Elastic-plastic Finite Element Analysis Research Articles

On relation between J-integral and heat energy dissipation at the crack tip in stainless steel specimens

In this paper, an experimental procedure to evaluate the elastic-plastic J-integral at the tip of a fatigue crack is presented. According to this new approach, the elastic component of the J-integral is derived from Thermoelastic Stress Analysis, while the plastic component of the J-integral is derived from the heat energy loss. An analytical link is proposed to apply this new experimental technique. Therefore, the elastic-plastic J-integral range was evaluated starting from infrared temperature maps measured in situ during crack propagation tests of AISI 304L stainless steel specimens. It was found that the range of the infrared thermography-based J-integral correlated well the crack growth data generated in small as well as large scale yielding conditions. Finally, the experimental values of the J-integral were successfully compared with the corresponding numerical values obtained from elastic-plastic finite element analyses.

New CMOD based η-factor equations considering R-O strain hardening for circumferential through-wall cracked pipe under bending moment

The fracture study of circumferential through-wall cracked (CTWC) pipe under bending load is of interest for integrity assessment of conventional piping system and especially important for Leak-Before-Break (LBB) analysis of primary heat transport piping system of nuclear power plants (NPP). The fracture study in the elastic-plastic regime needs to obtain material J-resistance curve where J-integral is usually calculated from test data using the η-factor methodology. The evaluation of J-R curve for CTWC pipe is also important for study of transferability of material fracture resistance data from small specimen to full scale components. Further, η-factor to evaluate J-integral may be based on either load-lone-displacement (LLD) or crack mouth opening displacement (CMOD). The conventionalη-factor equations for CTWC pipe are LLD based and derived based on the assumption that the material is elastic perfectly plastic. However, use of LLD based η-factor needs to subtract no-crack displacement which poses additional difficulty and real materials always show some form of strain hardening. Therefore, an effort has been made in this paper to obtain the CMOD based η-factor for CTWC pipe considering material strain hardening as per the Ramberg-Osgood (R-O) relation. In the present study, plastic η-factor (ηpl) has been evaluated by elastic-plastic finite element analyses (FEA) over a wide range of crack angles (2θ = 30°–150°) and R-O strain hardening exponent (n = 2–7) for three R/t ratios (5, 10 and 20). To capture the ovalization of pipe cross section during deformation, geometric non-linearity is also considered in FEA. Based on these FEA, new ηpl equations are proposed by 2-D surface curve fitting for different R/t ratios. For validation of FE model, a separate set of geometrically linear FEA was also carried out for comparison of FE J-integral with EPRI Handbook solutions. Further, semi-analytical η-factor derived from EPRI relations of J-integral and CMOD were also compared with the present (geometric-linear) finite element results. In both the cases, the matching was very good.

On the evaluation of energy release rate and mode mixity for ductile asymmetric four point bend specimens

A method for evaluating the contributions from mode I and II components of loading to the energy release rate J in ductile asymmetric four-point bend (4-PB) specimens is proposed. The validity of the method is established by conducting elastic-plastic finite element analysis of several asymmetric 4-PB specimens exhibiting a range of mode mixities from pure mode I to II and having different crack length to width (a / W) ratios. Further, a definition of plastic mode mixity is introduced based on the near-tip opening and sliding displacements. This definition and the proposed method to evaluate J are easy to apply since the required crack opening and sliding displacements can be determined from in-situ optical imaging coupled with Digital Image Correlation (DIC) technique. The application of the proposed methodology is demonstrated by analyzing mixed-mode fracture experiments being conducted with a magnesium alloy. It is found that the critical value of J at crack initiation reduces as loading changes from mode I to II.

