Fracture in Materials

10 Key excerpts on "Fracture in Materials"

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  eBook - PDF

  Mechanics of Materials

  A Modern Integration of Mechanics and Materials in Structural Design

  • Christopher Jenkins, Sanjeev Khanna(Authors)
  • 2005(Publication Date)
  • Academic Press

    (Publisher)

  7 Fracture The worst sin in an engineering material is not lack of strength or lack of stiffness . . . , but lack of toughness, that is to say, lack of resistance to the propagation of cracks. —J. E. Gordon, The New Science of Strong Materials (1976) Objective: To understand cracking and fracture behavior of materials for designing safe and fracture resistant structures. Two DDOF are introduced: a, K C . What the student will learn in this chapter: . Why we must consider fracture mechanics and its relationship with different materials in the design of structures . Introduction to fracture mechanics . The atomistic process of fracture . Design of simple structural elements with crack-like defects . An introduction to materials selection for fracture-resistant structures 7.1 Introduction to Fracture in Materials Þ : The aim of fracture mechanics is to provide engineers with a quantitative tool for designing against fracture in engineering structures. Fracture in a structure can lead to substantial financial loss and worse—loss of life. Some dramatic examples of fracture are the failure of the Liberty ship hulls in the early 1940s (see Figure 7-1), fracture of the Titanic passenger ship due to impact, the Comet aircraft in the 1950s, and more recently an Aloha Airlines aircraft whose outer skin fractured and peeled off in flight (see Figure 7-2). In all these examples, the structure underwent a catastrophic failure. In a vast majority of the cases though, a structure develops cracks and continues to function normally until the crack is detected during periodic inspection. For example, Figure 7-3 shows a large crack in the aluminum 7075-T73511 strut of a large commercial airliner. This particular failure occurred as a result of a ductile overload and had no other prior defects that caused the cracking.

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  Fundamentals of Materials Science and Engineering

  An Integrated Approach

  • William D. Callister, Jr., David G. Rethwisch(Authors)
  • 2022(Publication Date)
  • Wiley

    (Publisher)

  This allows quantification of the relationships among material properties, stress level, the presence of crack-producing flaws, and crack propagation mechanisms. Design engineers are now better equipped to anticipate, and thus prevent, structural failures. The present discussion centers on some of the fundamental principles of the mechanics of fracture. fracture mechanics 10.5 | | PRINCIPLES OF FRACTURE MECHANICS 1 Concept Check 10.2 Differentiate between ductile fracture and brittle fracture. [The answer may be found on the product page at www.wiley.com ] 10.5 Principles of Fracture Mechanics  385 Stress Concentration The measured fracture strengths for most brittle materials are significantly lower than those predicted by theoretical calculations based on atomic bonding energies. This discrepancy is explained by the presence of microscopic flaws or cracks that always exist under normal conditions at the surface and within the interior of a body of material. These flaws are a detriment to the fracture strength because an applied stress may be amplified or concentrated at the tip, the magnitude of this amplification depending on crack orientation and geometry. This phenomenon is demonstrated in Figure 10.8—a stress profile across a cross section containing an internal crack. As indicated by this profile, the magnitude of this localized stress decreases with distance away from the crack tip. At positions far removed, the stress is just the nominal stress σ 0 , or the applied load divided by the specimen cross- sectional area (perpendicular to this load). Because of their ability to amplify an applied stress in their locale, these flaws are sometimes called stress raisers.

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  Basic Fracture Mechanics and its Applications

  • Ashok Saxena(Author)
  • 2022(Publication Date)
  • CRC Press

    (Publisher)

  1 Fracture in Structural Components

  DOI: 10.1201/9781003292296-1

  The economic impact of fracture in engineering materials and components in the United States was once estimated at about 4.4% of its gross domestic product (GDP) [1 ]. By the size of the economy in 2021, this would be approximately one-trillion US dollars which is high even if one allows for uncertainties associated with such estimates. Thus, fracture in structural components must be prevented across industries such as ground, air, and sea transportation, chemical, power-generation, civil infrastructure, sports equipment, and biomedical prosthetics where stakes are high. The potential risk of fracture also cuts across all types of structural materials used in construction such as metals, ceramics, polymers, and composites. Consequently, fracture has been studied extensively since industrialization in the mid-nineteenth century and continues to be an important area of research in the twenty-first century, especially as new engineering materials evolve, and designs become more efficient. This chapter explores the significance of fracture and why it has been and continues to be an important engineering topic for academic and industrial research. The chapter also presents the early history of developments in understanding of fracture and recognizes the contributions of pioneers who led these developments.

