Fracture Mechanics Calculations Research Articles

Cavity growth – or lack thereof – in imperfectly roll bonded sheet metal

Roll bonding is a well-established solid-state joining method that has also found commercial use. In current industrial practice, a near-perfectly bonded interface is commonly aimed for, achieved by optimizing surface preparation and rolling parameters. On the other hand, an intriguing recent study has shown that roll bonding scrap metal has the potential to provide significant environmental benefits while not jeopardizing performance, despite the resulting imperfect interface with a distribution of cavities. This present work focuses on the mechanical aspects of this observation, aiming to provide a deeper understanding of the influence (or lack thereof) of the cavity content on the mechanical behavior of a roll bonded stainless steel, and a roll bonded mild steel. Imperfectly bonded samples of both steels are studied using mechanical tests and microstructure characterization, which both revealed that the interface cavities exhibit limited growth and no crack nucleation or propagation into the interface. A numerical finite element model of the imperfectly bonded sheet confirmed a tendency for low cavity growth by showing that opening stresses on the interface cavity remain low for various geometries and loading conditions, in line with linear elastic fracture mechanics calculations. Overall, this experimental-numerical study provides insights regarding the unexpected formability (and thus the wide applicability) of imperfectly roll bonded sheets.

A three-dimensional thermal-hydro-mechanical coupling model for simulation of fracturing driven by multiphysics

Geothermal mining, nuclear waste disposal, and other projects involve rock fracturing under the multiphysics effect. There is an urgent need for a numerical analysis tool that can consider both thermal-hydro-mechanical coupling (THM) effects and rock fracturing to analyze such projects. This paper presents a three-dimensional thermal-hydro-mechanical coupling model that can consider rock fracturing, which incorporates the advantages of the combined finite discrete element method (FDEM) for simulating fracture and fragmentation. The 3D thermal-hydro-mechanical coupling model includes three parts: fracture-pore mixed seepage model, heat transfer model (including heat conduction in solid and fluid, heat advection, heat exchange between solid and fluid), and FDEM fracture mechanics calculation model. Some examples with the analytical solution for seepage, hydromechanical, thermal–mechanical, hydrothermal, and thermal-hydro-mechanical coupling problems are used to verify the correctness of the FDEM based 3D THM model in detail. In addition, an example of rock fracturing caused by the thermal-hydro-mechanical coupling effect is also given. The simulation results show that the FDEM based 3D thermal-hydro-mechanical coupling model can simulate the complex fractures initiation, propagation, and extension caused by multiphysics effects, such as heat, fluid, and mechanics.

Weight function procedure for reduced order fracture analysis of arbitrary flaws in cylindrical pressure vessels

Fracture mechanics calculations using the finite element method can be computationally expensive, which makes them challenging to use in engineering evaluations of flaws in pressure vessels. The weight function (WF) technique is a reduced order fracture modeling method that is widely used to greatly reduce these computational costs. Its computational efficiency is essential for use in probabilistic fracture mechanics evaluations of embrittled nuclear reactor pressure vessels (RPVs), due to the large number of sampled flaws that must be evaluated. Although the WF technique is general, it is typically used only for axis-aligned flaws. Recent discoveries of off-axis flaws in operating nuclear reactors have necessitated detailed simulations of such flaws and the interactions between neighboring flaws. This paper presents a generalized WF approach applicable for analyzing arbitrary flaw geometries in thick-walled cylindrical vessels, including surface-breaking and subsurface flaws, which can either axis-aligned or off-axis, and can account for interactions with other flaws. This approach is demonstrated on representative simulations of multiple flaw geometries in a RPV subjected to transient loading conditions. In all cases, the WF technique gives good comparison with benchmark results from direct simulation with greatly reduced computational effort.

Fatigue Crack Initiation and Propagation Relation of Notched Specimens with Welded Joint Characteristics

This study focuses on predicting the fatigue life of notched specimens with geometries and microstructure representative of welded joints. It employs 26 series of fatigue tests on welded and non-welded specimens containing notches located in different material zones, including the parent material, weld metal, and heat-affected zone. Overall, 351 test samples made of six structural steels are included in the present evaluation. For each individual specimen, the stress concentration factor, as well as the stress distribution in the notched section, was determined for subsequent fracture mechanics calculation. The latter is employed to estimate the fraction of fatigue life associated with crack propagation, starting from a small surface crack until fracture. It was shown that the total fatigue life can be realistically predicted by means of fracture mechanics calculations, whereas estimates of the fatigue life until macroscopic crack initiation are subject to numerous uncertainties. Furthermore, methods of statistical data analyses are applied to explore correlations between the S–N curves and the notch acuity characterized by the notch radius, opening angle, and the stress concentration factor. In particular, a strong correlation is observed between the notch acuity and the slope of the S–N curves.

