Use Of Fracture Mechanics Research Articles

Application of interface finite elements to three‐dimensional progressive failure analysis of adhesive joints

ABSTRACT The paper presents a new model for three‐dimensional progressive failure analysis of adhesive joints. The method uses interface elements and includes a damage model to simulate progressive debonding. The interface finite elements are placed between the adherents and the adhesive. The damage model is based on the indirect use of fracture mechanics and allows the simulation of the initiation and growth of damage at the interfaces without considering the presence of initial flaws. The application of the model to single lap joints is presented. Experimental tests were performed in aluminium/epoxy adhesive joints. Linear elastic and elastoplastic analyses were performed and the predicted failure load for the elastoplastic case agrees with experimental results.

Prediction of compressive strength of carbon–epoxy laminates containing delamination by using a mixed-mode damage model

It is well known that composite laminates are easily damaged by low-velocity impact. The internal delaminations can drastically reduce the compressive strength of laminates. In this study, a numerical analysis for predicting the residual compressive strength of delaminated plates is proposed. The delaminated interfaces are modelled by using interface elements connecting the three-dimensional solid elements modelling the composite layers. Delamination propagation is modelled by using a damage model based on the indirect use of fracture mechanics. Due to the complex stress state of the problem, a mixed-mode analysis including the three modes of fracture was considered. Experimental studies were performed on carbon–epoxy [0 4, 90 4] s and [90 4, 0 4] s laminates. They included low-velocity impact tests, followed by X-ray damage characterisation and compression tests. Good agreement between experimental and numerical analysis was obtained.

On the use of fracture mechanics in designing a single lap adhesive joint

The design of adhesively bonded joints is a quite difficult task, due to the stress singularity that arises at the edges of the adhesive adjacent to the loaded substrate. This stress singularity makes any design approach based on elastic stress analysis inconvenient. A more convenient design tool for an adhesive joint should be based on its mode of failure. Most of the adhesive joints fail at the adhesive/adherend interface or very close to it in the adhesive layer. Therefore, a fracture theory such as linear elastic fracture mechanics (LEFM) can be used to analyse the failure of an adhesive joint. In this paper, the design of a single lap joint using a fracture mechanics parameter, i.e. the strain energy release rate (SERR), is discussed. The SERR is extracted from a finite element model using Irwin's virtual crack closure integral. A design equation relating the lap length to the adherend thickness through some design parameters is derived.

Review of empirical and semi-empirical Y factor solutions for cracked welded tubular joints

The practical use of fracture mechanics has been established for use on large turbine and electric generator rotor components used in the atomic power generation and the aircraft industry. Application areas in the offshore industry have also been identified. Fracture mechanics is currently used at the design stage of offshore facilities. It provides the basis for fatigue life prediction, steel selection and tolerance setting on allowable weld imperfections. Fracture mechanics is also used during the operational stage of a structure to make important decisions on inspection scheduling and repair strategies and as a tool for establishing limits on operational conditions. Linear elastic fracture mechanics relies on the use of the stress intensity factor concept. The stress intensity factor is a very important fracture mechanics parameter. Therefore, the accuracy of any fracture mechanics model for the prediction of fatigue crack growth in offshore structures for example will depend very much on the accuracy of the stress intensity factor solution used. Several empirical and semi-empirical solutions have been developed over the years with varying degrees of accuracy. This paper presents a review of some of these methods and attempts to assess their accuracy in predicting Y factors for welded tubular joints by comparing predicted results with experimental data obtained from fatigue tests conducted on large scale welded tubular joints. The experimental results were conducted under simulated service conditions, using a jack-up offshore standard load history (JOSH). A comparison between the experimental and predicted results shows that there may be other factors, which influence fatigue crack growth under variable amplitude conditions. Some of these factors have been identified and discussed in this paper.

A Technique to Measure Interfacial Toughness Over a Range of Phase Angles

An experimental technique using sandwiched Brazil-nut specimens to quantitatively characterize interfacial fracture toughness over a wide range of phase angles is presented. Specimens are made by sandwiching a thin layer of adhesive material between two metal substrates. Tensile loads are applied to the specimens at various loading angles. Through the use of fracture mechanics and finite element analysis, interfacial fracture toughness as a function of loading phase angle is determined from the experimentally obtained critical load and loading direction. The fracture toughness curves for several different Cu/adhesive systems are obtained. [S1043-7398(00)00302-9]

Use of Fracture Mechanics and Shape Optimization for Component Designs

About half of mechanical failures are due to repeated loading. Most of the failures are fatigue related, and the fatigue prohlem has been of major concern in the design of structures. The failure is a function of, among other factors, the external loads, material behavior, geometry of the structure, and crack characteristics. The relationship between structural geometry and number of life cycles to failure is investigated to improve the fatigue life of structural components. The linear elastic fracture mechanics (LEFM) approach is integrated with shape optimal design methodology. The primary ohjective of the design problem is to enhance the life of the structure. The results from LEFM analyses are used in the fatigue model to predict the life of the structure before failure is deemed to have occurred. The shape of the structure is changed using the natural shape optimal design methodology. Gradient-based nonlinear programming techniques are used with the computed sensitivity information to predict the required shape changes. Relevant issues such as problem formulation, finite element modeling, mesh generation, and regeneration are discussed. Two design examples are solved, and the results show that, with proper shape changes, the life of structural systems subjected to fatigue loads can be enhanced significantly.