  1.1 Fracture in Engineering Materials and Structures: Societal Relevance

  1.1.1 Safety Assessments

  Ensuring safety of people is one of the primary drivers of the need to prevent fractures in engineering structures. Fracture can lead to serious injuries and is threat to human life and are caused by failures in critical load-bearing components of automobiles, highways and bridges, trains, aircraft structures and engine components, pressure vessels used to store compressed combustible and non-combustible gases, and in host of other machinery and equipment used in our daily lives. Engineers are always aiming for fracture-safe design of components while designing them to be less bulky, using more economical materials, requiring less maintenance during service, and recyclable at the end of their design life. However, ensuring safety is paramount and any compromises cannot be justified by any of the above considerations. Thus, a thorough understanding of why components fail is an important aspect of safe designs. Quantifying risk of fracture is important in building adequate safety margins and redundancy in design of load-bearing components.

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  Practical Stress Analysis in Engineering Design

  • Ronald Huston, Harold Josephs(Authors)
  • 2008(Publication Date)
  • CRC Press

    (Publisher)

  It points to the necessity of characterizing the material ’ s behavior under stress in terms of new parameters. 27.2 PRACTICAL ASPECTS OF FRACTURE MECHANICS Fracture mechanics has been studied and documented as early as 1920 [2]. Since then, it has received considerable attention from many analysts with a focus on high-strength metals. A fracture is seen to occur even due to a low nominal stress setting off a brittle behavior phenomenon. Once 437 initiated, such a brittle process can propagate at a high velocity to the point of complete failure. Thus, failure can occur even if the yield strength is not reached. As a general guide, steels with yield strength above 180 ksi, titanium alloys above 120 ksi, and aluminum alloys above 60 ksi are in this high-strength but brittle category. They should thus be evaluated on the basis of fracture toughness rather than pure yield strength. Extensive experimentation and some recent developments in continuum mechanics have been aimed at de fi ning a quantitative relationship between stress, the size of a crack, and the mechanical properties. It is relevant to point out that the advent of fracture mechanics does not negate the traditional concepts of stress analysis, which allow us to design for stresses exceeding the yield strength in the vicinity of such structural discontinuities as holes, threads, or bosses, provided that the material deforms plastically and redistributes the stresses. This concept is still valid unless the material contains critical fl aws that produce unstable crack propagation below the design value of the yield strength. The dif fi culty with introducing the correction for fl aws in design is that, in many cases, fl aws cannot be easily detected. It becomes necessary, therefore, to develop a procedure that would de fi ne the maximum crack length permissible at a particular level of stress. According to the theory of fracture mechanics, this stress level is inversely proportional to the fl aw size.

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  Fracture Mechanics

  Fundamentals and Applications

  • Michael Janssen, Jan Zuidema, Russell Wanhill(Authors)
  • 2004(Publication Date)
  • CRC Press

    (Publisher)

  Part V Mechanisms of Fracture in Actual Materials 285 12 Mechanisms of Fracture in Metallic Materials 12.1 Introduction Since World War II there has been great progress in understanding the ways in which materials fracture. Such knowledge has proved essential to better formulation of fracture mechanisms. Nevertheless, it is still not possible to use this knowledge, together with other material properties, for predicting fracture behaviour in engineering terms with a high degree of confidence. Some insight into the problems involved is given in chapter 13, and it is the intention of the present chapter to provide the necessary background information on fracture mechanisms. Metallic materials, especially structural engineering alloys, are highly complex. An Figure 12.1. Schematic of microstructural features in metallic materials. Courtesy Gerling Institut für Schadenforschung und Schadenverhütung, Cologne, FRG. 286 Mechanisms of Fracture in Actual Materials indication of this complexity is given b y figure 12.1 , which shows various microstruc-tural features (not all of which need be present in a particular material) and also the two main types of fracture path, transgranular and intergranular fracture. Of fundamental importance is the fact that almost all structural materials are polycrystalline, i.e. they consist of aggregates of grains, each of which has a particular crystal orientation. The only exceptions are single crystal turbine blades for high performance jet engines. Before the various mechanisms of fracture are discussed some information will be given in sections 12.2 and 12.3 on the following topics: 1) The instruments used in fractography, which is the study of fracture surfaces. In par-ticular, the use of electron microscopes will be mentioned. 2) The concept of dislocations (se e figure 12. 1). The nucleation and movement of dis-locations causes shear, i.e. slip, on certain sets of crystal planes, and the overall ef-fect of slip is plastic de formation.

