (XRD) method by cutting off the backing plate. The measured WRSs are compared with those calculated by TEPFEA. It is found that the root WRSs in the PW specimens estimated by TEPFEA become much larger than those measured when creep strain is neglected. The SR specimen’s fatigue strength improvement ratio is estimated by using the mean stress effect formulas developed for toe-failure cases (IIW Fatigue Recommendations and MIL-HDBK-5D). The estimated improvement ratio shows fair agreement with that measured.

A parametric finite element study for determining burst strength of thin and thick-walled pressure vessels

To accurately predict the burst strength of both thin and thick-walled pressure vessels (PVs), a parametric study of PV burst strength was performed for a wide range of vessel geometries and materials using elastic-plastic finite element analysis (FEA). A valid FEA model was established through a detailed study of 2D versus 3D FEA models, the critical stress failure criterion versus the limit load criteria, and the thick-wall effect on the FEA simulations. The results show that the stresses and strains at the mean diameter, rather than outside diameter, determines a more accurate burst strength for both thin and thick-walled PVs. On this basis, a parametrized FEA script using the ABAQUS Python application programming interface (API) was used to create a large database of PV burst strengths for a variety of vessel geometries and materials, demonstrating that Python scripting is a powerful technique for performing parametric studies or generating large databases. From the FEA results, using the regression method, a new burst pressure model was developed as a function of the vessel geometry (D/t ratio) and material properties (UTS and n). As validated by a large number of full-scale burst test data, the proposed burst model can very accurately predict the burst strength for both thin and thick-walled PVs.

Elastic–Plastic Numerical Analysis of the Spinning Process of SA-372 Steel Used in High-Pressure Hydrogen Storage Cylinders (≥100 MPA)

Elastic-plastic numerical analysis of the spinning process of SA-372 steel is used in high-pressure hydrogen storage to analyze high-pressure hydrogen storage cylinders with high precision and excellent hydrogen embrittlement resistance. The spinning process of SA-372 steel used to form such a cylinder with a pressure of 100 MPa is investigated through elastic-plastic finite element analysis. The variations in the stress, strain, pressure, temperature, and wall thickness during the spinning processes are comprehensively examined, and the optimized processing parameters are determined based on the numerical analysis results. Finally, these optimal parameters are used to conduct actual spin-forming experiments. The numerical results are found to be in excellent agreement with the experimental results, which verifies the feasibility and effectiveness of the proposed elastic-plastic numerical analysis model for the optimization of spinning process parameters. Furthermore, the hydrogen embrittlement test based on ISO 11114-4:2005 method A proves that the cylinder shoulder has a good hydrogen embrittlement resistance.

The role of plasticity-induced crack closure in the non-propagation prediction of surface defect-initiated cracks near fatigue limit

The purpose of present work is to deepen the understanding of crack propagation, non-propagation, and fatigue limit. Quantitative prediction of fatigue crack non-propagation in constant amplitude loading is attempted through extensive 3D elastic–plastic finite element analysis of near-threshold propagation of short cracks nucleating from surface defects. Level of plasticity-induced crack closure is used to estimate the effective stress intensity factor range, which is evaluated in terms of non-propagation potential. It is shown that plasticity-induced crack closure alone is adequate in producing a local minimum in the development of effective stress intensity factor range, which gives a prerequisite to crack arrest.

A simple method to determine opening stress for the cracked plate considering thickness effect

In this paper, an approach is proposed to determine crack opening stress (COS) based on the variable quantity of maximum crack opening displacement (VMCOD) considering thickness effect. Based on the three-dimensional elastic-plastic finite element analysis of center cracked tension (CCT) specimens and single-edge cracked tension (SET) specimens, the explicit expressions of relationship between COS and VMCOD are put forward, considering the effect of specimen thickness, crack length, stress ratio, Young's modulus, yield stress and strain hardening. These expressions avoid adopting parameters around crack tip and are applicable to different specimen thicknesses. Further studies show these relationships can be applied to calculate the effective stress intensity factor range and predict crack growth rates for plates of different thicknesses, which correlate well with experimental results.

Effects of large plastic deformation and residual stress on the path independence of J-integral for cracks in ductile materials

Large plastic deformation and residual stress exist in the oil and gas transmission pipelines with mechanical damages that often contain a gouge or crack. Residual stresses can alter the mechanics behavior of the crack, and cause the standard J-integral to become path-dependent and unable to describe the crack driving force.This paper investigated the effects of large plastic deformation and residual stress on the path independence of the J-integral for a crack in ductile materials. The basic conditions required for the path independence of the standard J-integral were first reviewed, and the major factors that affect the path independence were then analyzed. This includes the theory of plasticity, finite strain formulation, and residual stresses. Then, a residual stress modified J-integral was introduced for ensuring the path independence. After that, the elastic–plastic finite element analyses were performed for a notched beam in terms of the incremental plasticity to create residual stresses and to simulate a crack at the notch root subject to three-point bending. The path independence of the standard and modified J-integrals was numerically evaluated for each of the major factors. Results showed that the modified J-integral is path-independent and able to describe the crack driving force for a crack in a residual stress field, but the standard J-integral cannot do so because of its nature of path dependence when residual stresses are present. Thus, the modified J-integral can be used as an appropriate fracture parameter to assess the pipeline integrity for line pipes containing cracks and residual stresses.

