Three-dimensional Elastic-plastic Finite Element Analysis Research Articles

Two-parameter characterization of elastic–plastic crack front fields: Surface cracked plates under tensile loading

In this paper the J–Q two-parameter characterization of elastic–plastic crack front fields is examined for surface cracked plates under uniaxial and biaxial tensile loadings. Extensive three-dimensional elastic–plastic finite element analyses were performed for semi-elliptical surface cracks in a finite thickness plate, under remote uniaxial and biaxial tension loading conditions. Surface cracks with aspect ratios a/c=0.2, 1.0 and relative depths a/t=0.2, 0.6 were investigated. The loading levels cover from small-scale to large-scale yielding. In topological planes perpendicular to the crack fronts, the crack stress fields were obtained. In order to facilitate the determination of Q-factors, modified boundary layer analyses were also conducted. The J–Q two-parameter approach was then used in characterizing the elastic–plastic crack front stress fields along these 3D crack fronts. Complete distributions of the J-integral and Q-factors for a wide range of loading conditions were obtained. It is found that the J–Q characterization provides good estimate for the constraint loss for crack front stress fields. It is also shown that for medium load levels, reasonable agreements are achieved between the T-stress based Q-factors and the Q-factors obtained from finite element analysis. These results are suitable for elastic–plastic fracture mechanics analysis of surface cracked plates.

Strain-rate dependence of mechanical behavior and hysteretic characteristics of TMCP steel (SM570-TMC) and its modeling

Abstract The stress–strain response of TMCP (Thermo-Mechanical Control Process) steels during dynamic deformation is different toward that during static deformation due to strain rate- and temperature-dependences of mechanical behavior. To predict static or dynamic behavior of SM570-TMC under monotonic and cyclic loadings, it is necessary to investigate characteristics of static–dynamic mechanical behavior by experimental approaches and to develop a strain rate-dependent model which can describe the non-linearity and hysteresis of complicated stress–strain relationship in the static and dynamic conditions. Therefore, strain-rate dependence of mechanical behavior and hysteretic characteristic of SM570-TMC is investigated by performing the tensile and low-cycle fatigue experiments as a function of strain rate. And based on the experiments, the strain rate-dependent hysteresis model is proposed by the authors. A three-dimensional elastic–plastic finite element analysis is developed by using the formulated hysteresis model and verified by comparing between the structural analyses and the experiments.

Behaviour of stresses in circumferential butt welds of steel pipe under superimposed axial tension loading

A computational procedure is presented for analyzing behaviour of stresses in circumferential butt welds of carbon steel pipe subject to superimposed mechanical loading. Three-dimensional uncoupled thermo-mechanical finite element (FE) analysis method is developed in order to predict the weld residual stress states in circumferentially butt-welded steel pipe. The FE method is verified through the experimental work. Then, three-dimensional elastic–plastic FE analysis is carried out to investigate the behaviour of stresses in steel pipe circumferential welds undergoing superimposed axial tension loading using the weld residual stresses and plastic strains obtained from the thermo-mechanical FE method. The simulated results show that spatial variations of the weld residual stresses are present along the circumference and a rapid change of the residual stresses exists at the weld start/stop position, therefore three-dimensional FE analysis is essential to accurately simulate the circumferential welding of steel pipe. Moreover, when axial tension loading is applied to the circumferentially welded steel pipe, bending moment is generated at the weld area caused by the circumferential shrinkage of the weld during welding, thus affecting the axial and hoop stress evolutions in the course of mechanical loading.

Characteristics of the Static and Dynamic Behavior of Steel Piles with a Welded Joint

During welding process to make joints, residual stress is inevitably produced and weld metal should be used. These influence the static and dynamic behavior of steel structures with welded joints, such as steel piles. In steel structures, dynamic mechanical behavior is different to static mechanical behavior. Therefore, to accurately predict the behavior of steel piles with a welded joint under static-dynamic loading, the research on influence of a welded joint on the static and dynamic behavior of steel piles is necessary. For that purpose, a rate-dependent plasticity model was used, considering strain rate hardening and temperature rise. In this paper, the distribution of welding residual stress in a welded joint was computed by using three-dimensional heat conduction analysis and three-dimensional thermal elastic-plastic analysis. The behavior of steel piles with a welded joint under axial static and dynamic loading was investigated by using three-dimensional elastic-plastic finite element analysis, which employed a rate-dependent plasticity model and included residual stress and mechanical properties of weld metal in a welded joint. The rate-dependent plasticity model used in this paper is proposed by the authors based on the static-dynamic loading tests. Numerical analysis results of steel piles with a welded joint were compared to those without a welded joint. In comparison, the characteristics of static and dynamic behavior of steel piles with a welded joint were investigated.

