Cracked Components Research Articles

Analysis of Material Properties for the Numerical Simulation of Fatigue Crack Growth under Variable Amplitude Loading

The numerical simulation of crack closure is employed to assist on the prediction of crack growth rate. Under fatigue load, the stress-strain response of metals is altered due to cyclic loading. For this reason, the material properties characterization is of prime concern as an input parameter to obtain reliable results. From numerical simulations, it was observed that simple material models do not provide accurate data for long crack lengths. In this paper, the effect that different hardening models have on the opening response of a cracked component when it is subject to variable amplitude loading is analyzed. The interaction effects (crack arrest/acceleration) for long crack length simulation are specially highlighted. For this purpose, a 6082-T6 aluminium alloy was analyzed experimentally and numerically in order to measure crack closure, and then, those data were used to predict fatigue crack growth rate under different patterns of overload. The Paris equation and the Elber crack closure concept were employed. The results showed that small variations in the opening stresses obtained from different material models produce high overestimated simulations of crack growth rate. Also, it was proved that the crack closure mechanism is able to take into account interaction effects due to variable amplitude loading.

On the Beauty of Analytical Models for Fatigue Crack Propagation and Fracture—A Personal Historical Review

Abstract Starting from James Rice’s classical work on cyclic plastic stresses and deformations in the plastic zone of a Mode III loaded crack, it will be shown that the crack tip opening displacement of a Mode I crack in a work hardening material can be written in analytical form. This result was then used to formulate the blunting line for J-integral testing and to estimate the fatigue crack propagation rate of a number of materials. In a similar manner—based on the strain distribution within the plastic zone of a work hardening material—the initiation of crack extension under static loading was estimated. The stress distribution ahead of a crack and the Ritchie, Knott. and Rice model were applied to the ductile-to-brittle transition of ferritic steels as well as the transition temperature shift due to neutron irradiation. Inspired by Fong Shih’s contribution to the Electric Power Research Institute Handbook, a simple but straightforward method for expressing the δ5 crack opening displacement as a crack driving force for fully plastic conditions was developed, finally ending up in a comprehensive assessment method for cracked components. The application to mismatched welded joints was demonstrated to be possible if the yield load for mismatch is available; this latter task was performed using both slip line theory and finite element (FE) analyses. Application examples of these models will be shown, and it will be seen that estimates using these models are in reasonable agreement with experimental results and FE analyses. Several elements of these models have made their way to international codes and standards.

Residual stresses in the quasi‐simultaneous laser transmission welding of amorphous thermoplastics

AbstractLaser transmission welding is frequently being used increasingly for joining complex, assembly‐oriented components, thanks to its small heat affected zone. As a result of the cooling processes, residual stresses can develop inside the components, potentially leading to stress cracking and premature component failure. One subgoal of process design should therefore be to reduce the level of residual stresses as far as possible when laser welding is employed. This work looks into experimental testing for residual stresses, as a factor for the weld parameters in quasi‐simultaneous laser transmission welding, with the objective of determining the optimum welding parameters. The ARAMIS optical measuring system for deformation analysis was used to this end, in conjunction with a modified hole‐drilling method. POLYM. ENG. SCI., 50:1520–1526, 2010. © 2010 Society of Plastics Engineers

Fracture Mechanics of Gray Cast Iron

The fracture mechanism of gray cast iron was investigated on tension loaded samples produced under different conditions. The parameters studied included the graphite morphology, the carbon content, the inoculation and the cooling condition. The observations made reveal the role of the microstructure on crack propagation. The cracks were found to always propagate parallel with the graphite flakes. The interaction between the metallic matrix precipitated as primary austenite and graphite has been interpreted by a simplified model of the austenite reinforced eutectic cell. The geometrical transcription gave a standard crack component configuration with known mathematical solution. The microstructure observed in the experiments has been analysed by means of a novel interpretation. The fictitious stress intensity at yield and the fictitious maximum stress intensity at failure are strongly related to the relative shape of the eutectic cell and the fraction primary austenite. A different slope is observed for the material cooled at high rate when the precipitation of primary carbide reduces the stress intensity. The observed relations indicate that the tensile strength of the grey cast iron is the result of the collaboration between the toughness of the metallic matrix precipitated as primary austenite and the brittleness of the graphite phase. The shape and distribution of the primary austenite and graphite can be influenced by chemical composition, by inoculation or by the cooling condition, but they will maintain equilibrium with respect to the stress intensity.

