The reliability of the fracture mechanics approach to environmentally assisted cracking: 1. Uniqueness of the v(K)-curve

This paper analyzes the reliability of the fracture mechanics approach to environmentally assisted cracking in engineering design. A wide collection of experimental evidences of uncertainty in the fracture mechanics characteristics of the phenomenon—the crack growth kinetics v(K)-curve and the threshold stress intensity factor K_th — is presented. Although these basic fracture mechanics items are supposed to depend solely on the material and the environment, they are notably sensitive to the influence of a wide family of test/service variables, producing loss of confidence in materials evaluation and structural integrity assessment.     

On the application of the damage work density as a new initiation criterion for ductile fracture

In this paper the ‘damage work’ proposed by Chaouadi et al. is used to formulate an energy crack initiation criterion to describe ductile crack initiation. The traditional assessment of structural integrity by the J-integral, a property of elastic-plastic fracture mechanics is compared. Two free-cutting and one structural steel are investigated. The measured values for the critical damage work density at initiation W_di are compared with values for copper and RPV steel. As the fracture mechanical approach is limited to sharp cracks in the material (high-constraint stress state) the present damage mechanics approach is regarded as important as a more general concept closer to reality. While old void growth models of damage mechanics cannot formulate a simple criterion for crack initiation the applied damage work reaches a constant value at initiation W_di which is independent of the stress state during the deformation process. We recommend W_di as a material property of toughness for testing and engineering purposes.     

The transition between stress corrosion crack growth and plastic fracture

The paper focuses on the behaviour of materials for which the onset of crack extension and unstable fracture coincide in a rising load fracture mechanics test. A theoretical analysis shows that use of the experimental test J_Ic value gives a non-conservative prediction of unstable fracture when a stress corrosion crack grows in a solid that is subject to a sustained high stress. Consequently, when an engineering component is to be used at high stress levels in an environment where stress corrosion cracking might be expected, there are clear advantages in having a material which exhibits stable crack growth in a fracture mechanics test.     

Fitness Considerations for Contemporary Composite Materials: (Who’s Afraid of the Composite Micro-Crack?)

Avoiding the catastrophic failure of a large structure demands the material’s microstructure be designed in such as a way as to render any crack present innocuous thereby raising the integrity of that structure. Structural integrity of a composite material embraces contributions from: materials science and engineering; processing science; design and fabrication technology. It combines a number of interacting factors: the criticality of the application; the accessibility for and ability to inspect vital parts and components; the intended use including load spectrum and time; the consequences of impact, fatigue, temperature and hostile environment; the nature of inherent flaws; the constituent properties of the material system utilized; and it takes into account human factors.     

Prediction of fatigue life with interspersed mode-I and mixed-mode (I and II) overloads by an exponential model: Extensions and improvements

The current work is an extension of the authors’ earlier work and presents a life prediction methodology under interspersed mode-I and mixed-mode (I and II) overloads. The important controlling parameter in the model is ‘specific growth rate’ (m). It depends on two crack driving forces i.e. stress intensity factor range and maximum stress intensity factor as well as material parameters i.e. fracture toughness, Young’s modulus, and yield stress. The dependence of ‘m’ on these parameters is correlated through a dimensionless parameter ‘l’. It is observed that the present model predicts the end life of post-overload period well in case of 7020 T7 and 2024 T3 Al-alloys.     

X-ray Diffraction Based Residual Stress Measurements for Assessment of Fatigue Damage and Rejuvenation Process for Undercarriages of Aircrafts

Assessment of fatigue damage during the service life of any component is important to ensure its continued integrity and predict the remnant life of the component. This is important to reduce the overall life cycle cost of the components. A component undergoing fluctuating stresses experiences fatigue damage and this is one of the major causes of failure of engineering components. Accumulation of fatigue damage takes place in undercarriages of aircrafts due to fluctuating stresses experienced after each landing. The accumulated fatigue damage has been assessed by carrying out residual stress measurements at stress critical regions of the undercarriages using X-ray diffraction technique. In the undercarriages, high compressive residual stresses are introduced as part of fabrication process, to enhance the fatigue resistance. These compressive residual stresses get redistributed due to the localized plastic deformation and become tensile with the increase in number of landings. The life of the undercarriages is extended by employing a rejuvenation treatment to overcome the surface tensile residual stresses, by first removing the material from stress critical regions, followed by shot peening treatment which introduces surface compressive stresses, thus enabling continued use of the undercarriages. The additional thickness provided at the design stage enables removal of fatigue damaged surface layers without affecting the overall structural integrity. The residual stress redistribution in stress critical regions of the struts of the undercarriages was measured and found to match qualitatively well with the values predicted from FEM based simulations.     

