Elastic-plastic FE Analysis Research Articles

Pipe geometry effect on fatigue cracking location of 90° elbows under in-plane bending

In this technical note, the criterion for fatigue cracking location for 90° elbows under in-plane bending is presented. The criterion is found using published elastic solutions and elastic-plastic FE analysis results. It is found that the most important parameter affecting fatigue crack location is the mean radius-to-pipe thickness ratio, rm/t. The circumferential crack at outer intrados is predicted for rm/t <4–5, and the axial crack at inner crown for rm/t >4–5. The exact value of rm/t depends slightly on the bend radius-to-mean pipe radius ratio. This conclusion is found to be appropriate from high cycle fatigue to very low cycle fatigue loading, and to be independent on the material.

Including effect of bending stress parallel to the crack plane on a developed local limit load model

A plate containing a semi-elliptical surface crack is selected as a typical surface crack case to investigate the effects of the bending stress parallel to the crack plane on the limit load and elastic-plastic J. Elastic and elastic-plastic FE analyses are used to obtain J values for the surface-cracked plate under stress normal to the crack plane or under biaxial stress plus through-thickness bending with/without bending stress parallel to the crack plane. The results show that the applied bending stress parallel to the crack plane does not affect the elastic J, and, therefore, the stress intensity factor (SIF), but it does affect the elastic-plastic J. A reference stress estimation method considering the bending stress parallel to the crack plane is developed, which shows good correlation to the elastic-plastic J for cases with/without the bending stress parallel to the crack plane. This method is then used to extend the developed local limit load model to include the effect of the bending stress parallel to the crack plane.

Computational analysis of welding radial deformation of typical pressure cylindrical shell with ring stiffener

We report on the evaluation of the radial deformation caused by the welding process on a typical pressure cylindrical shell with ring stiffeners. Welding experiments on butt and fillet welding were conducted beforehand, and temperature-dependent material properties were considered. The out-of-plane welding distortion and residual stress were measured using a three-coordinate measuring machine and X-ray diffraction, respectively. Effective thermal elastic plastic FE analysis based on parallel computation technology was performed to examine the mechanical behaviors. Computed results were validated by comparison with experimental measurements. Welding inherent deformations of the examined butt and fillet joints were then evaluated by integrating computed plastic strains. The elastic FE analysis, with welding inherent deformation as mechanical loading, was employed to examine the dimensional variation of the considered pressure cylindrical shell. The influence of ring stiffener on welding radial deformation was also discussed. Moreover, the application of welding sequence modification and inverse deformation was numerically examined with the proposed elastic FE analysis to reduce the welding radial deformation and enhance the fabrication accuracy. • Thermal and mechanical behaviors of welding experiments were holistically examined with advanced measurement approach. • TEP FE analysis was employed to represent welding response, and computed results have good agreement with measurement. • Ring stiffener has significant influence on dimensional accuracy by elastic FE analysis with welding inherent deformation. • Welding sequence and inverse deformation have significant effect to prevent radial deformation of pressure cylindrical shell.

A study on scantling formulae of plate members due to lateral pressure under the effect of axial loads

Existing rule scantling formulae of plate members are based on conventional plastic design theory, and do not necessarily reflect complicated plate bending phenomena under axial loads. In this study, we first formulated the effect of axial load on the fully plastic moment based on the von Mises yield criterion for longitudinally stiffened plate in addition to the well-known formula for transversely stiffened plate. In addition, we derived a theoretical formulation of the lateral pressure corresponding to 2-point hinge and 3-point hinge formation taking account of the effect of the additional lateral force due to the axial loads on the deflected plating, using a simple plate strip bending model assuming a long plate with a large aspect ratio.Then, a series of elastic-plastic FE analyses was carried out to verify the structural behavior and the effect of axial load on the plate plastic bending strength. The plate strength was evaluated based on the residual deflection criteria of two cases (0.26 mm and 4.0 mm), and the results were compared with the theoretical derivation. As a result, it was found that assumption of linear strength reduction to the axial stress can cover the transversely stiffened plate under compressive axial stress conservatively. As to the transversely stiffened plate under tensile axial stress and the longitudinally stiffened plate, the strength reduction was in accordance with the reduction in the fully plastic moment based on the von Mises yield criterion in the conservative side. Finally, based on the findings, the required plate thickness coefficients were proposed on an empirical basis both for transversely and longitudinally stiffened plate under compressive and tensile axial loads.