A Three-Dimensional Finite Element Analysis of the Stress Intensity Factors for Different Fracture Modes of Homogeneous Bimaterial

Abstract The failure of cracked components is governed by the stresses in the vicinity of the crack tip. The singular stress contribution is characterized by stress intensity factors. The stress intensity factors depend on the geometry of the component and on loading condition. This paper addresses the evaluation of stress intensity factors (SIFs) of opening, shearing and tearing modes for compact tension specimens for bonding homogeneous materials. The aim of this work is to find the optimal pre-cracked length, crack notch radius, and crack notch angle in order to eliminate the effect of them on the SIF and then on the fracture toughness. To achieve this goal, a three- dimension finite element analysis (FEA) model using the ANSYS program is constructed for specimens made of homogeneous materials such as stainless steel bonding with epoxy as a filler material. The effects of notch angle, notch tip radius and pre-crack length on the stress intensity factors are studied for different fracture modes. The results for the stress intensity factors KI, KII and KIII are obtained using the linear elastic fracture mechanics (LEFM) approach.

An approximation for the cyclic state of stress ahead of cracks and its implications under fatigue crack growth

Abstract Numerical methods are mostly used in the field of fatigue to derive the stress intensity factor (SIF) or J -integral solutions to be employed in damage tolerance analysis of cracked components. In this frame, simple assumptions about material properties are taken into account. More refined approaches try to describe the plasticity-induced crack closure in order to account for retardation effects under variable amplitude loading. In these approaches, the cyclic plasticity is used and cyclic finite element analyses are carried out. In the present work, a novel strategy is presented for the calculation of the relevant parameters to the fatigue crack growth, based on the evaluation of local field parameters ( J -integral, T -stress) and cyclic material properties. It is demonstrated that, in case of mild steels and under the assumption of a stress ratio R = −1, the global constraint factor α g widely employed in fatigue crack growth algorithms such as the strip-yield model, can be calculated in a closed-form on the basis of the expression of the crack-tip fields. Moreover, α g provides a reasonable explanation of the fatigue crack growth behaviour of the A1N steel for different geometrical and loading configurations. Further investigations carried out on different medium and high strength steel grades show that the plastic radius ahead of small and long cracks at their fatigue limits can be considered as a constant for the material.

Coupled phenomenological and fracture mechanics approach to assess the fracture behaviour of TWC piping component

The present study demonstrates the numerical prediction of experimental specimen J-R curve using Gurson–Tvergaard–Needleman phenomenologically based material model. The predicted specimen J-R curve is used to determine the geometric independent initiation fracture toughness ( J SZWc) value that compares well with experimental result. Using the experimentally determined and numerically predicted J SZWc values and specimen J-R curves, the accuracy of predicting the fracture behaviour of the cracked component is judged. Thus the present study proposed a coupled phenomenological and fracture mechanics approach to predict the crack initiation and instability stages in cracked piping components using numerically predicted specimen J-R curve obtained from tensile specimens testing data.

Surface Deformation Nanostructures and Stress Corrosion Crack Precursors Originating from Surface Grinding

AbstractStress corrosion cracking (SCC) in light water reactor components has long been studied from a post mortem perspective, yielding insights into water chemistries and effects on crack propagation. Analysis of a cracked component does not effectively provide information on the corrosion events or on SCC initiation. It is important that microstructures of these early stages be understood because the original surface of the component formed during fabrication is often not the final surface condition that is exposed to reactor water. Pre-service grinding of reactor components and welds is performed for a variety of reasons, from aesthetics to preparation for non-destructive testing. It is this final surface microstructure that often controls SCC initiation. Surface and near-surface characteristics have been investigated in 304SS metal coupons on which controlled grinding was performed. These examinations indicate the extent of subsurface microstructural damage before high-temperature water exposure. Analytical electron microscopy techniques have been used to gain insights into possible surface precursors to corrosion damage and SCC initiation. Nanocrystalline grains were commonly found at the surface in lightly ground to heavily abraded materials within the first ˜0.5-10 ųm along with high dislocation densities, twinning and lath structures.