Evaluation of fatigue life and fatigue limit of circumferentially-notched Type 304 stainless steel in air and hydrogen gas based on crack-growth property and cyclic stress-strain response

Fatigue tests were performed using circumferentially-notched, round bar specimens with a stress concentration factor, Kt, of 6.6 for Type 304, metastable, austenitic stainless steel. The tests were carried out in ambient air and in 0.7 MPa hydrogen gas at room temperature. In a relatively higher stress amplitude regime (i.e., the amplitude resulting in Nf < 105), the hydrogen gas environment caused a marked degradation in fatigue life. In contrast, in a relatively lower stress amplitude regime (i.e., the amplitude resulting in Nf > 105), it appeared that fatigue life did not differ between air and hydrogen gas. It was also confirmed that the fatigue limit appeared not have been degraded in the hydrogen environment though there was a slight difference between the data obtained in two environments. The fatigue life curve and fatigue limit were predicted by assuming that the notch was equivalent to a circumferential crack. Consequently, there was a significant disparity between the prediction and the experimental results. As a result of microscopic observations of the fracture process in combination with elastic-plastic finite element analyses, these discrepancies were attributed to (i) complex cyclic plastic deformation behavior under large- and small-scale yielding conditions within the vicinity of the notch root, (ii) the retardation of crack initiation in the finite life regime, and (iii) the absence of non-propagating cracks at the fatigue limit, all of which are typical characteristics of metastable austenitic stainless steel.

Interrupted fatigue testing with periodic tomography to monitor porosity defects in wire + arc additive manufactured Ti-6Al-4V

Porosity defects remain a challenge to the structural integrity of additive manufactured materials, particularly for parts under fatigue loading applications. Although the wire + arc additive manufactured Ti-6Al-4 V builds are typically fully dense, occurrences of isolated pores may not be completely avoided due to feedstock contamination. This study used contaminated wires to build the gauge section of fatigue specimens to purposely introduce spherical gas pores in the size range of 120–250 micrometres. Changes in the defect morphology were monitored via interrupted fatigue testing with periodic X-ray computed tomography (CT) scanning. Prior to specimen failure, the near surface pores grew by approximately a factor of 2 and tortuous fatigue cracks were initiated and propagated towards the nearest free surface. Elastic-plastic finite element analysis showed cyclic plastic deformation at the pore root as a result of stress concentration; consequently for an applied tension-tension cyclic stress (stress ratio 0.1), the local stress at the pore root became a tension-compression nature (local stress ratio −1.0). Fatigue life was predicted using the notch fatigue approach and validated with experimental test results.

Infrared thermography-based evaluation of the elastic-plastic J-integral to correlate fatigue crack growth data of a stainless steel

The elastic-plastic J-integral is adopted to correlate fatigue crack growth data of ductile metals. An analytical link is known to exist between the J-integral and the strain energy density averaged in a control volume embracing the crack tip. On the other hand, the strain energy fluctuation is the source of temperature variations close to a fatigue crack tip of a metal material; hence the possibility to measure the J-integral from infrared thermographic scanning at the crack tip is envisaged and it is the focus of this paper. It is proposed that the elastic component of the J-integral is derived from a thermoelastic stress analysis, while the plastic component of the J-integral is derived from the heat energy loss. An analytical expression is formalised to apply this novel approach. Therefore, the elastic-plastic J-integral range was evaluated starting from infrared temperature maps measured in situ during crack propagation tests of AISI 304L stainless steel specimens. The range of the infrared thermography-based J-integral correlated well the crack growth data generated in small as well as large scale yielding conditions. Finally, the experimental values of the J-integral were successfully compared with the corresponding numerical values obtained from elastic-plastic finite element analyses.

Proposal of residual stress mitigation in nuclear safety-related austenitic stainless steel TP304 pipe bended by local induction heating process via elastic-plastic finite element analysis

Abstract This paper proposes a residual stress mitigation of a nuclear safety-related austenitic stainless steel TP304 pipe bended by local induction heating process via performing elastic-plastic finite element analysis. Residual stress distributions of the pipe bend were calculated by performing finite element analysis. Validity of the finite element analysis procedure was verified via comparing with temperature histories measured by using thermocouples, ultrasonic thickness measurement results, and residual stress measurement results by a hole-drilling method. Parametric finite element stress analysis was performed to investigate effects of the process and geometric shape variables on the residual stresses on inner surfaces of the pipe by applying the verified procedure. As a result of the parametric analysis, it was found that it is difficult to considerably reduce the inner surface residual stresses by changing the existing process and geometric shape variables. So, in order to mitigate the residual stresses, effect of an additional process such as cooling after the bending on the residual stresses was investigated. Finally, it was identified that the additional heating after the bending can significantly reduce the residual stresses while other variables have insignificant effect.