Effect of damage evaluation method and cyclic hardening models on strain-based fatigue assessment to a piping system under seismic loads

In this paper, strain-based damage assessment based on elastic-plastic FE analysis was carried out for the piping system test under seismic loads conducted at Bhabha Atomic Research Center (BARC, India) to suggest relevant damage evlaution method and cyclic hardening model. For the damage evaluation method, the cumulative plastic damage and cumulative fatigue damage assessment methods, suggested in ASME BP53 % of the test result, and the use of the cumulative plastic damage method is found to be more conservative than the cumulative fatigue damage method. The effect of the hardening model on evaluation results is found to be not so significant.

Prediction of fatigue crack growth life under variable-amplitude loading using finite element analysis

This article presents an elastic-plastic study aiming at predicting the fatigue crack growth (FCG) of 2024-T3 aluminum alloys under variable-amplitude loading. The proposed analysis needs the estimation of the residual stress distribution ahead of the crack tip during propagation. An elastic-plastic FE analysis has been implemented for modeling FCG using Chaboche's model. The FE study has been carried out through consideration of the loading history effect using the memory rules. Three different loading spectra have been applied in this work. The obtained results have been compared to the experimental ones and it has been proved that the suggested model has a better prediction of the FCG lives of cracked 2024-T3 aluminum alloy structures subjected to variable-amplitude loading.

Limit load based evaluation of plastic η factor for C(T) specimen with a mismatched weld

Plastic η factor is adopted to account crack tip plasticity while evaluating the fracture toughness of the materials as per ASTM E1820. It is valid only for homogeneous materials. The plastic η factor for compact tension geometry (CT) with type 316LN stainless steel weld has been evaluated based on elastic-plastic FE analysis. The incremental elastic-plastic material model with various values for strength mismatch level (M), from 1.2 to 2.2 has been considered for the weld. The weld width (h) parallel to the crack plane is varied from 4 mm to 16 mm. The η values thus obtained are analyzed and the inferences are discussed.

Effect of sequence and stiffener shape on welding distortion of stiffened panel

Welding is extensively used in industries for the assembly of different products including ships, automobiles, trains, bridges etc. Welding distortion is usually a source of dimensional imprecision in assembly and higher manufacturing costs. So, it is of crucial importance to predict and minimize welding-induced distortion by improving the quality of the welded structure. The purpose of this research is to reduce the distortion in large ship panels. The study uses two methods. First, distortion prediction by thermal elastic plastic FE analysis is employed to estimate the inherent deformations of different SM490A steel welded joints. Then, the welding process of a large ship panel is elastically analyzed on the basis of the theory of inherent strains. The elastic analysis reveals some distortions on the edge and inside of the panel. The distortions can be minimized by changing welding sequence of panel stiffeners to symmetrical welding of type B and changing shape to L-stiffener as well as changing stiffener material to the SM570.

Development of new ηpl, β and limit load equations to evaluate fracture parameters of pre-cracked small punch test specimens

