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Stress Intensity Factors and Effective Spring Stiffness for Interfaces with Two and Three Dimensional Cracks at the Interface between Two Dissimilar Materials

Lekesiz, Huseyin

Abstract Details

2010, Doctor of Philosophy, Ohio State University, Mechanical Engineering.

Stress intensity factors and effective spring stiffnesses for two-dimensional and three-dimensional cracks at the interface between dissimilar solids are investigated. First explicit analytical expressions are obtained for the longitudinal and transverse effective spring stiffnesses of a planar periodic array of collinear cracks at the interface between two dissimilar isotropic materials; they are shown to be identical in a general case of elastic dissimilarity. The effects of elastic dissimilarity, crack density and crack interaction on the effective spring stiffness are clearly represented in the solution. It is shown that in general the crack interaction weakly depends on material dissimilarity and, for most practical cases, the crack interaction is nearly the same as that for crack arrays between identical solids. This allows approximate factorization of the effective spring stiffness for an array of cracks between dissimilar materials in terms of an elastic dissimilarity factor and two factors obtained for cracks in a homogeneous material: the effective spring stiffness for non-interacting cracks and the crack interaction factor.

Second, the longitudinal and transverse effective spring stiffnesses of non-interacting penny-shaped cracks at the interface between two dissimilar, isotropic, linearly elastic materials is obtained based on classical fracture mechanics. For linear ultrasound applications, it is shown that the expression obtained for transverse springs can be used for most isotropic, linearly elastic material combinations, if the initial maximum crack opening displacement is more than 0.000001 of the crack radius.

Third, based on Kachanov’s approximate method for crack interaction problems, the stress intensity factors for a periodic array of coplanar penny-shaped cracks are obtained as a function of angle around the crack circumference and crack density for square and hexagonal crack configurations. Numerical errors and errors due to the approximate nature of the method are estimated, and obtained results are shown to be valid within 8% error for crack density up to 95%.

Fourth, following the approximate factorization of the effective spring stiffness for an array of cracks between dissimilar materials, approximate expressions for the longitudinal and transverse effective spring stiffnesses of co-planar penny-shaped cracks with square or hexagonal configurations at the interface between two dissimilar isotropic materials are proposed. They are based on elastic dissimilarity factors and two factors obtained for cracks in a homogeneous material: the effective spring stiffnesses for non-interacting cracks and the crack interaction factor. The crack interactions as a function of crack density for square and hexagonal configuration are obtained by comparing the effective spring stiffnesses for coplanar penny shaped cracks and those for non-interacting cracks. By comparing expressions of the effective spring stiffnesses for non-interacting penny shaped cracks at the interface between two dissimilar materials and those in a homogeneous material, the effect of material dissimilarity on the equivalent spring stiffnesses are expressed in terms of material dissimilarity functions. Since the interfacial spring stiffnesses can be experimentally determined from ultrasound reflection and transmission analysis, the obtained expressions can be useful in estimating the percentage of disbond area between two dissimilar materials, which is directly related to the residual strength of the interface.

Noriko Katsube, Professor (Advisor)
Stanislav Rokhlin, Professor (Committee Member)
Robert Seghi, Professor (Committee Member)
Mark Walter, Professor (Committee Member)
274 p.

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Citations

  • Lekesiz, H. (2010). Stress Intensity Factors and Effective Spring Stiffness for Interfaces with Two and Three Dimensional Cracks at the Interface between Two Dissimilar Materials [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1293574318

    APA Style (7th edition)

  • Lekesiz, Huseyin. Stress Intensity Factors and Effective Spring Stiffness for Interfaces with Two and Three Dimensional Cracks at the Interface between Two Dissimilar Materials. 2010. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1293574318.

    MLA Style (8th edition)

  • Lekesiz, Huseyin. "Stress Intensity Factors and Effective Spring Stiffness for Interfaces with Two and Three Dimensional Cracks at the Interface between Two Dissimilar Materials." Doctoral dissertation, Ohio State University, 2010. http://rave.ohiolink.edu/etdc/view?acc_num=osu1293574318

    Chicago Manual of Style (17th edition)