Inelastic Finite Element Analysis Research Articles

Vertical Seismic Isolation Device for Three-Dimensional Seismic Isolation of Nuclear Power Plant Equipment—Case Study

The purpose of this study was to develop a vertical seismic isolation device essential for the three-dimensional seismic isolation design of nuclear power plant equipment. The vertical seismic isolation device in this study has a concept that can be integrally combined with a conventional laminated rubber bearing, a horizontal seismic isolator with a design vertical load of 10 kN. To develop the vertical seismic isolation device, the vertical spring and the seismic energy dissipation device capable of limiting the vertical displacement of the spring were designed and their performances were verified through actual tests. In this study, the target elevation of the floor is 136 ft, where safety-related nuclear equipment, such as cabinet and remote shutdown console, etc., is installed. The sensitivity studies were carried out to investigate the optimal design vertical isolation frequencies for the target building elevation. Based on the results of the sensitivity study, a disc spring and a helical coil spring were selected for the vertical stiffness design, and the steel damper was selected for the seismic energy dissipation, and their performance characteristics were tested to confirm the design performance. For the steel damper, three types were designed and their energy dissipation characteristics by hysteretic behavior were confirmed by the inelastic finite element analyses and the tests in static fully reversed cyclic conditions. Through the study of the vertical seismic isolation device, it was found that 2.5 Hz~3.0 Hz is appropriate for the optimal design vertical isolation. With results of the vertical seismic isolation performance analysis, the appropriate number of steel dampers are proposed to limit the vertical seismic displacement of the spring within the static displacement range by the design vertical load.

Quickly analyze the limit load of thinning defect elbows with elastic modulus adjustment method

In the process of production and service of pressure pipeline, local thinning defects may occur due to dielectric corrosion, manufacturing defects and other reasons. These defects reduce the carrying capacity of the pipeline and lead to leakage and rupture of the pipeline. Therefore, the integrity assessment of components and structures is required. Traditionally, the inelastic finite element method (FEM) is highly dependent on the specification of adequate mesh density and an assurance of numerically stable solutions. However, in engineering design, independent validation methods, such as Elastic Modulus Adjustment Procedures (EMAP), provide fast and stable solutions at relatively low cost. On the basis of elastic finite element analysis (FEA), the upper and lower bounds of limit load can be obtained by specifying the variations of elastic modulus in EMAP method. In this paper, an elastic modulus adjustment parameter k, which can improve the convergence of EMAP, is used to achieve stable convergence in the application of elbow with double defects. The EMAP method is also proved to be more efficient than the inelastic finite element analysis (FEA). Furthermore, the effect of defect size and distribution on the limit load of the elbow is studied.

Assessment of Failure Life Evaluation Methods for Structural Discontinuities With Fatigue and Creep-Fatigue Tests on Multiperforated Plate Made of Mod.9Cr-1Mo Steel

Abstract In the design of components for service at elevated temperatures, fatigue and creep-fatigue due to cyclic loading are some of the most important failure modes, and the assessment of failure life at structural discontinuities is a key issue within the evaluation of the integrity of the components. Since several fatigue and creep-fatigue life evaluation methods have been proposed, this study compares and assesses these different methods by performing fatigue and creep-fatigue tests of perforated plate made of Mod.9Cr-1Mo steel. Multiperforated plate was subjected to mechanical cyclic loading at 550 °C, and crack initiation and propagation at the surfaces of the holes were observed. The stress distribution was varied by changing the hole arrangement and loading level. A series of finite element analyses (FEA) were carried out to predict the number of cycles to failure by the several failure life evaluation methods, and these predictions were then compared with the test results. Several types of evaluation methods that use the elastic FEA were applied, namely, the stress redistribution locus (SRL) method, simple elastic follow-up method, and the methods described in the design and construction code for fast reactors (FRs) published by the Japan Society of Mechanical Engineers (JSME FRs code). In addition to these, evaluation was also carried out using the results of inelastic FEA to compare these elastic FEA-based estimation methods. The comparisons indicate that, for all conditions tested, the SRL method provided a rational prediction of the fatigue and creep-fatigue life when κ = 1.6 was applied, where κ = 1.6 is the recommended reduction factor for this method in general use. A comparison of the SRL method and the results of the inelastic FEA indicated that the applicability of the value of factor κ in the SRL method depends on the elastic region remaining in the cross section including the evaluated point and the spread in the plastically deformed region in the specimen.