A FDEM-based 2D coupled thermal-hydro-mechanical model for multiphysical simulation of rock fracturing

A coupled thermal-hydro-mechanical (THM) model based on the combined finite-discrete element method (FDEM) is presented for simulating rock cracking driven by multi-physics. The THM model contains three parts: a fracture-pore mixed seepage model, a heat transfer model , and a fracture mechanics calculation model. By combining any two of the above three models, a coupled thermal-mechanical (TM) model, a coupled hydrothermal (TH) model, and a coupled hydromechanical (HM) model are constructed. Then, the TM model, TH model, and HM model are combined to build the THM model, which is implemented in a GPU parallel multiphysics finite-discrete element software, namely MultiFracs. Finally, we use this THM model to study the hydraulic fracturing process of hot dry rock. The simulation results indicate that in addition to the primary fracture perpendicular to the direction of the minimum in situ stress , branching fractures along the direction of the minimum in situ stress are also produced during the hydraulic fracturing process. The proposed THM model can simulate heat and fluid transfer in fractured reservoirs, crack initiation, propagation, and intersection.

Set-up of a Generalized Dataset for Crack-Closure-Mechanisms of Cast Steel

In components, crack propagation is subjected to crack-closure-mechanisms which affect the build-up of the relevant threshold stress intensity factor range during cyclic loading. As structural parts are exposed to service loads incorporating a variety of load ratios, a significant change of the long-crack threshold value occurs, leading to a severe stress ratio dependency of crack-closure-mechanisms. Thus, an extensive number of crack propagation experiments is required to gain statistically proven fracture mechanical parameters describing the build-up of closure effects as crack growth resistance curves.The article presents a generalized dataset to assess the formation of crack-closure-mechanisms of cast steel G21Mn5+N. Numerous crack propagation experiments utilizing single edge notched bending (SENB) sample geometries are conducted, incorporating alternate to tumescent stress ratios. The statistically derived, generalized crack growth resistance curve features the impact of closure effects on the crack propagation rate in a uniform manner. To extend the dataset to arbitrary load ratios, the long-crack threshold approach according to Newman is invoked. The generalized dataset for the cast steel G21Mn5+N is validated by analytical fracture mechanical calculations for the utilized SENB-sample geometries. Incorporating a modified NASGRO equation, a sound correlation of analytical and experimental crack propagation rates is observed. Moreover, the derived master crack propagation resistance curve is implemented as a user-defined script into a numerical crack growth calculation tool and supports a local, node--based numerical crack propagation study as demonstrated for a representative SENB-sample. Concluding, the derived dataset facilitates the calculation of fatigue life of crack-affected cast steel components subjected to arbitrary stress ratios.

Numerical Fracture mechanics based prediction for the roughening of brittle cracks in 2D disordered solids

The behavior of fractures in 2D brittle disordered materials results from the competition between the microstructural disorder that roughens cracks and the material elasticity that straightens them. The experimental fracture surfaces left behind are generally scale invariant and their complex geometry are still largely unexplained. Here, this issue is addressed numerically using the boundary element method that predicts incrementally the trajectory followed by cracks in an infinite elastic medium with a heterogeneous field of fracture energy. The predicted fracture profiles are characterized using their height-height correlation function and show scale invariant properties. In particular, simulated cracks are shown to follow a random walk with roughness exponent $$\zeta = 0.5$$ , irrespective of the level of microstructural disorder, indicating that the crack behavior is neither persistent nor anti-persistent, but instead, that the orientation of the next propagation increment is chosen randomly, independently of the past trajectory. This behavior is then interpreted from fracture mechanics calculations that show that the restoring force emerging from elasticity that generally straightens cracks vanishes in the limit of large specimens with respect to the characteristic size of the material heterogeneity. Our findings shed light on some experimental fracture patterns recently reported and suggests an explanation for the observation of two different types of fracture morphologies in 2D disordered brittle solids.

