Elastic-plastic Fracture Mechanics Parameters Research Articles

Efficient technique for evaluation of three-dimensional elastic–plastic fracture mechanics parameters based on equivalent distributed stress concept

This study proposes an efficient technique for the evaluation of the elastic–plastic fracture mechanics (EPFM) parameters of three-dimensional (3D) cracks based on the modified crack cohesive force (CCF) model. In the current method, the 3D crack’s EPFM parameters are analyzed by applying the pseudo crack face traction (CFT) to a two-dimensional (2D) center crack in an infinite plate. This pseudo traction is called the equivalent distributed stress (EDS). The EDS to be applied on the 2D center crack is determined in a manner that reproduces the relationship between crack length and stress intensity factor (SIF) of the intended 3D crack. Once EDS is determined, EPFM parameters for 3D cracks can be obtained instantly by using the center crack’s analytical closed-form solutions. This approach can compute the 3D crack’s EPFM parameters in dramatically less computation time than 3D finite element (FE) analysis. The effectiveness of the proposed method is validated by comparing the EPFM parameters of a 3D penny-shape crack obtained from this method against the reference analytical solutions and numerical FE analysis results. The parameters determined by the present method show excellent agreement with the reference solutions.

Static assessment of flawed thin AlSi10Mg parts produced by Laser Powder Bed Fusion

Several factors must be considered within the assessment of parts produced by Additive Manufacturing (AM) such as, for example, heterogeneous microstructure, process-induced defects, surface quality, residual stresses, and dependence on the material’s properties with the building orientation. All these factors severely affect the resistance to static and fatigue loadings of AMed components. Among the possible failure mechanisms, the failure promoted by static loadings when cracks are present is one of the most important failure conditions, in particular for the as-built parts, which might have reduced fracture toughness and ductility compared to the wrought alloy counterpart. In this work, we present a comprehensive approach to the static assessment of AlSi10Mg parts manufactured by Laser Powder Bed Fusion. Two benchmark fracture geometries were designed to investigate the typical AM geometrical features: i) thin walls in tension and ii) notched components in bending. Finite Element analyses of the benchmark specimens showed that an approach based on elastic–plastic fracture mechanics parameters is needed to correctly predict the experimental failures, despite the quasi-brittle behaviour shown by the AlSi10Mg alloy. In view of these results, this paper explores the applicability of the Failure Assessment Diagram (FAD), a tool used for conventional ductile materials, to static assessment of AMed parts. The results show that the assessment approach based on the FAD makes it possible to properly predict the experimental failures of the benchmark specimens.

EPFM Analyses of a Complex Crack in Dissimilar Metal Welded Pipes

Abstract Accurate estimation of elastic-plastic fracture mechanics (EPFM) parameters for a crack in nuclear pipes was considered as an important factor for leak-before-break design and evaluation. Yet few EPFM studies have been made to predict the crack opening displacement and J-integral of dissimilar metal welded pipes, which consist of two-layered materials (TLMs), due to the difficulty of complicate analysis encompassing both through-wall crack and internal surface crack in radial and circumferential directions. In this study, a series of finite element analyses to determine the typical EPFM parameters were carried out considering idealized complex-cracked pipes with TLMs. The analyses were elaborated through applying three loading conditions of axial tension, bending moment, and internal pressure. Both J-integral and crack opening displacement values were calculated by assuming two kinds of equivalent materials based on weighted average concepts as well as two different materials. The proposed equivalent schemes can be utilized in not only improving the expansion to existing solutions but also in more accurate detailed leak-before-break assessment of complex cracked nuclear piping with TLMs.

Short fatigue crack behaviour of LZ50 railway axle steel under multi-axial loading in low-cycle fatigue

An experimental study was carried out on the low-cycle fatigue of LZ50 railway axle steel under multi-axial loading. The initiation and propagation behaviour of a short fatigue crack was observed and analysed as per the principles of effective short fatigue crack. Our results showed that in the microstructurally short crack (MSC) stage, the crack propagation was strongly influenced by the microstructural features of the material and did not satisfy the linear elastic fracture mechanics. At the physically short crack (PSC) stage, the crack was long enough to not be directly influenced by the microstructures; nevertheless, linear elastic fracture mechanics still could not explain the law of crack propagation properly owing to the large-scale yield range of the crack tip. Based on these observations, a crack growth rate model under multi-axial loading was presented to explain the short fatigue crack behaviour. The non-linear elastic-plastic fracture mechanics parameter, J-integral (cyclic), was adopted as the driving parameter in this model and the crack closure effect was also taken into account. In the MSC stage, the crack growth rate fluctuated significantly when the cyclic J-integral was used owing to the influence of the microstructure. However, at the PSC stage, the crack growth rate fluctuations were small. A linear correlation for the PSC was obtained with R = 0.934 and this model could be applied to describe the short fatigue crack behaviour in the PSC stage.