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  Practical Fracture Mechanics in Design

  • Arun Shukla(Author)
  • 2004(Publication Date)
  • CRC Press

    (Publisher)

  1 Historical Developments in Fracture Mechanics and Overview Several structural failures can be associated with the fracture of one or more of the materials making that structure. When such events occur, they are mostly unexpected, sudden, and unfortunate, and it is natural for us to focus attention on minimizing the undesired consequences when designing and analyzing modern-day structures. The study of crack behavior, prevention and analysis of fracture of materials is known as fracture mechanics . In every discipline, including fracture mechanics, it is of critical import-ance to examine the historical antecedents. Progress not only depends on revolu-tionary ideas, but a significant part of it depends on retentiveness as well. People who tend to ignore the past are more prone to repeat mistakes. Although devel-opments in fracture mechanics concepts are quite new, designing structures to avoid fracture is not a new idea. The fact that many ancient structures are still standing is a testimony to this. The stability of some of the ancient structures is quite amazing when we consider the fact that the choice of construction material was limited at that time. Brick and mortar, which were relatively brittle and unreliable for carrying tensile loads, were the primary construction materials. Even though the concept of brittle fracture did not exist, the structures were inad-vertently designed against fracture by ensuring that the weaker components of the structure were always in compression. An arch-shaped Roman bridge design, as shown in Fig. 1.1, is an excellent example of a structure where fracture was avoided by virtue of design. The possibility of fracture in the bridge design 1 was avoided as the arch shape of the bridge results in compressive rather than tensile stresses being transmitted through the structure.

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  The Theory of Critical Distances

  A New Perspective in Fracture Mechanics

  • David Taylor(Author)
  • 2010(Publication Date)
  • Elsevier Science

    (Publisher)

  Bruckner-Foit et al., 2004 ) have revealed the large extent of these local variations in stress and strain, which can be as high as a factor of 10.

  These effects may be of relatively little importance if the scale of the fracture process is large – for example, if the size of the plastic zone (see Section 1.5.2 ) is much larger than any microstructural feature, in which case it may be satisfactory to think of the stresses calculated by continuum analysis as average quantities, ignoring their local variations. However, the fact is that many failure processes happen on the microstructural scale. For example, the sizes of zones of plasticity and damage during the fracture of brittle materials and the HCF of metals are generally the same as the sizes of grains and other components of the microstructure. Under these circumstances it is rather remarkable that we can make meaningful predictions of failure using continuum mechanics theory. This implies that, at least under some circumstances, we will need to modify continuum mechanics to take account of crucial length scales in a material; this is the main subject of this book.

  1.5 Fracture Mechanics

  Fracture mechanics – the science which describes the behaviour of bodies containing cracks – is one of the most important developments in the entire field of mechanics. The great success of fracture mechanics has been to show that, under certain well-defined conditions, the propagation of the crack can be predicted using some very simple linear elastic analysis. When these conditions prevail, we are in the realm of Linear Elastic Fracture Mechanics (LEFM). We will first describe the basic theory of LEFM, leaving discussion of its limitations and assumptions for later. What follows is necessarily only a brief outline: for more detailed treatment the reader is referred to some of the excellent books which have been written on this subject (Broberg, 1999 ; Janssen et al., 2002 ; Knott, 1973

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  Materials

  Engineering, Science, Processing and Design

  • Michael F. Ashby, Hugh Shercliff, David Cebon(Authors)
  • 2009(Publication Date)
  • Butterworth-Heinemann

    (Publisher)

  Chapter 8 Fracture and fracture toughness

  Chapter contents

  • 8.1 Introduction and synopsis 166
  • 8.2 Strength and toughness 166
  • 8.3 The mechanics of fracture 167
  • 8.4 Material property charts for toughness 174
  • 8.5 Drilling down: the origins of toughness 176
  • 8.6 Manipulating properties: the strength–toughness trade-off 180
  • 8.7 Summary and conclusions 183
  • 8.8 Further reading 183
  • 8.9 Exercises 184
  • 8.10 Exploring design with CES 185
  • 8.11 Exploring the science with CES Elements 185

  It is easy to set a value on the engineering science that enables success, that makes things happen, but much harder to value engineering science that prevents failure, that stops things happening. One of the great triumphs of recent engineering science has been the development from the 1960s onward of a rigorous mechanics of material fracture. We have no numbers for the money and lives it has saved by preventing failures; all we know is that, by any measure, it is enormous. This chapter is about the ways in which materials fail when loaded progressively, and design methods to ensure that fracture won’t happen unless you want it to.

  Ductile and brittle fracture. (Image of bolt courtesy of Boltscience; www.boltscience.com )

  8.1 Introduction and synopsis

  It is easy to set a value on the engineering science that enables success, that makes things happen, but much harder to value engineering science that prevents failure, that stops things happening. One of the great triumphs of recent engineering science has been the development from the 1960s onward of a rigorous mechanics of material fracture. We have no numbers for the money and lives it has saved by preventing failures; all we know is that, by any measure, it is enormous. This chapter is about the ways in which materials fail when loaded progressively, and design methods to ensure that fracture won’t happen unless you want it to.