The small punch test (SPT) is an alternative method for determination of the mechanical properties when enough material is not available for conventional testing. Recently SPT specimen configuration is changed to have a crack (known as pre-cracked SPT) for more accurate determination of material fracture properties. Use of p-SPT specimens needs limit and maximum load values and geometric parameters, β and ηpl for evaluation of Stress Intensity Factor (SIF) and plastic J-integral respectively. However, general equations for these parameters are not available in the open literature. The present paper is an attempt to address this aspect of p-SPT specimens. Finite element analysis has been employed to evaluate the above parameters. Square pre-cracked specimens with crack parallel and perpendicular to the thickness direction are considered in this paper. The range of crack size a/W = 0.40–0.60 is considered for the present analysis. The load–displacement curves are extracted for both specimens using 3-D elastic–plastic FE analysis assuming elastic perfectly plastic material behaviour. Maximum load is directly obtained from the FEA load–deflection curves. The maximum load helps to assess the machine capacity to perform the SPT. Using the elastic–plastic J-integral and load–displacement data from FEA, ηpl values are calculated. Limit analysis using Plastic Work Curvature (PWC) criterion is carried out to obtain the limit loads. The geometric factor (β) is found out using elastic FE analysis for SIF calculation. Based on these FEA results, new equations have been proposed for limit load, maximum load, geometry factor (β) and ηpl for both types of p-SPT specimen configurations.

New load-line-displacement based η factor equation to evaluate J-integral for SE(B) specimen considering material strain hardening and no-crack displacement effect

The η factor plays an important role in the experimental evaluation of J-integral and J-R curve. While for a deeply cracked SE(B) specimen, established η factor value is available; for shallow cracked specimen, there is a variation in the η values proposed by different researchers. Although, it has been found that η factor depends on the material strain hardening behavior, most of the available equations are derived based on elastic-perfectly plastic material behavior. Additionally, almost all the existing η factor solutions do not consider the subtraction of no-crack displacement while calculating the strain energy although basic definition demands it. Hence effort has been made in this work to cover these gap areas. Plastic η factors (ηpl) have been calculated for a wide range of relative crack depth (a/W) and Ramberg-Osgood material strain hardening exponent ‘n’ with the help of elastic-plastic FE analysis. Calculated results are validated using literature values. The variation of ηpl with a/W and ‘n’ has been studied considering the effect of no-crack displacement. Based on these analyses, a closed-form equation has been proposed which is applicable for a wide range of a/W and material strain hardening exponents. The ηpl was shown to be independent of applied load level and various R-O parameters.

Low cycle fatigue life assessment of welded high-strength structural steels based on nominal and local design concepts

Fatigue life curves of butt joints, transverse stiffeners and sample components with tube-clevis connections, manufactured by active gas metal arc welding (GMAW) of S960QL, S960M and S1100QL high-strength steels, show a linear extension into the low cycle fatigue (LCF) regime with a constant slope up to the yield strength of the material. An extended S-N design curve based on fatigue class FAT 160 (k=5) gives conservative results for high quality butt welds below the ultimate tensile strength. In comparison to high frequency hammer peening and grinding, TIG dressing of S1100QL butt joints is most favorable for the increase of fatigue life.The effective notch stress approach with rref=1.00mm and measured radii of post treated welds leads to a reliable fatigue assessment up to at least N=5·103cycles to failure, which confirms FAT 225. The stress averaging approach using the microstructural support increases the assessment quality. A similar assessment reliability for damage parameter Wöhler lines, derived from elastic-plastic FE-analysis, is achieved, if support effects are considered.

Theoretical and experimental studies of battened buckling-restrained braces

A new type of core-separated buckling-restrained braces, namely a core-separated battened buckling-restrained brace (B-BRB) has been proposed. Its load-carrying capacity and hysteretic response are investigated theoretically and experimentally in this paper. The B-BRB has a remarkable advantage over a common buckling-restrained brace (BRB), in which the newly formed cross-section of the B-BRB is spread outwards by spacing two cores, hence resulting in higher material utilization efficiency in its structural design. In addition, the two independent all-steel BRBs, each having a single plate core simply in-filled in a narrow hollow section, are connected by longitudinally distributed battens rather than continuous plates. Based on the elastic-plastic FE analysis of a B-BRB under monotonic compressive load, its ultimate resistance and failure modes are investigated numerically, considering the effect of its overall initial geometric imperfection. An interaction formula between normalized slenderness ratio and buckling factor of the B-BRB is proposed for predicting its ultimate load-carrying capacity. Consequently, the hysteretic response of the B-BRB is explored through elastic-plastic FE analysis. The maximum normalized slenderness ratios of the B-BRBs required for a load-bearing type and an energy-dissipation type are proposed in their strength designs, respectively. Ultimately, hysteretic responses of five B-BRB specimens have been experimentally investigated. The experimental results are compared with the FE numerical analysis, which considers plate local buckling of all components of the B-BRBs. The comparison has verified the rationality of the proposed design method.