Thermomechanical topology optimization of shape‐memory alloy structures using a transient bilevel adjoint method

SummaryWe present a novel method for computational design of adaptive shape‐memory alloy (SMA) structures via topology optimization. By optimally distributing a SMA within the prescribed design domain, the proposed algorithm seeks to tailor the two‐way shape‐memory effect (TWSME) and pseudoelasticity response of the SMA materials. Using a phenomenological material model, the thermomechanical response of the SMA structure is solved through inelastic finite element analysis, while assuming a transient but spatially uniform temperature distribution. The material distribution is parameterized via a SIMP formulation, with gradient‐based optimization used to perform the optimization search. We derive a transient, bilevel adjoint formulation for analytically computing the design sensitivities. We demonstrate the proposed design framework using a series of two‐dimensional thermomechanical benchmark problems. These examples include design for optimal displacement due to the TWSME, and design for maximum mechanical advantage while accounting for pseudoelasticity.

On the Plastic Strain Accumulation in Notched Bars During High-Temperature Creep Dwell

ABSTRACTStructural integrity plays an important role in any industrial activity, due to its capability of assessing complex systems against sudden and unpredicted failures. The work here presented investigates an unexpected new mechanism occurring in structures subjected to monotonic and cyclic loading at high temperature creep condition. An unexpected accumulation of plastic strain is observed to occur, within the high-temperature creep dwell. This phenomenon has been observed during several full inelastic finite element analyses. In order to understand which parameters make possible such behaviour, an extensive numerical study has been undertaken on two different notched bars. The notched bar has been selected due to its capability of representing a multiaxial stress state, which is a practical situation in real components. Two numerical examples consisting of an axisymmetric v-notch bar and a semi-circular notched bar are considered, in order to investigate different notches severity. Two material models have been considered for the plastic response, which is modelled by both Elastic-Perfectly Plastic and Armstrong-Frederick kinematic hardening material models. The high-temperature creep behaviour is introduced using the time hardening law. To study the problem several results are presented, as the effect of the material model on the plastic strain accumulation, the effect of the notch severity and the mesh element type and sensitivity. All the findings further confirm that the phenomenon observed is not an artefact but a real mechanism, which needs to be considered when assessing off-design condition. Moreover, it might be extremely dangerous if the cyclic loading condition occurs at such a high loading level.

Design and analysis of formed bellows for nuclear applications- Case study

Bellows are highly engineered components which find large number of applications in nuclear industry. Formed bellows are the most commonly used type of bellows especially when stoke is less than one thirds of bellows free length. Conventionally, design and manufacturing of the formed bellows are extensively addressed in standards of Expansion Joint Manufacturers Association (EJMA). In nuclear applications, design of the bellows shall comply with standard nuclear design codes such as ASME section-III, RCC-MR etc, which follow design by analysis. Hence, the design of the bellows for nuclear systems needs detailed Finite Element Analysis (FEA) and fatigue life estimation as per the design curves given in the codes. In this work, a case study of design of formed bellows, made of SS316LN, operating below creep range for nuclear application is presented. The bellows are preliminarily designed by EJMA and the geometry arrived based on preliminary design is analyzed using FEA. The stress/ strain range in the bellows is estimated by both linear elastic and inelastic FEA. Non-linear isotropic-kinematic hardening constitutive model is employed for inelastic analysis of the bellows. The fatigue life of the bellows is estimated as per the guidelines given in RCC-MR. It is found that the fatigue life estimated by linear elastic analysis is more conservative as compared to inelastic analysis. In the design fatigue curves given in the nuclear design codes, factor of safety (FOS) of 2 on stress range is considered. By considering similar factor of safety on the equivalent stress given in EJMA, the cycle life of the bellows is estimated and compared with the design life obtained by detailed stress analysis. It is found that after including FOS of 2 on equivalent stress, the life predicted by EJMA design curve is conservative. Hence, FOS modified EJMA equation can be used for design of the nuclear bellows when operating temperature is less than creep range of the bellows material. Use of FOS modified EJMA design equation is easy and eliminates the need for detailed stress analysis by the bellows suppliers. However, other aspects such as manufacturing tolerances, inspection, testing and qualification of the bellows shall comply with standard nuclear design codes.