Component Tests and Numerical Investigations to Determine the Lifetime and Failure Behavior of End Stage Blades

Abstract The paper focuses on experimental and numerical fatigue assessment procedures to evaluate the influence of multi-axial stress state caused by high centrifugal forces superimposed with bending loads due to blade vibrations on the lifetime of end stage blades from steam turbines. The experimental investigations on original-sized end stage blades were carried out on a test rig specially developed for high forces and multicomponent force application. This was based on detailed numerical simulations by the MPA University of Stuttgart. During the fractographic postexaminations of the tested blades using magnetic particle inspection, light and scanning electron microscopes, two competing damage mechanisms were identified that occurred at different locations. Numerical investigations by means of elastic–plastic finite element analyses were carried out to estimate the local stress conditions acting in the blade root. The local stresses and strains were postprocessed using the critical plane approach and advanced multi-axial fatigue damage parameters. Due to the high stress gradients at the edge of contact, over-conservative predictions may result if their effects are not taken into account. Based on the critical plane method in conjunction with fatigue damage parameters, an approach taking the stress gradient into consideration was developed to predict the fatigue life of the end stage blades. The approach is verified by the component tests on original-sized blades.

Study on thermal deformation of hybrid printed circuit heat exchanger for advanced nuclear reactor

The intermediate heat exchanger (IHX) is one of the key components in advanced nuclear reactor power generation system. Printed circuit heat exchanger (PCHE) with mini-channels is a good candidate for the IHX. But the whole PCHE with tens of thousands of mini-channels is hard to be modeled and calculated at high temperature. Thus, the homogenization method, which can calculate the thermal deformation of the whole hybrid mini-channel PCHE, is conducted in this study and both the elastic and elastic-plastic finite element analysis methods are used. Here, the performance of the PCHE is assumed to be isotropic in the simulation. The results show that the macroscopic thermal deformation of the whole PCHE follows a gradually downward trend from hot side to cold side, while obvious thermal stress concentration is observed around the junctions between the PCHE core and cover plate. The stress and strain calculated by elastic and elastic-plastic methods under different constraints show quite different patterns. For the thermal deformation analysis of PCHE under weak constraint or small temperature difference conditions, the stress and strain results by elastic analysis and elastic-plastic analysis are similar so that the elastic analysis can be used. Under the strong condition, the stress of PCHE calculated by elastic analysis is much higher than that of elastic-plastic analysis, while the strain is lower than that of elastic-plastic analysis. The relative deviations of stress are 100.883% and 120.786% along path 1 and path 2 respectively. And the relative deviations of strain are 6.987% and 10.139% along path 1 and path 2 respectively. The elastic-plastic analysis should be used instead of the elastic analysis.

Effects of yield point and plastic anisotropy on results of elastic–plastic finite element analysis of tension leveling

Tension leveling is an important industrial process to eliminate the flatness defects and residual stresses of metal strips to provide high-quality sheet metals for subsequent sheet metal forming. The finite element (FE) method can be applied to elucidate the effects of process parameters on the quality of sheets after tension leveling for various materials. In our previous investigation, an accurate FE model has been established for the elastic–plastic FE analysis of tension leveling. In this study, we further studied the effects of the yield point and plastic anisotropy on tension leveling using the FE model established in our previous investigation. Aiming at improving the accuracy of simulation, a modified constitutive model was developed to describe the anisotropic hardening of materials under cyclic loading. The modified constitutive model was implemented into Abaqus/Standard as a user-defined material subroutine to simulate the development of the anisotropy in materials during tension leveling. The modified model was also applied to the FE analysis of sheet metal forming processes to demonstrate its simulation capability and accuracy.

Elastic-Plastic Finite Element New Method for Lower Bound Shakedown Analysis

Shakedown analysis methods have been well developed to determine the shakedown limit load of structures under various repeated loading situations. However, to take the limited kinematic hardening, geometric effect, and deformation into account, further research is required. A new numerical method is proposed for the lower bound shakedown analysis that applies the extended static shakedown theorem for limited kinematic hardening. The new method determines the shakedown limit load with two kinds of elastic-plastic finite element (FE) analyses: (1) the elastic-plastic loading and unloading analysis is carried out using the hardening model with the actual material parameters and (2) the elastic-perfectly plastic model with ultimate stress as the yield stress is used for the limit analysis. An incremental FE technique for finite strain plasticity is utilized to take the geometric effect into account. Furthermore, the deformation of the structure is monitored by checking the calculated deformation parameters. The method is applied to a square plate with a small central hole subjected to cyclic tensile load. The corresponding physical shakedown experiment of the above square plate was conducted for verification. The numerical result shows a good agreement with the experimental result. The new method provides a valid method for the structural lower bound shakedown analysis taking into account limited kinematic hardening, geometric effect, and deformation.