A study on the prediction of inherent deformation in fillet-welded joint using support vector machine and genetic optimization algorithm

The inherent deformation method has a significant advantage in evaluating the total welding deformations for large and complex welded structures. The prerequisite for applying this approach is that the inherent deformations of corresponding weld joints should be known beforehand. In this study, an intelligent model based on support vector machine (SVM) and genetic algorithm (GA) was established to predict the inherent deformations of a fillet-welded joint. The training samples were obtained from numerical experiments conducted by the thermal–elastic–plastic finite element analysis. In the developed SVM model, the welding speed, current, voltage and plate thickness were considered as input parameters, and the longitudinal and transverse inherent deformations were corresponding outputs. The correlation coefficients and percentage errors for all the samples were calculated to evaluate the prediction performance of the SVM model. The research results demonstrate that the SVM model optimized by GA can be used to assess the longitudinal and transverse inherent deformations for the T-joint fillet weld with acceptable accuracy.

Mixed mode I/II failure prediction of thin U-notched ductile steel plates with significant strain-hardening and large strain-to-failure: The Fictitious Material Concept

In wide range of ductile materials, the strain-to-failure and the strain-hardening are simultaneously significant, for which, there is no valid K-based fracture toughness (KIc or Kc) based on the standard test methods. So, prediction of the load-carrying capacity (LCC) of notched specimens made of these materials by means of the Equivalent Material Concept (EMC) is impossible. On the other hand, because of large value of the predicted failure load resulted from the large strain-to-failure, the modified EMC (MEMC) seems inefficient in LCC prediction of notched members. Consequently, for such ductile materials, both EMC and MEMC are null. The Fictitious Material Concept (FMC) is proposed in the present study to overcome this major limitation, by which fictitious values of Young's modulus and fracture toughness are defined and calculated for the real ductile material to predict LCC of notched ductile specimens. For this aim, first, U-notched specimens made of SUS 316 stainless steel with good ductility, large strain-to-failure, high elastic modulus, and significant strain-hardening, are evaluated for fracture under pure mode I and mixed mode I/II loadings both experimentally and theoretically. The U-notched specimens with different notch tip radii and notch inclination angles are produced and tested, and their failure loads are experimentally recorded. Then, the test results are theoretically predicted by linking FMC to the maximum tangential stress (MTS) and mean stress (MS) brittle fracture criteria with no need for time-consuming and complex elastic-plastic analyses. A good agreement is observed between the predictions of both FMC-MTS and FMC-MS combined criteria and the experimental results. Meanwhile, the experimental observations as well as the results of elastic-plastic finite element analysis confirm that all of the specimens tested fail by the gross-yielding (GY) regime.

Load resistance and hysteretic response of multiple cross-arm pre-tensioned cable stayed buckling-restrained braces

This paper investigates the elastic buckling loads, load resistance and hysteretic responses of the multiple cross-arm pre-tensioned cable stayed buckling-restrained braces (MPCS-BRBs) with circular rigid plates as the cross-arms that are fixed to the external tube, and the circular rigid plates are considered equivalent as stays with infinite stiffness in the finite element analysis (FEA). The span and elastic buckling load efficiency of the MPCS-BRBs could be increased and improved effectively by adopting multiple cross-arms that are considered to possess infinite stiffness. Explicit expressions for the elastic buckling loads of the MPCS-BRBs are obtained in closed form through curve fitting, by adopting the FEA results on a generalized structural design parameter β that is deduced from a single cross-arm PCS-BRB (SPCS-BRB). In addition, a protocol has been proposed for the height of stays so as to achieve a convenient and generalized design guide, where the outermost point at each stay falls on the same circular arc. Furthermore, the load resistance and hysteretic responses of the MPCS-BRBs subjected to monotonic and cyclic axial loads are explored through an elastic-plastic FEA. It is found that a lower limit of restraining ratio exists, which would ensure overall instability of the MPCS-BRBs not to occur by considering an optimal initial pre-tensioning force in the cables so that they do not become slack before the MPCS-BRBs reach their ultimate failures, and ensure maximum ultimate load-carrying capacities of the braces to be obtained. The investigation and its findings on the elastic buckling loads, load resistance and hysteretic responses of MPCS-BRBs provide fundamentals and guidance for their preliminary design in actual engineering applications.