System reliability-based Direct Design Method for space frames with cold–formed steel hollow sections

Design-by-analysis methods for steel structures are receiving considerable attention from professional engineers, researchers and standard-writing groups. Designing by analysis, termed as the Direct Design Method (DDM), is premised on the use of geometric nonlinear inelastic finite element analysis to determine the ultimate strength of steel structural frames and subsequently incorporating a system resistance factor (ϕs) to account for the effects of uncertainties in geometric parameters, stiffness and strength. This paper outlines the DDM in the context of cold-formed compact Hollow Steel Sections (HSS), including the reliability analysis framework at system level underpinning the Method. The system resistance factors for a series of representative 3D frames with hollow locally stable cross-sections are derived.

Column Moment Demands from Orthogonal Beam Twisting

Beam column joint subassemblies in steel moment frames often have simply-supported gravity beams framing into the joint in the perpendicular direction. When these subassemblies undergo lateral displacement, moments enter the column from the beams. Some of these moments are directly applied from the in-plane beam and slab stresses as they contact the column, and additional moments occur as the slab causes the perpendicular simply supported beams to twist. In most design codes around the world, no explicit consideration of these moments is performed even though they may increase the likelihood of column yielding and a soft-storey mechanism. This paper quantifies the magnitude of these perpendicular beam twisting moments in typical subassemblies using inelastic finite element analysis. It is shown that for beam-column-joint-slab subassemblies where the primary and secondary beams are fully welded to the column, the addition of slab effects significantly increases the total stiffness and strength of the composite frame structure. In addition to this, it is also shown the twisting moment demand of the secondary beams increased the frames strength by approximately 2% for an imposed drift of 5% for the subassembly investigated when no gap was provided between slab and the column. It was also shown the twisting moment demand of the secondary beams increased the frames strength by approximately 10% for a maximum imposed drift of 5% for the subassembly investigated when a gap was provided between the slab and the column.

Shakedown Analysis of Thick Cylinder with a Radial Opening with Primary Load Cycling In-Phase with Secondary Load

Shakedown and ratcheting behaviour of thick cylinder with and without radial crosshole is investigated in this paper by inelastic finite element analysis. Bree diagram was developed for the case of constant primary and cyclic secondary loading where the thermal gradient is varying linearly through the thickness for a thin cylindrical vessel. In the presented analysis the primary load is considered to be cycling strictly in-phase with the secondary loading and elastic-perfectly plastic material model is used. The results of FE analysis carried over thin cylinder was used to validate the methodology incorporated for distinguishing between cyclic behaviours (i.e. elastic shakedown, plastic shakedown and ratcheting). The thick cylinders considered have thickness ratio (Ri/t) = 2 and opening radius ratio (ri/Ri) = 0.2. The results indicate that the modified Bree diagram (i.e. considering both the loadings to be in-phase) derived for thin cylinder is sufficiently conservative and can be used to predict the shakedown behaviour of thick cylinders. However for thick cylinders with crosshole the ratcheting/shakedown boundary is significantly different and using the results of thin cylinder would be unsafe. The importance of selecting the most appropriate loading condition for analysis is also highlighted.

Creep-fatigue evaluation method for weld joint of Mod.9Cr-1Mo steel Part II: Plate bending test and proposal of a simplified evaluation method

In the present study, to develop an evaluation procedure and design rules for Mod.9Cr-1Mo steel weld joints, a method for evaluating the creep-fatigue life of Mod.9Cr-1Mo steel weld joints was proposed based on finite element analysis (FEA) and a series of cyclic plate bending tests of longitudinal and horizontal seamed plates. The strain concentration and redistribution behaviors were evaluated and the failure cycles were estimated using FEA by considering the test conditions and metallurgical discontinuities in the weld joints. Inelastic FEA models consisting of the base metal, heat-affected zone and weld metal were employed to estimate the elastic follow-up behavior caused by the metallurgical discontinuities. The elastic follow-up factors determined by comparing the elastic and inelastic FEA results were determined to be less than 1.5. Based on the estimated elastic follow-up factors obtained via inelastic FEA, a simplified technique using elastic FEA was proposed for evaluating the creep-fatigue life in Mod.9Cr-1Mo steel weld joints. The creep-fatigue life obtained using the plate bending test was compared to those estimated from the results of inelastic FEA and by a simplified evaluation method.