J-Integral Estimation for the 3-D Through-Thickness Centre-Cracks in Welds of Structural Steels

For the fracture analysis of a crack in welds, residual stress analysis and fracture mechanics analysis must be performed sequentially. In this study, characteristics of residual stresses in welds of structural steels (SM490, SM520, SM570) were presented by carrying out three-dimensional (3-D) thermal elastic-plastic finite element (FE) analysis. Then, an FE analysis method which was able to calculate domain-independent values of the J-integral for a crack in a 3-D residual stress bearing body was developed to evaluate the J-integral for a mode-I centre-crack in welds of structural steels when mechanical stresses were applied in conjunction with residual stresses. The results show that the longitudinal residual stresses in welds increase with increasing yield stress of the welded steel (SM490<SM520<SM570). For the through-thickness centre-cracks in welds of structural steels where only residual stresses are present, the J-integral values increase with increasing yield stress of the welded steel. This is because the longitudinal residual stresses in welds, which in this case act as the crack driving force, increase with increasing yield stress of the welded steel. Furthermore, the values of the J-integral for the case when mechanical stresses, applied in conjunction with residual stresses, are larger than those for the case when only residual stresses are present. This is because tensile stresses by mechanical loading are added to the existing residual stresses; hence the crack driving force is larger.

Three-parameter approach for elastic–plastic fracture of the semi-elliptical surface crack under tension

Systematic three-dimensional elastic–plastic finite element analyses are carried out for a semi-elliptical surface crack in plates under tension. Various aspect ratios ( a/ c) of three-dimensional fields are analyzed near the semi-elliptical surface crack front. It is shown that the developed J– Q annulus can effectively describe the influence of the in-plane stress parameters as the radial distances ( r/( J/ σ 0)) are relatively small, while the approach can hardly characterize it very well with the increase of r/( J/ σ 0) and strain hardening exponent n. In order to characterize the important stress parameters well, such as the equivalent stress σ e, the hydrostatic stress σ m and the stress triaxiality R σ , the three-parameter J– Q T– T z approach is proposed based on the numerical analysis as well as a critical discussion on the previous studies. By introducing the out-of-plane stress constraint factor T z and the Q T term, which is determined by matching the finite element analysis results, the J– Q T– T z solution can predict the corresponding three-dimensional stress state parameters and the equivalent strain effectively in the whole plastic zone. Furthermore, it is exciting to find that the values of J-integral are independent of n under small-scale yielding condition when the stress-free boundary conditions at the side and back surfaces of the plate have negligible effect on the stress state along the crack front, and the normalized J tends to a same value when φ equals about 31.5° for different a/ c and n. Finally, the empirical formula of T z and the stress components are provided to predict the stress state parameters effectively.

Effect of local wall thinning on the collapse behavior of pipe elbows subjected to a combined internal pressure and in-plane bending load

The objective of this study was to investigate the effect of local wall thinning on the collapse behavior of pipe elbows subjected to a combined internal pressure and in-plane bending load. This study evaluated the global deformation behavior and collapse moment of the elbows, which contained various types of local wall-thinning defects at their intrados or extrados, using three-dimensional elastic–plastic finite element analysis. The analysis results showed that the global deformation behavior of locally wall-thinned elbows was largely governed by the mode of the bending and the elbow geometry rather than the wall-thinning parameters, except for elbows with considerably large and deep wall thinning that showed plastic instabilities induced by local buckling and plastic collapsing in the thinned area. The reduction in the collapse moment with wall-thinning depth was considerable when local buckling occurred in the thinned areas, whereas the effect of the thinning depth was small when ovalization occurred. The effects of the circumferential thinning angle and thinning length on the collapse moment of elbows were not major for shallow wall-thinning cases. For deeper wall-thinning cases, however, their effects were significant and the dependence of collapse moment on the axial thinning length was governed by the stress type applied to the wall-thinned area. Typically, the reduction in the collapse moment due to local wall thinning was clearer when the thinning defect was located at the intrados rather than the extrados, and it was apparent for elbows with larger bend radius.

