Use Of Fracture Mechanics Research Articles

Use of equivalent interface samples during fracture mechanics investigations for the design of adhesively bonded composite reinforcements on steel structures

During an international Joint Industry Project called SBO (Strength Bond Offshore), a design strategy of adhesively bonded composite reinforcements for steel structures was developed and assessed. It relied on the use of fracture mechanics. Yet, an adaptation of the characterization tests was needed to reduce the number of samples while remaining representative of the studied reinforcement. This adaptation was called “equivalent interface samples”.This paper aims at presenting the proposed adaptation of fracture mechanics tests for mode I, mode II and mixed mode, and its use during the design strategy. First, the geometry of the samples will be presented. Then, the obtained results during the fracture mechanics experimental campaign will be introduced. Those investigations relied on the use distributed optical fiber sensor to monitor the crack propagation during the tests. The obtained toughness characterizations allowed us proposing a design strategy that was assessed in regards with experimental tests conducted on large size steel samples reinforced with adhesively bonded composite.

Extracting fracture properties from digital image and volume correlation displacement data: A review

AbstractThe advent of digital image and volume correlation has attracted wide use in fracture mechanics. The full‐field nature of digital image and volume correlation allows for the integration of computational fracture mechanics to analyse cracked samples quantitatively. This review provides a comprehensive overview of current methods used to extract fracture properties from full‐field displacement data. The term full‐field fracture mechanics is introduced to highlight the uniqueness of using inherently noisy experiential data to extract fracture properties. The review focuses on post‐processing‐based approaches rather than integrated approaches, as these have less limitations and are more commonly employed. There are four approaches that are discussed in extracting fracture properties from experimentally computed displacement data: field‐fitting, integral, crack‐opening and cohesive zone modelling approaches. This is further developed to discuss problems associated with using digital image and volume correlation to extract properties, including application examples.

A probabilistic model for quantifying uncertainty in the failure assessment diagram

Failure assessment diagrams are an integral component of asset integrity management in a variety of industrial sectors. They allow for the assessment of the significance of cracks in structures, between the domains of brittle fracture and plastic collapse. Numerical modelling, or empirically determined assessment lines across this continuum, are the basis of the guidance in current industrial standards. However, as the requirement of such assessments progresses from demonstrating safety to optimising resilience and resource allocation, it will become necessary to compute more informative (probabilistic) estimates, which are compatible with decision analysis.In this paper, Bayesian regression models are proposed as a suitable method of quantifying (aleatory and epistemic) uncertainty in the limit state on a failure assessment diagram. The data considered in this study consists of laboratory tests completed on wide plate fracture specimens. This work is intended to address the inconsistencies in current editions of industrial standards, and limitations (regarding flexibility and application) of existing scientific literature on the topic.Potential applications are discussed, including the use of fracture mechanics in meaningful reliability analysis, quantitative risk management, and optimising experimental design for future material tests.

Assessment of fracture toughness of cemented carbides by using a shallow notch produced by ultrashort pulsed laser ablation, and a comparative study with tests employing precracked specimens

The use of fracture mechanics for rationalizing the fracture behavior of cemented carbides is valid, as far as sharp cracks, free of residual stresses and subjected to a well-defined stress state are used for assessing fracture toughness. However, machining a very sharp notch on the surface of hardmetals for fracture toughness testing has been a critical issue during many years. Within this context, introduction of surface “through-thickness” micronotches (SEμVNB) by means of ultrashort pulsed laser ablation (UPLA) is here proposed, implemented and analyzed as an innovative precracking-like route within flexural testing procedures for appropiated evaluation of fracture toughness of cemented carbides. UPLA parameters used for introducing the micronotch are optimized in terms of induced damage ahead of the notch tip. For comparison purposes, fracture toughness is also determined by means of flexural testing of previously cracked single-edge notch beams (SENB-Cracked) as well as specimens with V-notch tips sharpened through diamond polishing using a razor blade, and Palmqvist indentation microfracture method. The satisfactory agreement found between values measured using UPLA-micronotched and SENB-Cracked (reference) specimens allows to conclude that flexural testing of SEμVNB samples is a valid methodology for reliable determination of fracture toughness of hardmetals. This is feasible because of the extremely short time of laser-matter interaction. It yields small and somehow controlled damage in front of the notch tip as a result of shock wave propagation during ablation, which translates into effective precracking of SEμVNB specimens.