Quantification and modelling of the stomatal, cuticular and crack components of peach fruit surface conductance

This study describes the components of fruit surface conductance. It aims to revise a modelling framework examining water loss across the fruit epidermis in relation to time and fruit growing conditions. For this purpose, cuticular crack surface area, healing artificial wounds in vivo, stomatal number and total fruit surface conductance were quantified during nectarine (Prunus persica L. nucipersica) fruit growth under contrasted irrigation regimes or thinning intensities. The contribution of stomatal component to total conductance decreased very early. A sub-model of the specific cuticular conductance according to fruit age was proposed that accounted for the complex temporal variation of the cuticular component. The occurrence of cracks was modelled by considering the relative expansion rate of the cuticle as a function of fruit fresh mass and relative expansion rate of the fruit. Healing decreased with fruit age. The observed temporal variations of fruit surface conductance and cuticular crack surface area were well simulated by the modified model whatever the fruit growing conditions. Tests on independent data revealed that the model was highly sensitive to parameters related to cuticular crack development and to cuticular properties.

Enhancement of leak rate estimation model for corroded cracked thin tubes

During the last couple of decades, lots of researches on structural integrity assessment and leak rate estimation have been carried out to prevent unanticipated catastrophic failures of pressure retaining nuclear components. However, from the standpoint of leakage integrity, there are still some arguments for predicting the leak rate of cracked components due primarily to uncertainties attached to various parameters in flow models. The purpose of present work is to suggest a leak rate estimation method for thin tubes with artificial cracks. In this context, 23 leak rate tests are carried out for laboratory generated stress corrosion cracked tube specimens subjected to internal pressure. Engineering equations to calculate crack opening displacements are developed from detailed three-dimensional elastic-plastic finite element analyses and then a simplified practical model is proposed based on the equations as well as test data. Verification of the proposed method is done through comparing leak rates and it will enable more reliable design and/or operation of thin tubes.

Reference stress method for evaluation of failure assessment curve of cracked pipes in nuclear power plants

In order to obtain a precise failure assessment curve (FAC) in the R6 defect assessment procedure, it is necessary to evaluate the J-value of cracked components. The reference stress method can be used for estimating J-values. However, the accuracy of estimation depends on the limit load used for evaluating the reference stress. In this study, the applicability of several limit load solutions was investigated through comparison with the results of elastic-plastic finite element analyses (FEA). A pipe containing a circumferential surface crack was analyzed under pure bending load. Six materials used in nuclear power plants were assumed. It was shown that the reference stress method is valid for FAC evaluation. The maximum non-conservativeness caused by using the reference stress method is less than 20% compared to the results obtained by FEA.

복합응력이 작용하는 균열 배관에 대한 천이 크리프 조건에서의 C(t)-적분 예측 (II) - 탄-소성-크리프 -

The C(t)-integral describes amplitude of stress and strain rate field near a tip of stationary crack under transient creep condition. Thus the C(t)-integral is a key parameter for the high-temperature crack assessment. Estimation formulae for C(t)-integral of the cracked component operating under mechanical load alone have been provided for decades. However, high temperature structures usually work under combined mechanical and thermal load. And no investigation has provided quantitative estimates for the C(t)-integral under combined mechanical and thermal load. In this study, 3-dimensional finite element analyses were conducted to calculate the C(t)-integral of elastic-creep material under combined mechanical and thermal load. As a result, redistribution time for the crack under combined mechanical and thermal load is re-defined through FE analyses to quantify the C(t)-integral. Estimates of C(t)-integral using this proposed redistribution time agree well with FE analyses results.