Fatigue life extension of existing welded structures via high frequency mechanical impact (HFMI) treatment

High Frequency Mechanical Impact (HFMI) is one of the post-weld treatment methods. In this study, comparative axial fatigue tests were conducted on as-welded and HFMI-treated welded transverse attachment details. The test results demonstrated the efficiency of HFMI-treatment in fatigue life extension of cracked welded structures, providing that the existing crack size is less than 1.2 mm. Cracks were created in some specimens through fatigue testing before HFMI-treatment, while other specimens were not subjected to any fatigue loading prior to treatment. Many of the treated specimens ran-out after 10 million cycles of loading when tested at a stress range of 150 MPa. Therefore, the stress range was increased to 180 MPa or 210 MPa. No remarkable difference was found between the fatigue strength of the crack-free and the cracked treated specimens. It was found that the induced compressive residual stress can exceed the material yield limit, and reach a depth larger than 1.5 mm in most of the cases. The induced compressive residual stress, the local material hardening, the increase in weld toe radius, the change in crack orientation and the shallowness of the crack size were the causatives of the obtained long fatigue lives of the HFMI-treated specimens. Besides, linear elastic fracture mechanics calculations were conducted to predict the fatigue lives of as-welded and HFMI-treated details. The results were in agreement with the experiment. Moreover, the calculations showed that the initial crack size, the clamping stress and the induced compressive residual stress were the main factors behind the scatter in fatigue lives.

Damage tolerance-based methodology for fatigue lifetime estimation of a structural component produced by material extrusion-based additive manufacturing

Abstract While additive manufacturing of polymers, especially material extrusion-based methods such as fused filament fabrication, has become increasingly popular for design studies, rapid prototyping and the production of non-critical spare parts, its application in structurally loaded components is still scarce. One of the reasons for this might be scepticism of engineers due to the lack of knowledge regarding the expected lifetime and reliability of these components under stress. Therefore, it is necessary to find fast, easy and reliable ways to determine the expected lifetime of a component without the need to apply expensive full-scale component testing for every new part. To realise this, finite element analysis combined with fracture mechanical lifetime calculations can be applied. In this paper, crack growth kinetics of the commonly used material poly(lactic acid) have been utilised to estimate the lifetime of a component under complex loading conditions, namely fatigue and friction. The calculated lifetime, based on a damage tolerant fracture mechanics approach, was found to be in good agreement to the results of full-scale component tests, proving the applicability of the chosen approach. Applying this knowledge can vastly decrease the necessary time during component design and encourage the additive manufacturing community towards applying their components also in structurally loaded applications.

Numerical simulation and experimental investigation on a steam turbine blade fractured from the lacing hole

Failure analysis of a 17th stage blade of a steam turbine fractured in the vicinity of the lacing hole is discussed in this study. For this purpose, visual inspection, chemical and structural analyses, hardness and uniaxial tensile tests, macro and micro-fractography, fracture mechanics calculations, as well as computer simulations have been carried out. According to the results of the hardness and tensile tests and a comparison with the properties of AISI 410 martensitic stainless steel, it can be claimed that the blade did not experience any deterioration of mechanical properties during the service. Fractographic observations revealed the high cyclic fatigue as the main failure mechanism of the blade and showed that the fatigue crack is initiated and propagated adjacent to the lacing hole, from the brazing interface between the rod and the blade due to a lack of proper filler attachment as well as the presence of micro cracks within the brazing metal. In addition, estimation of the failure stresses based of fractographic observations, fracture mechanics and computer-aided calculations indicated that the failure of the blades has not been due to any abnormal stresses. Finally, a computer simulation of the fatigue crack growth indicated that after the crack initiation, about 3.75 h should be enough for the crack to reach the critical crack dimensions.

Fracture studies on carbon steel straight pipes having off-centred circumferential through-wall crack under finite compliance

The level-3 Leak-Before-Break (LBB) assessment of nuclear piping system is based on simplified fracture mechanics calculations. A postulated through-wall circumferential crack is shown to be stable even under extreme loading conditions. An important aspect of this fracture assessment, which is generally not considered, is the reduction in load at the cracked section that occurs due to the local and global compliance of the piping system. In this study, the effect of piping system compliance, crack size and crack location on the load carrying capacity of SA-333 Gr. 6 carbon steel pipes was analysed. Experimental investigations were performed on 8״ NB Schedule 100 pipes (Outer diameter 219 mm and wall thickness of approx. 12.6 mm) under quasi-static four point bending loads. Out of the six fracture tests, one specimen had a through-wall circumferential crack at the centre (along the length of pipe) and the remaining five tests had off-centred cracks. While the initial crack size showed a weak influence on the load carrying capacity of a stiff piping system, the effect of crack location was, however, quite significant. Calculations based on twice-elastic slope (TES) method and limit analysis of uncracked piping system (in some cases) for evaluation of load carrying capacity of pipes under finite compliance may lead to large safety margins.