Fracture mechanics for fatigue design of metallic components and small defect assessment

The use of fracture mechanics based methodologies to assess the influence of defects on the high cycle fatigue resistance of mechanical components has become increasingly important for industrial applications and design. This presentation introduces the most commonly used fracture mechanics methods, emphasizing the assumptions on which they are based and analyzing their potential in predicting the influence of the main geometrical, mechanical and microstructural variables involved in the definition of the fatigue resistance of the components. Underlying hypotheses are discussed thoroughly and possible directions for future research are suggested. Applications examples on different configurations with small defects are presented. Finally, the potential of the fracture mechanics methodologies is analyzed when proposing simplifications suitable for use in the development of design documents for engineering applications.

Crack propagation in flexural fatigue of concrete using rheological-dynamical theory

The concrete fatigue analysis can be performed with the use of fracture mechanics. The fracture mechanics defines the fatigue crack propagation as the relationship of crack growth rate and stress intensity factor. In contrast to metal, the application of fracture mechanics to concrete is more complicated and therefore many authors have introduced empirical expressions using Paris law. The topic of this paper is development of a new prediction of fatigue crack propagation for concrete using rheological-dynamical analogy (RDA) and finite element method (FEM) in the frame of linear elastic fracture mechanics (LEFM). The static and cyclic fatigue three-point bending tests on notched beams are considered. Verification of the proposed approach was performed on the test results taken from the literature. The comparison between the theoretical model and experimental results indicates that the model proposed in this paper is valid to predict the crack propagation in flexural fatigue of concrete.

The Archimedes’ Constant, π Seen by Mechanical Engineers

Probabilistic engineering mechanics is used to relate the value of π with one of the main parameters in fracture mechanics. It proposes an engineering method to obtain the value of it from engineering data without involving any geometrical Euclidian’s circle’s data measurement or analysis. It is the first trial in studying the use of fracture mechanics to determine the value of ratio of circumference and diameter of Euclidean’s circles indirectly, and subsequently evaluate the number of the digits actually needed in fracture mechanics and engineering purposes.

A simple fracture mechanics estimation of the fatigue endurance of welded joints

The use of fracture mechanics based methodologies to assess the influence of defects on welded components has become increasingly important for industrial applications and design, in the last decades. However, there are still objections against these approaches due to their complexity and the consequent need of qualified personnel with certain level of knowledge of fracture mechanics. Therefore, development of simplified methods to evaluate severity of defects can be valuable for practical purposes. In the present work, a manageable expression is proposed to calculate the applied stress intensity factor for crack growth, which is proportional to the square root of crack length and the stress concentration factor at the location of the crack in the un-cracked body. The latter was obtained with numerical simulation of transversely loaded butt, T and cruciform joints. By means of the resistance curve method that accounts for short crack behaviour, these results can be compared with threshold for crack propagation to estimate the fatigue resistance of welded joints. Besides, a simple expression was derived to estimate the fatigue endurance, which can be used to understand and analyse in a simplified manner the influence of the main geometrical and mechanical parameters, like weld geometry, residual stresses and size of defects, among others. Estimations were compared with experimental results from literature for different weld configurations, and they proved to be conservative. Methodology is valid for toe cracks in as-welded joints.

Experimental and Numerical Investigations of Damage Behaviour at the Fibre Mortar Composite Interfaces

This paper deals with the experimental investigation and the numerical modelling of fibre mortar composite interface. This study focuses on the determination of failure types and the characterisation of mechanical behaviour at a fibre mortar-composite interface. The mechanical properties of fibre mortar are determined through laboratory tests. Experiments are carried out using a series of pull-out and shear tests to study the behaviour of composite/glue/fibre mortar assemblage. Numerical simulations based on the finite element method are used to predict the interface damage parameters as well as mixed mode crack initiation and propagation at the fibre mortar-composite interface. An interfacial decohesion model based on the indirect use of fracture mechanics is used to simulate the damage process. The model assumes a bilinear softening behaviour of the interfacial provided with stress-relative displacement laws. The interface parameters at the interface between fibre mortar and composite are evaluated and the failure mode determined.