Welding distortion prediction with elastic FE analysis and mitigation practice in fabrication of cantilever beam component of jack-up drilling rig

How to predict and mitigate the welding distortion in fabrication of large offshore structures such as jack-up drilling rig, is always an essential engineering problem. In general, welding distortion can be estimated beforehand with experimental measurement of mock-up or numerical computation, and then practical techniques will be carried out to correct the possible welding distortion in the actual fabrication. In this paper, the possible welding distortion during the fabrication of I section welded structure in cantilever beam of jack-up drilling rig was studied with prediction and mitigation. First, an elastic FE analysis was employed, in which (a) the whole examined welded structure was meshed by coarse shell elements; (b) welding inherent deformations of typical welded joints were evaluated with thermal elastic-plastic FE analysis, and will be applied to the welding lines as load; (c) interface element was used to represent the fitting procedure before full welding. In order to eliminate these predicted welding distortions, some mitigation practices such as application of inverse distortion, optimization of welding sequence and constraint methods, were conducted and examined. In particular, welding sequence will intensively influence the final dimensional accuracy via straightening in fitting procedure and updated stiffness of current main welded structure.

Simulation of residual stress and fatigue strength of welded joints under the effects of ultrasonic impact treatment (UIT)

Ultrasonic impact treatment (UIT) is a remarkable post-weld technique, which applies mechanical impacts in combination with ultrasonic oscillations into welded joints introducing plastic deformation and beneficial compressive residual stress in the region of the weld toe. In this study, a novel 3D numerical analysis approach including thermo-mechanical welding simulation and dynamic elastic-plastic FE analysis of ultrasonic impact treatment process for welded joints is proposed. In the FE model, the actual process parameters and ultrasonic-induced material softening, which is appropriately adjusted to fit experimental results, are considered. The predicted residual stress distributions of a non-load-carrying cruciform joint before and after UIT are compared with experimental results, showing a fairly good agreement with each other. In addition, an evaluation of fatigue strength of welded joints based on fracture mechanics is carried out. The results not only clearly distinguish the fatigue strengths of as-weld and UIT processed weld joints, but also show the effects of preloads and stress ratios, so that the proposed solution method may provide an effective tool to simulate UIT process in engineering structures.

Design, development and qualification of a titanium to SS joint with groove

An improved lap type diffusion-bonded transition joint was developed between titanium (Ti) pipe and stainless steel (SS) pipe with grooves at the interface for use in high pressure-high temperature applications. The groove design was optimised using finite element method (FEM) so as to produce joint strength superior to the strength of the Ti pipe being joined. Elastic-plastic FE analyses were performed simulating large displacement and deformation involved. Further, joints were subjected to a simplified pull-out test to assess its strength. A good matching of joint strength, within 10% of FEM prediction and experimental results has been achieved. Design curves were generated using non dimensional parameters like r/t and a1/t (r-pipe radius, t- pipe thickness and a1-groove depth) to arrive at the groove depth for r/t range of 10, 15 and 20. It was demonstrated experimentally that the joint with groove performs better under thermal cycling loads. [Received 12 March 2016; Accepted 27 October 2016]

