Net Section Stress Research Articles

Fatigue driving force of riveted shear joints in bridges — Replacing the net section stress

Many old steel bridges contain hot riveted double strap butt joints. The fatigue life of these joints is subject of growing concern. We collected 629 fatigue tests, showing that the fatigue resistance expressed as the net section stress range is extremely scattered. Based on the theory of mechanics and the finite element method, we developed analytical equations to estimate the hoop stress range in the plate at the rivet hole. Using this stress parameter, the scatter in fatigue resistance reduces significantly. The model also gives insight into how the joint geometry influences the fatigue resistance.

Dynamic failure assessment analysis of 15MnTi steel supporting structure with a circumferential surface crack under impact loads

Supporting structures, whose strength have great influence on the safe operation of the whole equipment, are widely used in various ship equipment. In this paper, dynamic failure assessment analysis is carried out to discuss the structural integrity of the cracked supporting structure under impact loads. Considering the dynamic response characteristics of structures, the dynamic fracture toughness determined by the loading rate of dynamic J-integrals is used to calculate the failure assessment point (FAP). Due to the widespread uncertainties in practical engineering, such as crack size and mechanical properties of materials, the failure assessment results will also have uncertainty. To analyze the structural integrity affected by uncertain variables, the polygonal convex set (PCS) model is introduced to the failure assessment diagram (FAD) to propose a non-probabilistic failure assessment method. The FAP is extended to a failure assessment region, and structural integrity can be analyzed by the non-probabilistic reliability degree. Compared with the traditional interval model, the non-probabilistic reliability degree calculated by PCS model is closer to the probabilistic reliability degree, which avoids premature judgement of structural failure. For the 15MnTi supporting structure with a circumferential semi-elliptical surface crack under impact loads, the critical depth obtained by non-probabilistic methods decrease by 10% compared with deterministic results, and the failure mechanism is summarized as plastic collapse resulting from the excessive net section stress. In the absence of statistical data on crack size or mechanical properties, the non-probabilistic failure assessment method can be used as an effective alternative to the probabilistic method.

Allowable stresses related to crack growth stability and leak-before-break for circumferentially cracked pipes governed by limit loads: Part II, Pipes subjected to bending moment

If cracks are detected in power plant pipes and the cracks are allowable, the plants can continue operating without the need for repair/replacement. The allowability of cracks is determined by means of allowable stresses, based on failure stresses. Failure bending stress at crack penetration is estimated by applying the Local Approach of Limit Load Criteria, which is based on the net-section stress approach. Using the stress at crack penetration, the allowable bending stress can be calculated for a pipe with a circumferential part-through crack. The allowable bending stress decreases with increasing crack depth and angle, as expected. However, the allowable bending stress can have one of three characters, depending on crack size: i) leak-before-break (LBB) and crack growth stability, ii) non-LBB and crack growth stability, and iii) non-LBB and crack growth instability. Character iii) represents a severe crack, and special attention needs to be paid to such a crack, even if it is allowable. Frequent non-destructive inspection and precise calculation of subcritical crack growth are recommended in order to prevent unexpected failure, especially for small-diameter thin-walled pipes. The boundaries of leak-before-break and crack growth stability can be successfully expressed by appropriate equations.

Allowable stresses related to crack growth stability and leak-before-break for circumferentially cracked pipes governed by limit loads: Part I, Pipes subjected to tensile loading

When cracks are found in high toughness ductile pipes governed by limit loads at in-service inspections, and the applied stresses at the cracked locations are less than the allowable stresses, the cracks are allowable. The allowable stresses are generally determined in combination with failure stresses and safety factors. Failure of pipes with circumferential part-through cracks subjected to tensile loading occurs in a two-step sequence: first there is the onset of crack penetration, and then there is the break after the crack penetration. The Local Approach of Limit Load Criteria, which is based on the net-section stress approach, can estimate both crack penetration and break stresses for high-toughness ductile pipes. Using the Local Approach of Limit Load Criteria, allowable tensile stresses based on crack penetration stresses are determined by means of safety factors for plant service level conditions. The allowable stresses decrease with increasing crack angles and depths. The characters of the allowable tensile stresses are found to vary with changing sizes of crack angles and depths. These different characters involve the presence/absence of two parameters: leak-before-break (LBB) and crack growth stability. The crack size boundary on LBB vs non-LBB can be expressed by appropriate equations containing crack depths and angles. In addition, the boundaries of crack growth stability/instability are also expressed by crack depths and angles. These boundaries are taken into consideration during non-destructive inspection and crack growth evaluation.