Determination of Residual Fatigue Life of Welded Structures at Bucket-Wheel Excavators through the Use of Fracture Mechanics

This paper presents a methodological approach for the assessment of service life of vital welded structures of a bucket-wheel excavator Sch Rs 650/5x24 (’Thyssen Krupp’, Germany) boom, subjected to cyclic loading with a variable amplitude through the use of experimental tests carried out in order to determine operational strength and growth of a fatigue crack. Realized researches and results presented in this paper offer great possibilities for the analyses of behaviour of vital welded structures of the bucket-wheel boom. By the application of the measurement device with 8 channels for registration and processing of electric signals HBM Spider 8 and measurement tapes HBM 6/350xXY31 deformations were measured at vital welded structures of the boom in the area of the bucket-wheel, made of steels St 37.2 and St 52.3 in accordance with standard DIN 17100, or steels S235J2G3 and S355J2G3 in accordance with standard EN 10025-2. The objective of the test is to determine if there is a possibility of occurrence of plastic deformations or initial cracks due to fatigue at vital welded structures. Tests that refer to the growth of the fatigue crack located at the welded joint have been carried out by bending at three points with asymmetric load R = 0.5 (R = σmin / σmax) at the specimen with a single edge notch. Tests were performed through the use of controlled force, ranging between Fmax and Fmin at the high-frequency pulsator ‘Cracktronic’, while obtainment of data regarding the crack growth was carried out through the use of measurement gauge ARM A-10.

A new empirical formula for prediction of fracture energy of concrete based on the artificial neural network

Assessment of energy needed for crack growth in concrete structures has been an interesting topic since the use of fracture mechanics to concrete. For concrete as a quasi-brittle material, the fracture energy has been demonstrated to be an effective index in the safe design of structures and the failure behavior modeling. Since the nonlinear behavior of concrete in fracture process is very complicated, intensive debates on the precise prediction of fracture energy by means of available estimating formula have never ended. In the present study, a new empirical method to determine the fracture energy of concrete is explored. With an extensive experimental database including 246 fracture tests, a new artificial neural network (ANN) model relating the fracture energy to different effective parameters such as compressive strength, water to cement ratio, maximum aggregate size and age is trained and validated. Using the generalization capabilities of the ANN, an empirical design plot and some correcting equations are extended to make a user-friendly formula to determine the fracture energy of concrete in practical design. Results showed that predicted values from ANN are in rationally good agreement with the experimental data and also ANN give higher accuracy than existing regression models, especially with overcoming the high scattered predictions. The use of the new empirical method as an efficient technique for determining the fracture energy of concrete is thus proved.

Fatigue strength and life determination of weldments based on fracture mechanics

The paper provides an overview on the results of a German cluster project on the use of fracture mechanics to the determination of the fatigue strength of weldments with fatigue cracks originating at the weld toes. The approach includes (a) a concept for short crack propagation for which the common ΔK concept is not applicable and the crack closure effects are still being gradually build-up, (b) a method for determining fatigue life relevant initial crack sizes as they are needed in any fracture mechanics analysis and (c) multiple cracking and crack coalescence at load levels higher than the endurance limit. The analyses are stochastically performed. Both, the endurance limit and the finite life branch of the S-N curve are determined.Besides a brief introduction into the approach, validation examples are presented. These comprise different weldment types (butt welds, cross joints and longitudinal stiffened plates), two steels (S355NL and S960QL) of quite different strengths, different weld geometries due to different welding techniques (WIG, MAG), as-welded and stress relieved welds and different stress ratios varying from R = -1 to R = 0.5.