Use of fracture mechanics and shape optimization for component designs

Use of fracture mechanics and shape optimization for component designs

A MICROMECHANICAL DAMAGE THEORY FOR BRITTLE MATERIALS WITH SMALL CRACKS

For brittle solids containing numerous small cracks, a micromechanical damage theory is presented which accounts for the interactions between different small cracks and the effect of the boundary of a finite solid, and includes growth of the pre‐existing small cracks. The analysis is based on a superposition scheme and series expansions of the complex potentials. The small crack evolution process is simulated through the use of fracture mechanics incorporating appropriate failure criteria. The stress–strain relations are obtained from the micromechanics analysis. Typical examples are given to illustrate the potential capability of the proposed theory. These results show that the present method provides a direct and efficient approach to deal with brittle finite solids containing multiple small cracks. The stress–strain relation curves are evaluated for a rectangular plate containing small cracks.

An Overview of the Fracture Mechanics of Concrete

Abstract For the design of concrete structures where adequate ductility is a concern, it is becoming increasingly necessary to use concepts based on crack growth and propagation to account for ductility and avoid catastrophic failure. While fracture based methods exist for steel design, no standard method currently exists to quantify the fracture properties of concrete. In light of a multitude of recent investigations to describe the complex nature of concrete fracture, it is currently accepted that two parameters are required to characterize crack propagation in concrete. This paper provides a brief background for the use of fracture mechanics in concrete and appeals for the establishment of standardized testing procedures for use in concrete. If appropriately determined, fracture parameters can provide a valuable tool for the design of new higher performance concretes and concrete structures.

Mode II delamination failure mechanisms of polymer matrix composites

The failure process of mode II delamination fracture is studied on the basis of the microscopic matrix failure modes (microcracks and hackles) as well as fracture mechanics principles. The crack tip matrix stresses leading to delamination is analysed by examining an adhesive bond with a crack analogous to a delamination crack in the resin layer of a composite. Such crack tip stresses induce matrix microcracks involving two major events: (a) single microcrack initiation and (b) development of multiple microcracks with regular spacing. The microcrack initiation shear stress τ* is found by the use of fracture mechanics to be related to certain resin properties (shear modulus G and mode I fracture toughness GIC) and microcrack length of the order of the resin layer thickness t (related to resin content).

Strengthening of concrete prisms using the plate-bonding technique

This paper presents the use of fracture mechanics for the plate bonding technique. Plates of steel or carbon-fibre reinforced plastic are bonded with an epoxy adhesive to rectangular concrete prisms and loaded in shear up to failure, what is normally known in fracture mechanics as mode II failure. In this special application a linear and a nonlinear approach are presented. The nonlinear equation derived for a realistic shear-deformation curve can only be used for numerical calculations. However, for simplified shear-deformation curves, the derived formula can be solved analytically. Results from tests, which are compared with the theory, are also presented.

Crack modelling: A technique for the fatigue design of components

A new method of fatigue analysis for components is outlined; the novelty of the method is that it uses fracture mechanics concepts without introducing a crack into the component. Stress concentrations are analysed by examining their stress fields and comparing these with the stress fields of cracks of standard geometry. The method was tested by using it to assess three different design conditions for a large cast-iron component. This component suffered fatigue failures from a corner feature which had a sharp fillet radius; it was found in practice that increasing the fillet radius was ineffective, whereas reduction of operating loads eliminated the problem. By estimating the stress intensity range, ΔK, in service and comparing this with the threshold value, ΔK th the in-service observations could be predicted with a good degree of accuracy. The method, which is termed “crack modelling”, appears to have potential for the assessment of design features in components, extending the use of fracture mechanics into industries in which it is currently not used.

Mechanics of fretting fatigue

Several aspects of the mechanics of cracks originating at sites of fretting are considered. It is argued that the problem may be distilled into three separate parts: the contact problem itself in full or partial slip, the initiation of a crack from a surface suffering severe distress, and the propagation of a crack under combined contact and bulk loading. The first of these may be solved by either a classical or numerical means, whilst the last merely requires the careful use of fracture mechanics. However, it is the second element which remains elusive to quantify, and the influence of the intrinsic length scales in the problem, including contact length, surface roughness and amplitude of relative tangential displacement on initiation conditions, is discussed and explored.

Derivation of the singular integral equations for curvilinear cracks with computer algebra software

The classical Cauchy-type complex singular integral equation for the general curvilinear crack problem in plane isotropic elasticity is rederived by using an appropriate computer procedure, based on the MATHEMATICA computer algebra system. Both cases of one crack (or a system of cracks) and of a periodic array of cracks are considered in detail and the MATHEMATICA procedure is displayed. The approach can also be generalized to additional arrays of cracks (like a doubly-periodic or a star-shaped array of curvilinear cracks). The present approach permits the direct error-free construction of sufficiently complicated complex singular integral equations of direct use in fracture mechanics in a simple and powerful way, which rid us of complicated manual, probably error-prone, computations. The approach is based on the knowledge stored in the MATHEMATICA kernel and on additional knowledge (like the Plemelj formulae) provided to the procedure itself. The subsequent use of a numerical algorithm for the solution of the derived complex singular integral equation is also possible.