Einführung in die Grundlagen der Bruchmechanik. Teil 2: Abhängigkeit des bruchmechanischen Werkstoffkennwertes KIC von verschiedenen Parametern

Factors affecting the fracture toughness K_IC The fracture toughness of material, required to ensure the structural integrity of a component, is subject to several effects from the specific operational environments. In the following chapters these influencing parameters will be treated which are of particular importance for engineering application of fracture mechanics such as heat treatment, loading rate, environment, temperature, neutron irradiation and chemical composition of the material.     

Apparent fracture toughness of low-carbon steel CSN 411353 as related to stress corrosion cracks

The occurrence of cracks in structural components indicates a certain threat to their reliable operation, because these cracks can grow during operation and reach critical sizes, leading to fracture. The fracture resistance of a structural component is given by the fracture toughness of the material, determined on standardized specimens with a precycled fatigue crack, and the constraint. The fracture toughness itself depends also on the environment. There is enough evidence that in the conditions of the environment assisted cracking the fracture toughness can be significantly reduced by hydrogen mechanism. Our research results have confirmed this and have demonstrated a considerable reduction in the stress corrosion fracture toughness as compared to that related to fatigue cracks. This should be taken into account when assessing the integrity of structural components with stress corrosion cracks. This paper presents experimental results concerned with the stress corrosion fracture toughness of specimens from a DN150 gas line pipe made of low-C steel CSN 411353.     

Predicting remnant lifetime of high-temperature materials by a resistance degradation model

Abstract

Lifetime and remnant life of engineering materials at high temperature has been analyzed based on a resistance degradation model. It can be demonstrated that the lifetime includes two time processes: resistance degradation process before crack initiation and crack growth process after the crack initiation. Traditional lifetime prediction, via the crack growth model, was found to involve the paradox that the lifetime is in proportion to the initial crack size. Whereas, experiments of static fatigue using glass sheet specimens did not confirm this proportional relationship. For a smooth sample, fracture resistance depends on the strength of the material, so a strength degradation model was used to estimate the lifetime zone between an upper and lower bound. It is defined that the material fails when the residual strength decline to the working stress or deformation reaches a designed limit. It is concluded that the quantity of lifetime mainly depends on the rate of resistance degradation for a brittle component under applied load. Thus, lifetime prediction is simulated as a simple relationship between distance, rate and time, in which the distance is known, the rate can be obtained from experiments and then the lifetime can be calculated.     

Scale effects in the initiation of cracking of a scarf joint

The singular stress field at the interface-corner of a bi-material scarf joint is analysed for a strip of finite width, w, under remote tension and bending. The two substrates are taken as linear elastic and isotopic. The intensity of the singular stress field is calculated using a domain integral method, and is plotted as a function of joint geometry and material mismatch parameters. It is envisaged that the intensity of singularity can serve as a valid fracture criterion provided the zone of nonlinearity is fully embedded within the singular elastic field. It is assumed that fracture initiates when the magnitude of the corner singularity attains a critical value; consequently, the fracture strength of the joint depends upon the size of the structure. In addition, the interfacial stress intensity factor and the associated T-stress are determined for an edge interfacial crack. When the crack is short with respect to the width of the strip, the stress intensity factor is dominated by the presence of the corner singularity; a boundary layer formulation is used to determine the coupling between the crack tip field and the interface-corner field. The solution suggests that an interfacial crack grows unstably with a rapidly increasing energy release rate, but with only a small change in mode mix. This revised version was published online in July 2006 with corrections to the Cover Date.     

Application of fracture mechanics for weld integrity assessment

The structural integrity assessment of a weld joint by conventional techniques is inadequate, because of unavoidable defects in the weld composite. The stress situation in a component having a defect is quite different from that of a homogeneous material. The significance of fracture mechanics to deal with such integrity assessments is brought out. A brief review on the basic formulations in the application of fracture mechanics is followed by established guidelines for evaluating the integrity of engineering components containing crack-like defects.     