Behavior of a girth-welded duplex stainless steel pipe under external pressure

This study attempts to investigate the effects that external pressure has on the residual stress behavior in a girth-welded duplex stainless steel pipe. At first, FE simulation of the pipe girth welding is performed to identify the weld-induced residual stresses and depressions using sequentially coupled three-dimensional (3-D) thermo-mechanical FE formulation. Then, 3-D elastic–plastic FE analysis is carried out to evaluate the residual stress redistributions in the girth-welded pipe under external pressure. The residual stresses and plastic strains obtained from the thermo-mechanical FE simulation are employed as the initial condition for the analysis. The FE analysis results show that the hoop compressive stresses induced by the external pressure significantly alter the hoop residual stresses in the course of the mechanical loading, i.e. the hoop residual stress distributions on both surfaces of the pipe weld shift downward considerably, whilst the axial residual stresses are little affected by the superimposed external pressure.

FE analysis of residual stress relaxation in a girth-welded duplex stainless steel pipe under cyclic loading

This study intends to characterize the residual stress relaxation in a girth-welded duplex stainless steel pipe exposed to cyclic loading. FE thermal simulation of the girth welding process is first performed to identify the weld-induced residual stresses. 3-D elastic–plastic FE analyses incorporated with the cyclic plasticity constitutive model which can describe the cyclic stress relaxation are next carried out to evaluate reconstruction of the residual stresses under cyclic mechanical loading. The results unveils that considerable reduction of the residual stresses in and around the girth weld occur even after the initial few loading cycles and degree of the stress relaxation is dependent on the magnitude of applied cyclic loading.

材料の加工硬化特性を考慮した亀裂結合力モデルに基づく疲労亀裂の開閉口モデルと亀裂伝播解析

This paper presents a numerical simulation for fatigue crack propagation based on improved strip yield model, which enables the strain hardening effect of materials to consider. One-dimensional bar elements, which consist of the strain hardening materials, are plugged up the gap corresponding to the fictitious crack opening displacement in the plastic zone to describe the role of crack wake generated over fatigue crack surfaces. Validity of this numerical model under monotonic loading, unloading and reloading conditions was verified by comparison of the COD profile and plastic zones size with elastic-plastic FE analysis. Proposed model was implemented into the numerical simulation of fatigue crack propagation considering the crack opening / closing. Proposed simulation of fatigue crack propagation, which enables the strain hardening effect of materials, was validated by comparing fatigue crack propagation histories obtained by the numerical simulations with measured ones.

OS0919-412 原子炉圧力容器のクラッド直下亀裂に対する加圧熱衝撃時の応力拡大係数算出方法の検討

The elastic-plastic FE analysis is needed to know a plastic behavior of the RPV inner surface caused by rapid cooling during PTS events. However, the J-integral is not path-independent for elastic-plastic material in the unloading process. Therefore, the combination of the Stress Intensity Factor (SIF) derived from a FE analysis based on a model consisting of elastic-plastic cladding and linear elastic low alloy steel with the subsequent plastic zone correction is examined, since the stress level of low alloy steel remains within elastic region during PTS events. Furthermore, the method for including the effect of residual stress into the SIF is investigated.

FE Analysis of Buckling Behavior Caused by Welding in Thin Plates of High Tensile Strength Steel

The target of this study was to investigate buckling behavior during the entire welding process which consists of the heating and the cooling processes. For thin plate structures made of high tensile strength steel, not only residual buckling during or after cooling down but also transient buckling during heating may occur. The thermal elastic plastic FE analysis to investigate welding-induced buckling during the entire welding process is presented. Because of the high yield stress of high tensile strength steel, larger longitudinal compressive thermal stress is produced near the welding line compared with that in the case of carbon steel. Therefore, the plate may buckle due to thermal expansion, before the material nears yielding. During cooling down, the longitudinal compressive thermal stress close to the welding line disappears, and longitudinal tensile residual stress is produced due to contraction. Meanwhile, longitudinal compressive residual stress occurs far from the welding line to balance the tensile stress close to the welding line. This distribution of longitudinal residual stress would change the deformed dish shape of transient buckling into a saddle buckling type when the stress exceeds the critical buckling condition.