  Sometimes, of course, you do. Aircraft engines are attached to the wing by shear-bolts, designed to fail and shed the engine if it suddenly seizes. At a more familiar level, peel-top cans, seals on food containers and many other safety devices rely on controlled tearing or fracture. And processes like machining and cutting use a combination of plasticity and fracture.

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  eBook - PDF

  Cement-Based Composites

  Materials, Mechanical Properties and Performance, Second Edition

  • Andrzej M. Brandt(Author)
  • 2005(Publication Date)
  • CRC Press

    (Publisher)

  10 Fracture and failure in the structures of the material 10.1 Application of fracture mechanics to cement matrices 10.1.1 Principles of linear elastic fracture mechanics (LEFM) Fracture mechanics was first applied by A. A. Griffith (1921) as an approach to the analysis and evaluation of the material’s behaviour. For the basic principles of fracture mechanics and its present development, the reader is referred to one of a number of available books and manuals: Anderson (2005). It is sufficient here to recall a few of the most important notions necessary for considerations of the brittle matrix composites. Griffith’s theory is based on two assumptions. The first concerns the considerable difference between observed and calculated tensile strength of materials. Effective strength is lower by at least one order of magnitude than the theoretical one calculated on the basis of the interatomic bonds. That difference is attributed to stress concentrations at microcracks and defects existing in every solid body before the application of any external load. In materials that exhibit plastic deformations, these stress concentrations disappear without appreciable reduction of material strength. In contrast, in brittle materials, a stress concentration initiates microcracks and their propagation, thus leading to fracture. The second assumption is related to the condition of an energetic equi-librium at the crack tip when a crack may start to propagate. The relation between the strain energy release rate U c considered as the crack extension force and the rate of energy S c necessary to create new crack surface decides whether the crack is stable or is rapidly propagating. The strain energy is denoted by U and specific surface energy by S . The initial crack length is equal to 2 c . When: c S c U < (10.1) the crack driving force is too low and the initial crack remains stable. If the load is increased over the equilibrium state,

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  eBook - ePub

  Practical Engineering Failure Analysis

  • Hani M. Tawancy, Anwar Ul-Hamid, Nureddin M. Abbas(Authors)
  • 2004(Publication Date)
  • CRC Press

    (Publisher)

  Chap. 8 . It suffices to mention here that on a microscopic scale, plastic deformation occurs by motion of a crystal defect called dislocation. Barriers to dislocation motion increase the external force required to cause plastic deformation. Among those barriers are grain boundaries. Increasing the grain boundary area per unit volume by reducing the grain size can thus be expected to increase the yield strength consistent with Eq. (6.11).

  When dislocations are held up against a grain boundary, a state of localized stress concentration is developed. In comparison with a coarse-grained material (smaller density of grain boundaries), dislocations in a fine-grained material can move smaller distances before they are held up against grain boundaries, as further explained in Chap. 8 . However, as shown later, a coarse-grained material develops a higher level of stress concentration at a grain boundary. In general, stress concentration is relieved by either plastic deformation in a neighboring grain or opening a crack at the grain boundary. Because plastic deformation can occur more readily in a coarse-grained material, cracks are more likely to propagate by a ductile mechanism. In contrast, for a fine-grained material where deformation is suppressed, cracks tend to propagate by a brittle mechanism.

  As explained in Chap. 8 , phase transformations occurring in a material can also have a significant effect on its fracture behavior. For example, when an alloy is disordered, fracture occurs by a ductile mechanism, However, if it becomes ordered, fracture may occur by a brittle mechanism. Precipitation of secondary phases can also the change the fracture behavior from ductile to brittle, e.g., precipitation of σ phase.

  6.11 Basic Principles of Fracture Mechanics

  It is recalled from Chap. 4 that toughness of a material, a property combining both strength and ductility, is a measure of its resistance to fracture. Since toughness corresponds to the area under the uniaxial stress-strain diagram, its unit is energy per unit volume equivalent to force per unit length.

  Basically, fracture mechanics aims at developing means by which crack propagation can be described on a macroscopic scale in terms of some measurable quantities. From the definition of toughness given in Chap. 4 , it becomes evident that the resistance to crack propagation must be expressed in terms of a parameter having the unit of force per unit length, which is called the crack extension force G. Since force per unit length is equivalent to energy per unit area, they both have the same physical meaning. According to the Griffith theory of crack nucleation, surface energy per unit area or surface tension equivalent to force per unit area is essentially the energy required to form a crack in a perfectly brittle material. In contrast, G

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