Towards a Predictive Design Methodology Based on the Physical Modelling of the Fracture of Fiber Composites

A predictive design methodology based on modelling the fracture stress (notched tensile strength) and post-fatigue residual strength of laminated fiber composites is presented. The approach is based explicitly on the development of models of the physical processes by which damage accumulates at a notch-tip and the application of these models to cross-ply laminates for a variety of material systems, including thermosetting and thermoplastic matrices containing carbon, glass and Kevlar fiber reinforcements. The effects of temperature and humidity on composite fracture can also be examined in the context of this modelling strategy.A pre-requisite of the model is that it has to be calibrated for each material system by performing tensile tests on notched and unnotched cross-ply laminate. From this initial calibration, which takes relatively little time, it is possible to apply the model to a prediction of the dependence of fracture stress on notch size; to an understanding of the effects of laminate stacking sequence (within the same cross-ply family) on fracture stress; and to provide insight into the effects of thermal or load cycling history on fatigue damage-growth and residual or fatigue strength.The advantages and deficiencies of this modelling strategy are assessed, as well as the applicability of such a physical modelling approach to the predictive design and failure of composite materials in general.     

Fatigue design of wire-wound pressure vessels using ASME-API 579 procedure

The wire winding of high pressure vessels is a technique usually applied to introduce initial compressive stresses in the inner core of the vessel, with the aim to improve the fatigue life under cyclic pressure conditions. In this work, the procedure followed to calculate the number of design cycles is presented, using the fracture mechanics approach and the structural integrity concepts. In particular, the API 579-1/ASME FFS-1 procedure has been used to analyse the structural integrity of the vessel through the crack propagation stage. Starting from a postulated internal semi-elliptical crack the number of design cycles is determined, the flaw aspect ratio is updated and the structural integrity of the cracked vessel is evaluated using the Failure Assessment Diagram (FAD). Different propagation laws, which take into account for negative stress intensity ratio factors R = K_min/K_max < 0, are reviewed, because of their high influence on the fatigue life of wire-wound vessels. In addition, this paper presents a number of useful expressions to calculate the stress intensity factor (SIF) for internal semi-elliptical cracks in wire-wound pressure vessels, in order to carry out the numerical integration of the number of cycles, updating the flaw aspect ratio, during the fatigue crack growth.     

CONSIDERING ENVIRONMENTAL CONDITIONS IN THE DESIGN OF BONDED STRUCTURES: A FRACTURE MECHANICS APPROACH

The continued airworthiness of ageing aircraft and long-term durability of new airframes depends, in part, on the integrity of adhesive bonds used for repairs and joining structural components. Additionally, the advent of composite materials and advanced repair techniques incorporating composites has increased the number of adhesively bonded joints specified for use in aerospace structures. Traditionally, adhesive bonds have been analysed and designed using a dependable and rigorous stress-based approach. However, the need to address the effect of bondline flaws and to understand the fatigue characteristics of bonded joints has led to the adoption of a discipline already common in the design of metallic components—fracture mechanics. To understand the durability of bonded structures, however, it is further necessary to examine the effect of environmental exposure on the performance of the adhesive bondline. Familiarity with the stress-based and fracture mechanics analytical approaches, as well as an understanding of environmentally induced trends in bond performance is paramount to quality design. This paper will briefly discuss the attributes of the two main forms of bonded joint analysis, and will broadly outline a design approach that uses fracture mechanics and accounts for environmental effects. Experiments discussed in this paper were performed specifically to use fracture mechanics in assessing the environmental effects on a toughened epoxy adhesive. Results indicate that the Mode I fracture toughness and fatigue crack growth threshold of this adhesive are significantly reduced upon exposure to a high temperature, high humidity aircraft service environment. These results will be used to illustrate the philosophical arguments supporting the design approach.     