Identification of traction-separation parameters by means of peel testing and in situ confocal microscopy

Delamination owed to environmental stress is a relevant concern in the field of microelectronics packaging. This study is focused on the adhesion of a photosensitive insulator to inorganic passivation layers and metal caps. Peel testing has been combined with confocal laser scanning microscopy to image the bent shape of the peeled layer in situ. Elastic plastic beam theory and finite element analysis have been used to identify a cohesive traction-separation law matching both the work of separation and the peel arm profile. The results indicate that the actual adhesion energy amounts to ~30% of the external work, whereas the rest is dissipated by plasticity. Being the latter related to the curvature of the peel arm during delamination, these results confirm the relevance of in situ imaging in the field of microelectronics reliability.

Prediction of failure stages for double lap joints using finite element analysis and artificial neural networks

Abstract Prediction of failure stages of double lap bolted joints is an important task for design. Finite element (FE) and artificial neural networks (ANNs) methods are widely used in such tasks to reduce time, money, and efforts consumed in laboratory experiments. Three dimension elastic-plastic FE analysis was adopted to simulate the failure stages of double lap joint in the present work. After completing mesh sensitivity analysis for the present FE model, only nine experiments were conducted to verify the prediction of the present FE model. Taguchi technique was applied to reduce the number of loading cases (different joint geometry and tightening torque) from one hundred twenty five cases of loadings to only twenty seven cases of loadings. The FE results of twenty seven cases of loadings were accomplished to provide the training set of ANNs. Finally, a comparison between the results obtained from FE and ANNs was made. Results indicated that, either FE or ANNs can highly predict the failure stages of double lap bolted joints for different e/D, w/D, and tightening torque values. Therefore, FE and ANNs methods may be considered good candidates to predict the mechanical behavior and failure mode of such joint.

Determination and verification of triaxiality dependent cohesive zone parameters of SA333 Grade 6 steel

Cohesive zone models are employed to simulate crack propagation in fracture process zone. It has been demonstrated in the present study that the cohesive zone parameters depend not only on the material, but also on stress triaxiality. To determine cohesive zone parameters, experimental results of 14 three-point bend specimens (TPBB) made of SA333 Grade 6 steel were analyzed using 3D finite element model using WARP3D. Cohesive parameters were determined by carrying out parametric studies of these specimens by varying peak stress ‘T’ to match experimental load-displacement data with the computed data. An exponential traction separation law was used for this purpose. In addition, elastic-plastic finite element analyses (FEA) are conducted to determine the multi-axiality quotient ‘q’ at the crack tip for TPBB specimens and pipe components. This helped to get a relation between peak stress ‘T’ and ‘q’. To extend the range of validity of parameter ‘T’ as a function of ‘q’, experimental results of six piping components with through-wall circumferential crack made of SA333 Grade 6 steel tested earlier were also used similarly. A confidence interval band between q and T is then plotted to study the transferability of cohesive parameters. The variation in ‘T’ for the same value of ‘q’ is attributed to the microstructural changes in the material near crack tip.To test the accuracy of the cohesive parameters determined above, experimental results of six piping components were again used. Using the ‘q’ parameters determined from elastic-plastic FEA on pipes, the upper and lower limits of peak stress ‘T’ from the confidence band determined above were found out. This range of ‘T’ was then used to carry out cohesive zone analyses (CZA) of these piping components to determine load-displacement curves. For each piping component, a set of load-displacement curves were determined by assuming a normal variation of parameter ‘T’ over the maximum and minimum limits. The simulation results were compared with the experimental results and it has been observed that experimental results lie reasonably well within the computed results.