Measurement and simulation of residual stresses in laser welded CFRP/steel lap joints

In light of the demand for reducing the emission of climate-damaging gases such as CO2, it is very important to apply lightweight materials in the aerospace and automotive industries. In the past years, hybrid structures made of carbon fiber reinforced plastics (CFRP) and metals received high attention from numerous industries. Laser welding is an advanced approach for bonding dissimilar materials. However, in the welding process, residual stresses are induced in the joined part, which influence the mechanical performance of the bonded components. In the present work, residual stresses in laser welded CFRP and steel joints are experimentally determined using the hole drilling method (HDM) and numerically analyzed by thermal elastic–plastic finite element analysis. The non-uniform residual stress distribution through the thickness direction of the CRRP and steel plates can be successfully measured when the anisotropic material properties in CFRP are considered. Moreover, a numerical simulation was carried out for analyzing the residual stresses in the laser welded CFRP/steel joints, particularly their distribution characteristics at the CFRP/Steel interface. Specific discussions focus on the residual stress formation mechanism and the effect of laser welding process parameters on the residual stresses through experimental tools and numerical simulations.

Effect of printing speed on tensile and fracture behavior of ABS specimens produced by fused deposition modeling

The current paper deals with the influence of printing speed on the tensile and fracture strength of Acrylonitrile Butadiene Styrene (ABS) specimens made by Fused Deposition Modeling (FDM) technique. Four different printing speeds of 10, 30, 50, and 70 mm/s are used to fabricate dog-bone and Semi-Circular Bending (SCB) specimens for examining the mechanical and fracture performance of FDM-ABS parts, respectively. Due to the plastic deformation in the crack tip zone of SCB specimens prior to fracture initiation, the critical value of J-integral is chosen as the fracture characterizing parameter. Therefore, elastic–plastic finite element analyses are performed to calculate the critical values of J-integral (Jc). According to the experimental results, the fabricated specimens with a printing speed of 70 mm/s shows the best performance with the maximum elongation and fracture resistance compared to the other printed specimens with different nozzle speeds. For exploring the failure mechanisms in the tensile specimens Scanning Electron Microscopy (SEM) is utilized and various failure mechanisms have been presented and discussed. These observations are then linked to the tensile and fracture properties of the studied specimens.

Study on welding crack sensitivity assessment method based on thermal elastic plastic finite element analysis

This study presents a new welding crack sensitivity assessment method with the equivalent plastic strain increment as an indicator, and the reliability is verified by comparing the computed results and experimental results of bead-on-plate joint under different welding conditions. Then the proposed method is applied to assess the welding crack sensitivity of multi-pass joints in the bridge rehabilitation engineering. The results show that the equivalent plastic strain increment increases with increasing heat input and constraint degree, and decreases with increasing preheat temperature. The equivalent plastic strain increment can be used as an indicator for assessing welding crack sensitivity assessment of joints. With regard to multi-pass welded joints, the welding crack sensitivity decreases with the increase of number of weld passes in terms of equivalent plastic strain increment. The welding crack sensitivity assessment method proposed in this study is reliable and can provide a practical tool for assessing the performance of welded joints.

Ensemble Smoother with Multiple Data Assimilationによる弾塑性有限要素解析のパラメータ推定

Data assimilation is a technique for estimating uncertain parameters and states in a simulation by integrating observed data into a numerical simulation. In this study, the applicability of the data assimilation algorithm, Ensemble Smoother with Data Assimilation (ES-MDA), to parameter estimation in elastoplastic finite element analysis was verified through twin experiments using pseudo-observational data. The results confirm the applicability of ES-MDA to parameter estimation in elastic-plastic finite element analysis.

On the evaluation of overload effects on the fatigue strength of metallic materials

In this paper, experimental and numerical studies are performed to quantify the influence of overloads on the fatigue behaviour of the quenched and tempered steel 42CrMoS4 and the wrought aluminium alloy EN AW-6082 T6. The main objective is to incorporate the influence of overloads in the fatigue assessment. Three series of fatigue tests per material were performed, each under load control conditions, at R ═—1:i) constant amplitude loading (CAL) tests with no overloads; ii) CAL tests after five overload cycles of the magnitude OL 1; iii) CAL tests after five overload cycles of the magnitude OL 2. The respective overload levels are selected to achieve 75 % of the static strength of the test samples either estimated according to the FKM Guideline (2020) for OL 1 or determined directly by specimen testing for OL 2. During the overload cycles, the local notch strains were monitored by means of the digital image correlation (DIC) technique. X-ray diffraction was applied to quantify the residual stresses in the specimens due to manufacturing, after applying overload cycles, as well as after completing tests on runouts. Fatigue test results demonstrate that, depending on the material and the overload level, the fatigue strength can either decrease or increase or, in some cases, be only slightly affected by overloads. To explain the experimental findings, residual stresses determined from both experimental measurements and elastic-plastic finite-element analyses are included in the calculations of the notch stresses and strains and a fatigue damage parameter. The latter is then involved in the damage calculations to quantify the effect of overloads in terms of the magnitude and number of cycles to failure.