By Yoichi Sumi
ISBN-10: 443154934X
ISBN-13: 9784431549345
ISBN-10: 4431549358
ISBN-13: 9784431549352
This publication is set the trend formation and the evolution of crack propagation in engineering fabrics and buildings, bridging mathematical analyses of cracks in keeping with singular quintessential equations, to computational simulation of engineering layout. the 1st elements of this ebook specialize in elasticity and fracture and supply the foundation for discussions on fracture morphology and its numerical simulation, that may bring about a simulation-based fracture regulate in engineering buildings. numerous layout innovations are mentioned for the prevention of fatigue and fracture in engineering constructions, together with safe-life layout, fail-safe layout, harm tolerant design.
After beginning with simple elasticity and fracture theories in elements one and , this ebook makes a speciality of the fracture morphology that develops because of the propagation of brittle cracks or fatigue cracks.
In half 3, the mathematical research of a curved crack is exactly defined, in response to the perturbation procedure. the steadiness conception of interactive cracks propagating in brittle solids can help readers to appreciate the formation of a fractal-like cracking styles in brittle solids, whereas the soundness concept of crack paths is helping to spot the immediately as opposed to sharply curved or occasionally wavy crack paths saw in brittle solids.
In half 4, the numerical simulation approach to a procedure of a number of cracks is brought by way of the finite aspect process, that could be used for the higher implementation of fracture regulate in engineering structures.
This e-book is a part of a chain on “Mathematics for undefined” and should attract structural engineers looking to comprehend the elemental backgrounds of analyses, but in addition to mathematicians with an curiosity in how such mathematical ideas are evaluated in commercial applications.
Read or Download Mathematical and Computational Analyses of Cracking Formation: Fracture Morphology and Its Evolution in Engineering Materials and Structures PDF
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Extra info for Mathematical and Computational Analyses of Cracking Formation: Fracture Morphology and Its Evolution in Engineering Materials and Structures
Sample text
Using Eq. 11) This result means that fracture takes place when the first variation of the total potential energy vanishes or decreases with arbitrary positive crack extension (ıa > 0). We shall first consider a Mode-I crack under the displacement-controlled loading condition. In this case the variation of the mechanical potential energy coincides with the variation of strain energy. Since the change of strain energy corresponds to the work necessary to release the crack tip stress so as to open a crack tip by the extension length ıa (see Fig.
I D 1; 2/ is the external unit normal vector on the newly created crack surfaces. Using the stress and displacement near a crack tip given by Eqs. 13) where GI is the energy release rate of Mode-I. 1 Theory of Brittle Fracture 51 Fig. 3 Small crack extension at a crack tip in terms of the stress intensity factor, Irwin (1957, 1958). 15) depends entirely on the material properties called fracture toughness. 16) is called the plane-strain fracture toughness. 17) for the problem illustrated in Fig.
D 4 (see Fig. 7b). 29) where the lengths of the major and minor axes of the ellipse are denoted by a and b, respectively (Inglis 1913). 30) so that one can rewrite Eq. 6 Elliptic Hole in Tension 25 a b Fig. 7 Stress concentration under (a) biaxial tension and (b) pure shear Fig. 8 Stress concentration due to a defect under uniaxial tension This expression is known to be applicable to the estimation of the stress concentration factor of a wider range of internal defects whose projected length on the plane perpendicular to the principal loading direction is 2a and its tip radius is (see Fig.
Mathematical and Computational Analyses of Cracking Formation: Fracture Morphology and Its Evolution in Engineering Materials and Structures by Yoichi Sumi
by Ronald
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