Shakedown analysis of thick cylinders with multiple radial openings

Shakedown and ratcheting behaviour of thick cylinder with multiple radial crossholes is investigated in this paper by inelastic finite element analysis. Effect of opening radius (ri/Ri), thickness of the vessel i.e. thickness ratios (R0/Ri) and availability of ligament between two openings (L/1) is studied. In order to normalise the applied pressure, limit load for thick cylindrical vessel without any opening was considered and it was found to be highly conservative. Later, interaction diagram normalised with respect to the limit load for thick cylinder taking into account the effects of opening was plotted. In order to distinguish between plastic shakedown and ratcheting, thickness advantage is taken into consideration. A more practical assessment technique is also discussed where the maximum range of thermal stress is computed through finite element analysis and the results were found to be in accordance with the Bree diagram. However the elastic-plastic shakedown boundary was found to be affected significantly with the incorporation of discontinuities and with changes in the parameters.

Evaluation of multiaxial low cycle fatigue life for type 316L stainless steel notched specimen under non-proportional loading

This study discusses a multiaxial low cycle fatigue (LCF) life of notched specimen under proportional and non-proportional loading conditions at room temperature. Multiaxial LCF tests controlled by strain were carried out using a smooth and a circumferentially notched round-bar specimens of type 316L stainless steel (316LSS). Four kinds of notched specimens of which elastic stress concentration factors Kt are 1.5, 2.5, 4.2 and 6.0 were employed. The strain paths employed were proportional loading and non-proportional loading. The former is push–pull loading and reversed torsion loading and the latter is circular loading achieved by the strain path of which axial and shear strains are loaded by 90° sinusoidal out-of-phase. Total axial strain and total shear strain ranges were the same ranges based on von Mises. An evaluation of the fatigue life for the notched specimen is discussed based on the experimental results and also by employing an inelastic finite element analysis (FEA). The fatigue life is decreased with increase in Kt at each strain path and is underestimated by a maximum local strain range evaluated by FEA result. A proposed strain range defined by a local mean strain value near the notch calculated from FEA by taking into account the non-proportional effect is an appropriate parameter for life evaluation of 316LSS notched specimen under non-proportional loading.

Fatigue Evaluation of Autofrettaged Thick-Walled Cylinders with a Radial Cross-Bore

The fatigue life of autofrettaged thick-walled cylinders with a radial cross-bore is investigated by applying inelastic finite element analysis with cyclic pressure loading. A non-linear kinematic hardening model considering bauschinger effect is used for determining cyclic plastic strain ranges in fatigue evaluations. A macro is written in ANSYS to calculate the equivalent alternating stress intensity, based on the ASME Boiler and Pressure Vessel Code. For a specific cyclic load level, a distinct optimum autofrettage pressure is identified by plotting autofrettage pressure against the equivalent alternating stress intensity and the number of cycles from design fatigue data. The optimum autofrettage pressure was found in the range of 80.5%-92.5% of limit pressure. The hydrotest had little influence on the fatigue life when the thick-walled cylinder was autofrettaged with an optimum autofrettage pressure.