Fracture mechanics ? theoria or tekhne?

Ideally a method for use in fracture mechanics should be a harmonious combination of theoria and techne, of contemplation and engineering skill. The main objective of fracture mechanics is to tell whether fracture is likely to occur in a structure under given conditions. This requires a theory of fracture and access to necessary material data, obtainable through laboratory testing.

Criteria of Leakage Occurrence and Pressure Vessel Failure as Applied to Reactors

This paper reports that the safety concept of a nuclear district heating plant (NDHP) reactor for emergency coolant losses is based on the realization of the leak before break criterion. Its acceptance became possible owing to the large experience of designing and operating the different type NPPs, as well as due to the modern achievements in the practical use of fracture mechanics. It is known that a metal's destruction is associated with the presence or birth and subsequent development of a crack under cyclic thermo-mechanical loading due to a plant's unsteady operating regime. That is why the study of the realization of hazardous states as the consequences of crack development up to local instability occurrence is the main task of investigations. The experimental part of the research program included tests of full-scale vessel models. This enabled us to reproduce with maximum possible accuracy the stress-strain state in the crack's mouth and to thereby remove the problem of carrying the results obtained over to the realone.

Fracture Mechanics of Ship Structures

Using international cooperative exchange programs, the Department of Defense is currently working with U.S. steel makers to improve the technology base so that they can produce new highly weldable, low alloy, high strength alloys. The development program for these alloys should insure adequate strength and toughness, but not impose excessive requirements. That program justifies the need for a greater understanding of the use of fracture mechanics for the selection of structural materials. There have been several recent independent extensive studies of the application of fracture mechanics to ship structures sponsored by the Ship Structure Committee, the Naval Research Laboratory, David Taylor Research Center, and the Admiralty Research Establishment. The recommendations of these experts range from continued use of existing material parameters, use of linear elastic fracture mechanics, and the use of ductile fracture mechanics for determining the requirements for hull material. This paper reviews the results of these studies and recommends an approach to the development of rational criteria. The Navy is starting an extensive research and development program to verify the chosen methodology, including the testing of large scale sections that will replicate ship hulls. The result of this application of theory and verification through testing will be a new basis for the determination of the toughness requirements for ship structures, avoiding excessive requirements as we seek to use the latest materials that will be available during this decade and in the twenty-first century.

On the fracture parameters in a clamped cracked lap shear adhesive joint

A stress analysis using a beam theory approach similar to that suggested by Goland and Reissner is undertaken for a clamped crack lap shear ( cls) adhesively bonded joint. Analytical solutions of the normal and shear stresses in the adhesive are derived for the simple case where the lap and the strap have equal thickness and moduli. In a subsequent step, these expressions are used in the framework of a crack-closure technique to obtain the Mode I, Mode II and total energy release rates for a crack propagating along the bondline. For an illustrative example, a comparison with a finite element analysis showed reasonably good agreement. This closed-form approximation of both the Mode I and Mode II components of the energy release rate allows the use of fracture mechanics to describe debond growth in mixed-mode conditions representative of actual structures.

A UK regulatory view of fracture mechanics

The regulatory framework in the UK is outlined, and its particular application in considering the use of fracture mechanics in the construction of structural integrity cases is discussed. Some differences with other countries are outlined. Fracture mechanics has advanced a long way in techniques and acceptance since its introduction, but still has limitations, particularly from a regulatory viewpoint. This is especially so in today's society, with an increasing emphasis on safety in the light of recent events. Areas of uncertainty, and areas where future work would be useful in clarifying these are given.

Characterization of small crack growth in 12% CrMoV steel under high temperature, low cycle fatigue conditions

Cylindrical specimens of 12% CrMoV steel were tested under high temperature, low cycle fatigue (HTLCF) conditions to investigate the growth of microcracks which nucleate at the surface. Results are presented which indicate that the microcracks maintain an equilibrium shape under HTLCF conditions, making it possible to estimate crack depth from a measure of the crack lenght along the surface. The individual growth of these microstructurally small cracks was monitored using a surface replication technique during periodic interruptions of the experiments. Crack growth rate data for different microcracks are compared on the basis of the cyclic J-integral ΔJ to examine the use of fracture mechanics for predicting HTLCF microcrack growth. A determination of ΔJ is shown to be successful in characterizing the growth of fatigue microcracks in 12% Cr steel at elevated temperatures despite differences in overall orientation at the surface. Good agreement with fatigue crack growth data for through-cracks in CrMoV steels at high temperatures further demonstrates the usefulness of ΔJ for predicting HTLCF microcrack growth. The results also suggest that large extrapolations of the observed correlation between ΔJ and crack growth rate could result in unacceptable errors owing to the relative contribution of oxidation damage at the crack tip.