Fracture Mechanics of Composites

Two systems of non-homogeneous linear equations with 8 unknowns are obtained. This is done by introducing two stress functions containing 16 undetermined coefficients and two real stress singularity exponents with the help of boundary conditions. By solving the above systems of non-homogeneous linear equations, the two real stress singularity exponents can be determined when the double material parameters meet certain conditions. The expression of the stress function and all coefficients are obtained based on the uniqueness theorem of limit. By substituting these parameters into the corresponding mechanics equations, theoretical solutions to the stress intensity factor, the stress field and the displacement field near the crack tip of each material can be obtained when both discriminants of the characteristic equations are less than zero. Stress and displacement near the crack tip show mixed crack characteristics without stress oscillation and crack surface overlapping. As an example, when the two orthotropic materials are the same, the stress singularity exponent, the stress intensity factor, and expressions for the stress and the displacement fields of the orthotropic single materials can be derived.

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“…Let U j = U (x + s j y), then the characteristic equation of the governing equation (4) can be obtained [8,14] :…”

Section: Undetermined Coefficients Methodsmentioning

confidence: 99%

“…In the absence of body forces, the governing equation of the orthotropic materials may be expressed as follows [11,14] :…”

Section: The Fundamental Equationsmentioning

confidence: 99%

Crack-tip field on mode II interface crack of double dissimilar orthotropic composite materials

Zhang

Cui

Yang

et al. 2009

Appl. Math. Mech.-Engl. Ed.

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“…From (32), (43), (47), and (50), the same stress expressions in the vicinity of mode II crack tip of the orthotropic single material as those in Refs. [15,17] can be deduced.…”

Section: (48)mentioning

confidence: 99%

“…Putting (15) and (16) into the relationships between the stresses and the stress functions [10,15,16] , and noticing (17), we get…”

Section: Stress Functionmentioning

confidence: 99%

Interface crack problems for mode II of double dissimilar orthotropic composite materials

Yang

Zhang

et al. 2009

Appl. Math. Mech.-Engl. Ed.

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The fracture problems near the interface crack tip for mode II of double dissimilar orthotropic composite materials are studied. The mechanical models of interface crack for mode II are given. By translating the governing equations into the generalized bi-harmonic equations, the stress functions containing two stress singularity exponents are derived with the help of a complex function method. Based on the boundary conditions, a system of non-homogeneous linear equations is found. Two real stress singularity exponents are determined be solving this system under appropriate conditions about bimaterial engineering parameters. According to the uniqueness theorem of limit, both the formulae of stress intensity factors and theoretical solutions of stress field near the interface crack tip are derived. When the two orthotropic materials are the same, the stress singularity exponents, stress intensity factors and stresses for mode II crack of the orthotropic single material are obtained.

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“…In this paper, we use a complex function method as is used in papers [ 3 ] ~ [ 5 ] to solve and analyse the boundary value problem (1), (2) and (3). The solution for partial differential Eq.…”

Section: Mechanical Modelmentioning

confidence: 99%

The crack tip fields of orthotropic composite plate under bending

et al. 1999

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The fracture problem which is the same as that in paper [ 1 ] is further discussed in this paper. The analysis of fracture behaviours near crack tip for infinite linear elastic orthotropic composite plate with a central through crack of length 2 a is carried out. The geometry and loading conditions are shown in Fig. 1. To solve such a problem, we need to solve the partial differential equation with the following boundary conditions: QII 34w 34w c94w 3x---2-+ 2( Q12 + 2Q66) 3x2ay 2 + Q22 --

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Fracture Mechanics of Composites

Cited by 53 publications

References 25 publications

Crack-tip field on mode II interface crack of double dissimilar orthotropic composite materials

Crack-tip field on mode II interface crack of double dissimilar orthotropic composite materials

Interface crack problems for mode II of double dissimilar orthotropic composite materials

The crack tip fields of orthotropic composite plate under bending

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