A critical review of fracture mechanics as a tool for multiaxial fatigue life prediction of plastics

Plastics belong to the most complex and probably least understood engineering materials of today. Combining the best aspects of design, mechanical properties and manufacturing, the structural integrity of plastics is on par with aluminium and can in some cases even rival those of steels. One of the most important aspects of plastics is the ability to tailor-drive their material properties for a specific purpose or towards a specific strength value. The morphology of plastics is directly dependent on the manufacturing process, e.g. injection moulding, extruding and casting. Plastics contain multiple phases (crystalline, amorphous, oriented), and are in no sense at all isotropic, although integrally deduced mechanical properties may appear to claim the opposite. As such, it becomes obvious that attempting to analyse such materials using conventional material models and explanations of mechanics is an inherently complex task. The static situation alone requires concepts such as creep, relaxation and rate effects to be incorporated on a numerical level. If the load situation changes, such that cyclic loading is acting on the continuum, with the morphology taken into account (without considering the actual geometrical shape), then the result is that of a complex multiaxial fatigue case. Classical theories used for treating fatigue such as SN or eN analysis have proven much less successful for plastics than they have for metals. Fatigue crack propagation using fracture mechanics has seen some success in application, although appropriate crack initiation criteria still need to be established. The physical facts are more than intriguing. For injection moulded parts (being the most common manufacturing process in place), fracture is in most cases seen to initiate from inside the material, unless the surface has been mechanically compromised. This appears to hold true regardless of the load case. In this review, we have scrutinised physically useful methods of crack initiation, as well as the use of fracture mechanics for multiaxial fatigue life prediction of injectionmoulded plastics. Numerical tools have been utilised alongside experimental experience and public domain data to offer what we hope will be a contemporary overview, and offer an outlook for future research into the matter.

Brittle fracture in structural steels: perspectives at different size-scales.

This paper describes characteristics of transgranular cleavage fracture in structural steel, viewed at different size-scales. Initially, consideration is given to structures and the service duty to which they are exposed at the macroscale, highlighting failure by plastic collapse and failure by brittle fracture. This is followed by sections describing the use of fracture mechanics and materials testing in carrying-out assessments of structural integrity. Attention then focuses on the microscale, explaining how values of the local fracture stress in notched bars or of fracture toughness in pre-cracked test-pieces are related to features of the microstructure: carbide thicknesses in wrought material; the sizes of oxide/silicate inclusions in weld metals. Effects of a microstructure that is 'heterogeneous' at the mesoscale are treated briefly, with respect to the extraction of test-pieces from thick sections and to extrapolations of data to low failure probabilities. The values of local fracture stress may be used to infer a local 'work-of-fracture' that is found experimentally to be a few times greater than that of two free surfaces. Reasons for this are discussed in the conclusion section on nano-scale events. It is suggested that, ahead of a sharp crack, it is necessary to increase the compliance by a cooperative movement of atoms (involving extra work) to allow the crack-tip bond to displace sufficiently for the energy of attraction between the atoms to reduce to zero.

ON DUALITY, SYMMETRY AND SYMMETRY LOST IN SOLID MECHANICS

The paper recalls the concept of duality in mathematics and extends it to solid mechanics. One important application of duality is to restore some symmetry between current fields and their adjoint ones. This leads to many alternative schemes for numerical analyses, different from the classical one as used in classical formulation of boundary value problems (finite element method). Usually, conservation laws in fracture mechanics make use of the current fields, displacement and stress. Many conservation laws of this type are not free of the source term. Consequently, one cannot derive path-independent integrals for use in fracture mechanics. The introduction of variables and dual or adjoint variables leads to true path-independent integrals. Duality also introduces some anti-symmetry in current fields and adjoint ones for some boundary value problems. The symmetry is lost between fields and adjoint fields. The last notion enables us to derive new variational formulation on dual subspaces and to exactly solve inverse problems for detecting cracks and volume defects.

