Publisher Summary This chapter describes the mixed mode cracking in layered materials. There is ample experimental evidence that cracks in brittle, isotropic, homogeneous materials propagate such that pure mode I conditions are maintained at the crack tip. An unloaded crack subsequently subject to a combination of modes I and II will initiate growth by kinking in such a direction that the advancing tip is in mode I. The chapter also elaborates some of the basic results on the characterization of crack tip fields and on the specification of interface toughness. The competition between crack advance within the interface and kinking out of the interface depends on the relative toughness of the interface to that of the adjoining material. The interface stress intensity factors play precisely the same role as their counterparts in elastic fracture mechanics for homogeneous, isotropic solids. When an interface between a bimaterial system is actually a very thin layer of a third phase, the details of the cracking morphology in the thin interface layer can also play a role in determining the mixed mode toughness. The elasticity solutions for cracks in multilayers are also elaborated.

Mixed mode cracking in layered materials

A fracture theory for a heterogenous aggregate material which exhibits a gradual strain-softening due to microcracking and contains aggregate pieces that are not necessarily small compared to structural dimensions is developed. Only Mode I is considered. The fracture is modeled as a blunt smeard crack band, which is justified by the random nature of the microstructure. Simple triaxial stress-strain relations which model the strain-softening and describe the effect of gradual microcracking in the crack band are derived. It is shown that it is easier to use compliance rather than stiffness matrices and that it suffices to adjust a single diagonal term of the complicance matrix. The limiting case of this matrix for complete (continuous) cracking is shown to be identical to the inverse of the well-known stiffness matrix for a perfectly cracked material. The material fracture properties are characterized by only three parameters—fracture energy, uniaxial strength limit and width of the crack band (fracture process zone), while the strain-softening modulus is a function of these parameters. A method of determining the fracture energy from measured complete stres-strain relations is also given. Triaxial stress effects on fracture can be taken into account. The theory is verified by comparisons with numerous experimental data from the literature. Satisfactory fits of maximum load data as well as resistance curves are achieved and values of the three material parameters involved, namely the fracture energy, the strength, and the width of crack band front, are determined from test data. The optimum value of the latter width is found to be about 3 aggregate sizes, which is also justified as the minimum acceptable for a homogeneous continuum modeling. The method of implementing the theory in a finite element code is also indicated, and rules for achieving objectivity of results with regard to the analyst's choice of element size are given. Finally, a simple formula is derived to predict from the tensile strength and aggregate size the fracture energy, as well as the strain-softening modulus. A statistical analysis of the errors reveals a drastic improvement compared to the linear fracture theory as well as the strength theory. The applicability of fracture mechanics to concrete is thus solidly established.

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Crack band theory for fracture of concrete

A balanced mechanics-materials approach and coverage of the latest developments in biomaterials and electronic materials, the new edition of this popular text is the most thorough and modern book available for upper-level undergraduate courses on the mechanical behavior of materials To ensure that the student gains a thorough understanding the authors present the fundamental mechanisms that operate at micro- and nano-meter level across a wide-range of materials, in a way that is mathematically simple and requires no extensive knowledge of materials This integrated approach provides a conceptual presentation that shows how the microstructure of a material controls its mechanical behavior, and this is reinforced through extensive use of micrographs and illustrations New worked examples and exercises help the student test their understanding Further resources for this title, including lecture slides of select illustrations and solutions for exercises, are available online at wwwcambridgeorg/97800521866758

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Mechanical Behavior of Materials

There have been a number of review papers on layered silicate and carbon nanotube reinforced polymer nanocomposites, in which the fillers have high aspect ratios. Particulate–polymer nanocomposites containing fillers with small aspect ratios are also an important class of polymer composites. However, they have been apparently overlooked. Thus, in this paper, detailed discussions on the effects of particle size, particle/matrix interface adhesion and particle loading on the stiffness, strength and toughness of such particulate–polymer composites are reviewed. To develop high performance particulate composites, it is necessary to have some basic understanding of the stiffening, strengthening and toughening mechanisms of these composites. A critical evaluation of published experimental results in comparison with theoretical models is given.

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Effects of particle size, particle/matrix interface adhesion and particle loading on mechanical properties of particulate–polymer composites

On fracture locus in the equivalent strain and stress triaxiality space

Nearly double the size of the previous edition, the third edition of this classic reference provides a comprehensive, easy-to-access collection of elastic stress solutions for crack configurations. For each configuration, The Stress Analysis of Cracks Handbook present crack tip stress intensity formulas along with other relevant information, such as displacements, crack opening areas, basic stress functions source references, accuracy of solutions, and more. Throughout, it stresses formulas for application to test configurations. The introductory section details the methods of developing the informatio A series of appendices represents special methods and special applications. Now in a hardbound format, the current Handbook offers a number of new features including: * Ne Stress Solutions * Cracked Configurations * Plates with Pinching Loads * Dislocations and Cracks Solutions * Plastic Zone Instability (Expanding a Potentially Interceding "Elastic" Failure Mechanism) * Estimation Methods for Stress Intensity Formulas * J-Integral Methods * Pure Shear Plasticity Solutions. The authors provide 30 new solution pages, plus modifications of older solutions. Contents Include: * Introductory Information Stress Analysis Results for Common Test Specimen Configurations with Cracks * Cracks Along a Single Line * Parallel Cracks * Cracks and Holes or Notches * Curved, Angled, Branched, or Radiating Cracks * Cracks in Reinforced Plates * Three-Dimensional Cracked Configurations * Crack(s) in a Rod or a Plate by Energy Rate Analysis * Strip Yield Model Solutions * Cracks(s) in a Shell * Appendices.

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The stress analysis of cracks handbook

The general equations for crack-tip stress fields in anisotropic bodies are derived making use of a complex variable approach. The stress-intensity-factors, which permit concise representation of the conditions for crack extension, are defined and are evaluated directly from stress functions. Some individual boundary value problem solutions are given in closed form and discussed with reference to their companion solutions for isotropic bodies.

On cracks in rectilinearly anisotropic bodies

The Stress Analysis of Cracks Handbook, Third Edition

Fracture Toughness and Slow-Stable Cracking

: An investigation and analysis of aircraft structural failures was conducted to assess the condition surrounding early life failures and initiate improved methods for the structural analysis of such failure problems. The primary objective was to identify critical structural component areas and define an analysis approach which would consider the useful life of a flawed or damaged structure. Initial program efforts involved the survey of Government and Industry organizations concerned with engineering and maintenance of present operational aircraft. Failure data was gathered on airframe structures, landing gear components and highly stressed aircraft sub-components which experienced operational failures. The data gathered was tabulated under various categories related to component description, failure circumstances, stress history and environmental influences in an attempt to identify significant or contributing variables. Results of these failure correlations are presented in tabular form.

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George R. Irwin

Papers

The stress analysis of cracks handbook

On cracks in rectilinearly anisotropic bodies

The Stress Analysis of Cracks Handbook, Third Edition

Fracture Toughness and Slow-Stable Cracking

Investigation and Analysis Development of Early Life Aircraft Structural Failures