Safety assessment of allowable through-wall crack angles for pipes subjected to tensile loading

Fully plastic collapse stresses for high toughness ductile pipes with circumferential cracks subjected to tensile loading can be predicted by means of Limit Load Criteria based on the net-section stress approach. The Limit Load Criteria are provided by the ASME Code Section XI. Allowable membrane stresses for part-through cracks were determined by plastic collapse stresses in combination with safety factors. The allowable stresses decrease with increasing angles of the part-through cracks. When crack angles are large, the allowable stresses of the part-through cracks are larger than the collapse stresses of through-wall cracks. For such large cracks, allowable stresses greater than the collapse stresses cause instability, and are thus detrimental to pipe integrity, especially in thin-wall pipes, even though the stresses are allowed. In order to avoid the anxiety associated with this, it is necessary to establish maximum allowable crack angles. This paper proposes maximum allowable crack angles for allowable stresses based on the collapse stresses of through-wall cracks. The maximum allowable crack angles can be expressed by equations for various service level conditions.

Fully Plastic Failure Stresses and Allowable Crack Sizes for Circumferentially Surface-Cracked Pipes Subjected to Tensile Loading

Abstract Fully plastic failure stresses for circumferentially surface-cracked pipes subjected to tensile loading can be estimated by means of limit load criteria based on the net-section stress approach. Limit load criteria of the first type (labeled LLC-1) were derived from the balance of uniaxial forces. Limit load criteria of the second type are given in Section XI of the ASME (American Society of Mechanical Engineering) Code, and were derived from the balance of bending moment and axial force. These are labeled LLC-2. Fully plastic failure stresses estimated by using LLC-1 and LLC-2 were compared. The stresses estimated by LLC-1 are always larger than those estimated by LLC-2. From the literature survey of experimental data, failure stresses obtained by both types of LLC were compared with the experimental data. It can be stated that failure stresses calculated by LLC-1 are better than those calculated by LLC-2 for shallow cracks. On the contrary, for deep cracks, LLC-2 predictions of failure stresses are fairly close to the experimental data. Furthermore, allowable circumferential crack sizes obtained by LLC-1 were compared with the sizes given in Section XI of the ASME Code. The allowable crack sizes obtained by LLC-1 are larger than those obtained by LLC-2. It can be stated that the allowable crack size for tensile stress depends on the condition of constraint of the pipe, and the allowable cracks given in Section XI of the ASME Code are conservative.

Failure bending stresses for pressurized pipes with circumferentially part-through cracks

Stress corrosion cracks detected in austenitic stainless pipes were circumferential cracks at inside of the pipes. Failure stresses for the cracked pipes were developed by net-section stress concept. Limit Load Criterion provided by the ASME Code based on the net-section stress concept can estimate fully plastic collapse stress, which is called as failure stress. Local Approach of Limit Load Criteria for estimating stress at crack penetration had developed for a part-through cracked pipe based on the Limit Load Criteria. Advanced Local Approach of Limit Load Criteria for estimating stress at crack penetration is newly developed based on the Local Approach in this paper. In comparing with experimental stresses of pipe crack penetrations, the Limit Load Criteria give un-conservative estimation, and the Local and the Advanced Local Approaches are close to the experimental stresses. In addition, the Advanced Local Approach always gives higher stresses than the Local Approach for internal cracks, and it is shown that the Advanced Local Approach is beneficial for thick wall pipes with large angle cracks.

Crack initiation, propagation, and arrest in sintering powder aggregates

AbstractCracking during sintering is a common problem in powder processing and is usually caused by constraint that prevents the sintering material from shrinking in one or more directions. Different factors influence sintering‐induced cracking, including temperature schedule, packing density, and specimen geometry. Here we use the discrete element method to directly observe the stress distribution and sinter‐cracking behavior in edge notched panels sintered under a uniaxial restraint. This geometry allows an easy comparison with traditional fracture mechanics parameters, facilitating analysis of sinter‐cracking behavior. We find that cracking caused by self‐stress during sintering resembles the growth of creep cracks in fully dense materials. By deriving the constrained densification rate from the appropriate constitutive equations, we discover that linear shrinkage transverse to the loading axis is accelerated by a contribution from the effective Poisson's ratio of a sintering solid. Simulation of different notch geometries and initial relative densities reveals conditions that favor densification and minimize crack growth, alluding to design methods for avoiding cracking in actual sintering processes. We combine the far‐field stress and crack length to compute the net section stress, finding that it characterizes the stress profile between the notches and correlates with the sinter‐crack growth rate, demonstrating its potential to quantitatively describe sinter‐cracking.