Remarks on quasi-static and interlaminar fracture toughness tests of composite structures

The critical energy release rate is one of the most important material properties used in fracture mechanics calculations, in particular, an estimation of a structural residual life. The determination of this material property can be performed in numerous standardized tests, depending on the desired crack extension mode. However, some parameters of such tests are not discussed in standards and are not taken into consideration during the determination of the critical energy release rate. In this study, the authors present results of their experimental studies for quasi-static and fracture tests on double cantilever beam specimens made of glass and carbon reinforced polymeric composite structures. The results of these studies show the influence of technological aspects of the specimens’ preparation as well as data acquisition during performing experiments on the final results. These results will be used for a developed reversed numerical model for a prediction of the residual life of composite structures containing barely visible impact damage.

Treatment of reliability in fracture assessments using BS 7910 Annex K

This paper presents the background to the development of Annex K (‘Probabilistic assessment’) of BS 7910:2013, in particular the use of Partial Safety Factors (PSFs) in fracture assessment. These were originally derived using Probabilistic Fracture Mechanics (PFM) calculations, and in principle allow the user to estimate the probability of failure (Pf) associated with a deterministic fracture assessment simply by dividing (or multiplying) the inputs by a series of PSFs given in look-up tables.Calculations carried out using modern PFM software have shown that the PSFs given in Annex K are appropriate only for a narrow range of fracture scenarios, reflecting the conditions used to derive the PSFs in the first place – namely, thick-section plates with low fracture toughness and large through-thickness flaws. The use of Annex K tends to over-estimate Pf for other situations, and the use of direct PFM calculations is preferable where possible. The implications for the next revision of BS 7910 are discussed.

Cracking and spalling of the oxide layer developed in high-burnup Zircaloy-4 cladding under normal operating conditions in a PWR

In this paper, the evolution of cracks from the surface of a thick oxide layer on Zircaloy-4 cladding has been analyzed for the normal operation of pressurized-water reactors. The conditions for the propagation of radial cracks towards the interface, channeling along the axis of the cladding, and the possible subsequent spalling of the oxide have been studied. The analysis was conducted by first calculating how the stresses in the oxide developed during operation, using a numerical model that incorporates multiple mechanisms such as creep, swelling and oxidation. These calculations demonstrate that the circumferential stresses within the oxide increase as oxidation proceeds and as the cladding expands under the effect of fuel swelling. Although the intrinsic growth stresses of the oxide are compressive, tensile stresses can eventually develop in the outer region of the oxide. Within this regime, the energy-release rate for the radial propagation of a crack was determined using the J-integral along with the calculated stress profile. By assuming a suitable value of toughness for the oxide, it is possible to determine the depth to which such a radial crack can grow. A second fracture-mechanics calculation was then conducted to explore the conditions under which such a surface crack can subsequently channel along the axial direction of the cladding. A third fracture-mechanics analysis considered oxide spalling. This showed the possibility of spalling from the radial cracks, which leaves a thin layer of the oxide adhered to the metal that can result in a local cold spot responsible for hydride formation.

On repair weld residual stresses and significance to structural integrity

This paper starts with a brief state of the art assessment on what has been learned over the last few decades in understanding residual stress development mechanisms, particularly those uniquely associated with weld repairs. A special emphasis will be given to how some of the residual stress features contribute to structural integrity of a component containing weld repairs. In contrast to initial fabrication welds, residual stresses associated with finite length repair welds tend to exhibit important invariant features, regardless of component configurations, materials, and to some degree, welding procedures. Such invariant features are associated with the severe restraint conditions present in typical repair situations. A number of weld repair cases are examined in this paper. In addition to highlighting important residual stress distribution features, fracture mechanics calculations are performed to examine how repair weld residual stresses quantitatively contribute to crack driving force as a function of crack location and size. One simple and effective technique for mitigating detrimental residual stress effects on structural integrity is also demonstrated by considering overall weld repair dimensions.

Critical defect size assessment in pipelines on a nuclear power plant

In many energy industry structures, pipeline systems are subject to the impact of mechanical forces, moments of forces and fluid flows of high pressure and temperature. These load factors cause defects in the pipeline metal. As the years of operation increase, defects may occur and grow, which may lead to the destruction of pipeline walls. Special measures have been planned and implemented to ensure the safe operation of high-energy facilities. This study focused on pipelines and nozzles of nuclear power plant equipment with bimetal welded joints on which the size of critical defects was assessed. The base of assessment covers material properties, temperature and stress fields, fracture mechanics calculations. This study involves developing of finite element models and implementing simulations on them in order to obtain temperature fields and determine the stress-strain state of the component.