Application of a New, Energy-Based ΔS* Crack Driving Force for Fatigue Crack Growth Rate Description.

This paper presents the problem of the description of fatigue cracking development in metallic constructional materials. Fatigue crack growth models (mostly empirical) are usually constructed using a stress intensity factor ΔK in linear-elastic fracture mechanics. Contrary to the kinetic fatigue fracture diagrams (KFFDs) based on stress intensity factor K, new energy KFFDs show no sensitivity to mean stress effect expressed by the stress ratio R. However, in the literature there is a lack of analytical description and interpretation of this parameter in order to promote this approach in engineering practice. Therefore, based on a dimensional analysis approach, ΔH is replaced by elastic-plastic fracture mechanics parameter—the ΔJ-integral range. In this case, the invariance from stress is not clear. Hence, the main goal of this paper is the application of the new averaged (geometrically) strain energy density parameter ΔS* based on the relationship of the maximal value of J integral and its range ΔJ. The usefulness and invariance of this parameter have been confirmed for three different metallic materials, 10HNAP, 18G2A, and 19th century puddle iron from the Eiffel bridge.

Mixed mode (I+II, I+III) fatigue crack growth description in S355/P355NL1 steel

Fatigue crack growth models (mostly empirical) are usually constructed using stress intensity factor – ΔK in linear-elastic fracture mechanics. Contrary to the kinetic fatigue fracture diagrams (KFFDs) based on ΔK, Kmax new energy diagrams based on strain energy density parameter ΔH, ΔS* demonstrates no sensitivity to mean stress effect expressed by the stress ratio R. According to the dimensional analysis approach ΔH, ΔS* is replaced by elastic-plastic fracture mechanics parameter based on the energy parameter associated with ΔJ energy parameter range. Hence, the main goal of this paper is the application of the new averaged strain energy density parameter ΔS* based on hysteresis loop curves for cracked components under uniaxial as well as multiaxial stress state. The presented approach assumes that the fatigue crack growth increment in the elastic-plastic range is caused by the combination of the maximum value of the energy parameter and its positive part of the range in each cycle of loading. The usefulness and invariance of this parameter have been confirmed in many works.

The heat energy dissipated in the material structural volume to correlate the fatigue crack growth rate in stainless steel specimens

The heat energy exchanged in a unit volume of material per cycle, Q¯, has been previously proposed and adopted by the authors as a fatigue damage indicator, because it accounts for the response of the material to the external applied loads as a result of energy conversion from the intrinsic mechanical dissipation. Q¯ can be determined by means of temperature measurements performed in situ during fatigue tests, at least for certain classes of metallic and composites materials. Originally conceived as a point-related physical quantity, recently a theoretical frame and an experimental procedure have been defined to average Q¯ inside a volume surrounding the tip of a fatigue crack. The resulting averaged heat energy per cycle Q¯∗ is an appropriate candidate to correlate crack growth data generated from fracture mechanics tests, especially at relatively high applied ΔK values, when the Linear Elastic Fracture Mechanics hypotheses are violated. The present paper is focussed on the use of Q¯∗ as an elastic-plastic fracture mechanics parameter. First of all, the size of the structural volume, where Q¯ is to be averaged to calculate Q¯∗, was defined with reference to an AISI 304L stainless steel. After that, the averaged heat energy Q¯∗ was determined during crack propagation tests starting from the temperature maps measured in situ by means of an infrared camera. The use of Q¯∗ resulted promising because it could take into account crack acceleration due to excessive plasticity. Finally, in the context of energy-based approaches to fatigue crack propagation problems, a link between the averaged heat energy Q¯∗ and Rice’s J-integral has been discussed and formalised.