Structural integrity of nuclear reactor pressure vessels

The paper starts from concerns expressed by Sir Alan Cottrell, in the early 1970s, related to the safety of the pressurized water reactor (PWR) proposed at that time for the next phase of electrical power generation. It proceeds to describe the design and operation of nuclear generation plant and gives details of the manufacture of PWR reactor pressure vessels (RPVs). Attention is paid to stress-relief cracking and under-clad cracking, experienced with early RPVs, explaining the mechanisms for these forms of cracking and the means taken to avoid them. Particular note is made of the contribution of non-destructive inspection to structural integrity. Factors affecting brittle fracture in RPV steels are described: in particular, effects of neutron irradiation. The use of fracture mechanics to assess defect tolerance is explained, together with the failure assessment diagram embodied in the R6 procedure. There is discussion of the Master Curve and how it incorporates effects of irradiation on fracture toughness. Dangers associated with extrapolation of data to low probabilities are illustrated. The treatment of fatigue-crack growth is described, in the context of transients that may be experienced in the operation of PWR plant. Detailed attention is paid to the thermal shock associated with a large loss-of-coolant accident. The final section reviews the arguments advanced to justify ‘Incredibility of Failure’ and how these are incorporated in assessments of the integrity of existing plant and proposed ‘new build’ PWR pressure vessels.

Fractographic Observation of Various Loading Modes of Fibre Reinforced Laminates

One of the major disadvantages of laminated composites is their tendency to delaminate. Unidirectional glass/epoxy laminates have been tested under static conditions by the use of fracture mechanics. Mode I, mode II, mixed mode I-II, mode III and mixed mode II-III tests were performed. Double cantilever beam (DCB), end-notched flexure (ENF), mixed-mode bending (MMB) and edge crack torsion (ECT) specimens were used. Scanning electron microscopy technique was used to identify distinguishing fractographic features and to establish the differences between the various modes of fracture after specimens testing. The propagated orientation of the delamination could be specified from the patterns of fracture surface. Scanning electron micrographs of fractured surfaces showed that the most predominant fractographic features in mode I and mode II are the large amount of fibre pull-out and the cusps markings respectively. In the MMB specimen the fracture surfaces are characterized by fibre breakage under shearing with fractures localized in the resin with cusps having an orientation of 90º (mode II) and also fractures localized in the resin and along the resin/fibre interface (mode I). Mode III characterization concluded that some limited mixed mode II-III seems to be present for ECT specimen on delamination initiation and growth, but a large majority of mode III delamination is present.

Non destructive testing techniques for risk based inspection

Ensuring the safety of offshore structures is of vital importance for the reliability of oil and gas drilling rigs.Risk based inspection (RBI) is becoming an industry standard for management of equipment integrity. Theobjective of risk based inspection is to determine the likelihood of equipment failure (probability) and theconsequences of such an event. Combining the probability of an event with its possible consequencesallows determining the risk of an operation. Risk based inspection enables to optimize the frequency ofinspection, by moving from periodic inspection (based on arbitrary calendar dates) to an informedinspection program (based on equipment condition).One of the most important tools to determine the condition of the equipment, and to calculate its reliability,is the use of non destructive testing (NDT) techniques to detect cracks, flaws and defects. The probability ofdetection and the probability of sizing depend on the type of NDT method used. Combining NDTinformation on crack size and depth with fracture mechanics based damage models, allows predicting theremaining life time of a component.In this paper, the philosophy of risk based inspection is introduced and recent advances in non destructivetesting (in particular ultrasonic and electromagnetic techniques) are reviewed. Then, the use of fracturemechanics based damage models is demonstrated to predict fatigue failure for offshore structures.

Energy density mechanics applied to coating blistering problems

The use of fracture mechanics outside the area of mechanics, including materials science, is evidence that the concept is capable of handling failures involving almost any types of crack propagations. This paper outlines the simple method on how to use fracture mechanics concepts in coating study by using a concrete example that is easy to follow. The example presented here is the use of fracture mechanics to develop equation governing the blister propagation using the concept pioneered by Sih, the SED concept. Despite being simple, the method gives excellently good agreement with those available solutions derived by other methods.

Fatigue Prediction for Pump End of High Pressure Fracturing Pump

The unexpected in-service failure of fluid pump end of fracturing pump motivated the present investigation. The model of three-cylinder single-action fluid pump end had been established by using the Pro/E software for improving the level of fracturing pump design. The combined use of fracture mechanics concepts as well as the finite element method demonstrated that local failure was due to the specific intersection region between plunger-chamber and cylinder-cavity. The predicted fatigue lives based on the FE stress analysis agree well with the application observations.