Net-section limit moments and approximate J estimates for circumferential cracks at the interface between elbows and pipes

This paper firstly presents net-section limit moments for circumferential through-wall and part-through surface cracks at the interface between elbows and attached straight pipes under in-plane bending. Closed-form solutions are proposed based on fitting results from small strain FE limit analyses using elastic–perfectly plastic materials. Net-section limit moments for circumferential cracks at the interface between elbows and attached straight pipes are found to be close to those for cracks in the centre of elbows, implying that the location of the circumferential crack within an elbow has a minimal effect on the net-section limit moment. Accordingly it is also found that the assumption that the crack locates in a straight pipe could significantly overestimate the net-section limit load (and thus maximum load-carrying capacity) of the cracked component. Based on the proposed net-section limit moment, a method to estimate elastic–plastic J based on the reference stress approach is proposed for circumferential cracks at the interface between elbows and attached straight pipes under in-plane bending.

Using Thermomechanical Conditioning Cycles to Improve Fracture Toughness of Low Carbon Steel

The improvement of material toughness has significant industrial applications. In this article, the thermomechanical conditioning (TMC) cycle (which involves simultaneous application of heat to a moderate temperature combined with a tensile load, followed by unloading and cooling to room temperature) was used to improve the fracture toughness of the material. Apparent fracture toughness (Ka) is denoted to represent the fracture toughness of cracked components after the application of TMC cycles. The TMC cycles result in a significant increase in the apparent fracture toughness (Ka) of AS 1548 grade 7-460R steel as compared to the fracture toughness (KIC) of the original material. It is found that the improvement in the apparent fracture toughness of the material was due to the increase in plastic strain and the plastic zone size ahead of the crack tip that occurred after applying TMC. In this study, both the apparent and original fracture toughness (Ka and KIC) are evaluated using the cylindrical notched tensile (CNT) technique, which is considerably cost effective over the standard compact tension specimens (ASTM E399).

Fracture analysis of strength undermatched Al‐Alloy welds in edge cracked tensile panels using FITNET procedure

ABSTRACTThis paper presents a methodology for the assessment of the remaining load carrying capacity of thin‐walled components under tension containing highly strength undermatched welds and edge cracks. The analysis is based on the strength mismatch option of the fracture module, part of the newly developed European fitness‐for‐service (FFS) procedure FITNET. The mismatch option of the FITNET fracture module allows weld features such as weld tensile properties and weld geometry to be taken into account in the fracture analysis of cracked welded components. The methodology described was verified for centre cracked Al‐alloy large tensile panels containing undermatched welds in Ref. [1] and hence the present work provides validation with experimental results of the single edge cracked (SEC) and double edge cracked (DEC) panels. The material used is an age‐hardening aluminium alloy 6013 in T6 temper condition used in welded airframe components. The welds in the form of butt joints were produced using the CO2 laser beam welding process. The results show that by using the FITNET FFS methodology with an appropriate selection of the input parameters, safe acceptable predictions of the maximum load carrying capacity of the welded panels can be obtained. It should also be noted that one of the main difficulties that engineers encounter when applying mismatch analysis for first time is its apparent complexity. A step‐by‐step analysis is proposed here in order to provide guidance for this kind of assessments.

A scientific evaluation of the approximate 2D theories for composite repairs to cracked metallic components

In this paper, we show how the published literature reveals that the approximate two-dimensional solution for the stress intensity factor associated with cracked panel repaired using an externally bonded composite repair is inconsistent with experimental data, and that for short to mid-size cracks the fibre bridging effect is often a second-order effect. The result of this finding is that prediction of the effect of a composite repair on the structural integrity of cracked components repaired by an externally bonded composite repair is dramatically simplified. We also show why structures repaired using Glare patches have a fatigue performance that is superior to structures repaired using boron epoxy or carbon fibre patches.