Finite-Element Analysis of Crack Arrest Properties of Fiber Reinforced Composites Application in Semi-Elliptical Cracked Pipelines

In nowadays, repair method using fiber reinforced composites as the mainstream pipe repair technology, it can provide security for X100 high-grade steel energy long-distance pipelines in engineering. In this paper, analysis of cracked X100 high-grade steel pipe was conducted, simulation analysis was made on structure of pipes and crack arresters (CAs) to obtain the J-integral value in virtue of ANSYS Workbench finite element software and evaluation on crack arrest effects was done through measured elastic-plastic fracture mechanics parameter J-integral and the crack arrest coefficient K, in a bid to summarize effect laws of composite CAs and size of pipes and cracks for repairing CAs. The results indicate that the K value is correlated with laying angle λ, laying length L2/D1, laying thickness T1/T2of CAs, crack depth c/T1 and crack length a/c, and calculate recommended parameters for repairing fiber reinforced composite CAs in terms of two different crack forms.

Elastic-plastic fracture mechanics approach for stress corrosion cracking of nickel aluminium bronze under ammonia-containing artificial seawater

With the growth of urbanization and industries, the seawater near coastal areas has become polluted, and the nickel aluminium bronze components around coastal areas are affected by ammonia-containing seawater. Unfortunately, the influence of the ammonia concentration in seawater on the stress corrosion cracking of thin nickel aluminium bronze components with large plastic zones at the defects has not been evaluated before. In the present work, stress corrosion cracking experiments on nickel aluminium bronze components under artificial seawater and ammonia-containing artificial seawater were conducted using a four-point bending technique. The elastic–plastic fracture mechanics parameter ( J-integral) was evaluated using finite element analysis. The J-integral successfully characterized the crack growth rate under the present corrosive environments. Stress corrosion cracking was possible under both artificial seawater and ammonia-containing artificial seawater. The threshold J-integral for susceptibility to stress corrosion cracking ( JSCC) and fracture toughness ( JC) was the highest for stress corrosion cracking under artificial seawater and decreased as the amount of ammonium hydroxide added to the artificial seawater increased.

Structural integrity assessment of turbine disk on a plastic stress intensity factor basis

Based on a new fracture mechanics parameter, this study is concerned with assessing the integrity of a cracked steam turbine disk operating under startup-shutdown cyclic loading conditions. Damage accumulation and growth in service occurred on the inner surface of the key slot. To determine the elastic-plastic fracture mechanics parameters, full-size stress-strain state analysis of the turbine disk was performed for semi-elliptical cracks under startup loading conditions. As a result, the distributions of the elastic and plastic stress intensity factors along the crack front in the key slot of the turbine disk were defined according to the surface crack form. An engineering approach for predicting the lifetime of cracked turbine disks is proposed. The predictions of the crack growth rate and residual lifetime of the steam turbine disk are compared for elastic and elastic-plastic solutions. It is shown that the previously proposed elastic crack growth models overestimate the lifetime with respect to the model presented in this research. The expediency of using the plastic stress intensity factor to characterize the fracture resistance as the self-dependent unified parameter for a variety of turbine disk configurations rather than the magnitude of the elastic stress intensity factors alone is also discussed.

A plastic stress intensity factor approach to turbine disk structural integrity assessment

This study based on a new fracture mechanics parameter is concerned with assessing the integrity of cracked steam turbine disk which operate under startup-shutdown cyclic loading conditions. Damage accumulation and growth in service have occurred on the inner surface of slot fillet of key. In order to determine elastic-plastic fracture mechanics parameters full-size stress-strain state analysis of turbine disk was performed for a quote-elliptical part-through cracks under considering loading conditions. As a result distributions of elastic and plastic stress intensity factors along crack front in slot fillet of key of turbine disk depending on surface crack form are defined. An engineering approach to the prediction of carrying capacity of cracked turbine disk which is sensitive to the loading history at maintenance is proposed. The predictions of the rate of crack growth and residual lifetime of steam turbine disk are compared for elastic and elastic-plastic solutions. It is shown that the previously proposed elastic crack growth models provide overestimate the lifetime with respect to the present one. An advantage to use the plastic stress intensity factor to characterize the fracture resistance as the self-dependent unified parameter for a variety of turbine disk configurations rather than the magnitude of the elastic stress intensity factors alone is discussed.