Pressurized Thermal Shock analysis of the reactor pressure vessel

PTS analysis is a substantial part of the technical analyses supporting the license application for operation beyond design life. Guidance for the analysis’ concept is given by the Hungarian nuclear regulator which is in line with the relevant international rules. Involving technical support organizations and independent consultants as well as taking into account the changes in fuel management Paks NPP, Hungary, compiled a new PTS analysis. Subjects of the analysis were the RPV belt line region components as well as other circumferential welds of the RPV including nozzle region. Beyond the PTS initiating events selected on the basis of engineering judgment a PSA provided additional transients which showed a higher frequency than 10-5 /year. Thermal-hydraulic calculations completed for each selected PTS initiating event provided the necessary input for the structural analysis. Based on core configurations end-of-life fluence were calculated. Neutron dosimetry surveillance results were used to verify the calculations. Temperature and stress field calculations were performed by solving the system of equations of elasticity. Underclad crack was postulated for fracture mechanics calculation. KI was calculated at the crack tip and the boundary between the cladding and base / weld metal; KIc was calculated on the basis of the reference curve. Comparison of these two parameters (KI ≤KIc), i.e. evaluation of whether the postulated defect stability criteria was met, gave the result.

Experimental study of transverse attachment joints with 40 and 60 mm thick main plates, improved by high-frequency mechanical impact treatment (HFMI)

In recent years, high-frequency mechanical impact (HFMI) treatment has grown in popularity due to its efficiency in improving the fatigue strength of welded joints. The fatigue performance of HFMI-treated welded steel joints has, however, not been thoroughly studied for plate thicknesses above 30 mm. In this study, 40 and 60 mm thick main plates with non-load-carrying transverse attachments have been fatigue tested under constant amplitude four-point bending, both in as-welded and HFMI-treated condition to investigate the fatigue performance for large plate thicknesses, typical for weldments in bridges. Axial fatigue strengths were estimated by a modification of the experimental results with fracture mechanics calculations. The main conclusions are that HFMI treatment can result in significant fatigue strength improvement even for large main plate thicknesses and that the difference in fatigue strength between bending and axial loading is negligible for the specimen geometries used in this study.

Shot Peening Effect on Fatigue Crack Repaired Weldments

Fracture mechanics calculations are required to validate the safety level defined in design codes to prevent a fatigue failure. The periodic inspection-assessment cycle can lead to the implementation of a fatigue crack repair by crack removal. To improve the fatigue performance of the crack repair, residual compressive stresses induced by peening can be considered. This paper is in relation to the peening effect estimation on stress intensity factors in fatigue crack repaired weldments, since the stress intensity factor is a key parameter in fracture mechanics calculations. A set of T-butt specimens were experimentally fatigue tested and crack propagation data was gathered for the calculation of stress intensity factors. The experiments were designed to estimate the residual compressive stress depth layer and its effect on crack propagation inhibition. Experimental estimation of the peening effect on stress intensity factors in fatigue crack repaired weldments was validated by comparison against an analytical weight function solution. Experimental stress intensity factors determined from a set of fatigue tested T-butt specimens allowed estimating preliminarily that peening has a limited effect on fatigue crack propagation inhibition for edge repaired T-butt weldments subjected to bending loading.

Crack propagation analysis and rehabilitation by HFMI of pre-fatigued welded structures

This paper deals with a crack propagation analysis of welded structures and rehabilitation after pre-fatigue loading by the high-frequency mechanical impact (HFMI) post-treatment technique. The investigated specimen type is a thin-walled longitudinal stiffener made of mild steel S355. Fracture mechanical calculations are primarily performed on the basis of the weight-function approach. Thereby, the local residual stress condition at the weld toe is considered by the aid of a structural weld simulation, whereas the numerically evaluated residual stress distribution in depth agrees well to X-ray measurement results. The fracture mechanical analysis illustrates that by incorporating the residual stress state, the calculated lifetime is in good accordance to the conducted fatigue test results. By application of the HFMI-treatment as rehabilitation method, it is found that the beneficial post-treatment effect increases especially by a reduction of the applied load-level. Hence, particularly for minor nominal stress ranges near the high-cycle fatigue region, the mechanical post-treatment as repair method is utmost effective leading to almost equal fatigue strength as for the HFMI-treated specimens without pre-cycling. Finally, proposals for the crack growth assessment of welded structures and a conservative application of HFMI as rehabilitation method for mild steel joints are provided.