Modelling of a cracked aluminium plate repaired with composite octagonal patch in mode I and mixed mode

Adhesively bonded composite patch repair technique has been successfully applied in military aircraft repair and has recently been expanded to commercial aircraft industry. This technique is applied to extend the service life of cracked aluminium components. In this paper, the finite element method is applied to analyse the central crack’s behaviour repaired by a boron/epoxy composite patch. The effects of the mechanical and geometrical properties of the patch on the variation of the stress intensity factor at the crack tip were highlighted. The obtained results show that the stress intensity factor at the crack tip, repaired by an octagonal patch of height 2 c/3, is reduced by 5% with regard to the one repaired by an octagonal patch of size ‘ c’. For a height patch of c/3 the reduction is about 7%. The maximum reduction of composite patch of fibres in y-direction is about 30% compared to the aluminium patch. This reduction doubles when a composite patch of fibres in x-direction is used. The adhesive properties must be optimised to increase the performance of the repair of structures by such reinforcement.

FE analysis of the behaviour of octagonal bonded composite repair in aircraft structures

Bonded composite repair has been recognized as an efficient and economical method to extend the fatigue life of cracked aluminium components. In this work, the finite element method is applied to analyze the central crack’s behaviour repaired by a boron/epoxy composite patch. The knowledge of the stress distribution in the neighbourhood of cracks has an importance for the analysis of their repair according to the patch geometry. The effects of mechanical and geometrical properties of the patch on the variation of the stress intensity factor at the crack tip were highlighted. The obtained results show that the stress intensity factor at the repaired crack with composite patch of height 2c/3 is reduced about 5% compared to cracks repaired with octagonal patch of size c. For patch height of c/3 the reduction is about 7%. The adhesive properties must be optimised in order to increase the repair performances and to avoid the adhesive failure.

On the Use of Mechanical Weight Functions for Practical Evaluation of Thermal Shock SIF's in Flexibly Restrained Edge-Cracked Plates

Two practical methods have been used to estimate thermal shock stress intensity factors (TS-SIF`s) associated with a flexibly restrained cracked plate. The first method used a traditional mechanical weight function (MWF) methodology in conjunction with the MWF derived for an equivalent freely restrained cracked component. The second method used a traditional MWF methodology in conjunction with the MWF derived for an equivalent rigidly restrained cracked component. Fracture mechanic finite element analyses were also undertaken to construct a comparative benchmark for the TS-SIF`s associated with a flexibly restrained cracked plate. The results of this comparison demonstrate the errors associated with these MWF methods to be acceptable, if and only if, the crack size is small, the crack component aspect ratio is large or the flexible boundary restraint stiffness are deemed negligible or near rigid. In addition, the curves derived with these MWF methods do not intersect and there is no obvious transition to distinguish which MWF method would be more appropriate for a given a particular flexible boundary restraint configuration. In effect, this means that these MWF methods cannot be confidently used to evaluate the TS-SIF`s associated with a flexibly restrained cracked component.

A study on the evolution of crack networks under thermal fatigue loading

The crack network is a typical cracking morphology caused by thermal fatigue loading. It was pointed out that the crack network appeared under relatively small temperature fluctuations and did not grow deeply. In this study, the mechanism of evolution of crack network and its influence on crack growth was examined by numerical calculation. First, the stress field near two interacting cracks was investigated. It was shown that there are stress-concentration and stress-shielding zones around interacting cracks, and that cracks can form a network under the bi-axial stress condition. Secondly, a Monte Carlo simulation was developed in order to simulate the initiation and growth of cracks under thermal fatigue loading and the evolution of the crack network. The local stress field formed by pre-existing cracks was evaluated by the body force method and its role in the initiation and growth of cracks was considered. The simulation could simulate the evolution of the crack network and change in number of cracks observed in the experiments. It was revealed that reduction in the stress intensity factor due to stress feature in the depth direction under high cycle thermal fatigue loading plays an important role in the evolution of the crack network and that mechanical interaction between cracks in the network affects initiation rather than growth of cracks. The crack network appears only when the crack growth in the depth direction is interrupted. It was concluded that the emergence of the crack network is preferable for the structural integrity of cracked components.