On the influence of crystallography on creep of circular notched single crystal superalloy specimens

The present work contributes to a better understanding of the effect of stress multiaxiality on the creep behavior of single crystal Ni-base superalloys. For this purpose we studied the creep deformation and rupture behavior of double notched miniature creep tensile specimens loaded in three crystallographic directions [100], [110] and [111] (creep conditions: 950 °C and 400 MPa net section stress). Crystal plasticity finite element method (CPFEM) was used to analyze the creep stress and strain distributions during creep. Double notched specimens have the advantage that when one notch fails, the other is still intact and allows to study a material state which is close to rupture. No notch root cracking was observed, while microstructural damage (pores and micro cracks) were frequently observed in the center of the notch root region. This is in agreement with the FEM results (high axial stress and high hydrostatic stress in the center of the notched specimen). Twinning was observed in the notch regions of [110] and [111] specimens, and <112> {111} twins were detected and analyzed using orientation imaging scanning electron microscopy. The present work shows that high lattice rotations can be detected in SXs after creep fracture, but they are associated with the high strains accumulated in the final rupture event.

Tension failure analysis for bolted joints using a closed-form stress solution

Bolted joints are widely used to connect safety-critical parts in the aeronautical industry and require precise structural assessment tools. Focus of this paper is the development of an overall analytical calculation method to determine the stresses of a bolted joint with quasi-isotropic composite material, which is then used in a tension failure analysis. The stress solution is obtained by means of the Airy stress function. To predict crack initiation in the tension failure analysis use is made of the Theory of Critical Distances. Crack initiation occurs in the net section plane and its assessment requires precisely calculated net section stresses. For this purpose, the stress boundary conditions in load direction at the straight free edges must be fulfilled, which is reached by supplementing the field modelling the load introduction with auxiliary functions. This technique is a physically motivated means to deal with symmetric finite geometry problems involving straight free edges. However stress boundary conditions perpendicular to the load direction are not covered and some inaccuracies in the stress solution may arise. A failure analysis is conducted to investigate their impact on the predicted failure load using literature values based on Finite Fracture Mechanics as reference.

Microstructure evolution mechanisms in nickel-based single crystal superalloys under multiaxial stress state

Thin-walled plate specimens with square and triangular penetration pattern close-packed film cooling holes are used to study the evolution of the γ/γ′-microstructure of nickel-based single crystal superalloys during [001] orientation tensile creep. For both types of penetration patterns, the creep tests were performed at ligament efficiencies of 0.4 and 0.8 at 980 °C and a net section stress of 300 MPa. In contrast, the creep experiment of specimens with square penetration pattern film cooling holes at a ligament efficiency of 0.8 at 1050 °C was also carried out. Quantitative metallographic assessment is used to investigate the influence of the multiaxial stress state on the microstructural evolution of nickel-based single crystal superalloys. The results show that the evolution of the γ/γ′-microstructure in specimens with square and triangular penetration pattern film cooling holes is related to the kinetics of the stress redistribution during tensile creep. A minimum stress level is necessary for rafting to occur at a specific experimental temperature. The contrast between the mechanical results and microstructural findings shows the effect of the maximum principal stress and stress triaxiality on the microstructural evolution of nickel-based single crystal superalloy specimens with close-packed film cooling holes. The rafting orientation of the γ/γ′-microstructure is shown to be sensitive to the direction of the maximum principal stress. Finally, the γ/γ′ topological inversion is faster under higher ligament efficiency.

Experimental investigation and simulation on stress rupture behavior of a Ni-based DS superalloy affected by initial elastic-plastic multi-axial stress state

In this study, the stress rupture behavior of a Ni-based directionally solidified (DS) superalloy affected by initial elastic-plastic multiaxial stress state at 850 °C has been investigated. Smooth and three types of U-shape notched plate specimens have been adopted. The notch effect on stress rupture lives is exhibited as notch softening, and there is a positive correlation between the degree of notch softening and theoretical stress concentration factor. Scanning electron microscopy (SEM) observation is conducted to reveal failure mechanism. For both smooth and notched specimens, thickness dependence on crack initiation due to the changed crack tip stress state is exhibited. The initiation of microcracks is mainly caused by interfacial decohesion at the carbide/matrix interface, non-uniform deformation field at eutectic/matrix interface and stress concentration around cavities. The plastic fiber zone of smooth plate is located in the intermediate region, which is occurred throughout a wide region near notch root of notched specimen. Finally, a finite element analysis (FEA) is performed based on the transverses elastic viscoplastic constitutive model with the Kachanov-Rabotnov damage rule. The simulation results show that the effect of notch softening is due to the fact that the redistributed tensile stress is higher than the value of net section stress in a very wide region.