Behavior and Strength of Rib Stiffened SC Wall-slab Connection

강판콘크리트(SC)구조 벽-바닥접합부는 표면 강판에 의해 콘크리트가 나뉘게 되며 이 때문에 바닥 단부의 응력 전달기구가 RC구조의 것과 다를 것으로 예상된다. 따라서 본 연구에서는 리브가 부착된 SC구조 벽-바닥 실험체의 거동 및 내력평가를 수행하였다. 리브가 부착된 SC벽바닥 접합부의 접합성능을 확인하기위하여 7가지의 접합부 모형을 제작하고 단조 가력실험을 수행하여 구조내력 및 거동특성을 실험결과분석을 통해 고찰하였다. 제안식의 신뢰성을 확보하기위해 유한요소 해석을 수행하였다. 실험체 변수로는 가력지점, 마찰계수이며 이들의 영향에 대해 검토되었다. 실험체 파괴모드 분석을 통해 접합부 내력을 확인하였다. 제안식은 대부분 보수적인 값으로 확인되었다. Until now, wall-slab plate of steel plate concrete has been constructed by joint. But, the shear plate has problems in the workability as well as structural integrity. This study investigates the behavior and strength of rib stiffened SC wall-slab connection. Seven prototype specimens of wall-slab connections were fabricated and tested. the structural safety of the specimens was confirmed through the monotonic loading test. Based on the experimental observations, this study propose the strength formula of the joint was proposed. To enhance the reliability of the proposed strength formula, analytical verification was performed through inelastic finite element analysis. Effect of parameters, such as, load point, friction coefficient, on the joint strength was examined. The proposed formula yields a conservative value for most cases.

Plastic Response Estimation in Repeated Elastic Analyses for Strain Hardening Material Model

Simplified limit analysis techniques have already been employed for limit load estimation on the basis of linear elastic finite element analysis (FEA) assuming elastic-perfectly-plastic material model. Due to strain hardening, a component or a structure can store supplementary strain energy and hence carries additional load. In this paper, an iterative elastic modulus adjustment scheme is developed in context of strain hardening material model utilizing the “strain energy density” theory. The proposed algorithm is then programmed into repeated elastic FEA and results from the numerical examples are compared with inelastic FEA results.

A re-assessment of elastic follow-up in high temperature piping

Despite the availability of detailed inelastic finite element analysis, the design of complex pipework systems operating at high temperature, where creep has to be taken into consideration, can be problematic. Design can be based on elastic analysis alone provided the effect of ‘elastic follow-up’ – the possibility of large inelastic strain concentration at some locations due to elastic behaviour of the rest–is somehow taken into account. Over the years it has become common to adopt an ‘elastic follow-up factor’, based on simplified methods, which can provide some estimate of the accumulated strain. This type of approach was developed over the years from numerous studies (including the author's) of the phenomenon of elastic follow-up in various structures. In all of these studies the constitutive model for creep was based on the simple power law. However, it has recently been shown by the author that stress-range dependent constitutive creep models can lead to significantly different predictions for follow-up. This paper applies this finding to the author's previous results on elastic follow-up in high temperature: it is demonstrated that consequently there could be a need to re-assess current design practice.

Verification of the Estimation Methods of Strain Range in Notched Specimens Made of Mod.9Cr-1Mo Steel

Several methods of estimating strain range at a structural discontinuity have been developed in order to assess component reliability. In a component design at elevated temperature, estimation of strain range is required to evaluate the fatigue and creep-fatigue damage. Therefore, estimation of strain range is one of the most important issues when evaluating the integrity of a component during its lifetimes. To verify the methods of estimating strain range for discontinuous structures, low cycle fatigue tests were carried out with notched specimens. All the specimens were made of Mod.9Cr-1Mo steel, because it is a candidate material for a primary and secondary heat transport system components of Japan Sodium-cooled Fast Reactor (JSFR). Displacement control fatigue tests and thermal fatigue tests were performed by ordinary uniaxial push–pull test machine and equipment generating the thermal gradient in the notched plate by induction heating. Several notch radii were employed to vary the stress concentration level in both kinds of tests. Crack initiation and propagation process during the tests were observed by a digital microscope and the replica method to define the failure cycles. Elastic and inelastic finite element analyses were also performed to estimate strain range for predicting fatigue life. Then, these predictions were compared with the test results. Several methods such as stress redistribution locus (SRL) method, simple elastic follow-up (SEF) method, Neuber's law, and the procedures employed by elevated temperature design codes were applied. Through these comparisons, the applicability and conservativeness of these strain range estimation methods, which is the basis of the fatigue and creep-fatigue life prediction, are discussed.