Coupled Fatigue Crack Initiation and Propagation Model Utilizing a Single Blunt Notch Compact Tension Specimen

Many power generation facilities equipped with turbomachinery are designed to provide electric energy on an as-needed basis and, as a consequence, impart a mixture of fatigue and creep damage to high-value components at elevated temperatures. Cracks are often initiated on free surfaces of these parts near stress-raising features and propagate under thermal-mechanical cycling until the component is removed from service. Whether the emphasis is on creep or fatigue failure, most conventional structural life prediction approaches decouple crack initiation from crack propagation. Turbine designers are in need of approaches that span the full life cycle of components in which both initiation and propagation are the consequences of a variety of mechanical failure modes. Although recent fracture mechanics methods have been developed to account for fatigue- and creep-crack growth, a tacit assumption is that a precrack exists. Another main limitation of these approaches is the small scale yielding assumption, associated with linear elastic fracture mechanics, in which extensive plasticity invalidates such analyses. In this study, utilizing a blunt notch compact tensile specimen, experimental routines involving crack initiation and propagation within a single specimen at elevated temperatures with plastic-inducing loads and hold periods were conducted. Founded on existing elastic and elastic-plastic fracture mechanics (EPFM), a coupled crack initiation and propagation model is presented. Through the use of the EPFM parameter J, the proposed models are observed to accurately predict crack initiation and replicate crack propagation rates based on the imposed experimental conditions. The model is demonstrated on an austenitic stainless steel, type 304, subjected to moderate temperatures in air. Mechanical testing, metallurgical analysis, and analytical modeling allow for a simplified phenomenological life prediction model capable of predicting crack initiation and propagation at elevated temperatures. Consequently, structural analysis of critical locations of components can span the gamut of crack initiation, crack growth, and instability (i.e., total life assessment).

Evaluation of fracture mechanics parameters for bimaterial compact tension specimens

The elastic–plastic fracture mechanics parameter J and its analogous creep fracture parameter C* are widely used to measure the fracture resistance of a material. The non-linear component of the J and C* parameters can be evaluated experimentally using the η factor. For weldments, the η factor is dependent on the relative properties of the base (parent) and weld materials, particularly the mismatch in their yield strengths. In this work, the η factor has been evaluated using non-linear finite element analyses in a standard compact tension C(T) specimen for a power law material. A range of mismatches in base/weld material properties have been considered. A through thickness strip of weld material, of height 2h, has been modelled, which was positioned at the mid height of the specimen. The η factor has been evaluated for a range of crack lengths and power law hardening exponents under both plane stress and plane strain conditions and the results compared with literature where available. For a given crack length and weld width, the η solutions of the undermatched and overmatched conditions examined show a maximum variation of 12% from the mean value. A relationship has been proposed with respect to crack length for the C(T) specimen to describe the decrease in the η factor with an increase in mismatch ratio.

Fatigue crack growth behavior and mechanism of closed-cell PVC foam

The applicability of linear-elastic fracture mechanics parameters (DK and Kmax), elastic–plastic fracture mechanics parameter (DJ), and time-dependent fracture mechanics parameter (C*) to characterize fatigue crack growth (FCG) rate of closed-cell polyvinyl chloride foam was investigated in the present work. The effect of stress ratios (R ¼ 0.1 and 0.4) on FCGs was observed when the DK, Kmax and DJ were used as fracture mechanics parameters. As a fracture mechanics parameter that combines DK and Kmax, the K* successfully characterized FCGs (da/dN )a tR ¼ 0.1 and 0.4. While, a time-dependent fracture mechanics parameter (C*) successfully correlated da/dt of creep crack growth (CCG) test, but it failed to correlate da/dt of FCG tests. The FCGs at both R ¼ 0.1 and 0.4 were cyclic dependent, while the CCG was time dependent. For cyclic-dependent crack growth, the interaction between polymer-chain scission and small scale cracktip blunting was the main mechanism, whereas the interaction between polymer-chain pullout and large scale crack-tip blunting dominated fracture process for time-dependent crack growth. POLYM. ENG. SCI., 53:1719–1727, 2013. a 2012 Society of Plastics Engineers

1210 高温環境下におけるSUS304平板の疲労き裂進展評価(G02-4 疲労の特性および評価,G02 機械材料・材料加工部門)

High-temperature plants, such as nuclear and thermal power plants are used under severe conditions. High temperature plants are susceptible to micro-cracks in its structure. This is because there is the effect of cyclic fatigue and creep fatigue. To prevent serious accidents, including small defects in the structure, we predicted the destruction, we must use safely. In particular, the evaluation of fatigue crack development is important. And, it is desirable to develop a more accurate assessment method. In this study, fatigue tests conducted for SUS304 which is often used in high temperature plant. Then observe the behavior of crack development, we examined the relationship between crack growth rate and the elastic-plastic fracture mechanics parameter, J-integral. In addition, the model plate with central crack, the J-integral analysis was performed by the virtual crack extension method.