Determination of J-initiation toughness using pre-cracked small punch test specimens

Determination of fracture properties is important to assess the in-service degradation of nuclear structural materials subjected to thermal fluctuations and irradiation and to calculate the residual life of the component. The pre-cracked small punch test is an alternative method for the determination of fracture properties in case of limited availability of materials and is insufficient for conducting conventional standard tests. In this paper, pre-cracked small punch test (denoted as p-SPT) specimens are used to obtain the fracture J-initiation toughness of nuclear structural steel 20MnMoNi55 and T91.The size of the p-SPT specimen is 10 x 10 x 0.5 mm and wire EDM technique is used to generate through thickness crack profile from mid-point of one side to a point just passing the center of the specimen, producing a crack length to specimen width ratio (a/W) as 0.4. The tests are conducted to get load v/s displacement data. Elastic-plastic finite element analysis of the p-SPT specimen is carried out and numerically obtained load v/s displacement data are compared with the experimental results. This analysis also helped to compute J-integral near the crack tip as a function of load. FE analysis is then repeated using the micromechanical Gurson-Tvergaard-Needleman model to know the load at which crack is initiated. J-initiation is then calculated using J-integral v/s load data. Computed J-initiation using micromechanical GTN model has good matching with the value quoted in the literature, which shows the viability of the method. The methodology described in this paper has the potential to determine fracture initiation toughness of aged nuclear materials using pre-cracked small punch tests.

Ratcheting boundary of pressurized pipe under reversed bending

Ratcheting boundary is firstly determined by experiment, elastic-plastic finite element analysis combined with C-TDF and linear matching method, which is compared with ASME/KTA and RCC-MR. Moreover, based on elastic modulus adjustment procedure, a novel method is proposed to predict the ratcheting boundary for a pressurized pipe subjected to constant internal pressure and cyclic bending loading. Comparison of ratcheting boundary of elbow pipe determined by the proposed method, elastic-plastic finite element analysis combined with C-TDF and linear matching method, which indicates that the predicted results of the proposed method are in well agreement with those of linear matching method.

Validation of the two-parameter fracture criterion for various crack configurations made of 2014-T6 aluminum alloy using finite-element fracture simulations – Part 1 LT-Orientation

A two-parameter fracture criterion (TPFC), derived by Newman, related the linear-elastic stress intensity factor, KIe, and net-section stress, Sn, at failure with two material fracture parameters, KF and m. The objective of this work was to validate the TPFC using two-dimensional elastic–plastic finite-element analyses (FEA). The critical crack-tip-opening-angle (CTOA) fracture criterion and a plane-strain core were used to match the failure loads on middle-crack-tension, M(T), specimens made of thin-sheet 2014-T6 (LT) aluminum alloy. The same analyses were then used on other M(T), single-edge-crack-tension, SE(T), and bend, SE(B), specimens to predict failure loads and moments. Test data was not available on SE-type specimens. A wide range in specimen widths (w = 19–610 mm) were considered. The finite-element code, ZIP2D, was used to calculate critical stress-intensity factors at failure corresponding to all crack configurations for crack-length-to-width (ci/w) ratios of 0.05–0.95. The FEA results agreed very well with the TPFC predictions for net-section stresses less than the material proportional limit. Further studies are needed for net-section stresses greater than the proportional limit on both tension and bend specimens.