Failure bending moment of pipes containing multiple circumferential flaws with complex shape

Flaws due to stress corrosion cracking have been detected in stainless steel or nickel-based alloy dissimilar metal weld joints of piping systems in nuclear power plants. Generally, stainless steel and nickel-based alloy are ductile materials with high toughness, and the failure mode of flawed pipes made of ductile materials is expected to be net-section plastic collapse. Failure bending moment of a ductile pipe containing a circumferential flaw is predicted using the net-section stress approach according to ASME Code Section XI as a limit load criterion. However, in the current code, the failure bending moment can only be adopted for a pipe containing a single circumferential flaw with constant depth, although many flaws detected actually are multiple flaws, and the flaw shapes are generally complex. In this study, a failure estimation method for pipes containing multiple circumferential flaws with complex shapes was proposed. Furthermore, failure experiments were performed for 8-inch diameter Schedule 80 stainless steel pipes containing two circular circumferential flaws. The failure bending moments obtained from the experiments were compared with the estimated results. Based on the experimental results, it was concluded that the proposed failure estimation method satisfactorily represents the failure behavior of the pipes and can be applied in engineering application.

Plastic Collapse Stresses for Pipes With Inner and Outer Circumferential Cracks

Bending stresses at incipient plastic collapse for pipes with circumferential surface cracks are predicted by net-section stress approach. Appendix C-5320 of ASME B&amp;PV Code Section XI provides an equation of bending stress at the plastic collapse, where the equation is applicable for both inner and outer surface cracks. That is, the collapse stresses for pipes with inner and outer surface cracks are the same, because of the pipe mean radius at the cracked section being entirely the same. Authors considered the separated pipe mean radii at the cracked ligament and at the uncracked ligament. Based on the balances of axial force and bending moment, equations of plastic collapse stresses for both inner and outer cracked pipes were developed. It is found that, when the crack angle and depth are the same, the collapse stress for inner cracked pipe is slightly higher than that calculated by the Appendix C equation, and the collapse stress for outer cracked pipe is slightly lower than that by the Appendix C equation, as can be expected. The collapse stresses derived from the three equations are almost the same in most instances. However, for less common case where the crack angle and depth are very large for thick wall pipes, the differences among the three collapse stresses become large. Code users pay attention to the margins of plastic collapse stresses for outer cracked pipes, when using Appendix C equation.

Validation of the two-parameter fracture criterion for various crack configurations made of 2014-T6 aluminum alloy using finite-element fracture simulations – Part 2 TL-Orientation

In the present paper, the two-parameter-fracture-criterion (TPFC) validity and transferability are analysed using two-dimensional (2D) elastic-plastic finite-element fracture simulations with the critical crack-tip-opening-angle (CTOA) fracture criterion and plane-strain-core concept. Fracture simulations were performed on three crack configurations: (1) middle-crack-tension, M(T), (2) single-edge-crack-tension, SE(T), and (3) single-edge crack-bend, SE(B), specimens to predict failure loads and moments. They were made of 2014-T6 (TL) aluminum alloy. Fracture test data from Orange (NASA) were only available on M(T) specimens (one-half width, w = 38–152 mm), which were all tested at cryogenic (−200 °C) temperature. The critical crack-tip-opening-angle (CTOA) and a plane-strain-core height, hc, were selected to match the failure loads on the M(T) specimens. Fracture test data on the M(T) specimens were also used to determine the two fracture parameters (KF and m). All crack configurations were analysed over a very wide range of widths (w = 19–610 mm) and initial crack-length-to-width (ci/w) ratios ranged from 0.05–0.95. The TPFC was shown to fit the M(T) test data (±5%) and the simulated fracture data fairly well (within 6.5%) for all crack configurations for net-section stresses (Sn) less than the material proportional limit (σplσ). For M(T) specimens, a simple approximation was shown to work well for Sn > σpl. Further study is needed for Sn > σpl, for the SE(T) and SE(B) specimens.

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.

Stress Intensity Factors for Transformed Surface Flaws and Remaining Fatigue Lives Based on Flaw-to-Surface Proximity Rules

Subsurface flaws are sometimes found as blowholes near free surfaces of structural components. Net-section stress at the ligament between the free component surface and the subsurface flaw increases when the ligament size is short. It can be easily expected that the stress intensity factor at the tip of the subsurface flaw increases with decreasing the ligament size. Fitness-for-service (FFS) codes provide flaw-to-surface proximity rules, which are transformation from subsurface to surface flaw. Although the concepts of the proximity rules of the FFS codes are the same, the specific criteria for the rules on transforming subsurface flaws to surface flaws are significantly different among FFS codes. This study demonstrates the proximity criteria provided by the FFS codes and indicates that the increment of the stress intensity factors before and after the transformation depends on the flaw aspect ratio and the ligament size at the transformation from subsurface to surface flaws. In addition, it is shown that remaining fatigue lives for pipes with flaws are strongly affected by the ligament size at the transformation from subsurface to surface flaws.