Moment gradient correction factor and inelastic flexural–torsional buckling of I-girder with corrugated steel webs

Corrugated steel plates have several advantages such as high resistance for shear without stiffeners, minimization of welding process, and high fatigue resistance. To take advantage of these benefits, several researchers have attempted to use corrugated steel plate as a web for I-girders. The flexural–torsional buckling is the major design aspect of such I-girders. However, the flexural–torsional buckling of the I-girder with corrugated steel webs still needs to be investigated especially for a real loading condition such as non-uniform bending. This paper investigated the flexural–torsional buckling strength of an I-girder with corrugated steel webs under linear moment gradient by using finite element analysis. From the results, it was found that the buckling behavior of the I-girder with corrugated steel webs differed depending on the number of periods of the corrugation. Also, a simple equation for the moment gradient correction factor for the I-girder with corrugated steel webs was suggested. The inelastic flexural–torsional buckling strength of the I-girder with corrugated steel webs was then discussed based on current design equations for ordinary I-girders and inelastic finite element analysis considering initial imperfection and residual stresses.

Stress and Strain Locus of Perforated Plate in Inelastic Deformation—Strain-Controlled Loading Case

Plastic strain of structures having stress concentration is estimated by using the simplified method or the finite element elastic solutions. As the simplified methods used in codes and standards, we can cite Neuber’s formula in the work by American Society of Mechanical Engineers (1995, “Boiler and Pressure Vessel Code,” ASME-Code, Section 3, Division 1, Subsection NH) and by Neuber (1961, “Theory of Stress Concentration for Shear Strained Prismatic Bodies With Arbitrary Nonlinear Stress-Strain Law,” ASME, J. Appl. Mech., 28, pp.544–550) and elastic follow-up procedure in the work by Japan Society of Mechanical Engineers [2005, “Rules on Design and Construction for Nuclear Power Plants, 2005, Division 2: Fast Breeder Reactor” (in Japanese)]. Also, we will cite stress redistribution locus (SRL) method recently proposed as the other simplified method in the work by Shimakawa et al. [2002, “Creep-Fatigue Life Evaluation Based on Stress Redistribution Locus (SRL) Method,” JPVRC Symposium 2002, JPVRC/EPERC/JPVRC Joint Workshop sponsored by JPVRC, Tokyo, Japan, pp. 87–95] ad by High Pressure Institute of Japan [2005, “Creep-Fatigue Life Evaluation Scheme for Ferritic Component at Elevated Temperature,” HPIS C 107 TR 2005 (in Japanese)]. In the present paper, inelastic finite element analysis of perforated plate, whose stress concentration is about 2.2–2.5, is carried out, and stress and strain locus in inelastic range by the detailed finite element solutions is investigated to compare accuracy of the simplified methods. As strain-controlled loading conditions, monotonic loading, cyclic loading, and cyclic loading having hold time in tension under strain-controlled loading are assumed. The inelastic strain affects significantly life evaluation of fatigue and creep-fatigue failure modes, and the stress and strain locus is discussed from the detailed inelastic finite element solutions.

Shakedown of Thick Cylinders With Radial Openings Under Thermomechanical Loadings

Shakedown and ratcheting behaviors of thick-walled cylindrical vessels with radial openings subjected to cyclic thermomechanical loadings are investigated by the inelastic finite element analysis. Different shakedown and ratcheting responses are described in the modified Bree diagram considering the influences of various opening radius ratios ri/Ri, thickness ratios Ro/Ri as well as different axial stress states. Then, two simplified shakedown assessment methods of perforated cylinders are discussed. The results indicate that elastic/plasticity shakedown boundary reduces significantly owing to the presence of a radial opening while varies slightly with the opening radius, which can be defined as 1.2 approximately in the modified Bree diagram for conservative elastic/plasticity shakedown evaluation. Moreover, shakedown/ratcheting boundary decreases significantly with increasing the opening radius or decreasing the axial stress. Finally, comparing with the calculated results, the two simplified methods are verified to be accurate and intuitive to estimate the shakedown behaviors of perforated cylinders under various thickness and opening radius conditions.