Fatigue Growth Models for Multiple Long Cracks in Plates under Cyclic Tension Based on Δ<i>K<sub>I</sub></i>, ΔJ<i>-</i>Integral and <i>ΔCTOD </i>Parameter

This paper presents the implementation of fatigue crack growth power law equations based on ΔK,ΔJ-integral andΔCTODfracture mechanics parameters determined in an FE analysis, to plates with multiple site damage (MSD). Results of fatigue tests with constant amplitude tensile loading carried out on mild steel plate specimens damaged with a single central crack and with three collinear cracks are presented. A relatively larger plastic zone occurred in the crack tip region at higher fatigue crack growth rate (FCGR), from 10-7to 10-6m/cycle. The crack growth models based on the elastic-plastic fracture mechanics (EPFM) parameters describe better fatigue crack growth in this range as compared to the liner elastic models.

Limit loads and fracture mechanics parameters for thick-walled pipes

In this paper, information on plastic limit loads and both elastic and elastic-plastic fracture mechanics parameters is given for cracked thick-walled pipes with mean radius-to-thickness ratios ranging from two to five. It is found that existing limit load expressions for thin-walled pipes can be applied to thick-walled pipes, provided that they are normalized with respect to the corresponding un-cracked thick-walled pipe values. For elastic fracture mechanics parameters, FE values of the influence functions for the stress intensity factor and the crack opening displacement are tabulated. For elastic-plastic J, it is shown that existing reference stress based J estimates can be applied, provided that a proper limit load for thick-walled pipes is used.

A Proposal for Evaluation Method of Crack Growth Due to Cyclic Overload for Piping Materials Based on an Elastic-Plastic Fracture Mechanics Parameter

The magnitude of Niigata-ken Chuetsu-Oki earthquake in 2007 was beyond the assumed one provided in seismic design. Therefore it becomes an important issue to evaluate the crack growth behaviors due to the cyclic overload like large earthquake. Fatigue crack growth is usually evaluated by Paris's law using the range of stress intensity factor (ΔK). However, ΔK is inappropriate in a loading condition beyond small scale yielding. In this study, the crack growth behaviors for piping materials were investigated based on an elastic-plastic fracture mechanics parameter, J-integral. It was indicated that the crack growth due to the cyclic overload beyond small scale yielding could be the sum of fatigue and ductile crack growth. The retardation effect of excessive loading on the crack growth was observed after the loading. The modified Wheeler model using J-integral has been proposed for the prediction of retardation effect. Finally, an evaluation method for crack growth behaviors due to the cyclic overload is suggested.

Computational assessment of cracks under strain-gradient plasticity

With introducing the strain gradient into plasticity theory, the crack field singularity at the crack tip changes. Characterization of the crack in strain-gradient dependent materials has not found a common consensus. In the present work the crack tip field is systematically investigated within the frame of the strain-gradient plasticity using the element-free Galerkin method. Under both small scale yielding and finite yielding conditions the crack field in strain-gradient plasticity consists of three zones: The elastic K-field, the known plastic HRR-field dominated by the known energy release rate, \({\mathcal G}\), and the hyper-singular stress field which cannot be characterized by the known fracture mechanics parameters. Effects of the finite strains have been considered for both small scale yielding and finite cracked specimens. The computational results show that the finite strains do not change the characterization of the crack tip fields under the strain-gradient plasticity. In all investigated cases the hyper-singular zone is small (\({r < \mathcal G/\sigma_0}\)) and well contained by the HRR zone under the \({\mathcal G}\) dominance condition. The hyper-singular zone is in the size of \({r/(\mathcal G/\sigma_0)}\) and may grow with the material length, but decrease with applied load. The known elastic-plastic fracture mechanics parameter, \({\mathcal G}\), can be directly applied to characterize the crack under strain-gradient plasticity, within the intrinsic material length much smaller than the overall component size, l < 0.1%L0. In this case the strain-gradient term in the gradient plasticity will not affect description of cracks.

1004 弾塑性破壊力学パラメータに基づく繰返し過大荷重による配管材のき裂進展評価法の提案(OS10-1 供用エネルギー機器の経年変化と健全性評価-欠陥評価-)

1004 弾塑性破壊力学パラメータに基づく繰返し過大荷重による配管材のき裂進展評価法の提案(OS10-1 供用エネルギー機器の経年変化と健全性評価-欠陥評価-)