Failure pressure of straight pipe with wall thinning under internal pressure

The failure pressure of pipe with wall thinning was investigated by using three-dimensional elastic–plastic finite element analyses (FEA). With careful modeling of the pipe and flaw geometry in addition to a proper stress–strain relation of the material, FEA could estimate the precise burst pressure obtained by the tests. FEA was conducted by assuming three kinds of materials: line pipe steel, carbon steel, and stainless steel. The failure pressure obtained using line pipe steel was the lowest under the same flaw size condition, when the failure pressure was normalized by the value of unflawed pipe defined using the flow stress. On the other hand, when the failure pressure was normalized by the results of FEA obtained for unflawed pipe under various flaw and pipe configurations, the failure pressures of carbon steel and line pipe steel were almost the same and lower than that of stainless steel. This suggests that the existing assessment criteria developed for line pipe steel can be applied to make a conservative assessment of carbon steel and stainless steel.

Effect of Residual Stress and Weld Metal on Hysteretic Behavior of a Welded Tubular T-Joint

During the welding process to make welded joints, residual stress is inevitably generated and weld metal is used. Welding Residual stress is influenced on the behavior of welded joints under monotonic and cyclic loading. And the weld metals used in welding process have different mechanical characteristics than structural steels. Therefore, to accurately predict the hysteretic behavior of welded joints, the effect of residual stress and weld metal must be investigated. In this paper, the residual stress distribution in a welded tubular T-joint was investigated by carrying out three-dimensional non-steady heat conduction analysis and three-dimensional thermal elastic-plastic analysis. To consider a effect of base metal(SM490) and weld metal(E71T-1), a cyclic plasticity model was formulated based on monotonic and cyclic loading tests. And the formulated model was applied to three-dimensional elastic-plastic finite element analysis. The effect of residual stress and weld metal on hysteretic behavior of a welded tubular T-joint was investigated by carrying out numerical analyses considering residual stress and cyclic plasticity model of base metal and weld metal respectively.

Influence of the Welded Joint on the Mechanical Behavior of Steel Piles during Static and Dynamic Deformation

During manufacturing the welded joint of steel structures, residual stress is produced and weld metal is used inevitably. And residual stress and weld metal influence on the static and dynamic mechanical behavior of steel structures. Therefore, to predict the mechanical behavior of steel pile with a welded joint during static and dynamic deformation, the research on the influence of the welded joints on the static and dynamic behavior of steel pile is clarified. In this paper, the residual stress distribution in a welded joint of steel piles was investigated by using three-dimensional welding analysis. The static and dynamic mechanical behavior of steel piles with a welded joint is investigated by three-dimensional elastic-plastic finite element analysis using a proposed dynamic hysteresis model. Numerical analyses of the steel pile with a welded joint were compared to that without a welded joint with respect to load carrying capacity and residual stress distribution. The influence of the welded joint on the mechanical behavior of steel piles during static and dynamic deformation was clarified by comparing analytical results

Stability Analyses of the Three Gorges Dam Foundation against Sliding by Strength Reduction of Finite Elements

This paper studies the dam foundation stability of the representative no. 3 powerhouse-dam section of the Three Gorges Dam (TGD), China, using elastic-plastic finite element shear strength reduction technique. In the no. 3 powerhouse-dam section area, the low-angle discontinuities, such as joints and faults, are mostly developed in the dam foundation rock mass, and constitute deep foundation stability problems. These weak structure planes affecting the dam foundation stability are modeled as continuum bodies in the finite element modeling according to their respective spatial geometrical characteristics including inclination and dip angle. Three-dimensional elastic-plastic finite element analyses are performed to obtain the stress and deformation distributions of TGD foundation and concrete structures. The factor of safety (FOS) of TGD foundation stability against sliding and its failure mechanics are comprehensively evaluated with the following criteria: (a) The maximum of the trial factors of shear strength reduction can be reached by which the dam foundation is brought to the critical equilibrium state; (b) The inflection points of the curves of the displacements of dam heel, dam toe and dam top, vs. the trial factors of shear strength reduction are located; and (c) Plastic zones develop along the potential sliding paths consisting of the dam heel, long and large joints, and other weak structure planes as the trial factors increase. The results obtained show that the dam foundation of the no. 3 powerhouse-dam section is stable under the designed normal load combinations. The evaluations of the FOS of dam foundation stability presented may provide a significant reference for the safety assessment of TGD in the Three Gorges Project, China.