How evolving multiaxial stress states affect the kinetics of rafting during creep of single crystal Ni-base superalloys

Miniature tensile creep specimens are used to investigate the effect of mild circular notches on microstructural evolution during [001] tensile creep of a Ni-base single crystal superalloy. Creep deformed material states from a uniaxial (950 °C, uniaxial stress: 300 MPa) and a circular notched creep specimen (950 °C, net section stress in notch root: 300 MPa) are compared. For both types of tests, creep experiments were interrupted after 81, 169 and 306 h. Quantitative scanning electron microscopy (SEM) is used to assess the evolution of the γ/γ′-microstructure from rafting to topological inversion. Scanning transmission electron microscopy (STEM) was applied to study the evolution of dislocation densities during creep. As a striking new result it is shown that in circular notched specimen, the microstructural evolution is well coupled to the kinetics of the stress redistribution during creep. Rafting, the directional coarsening of the γ′-phase, and the increase of γ-channel dislocation density, start in the notch root before the center of the specimen is affected. When stresses in the circular notched specimens are fully redistributed, the microstructural differences between the notch root and the center of the circular notched specimen disappear. The comparison of the mechanical data and the microstructural findings in uniaxial and circular notched specimens contribute to a better understanding of the role of mild notches, of stress multiaxiality and of strain accumulation in the microstructure evolution of single crystal Ni-base superalloys during creep. The results obtained in the present work are discussed in the light of previous work published in the literature.

Creep tests on notched specimens of copper

In Sweden, spent nuclear fuel is planned to be disposed off by placing it in canisters which are made of oxygen free copper alloyed with 50 ppm phosphorus. The canisters are expected to stay intact for thousands of years. During the long term disposal, the canisters will be exposed to mechanical pressure from the surroundings at temperatures up to 100 °C and this will result in creep. To investigate the role of the complex stress conditions on the canisters, creep tests under multiaxial stress state are needed. In the present work, creep tests under multiaxial stress state with three different notch profiles (acuity 0.5, 2, and 5, respectively) at 75 °C with net section stresses ranging from 170 MPa to 245 MPa have been performed.To interpret the experimental results, finite element computations have been conducted. With the help of the reference stress, the rupture lifetime in the multiaxial tests was estimated. The prediction was more precise for the higher acuities than for the lower one. In order to predict the creep deformation of the canisters for the long service period, fundamental creep models are considered. Previously developed basic models are used to compute the creep deformation in the multiaxial tests. Although the scatter is large, the agreement with the experiments is considered as acceptable, indicating that the basic models which have been successfully developed for uniaxial creep tests can also be used to describe multiaxial creep tests. Notch strengthening was observed for copper.

Reliability-based fatigue life estimation of shear riveted connections considering dependency of rivet hole failures

Standards and guidelines for the fatigue design of riveted connections make use of a stress range-endurance (S-N) curve based on the net section stress range regardless of the number and the position of the rivets. Almost all tests on which S-N curves are based, are performed with a minimum number of rivets. However, the number of rivets in a row is expected to increase the fail-safe behaviour of the connection, whereas the number of rows is supposed to decrease the theoretical stress concentration at the critical locations, and hence these aspects are not considered in the S-N curves. This paper presents a numerical model predicting the fatigue life of riveted connections by performing a system reliability analysis on a double cover plated riveted butt joint. The connection is considered in three geometries, with different number of rivets in a row and different number of rows. The stress state in the connection is evaluated using a finite element model in which the friction coefficient and the clamping force in the rivets are considered in a deterministic manner. The probability of failure is evaluated for the main plate, and fatigue failure is assumed to be originating at the sides of the rivet holes, the critical locations, or hot-spots. The notch stress approach is applied to assess the fatigue life, considered to be a stochastic quantity. Unlike other system reliability models available in the literature, the evaluation of the probability of failure takes into account the stochastic dependence between the failures at each critical location modelled as a parallel system, which means considering the change of the state of stress in the connection when a ligament between two rivets fails. A sensitivity study is performed to evaluate the effect of the pretension in the rivet and the friction coefficient on the fatigue life.