Estimation of J-resistance curves of SA-508 steel from small sized specimens with the correction of crack tip constraint

Based on normalization method, experimental J-resistance (J-R) curves of SA-508 steel using five types of specimen configurations, such as C-shaped outside edge-notched compression (COEC), C-shaped inside edge-notched tension (CIET), miniature single edge notched bend (Mini-SENB), standard SENB and compact tension (CT) specimens are given. Great difference can be observed in these experimental J-R curves because of the various specimen configuration and dimension. The results show that, COEC specimens present the lowest J-R curves with high level of crack tip constraint, but the highest J-R curves are estimated from Mini-SENB specimens because of the lowest level of crack tip constraint they have. The classic crack tip constraint effect can explain these differences, so J-Q-M theory is applied to quantify this effect through 3D elastic plastic finite element analysis, and a family of constraint corrected J-R curves for SA-508 steel are consequently obtained, which match well with the experimental data for five types of specimen configurations with different dimensions. It is applicable to predict the J-R curves of actual cracked components as long as the crack tip constraint is determined.

A new weld material model used in welding analysis of narrow gap thick-walled welded rotor

A new weld material model was developed to improve simulation convergence and accuracy in welding stress analysis of thick-walled welded structure, taking use of the none-stiffness and none-strength properties of the weld metal corresponding to the globular transferring by controlling residual deformation in every weld bead. Single-pass welding model was employed to compare the new weld material model with the traditional one. Besides, the evolution of welding stress with the new weld material model was analyzed. Based on the new weld material model, welding stress in the thick-walled welded rotor was predicted by means of thermal elastic-plastic finite element analysis. Comparisons between the traditional weld material model and the new one were conducted during welding stress simulation upon thick-walled welded rotors. The results indicated that the new weld material model can make convergence practicable and quickly when the cut-off temperature is high in order to guarantee the accuracy. Comparisons between simulations and experimental data were also carried out to verify the effectiveness of the developed numerical analysis procedure.

Analysis of high-strength pressurized pipes (API-5L-X80) with local gouge and dent defect

In this study, indentation responses of high strength steel pipe with local wall thinning (gouge) under internal pressure have been studied through experimental procedure and numerical analysis. The experimental study was carried out on laboratory scale specimens from API 5 L X80 steel. Dent produced by a hemi-spherical indenter with diameter of 20 mm and axial gouge introduced to the pipe’s outer surface. In experimental work, the influence of some parameters such as depth of dent, axial gouges of different sizes and presence of the internal pressure have been investigated.A numerical modeling approach has also been employed. The current numerical simulation has first been validated by experimental results previously conducted by the authors. The numerical results show well agreement with the experimental results. Effects of internal pressure level, boundary condition and D/t ratio on the response of pipelines subjected to lateral impacts numerically studied and the results have then been compared with analytical equations provided in some design codes. The results show that the analytical relations estimate greater lateral resistance than numerical results. Validated model were then used to derive a semi-empirical equation for predicting structural behavior of locally damaged tubes as a function of internal pressure. Furthermore, the elastic-plastic finite element analyses were performed to estimate the variations of failure depth with several internal pressures and gouge sizes.

Numerical investigations of multiple cross-arm pre-tensioned cable stayed BRBs with pin-ended stays

This paper proposes Multiple cross-arm Pre-tensioned Cable Stayed Buckling-Restrained Braces (MPCS-BRBs) with pinned connections between stays and external tube. By adopting pin-ended stays, the additional bending moment that would be exerted on those connections can be effectively released instead of fixed connections. This eliminates premature strength failures at those connections and simplifies the tensioning process of the cables, thus making the pin-ended stays to be a very practical option in engineering applications. Comparative studies have been conducted on the elastic buckling, load resistance and cyclic behaviors of the MPCS-BRBs with and without additional minor diagonal cables through Finite Element Analysis (FEA). Explicit expressions for the elastic buckling loads of the two types of MPCS-BRBs are obtained in closed form through curve fitting based on a generalized structural design parameter β of the external restraining system. It is found that the elastic buckling performance of the MPCS-BRBs with additional minor diagonal cables could be enhanced dramatically as compared to those not possessing the minor diagonal cables. At last, by ensuring the major cables not to become slack before reaching ultimate failures of the MPCS-BRBs, the load resistance and cyclic behaviors subjected respectively to monotonic and cyclic axial loads are explored through an elastic-plastic FEA. Corresponding lower limits of restraining ratios are attained, where they would provide fundamentals and guidance for preliminary design of the MPCS-BRBs in actual engineering applications.