On the fundamental basis of fracture mechanics

Based on the crack tip stress and strain fields, the linear and the non-linear fracture mechanics have been developed. Their applications to the studies of fracture initiation and stable crack growth may differ because of the difference in the basic postulates of various fracture theories. The correct postulates will help to develop non-linear fracture mechanics for valid fracture toughness measurements and to extend fracture mechanics beyond the realms of K and J.The basic postulates of the linear elastic fracture mechanics are examined. The theory of global energy balance, the theory of sharp notch, and the theory of the characterization of crack tip stress and strain fields by K are analyzed. Fracture initiation and stable crack growth are local fracture phenomena. Therefore the global energy balance theory for crack initiation and stable crack growth without the study of the detailed fracture processes is fortuitous. The capability of the stress intensity factor to characterize the crack tip stress and strain fields for the localized fracture process is the basis for the validity of the linear elastic fracture mechanics.The concept of the characteristic crack tip field can be directly extended to the non-linear fracture mechanics. The fracture toughness and the tearing modulus of a tough material are measures of the fracture ductility of the material. The possibility to extend fracture mechanics beyond the realms of K and J are discussed.     

Some comparisons in the behaviour of materials at elevated temperatures under uniaxial and under multiaxial stress

Most data on the mechanical behaviour of materials at elevated temperature concerns the influence of a uniaxial stress. For many purposes such information may suffice but there is increasing awareness of its inadequacy when used in the design or service life estimation of engineering components operating under more complex stress systems. Such stress systems do not only arise from the external stresses that are applied but may also result from thermal effects, particularly at interfaces and joints, or from the special geometrical features of a component. Some experimental techniques to provide information on creep behaviour under multiaxial stresses are described together with a discussion and evaluation of the results obtained. It is noted that data from uniaxial stress tests can be used to predict such behaviour when the material is isotropic and is not subject to volume changes, microstructural instability or creep damage. Frequently, materials do not fulfill these conditions and information is presented on the influence of some of these complicating features both on creep rate and on fracture.     

Localization of deformation and failure around elliptical perforations based on a polar continuum

Stability analysis of elliptical shape perforations embedded in a compressive stress field is presented. The study is based on finite element analysis with an advanced material model capable of predicting surface buckling and localization of deformation in shear bands causing failure in a structure. The model is an extended flow theory of plasticity for a Mohr–Coulomb solid with Cosserat micro-structure. The application is related to the stability of perforation tunnels that are used for the flow of hydrocarbon in the wellbores. It is demonstrated that it is essential to carry out advanced localization analysis in order to reach correct results upon which a new perforation shape design can be based. Classical stress analysis predicts that an elliptical hole suffers less stress concentration than a circular hole when its major axis is aligned with the direction of the major principal stress and its axis ratio is the same as the applied stress ratio. However, failure analysis based on localization of deformation show that an elliptical hole will be stronger if its axis ratio is greater than the ratio of the applied stresses. Other practical applications can be found in the design of underground cavities in geotechnical, mining and petroleum engineering. Received 2 August 1999     

On the slow motion of a sphere in fluids with non-constant viscosities

We study a slowly moving sphere in fluids where the viscosity depends upon factors such as shear-rate, temperature and pressure, with the flow field approximated by the Stokes flow past a sphere. We derive an expression for the stresses generated in the fluid due to these various factors. This gives us information about both, the force imposed by the fluid upon the sphere and also the reaction force due to the sphere upon the fluid, referred to as the stress density. The values of the force and stress density are numerically computed in each of the cases and analyzed for various values of the flow and material parameters. Our computations show interesting variations in the distribution of stress density in the fluid for the various cases and also give us valuable information about the effect of walls. Our calculations also indicate that particle heating or cooling can serve as a significant control parameter since the drag force upon the sphere increases dramatically for a cold particle and can be reduced considerably upon heating it.     

A finite element model and experimental analysis of PTH reliability in rigid-flex printed circuits using the Taguchi method

The primary reliability concern in complex RFPC construction is PTH integrity as a result of thermo-mechanical deformation due to significant CTE mismatch between the copper and surrounding dielectric material. In this paper, a finite element model was developed to determine the maximum strain, by which the fatigue life could then be predicted and compared with the experimental thermal cyclic test results. The FEM results show that the maximum strain in the PTH of an RFPC depends on the varying properties of the dielectric materials. A Taguchi analysis indicated that higher fatigue life can be achieved by using high T_g and low CTE bonding material, increasing the plating thickness, reducing the board thickness and increasing the drill hole size. The results show a good agreement between the experimental data and the FEM analysis.