Coalescence evaluation of collinear axial through-wall cracks in steam generator tubes

To maintain the structural integrity of steam generator tubes, usually, 40% of wall thickness plugging criterion has been adopted. However, since the criterion is applicable only for the steam generator tube containing a single crack, the interaction effect of multiple cracks cannot be considered. In this paper, the coalescence pressure of tube with dual cracks is evaluated based on detailed three-dimensional elastic–plastic finite element analyses. In terms of the crack configuration, collinear axial through-wall cracks with various length, distance and ratio between individual cracks are selected. The applicability of failure pressure prediction models recently proposed by the authors was verified by comparing the finite element analyses results with corresponding experimental data for tubes with two identical cracks. Further, in order to quantify the effect of crack length ratio on failure behavior, the failure pressure prediction model was used expansively for tubes containing different-sized cracks and a coalescence evaluation diagram was developed.

Nanogranular Origins of the Strength of Bone

Here, we investigate the ultrastructural origins of the strength of bone, which is critical for proper physiological function. A combination of dual nanoindentation, three-dimensional elastic-plastic finite element analysis using a Mohr-Coulomb cohesive-frictional strength criterion, and angle of repose measurements was employed. Our results suggest that nanogranular friction between mineral particles is responsible for increased yield resistance in compression relative to tension and that cohesion originates from within the organic matrix itself, rather than organic-mineral bonding.

A new constraint based fracture criterion for surface cracks

A new methodology for predicting the location of maximum crack extension along a surface crack front in ductile materials is presented. Three-dimensional elastic–plastic finite element analyses were used to determine the variations of a constraint parameter ( α h) based on the average opening stress in the crack tip plastic zone and the J-integral distributions along the crack front for many surface crack configurations. Monotonic tension and bending loads are considered. The crack front constraint parameter is combined with the J-integral to characterize fracture, the critical fracture location being the location for which the product Jα h is a maximum. The criterion is verified with test results from surface cracked specimens.

소성거동을 고려한 원주방향 관통균열 열림에 미치는 압력유기굽힘의 구속효과 평가 모델

This paper presents the model for evaluating restraint effect of pressure induced bending (PIB) on the circumferential through-wall crack opening displacement (COD), which considers plastic behavior of crack. This study performed three-dimensional elastic-plastic finite element (FE) analyses for different crack angle, restraint length, pipe geometry, stress level, and material conditions, and evaluated the influence of each parameter on the PIB restraint effect on COD. Based on these evaluations and additional perfectly-plastic FE analyses, a closed-form model to evaluate the restraint effect of PIB on the plastic crack opening of circumferential through-wall crack, was proposed as functions of crack angle, restraint length, radius to thickness ratio, axial stress corresponding to an internal pressure, and normalized COD evaluated from linear-elastic crack opening condition.

Assessment of bending fatigue limit for crankshaft sections with inclusion of residual stresses

The fatigue limit of rolled, ductile cast iron crankshaft sections under bending was investigated experimentally and analytically. The relationship of different failure criteria – specifically, surface crack initiation, resonant shifts, and two-piece failures – on the fatigue limit of the crankshafts was explored from testing. A comparison showed that using the surface crack failure criterion decreased the apparent fatigue limit of the crankshaft significantly. This result supported the theory of crack arrest in the fillet area of crankshafts and raises a significant challenge to the use of the surface crack failure criterion due to its inconsistent correlation to two-piece failure. Also an engineering practice for residual stress simulation and fatigue limit estimation due to a fillet rolling process on a crankshaft was explored. The complete analytical process was validated by the resonant bending fatigue test results. The normal stress distribution from the fillet surface-to-depth of a crankshaft section under bending was first obtained by a three-dimensional elastic finite element analysis. The residual stress distribution near the crankshaft fillet induced by a fillet rolling process was then determined by a three-dimensional elastic–plastic finite element analysis. A resultant normal stress distribution along any possible crack growth plane originating from the fillet surface and extending into the component was defined by superimposing the normal stress components due to the bending moment and the rolling load. Based on these calculated normal stresses, two fatigue models (such as the SWT equivalent stress and the effective stress intensity factor range) used to estimate the fatigue limits on surface cracks and in-depth cracks were examined by the experimental data. The results showed that the SWT equivalent stress was not a good fatigue damage parameter for surface cracks and the effective stress intensity factor range derived on the technique of crack modeling did correlate reasonably to the experimental data.

Fully plastic J-integral solutions for surface cracked plates under biaxial loading

In this paper, surface cracked plates under biaxial tension are studied. Three-dimensional elastic–plastic finite element analyses have been carried out to calculate the J-integral for surface cracked plate for a wide range of geometry, biaxiality and material properties. Fully plastic J-integral solutions along the front of the surface cracks are presented for Ramberg–Osgood power law hardening material of n = 3, 5, 10 and 15. Geometries considered are a/ c = 0.2, 1.0 and a/ t = 0.2, 0.4, 0.6 and 0.8 and the biaxial ratios of 0, 0.5 and 1. Based on these results, the J-integral along the crack front for general elastic–plastic loading conditions can be estimated using the EPRI scheme. These solutions are suitable for fracture analyses for surface cracked plates under biaxial loading.

Determining the stress and convergence at Beypazari trona field by three-dimensional elastic–plastic finite element analysis: A case study

In this paper, deformation and failure characteristics of the main drift, T-2000, and a roadway, T-3000 excavated for Beypazari trona (natural soda) underground mine, which is located in Ankara, Turkey, were investigated by in situ measurements and numerical analysis. T-2000 was planed as a main drift with a length of 965 m, 14° inclined and excavated with an area of 18 m 2. The T-3000 roadway was driven in the trona ore body for the first stope. Load and convergence measurements were carried out at seven stations installed in main drift (T2000) and roadway (T3000). Measurement results indicate that the total convergences at all the stations were below 1% of the total gallery height and deformation rates were reduced significantly. Three-dimensional numerical modeling was performed to analyze the deformation and failure behavior of the drift for three different models using an elasto-plastic finite element method (FEM) approach considering Drucker–Prager failure criterion. The results of the numerical analyses were found to be comparable with in situ measurements.

The Effect of Load Reduction Scheme on Crack Closure in the Near-Threshold Regime

Abstract Three-dimensional elastic-plastic finite element analyses were conducted to model fatigue crack growth in an M(T) specimen. Variable amplitude loading with a continual load reduction was used to simulate the load history associated with fatigue crack growth threshold measurement. Load reductions with both constant load ratio R and constant maximum stress intensity Kmax were used. Results indicated that load reduction with constant R generated a plastic wake such that remote crack opening occurred during loading, with the crack front opening prior to a region remote to the crack front. The last region to open was located at the point at which the load reduction originally began, and at the free surface. In contrast, for load reduction with constant Kmax, the crack front was the last to open. The results also indicated the crack opening process is three-dimensional in nature, with regions in the interior opening prior to regions near the free surface.

Development of circumferential through-wall crack K-solutions for control rod drive mechanism nozzles

The US Nuclear Regulatory Commission (USNRC) has undertaken a program to assess the integrity of control rod drive mechanism nozzles in existing plants that are not immediately replacing their reactor pressure vessel heads. This paper summarizes some of the efforts undertaken on behalf of the USNRC for the development of circumferential crack-driving force solutions to be used in probabilistic determinations of the time from detectable leakage to failure. Detailed three-dimensional elastic–plastic finite element analyses of these nozzles were conducted to determine the effects of operating conditions, tube-to-head interference fit, tube yield strength, and nozzle-to-head angle on the crack-driving force. Three major observations to date are: • Conducting simple tube-only analyses can severely overpredict the actual crack-driving force in the control rod drive mechanism nozzles. • The crack-driving force is a strong function of the nozzle yield strength, nozzle-to-head angle, interference fit, and weld residual stress; and • In many cases, when the crack is made to be perpendicular to the wall of the nozzle, the operating conditions and residual stresses appear to create some crack closure along the crack faces, suggesting that cracks in service will grow at an angle through the thickness.