Size effect and asymptotic matching analysis of fracture of closed-cell polymeric foam |
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| Institution: | 1. Departments of Civil Engineering and Materials Science, Northwestern University, 2145 Sheridan Road, Tech-CEE, Evanston, IL 60208, USA;2. Department of Civil Engineering, Northwestern University, Evanston, IL 60208, USA;3. Departments of Civil and Mechanical Engineering, Northwestern University, Evanston, IL 60208, USA;1. University of Bucharest, 405 Atomistilor, 077125 Magurele-Bucharest, Romania;2. Institute of Materials Tecnology, University Politècnica of València, Camino de Vera s/n, 46022 Valencia, Spain;3. Centro Ricerche Fiat, Strada Torino 50, 46022 Orbassano, Italy;1. Department of Materials Science and Engineering, Inha University, Incheon 402-751, Republic of Korea;2. GiEVER, Inha University Dream Center, Incheon 22212, Republic of Korea;3. Mechanical and Materials Engineering Department, Portland State University, Portland 97207, USA;4. Division of Materials Science and Engineering, Hanyang University, Seoul 133-791, Republic of Korea;5. The Research Institute of Industrial Science, Hanyang University, Seoul 133-791, Republic of Korea;6. Korea Institute of Industrial Technology (KITECH), Incheon 21999, Republic of Korea |
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| Abstract: | The effect of structure size on the nominal strength of closed-cell PVC foam (Divinycell H100) is investigated experimentally, theoretically and numerically. Two types of size effect are considered––Type I, characterizing failure of structures with large cracks or notches, and Type II, characterizing failure at crack initiation. Geometrically similar single edge-notched prismatic specimens of cross section widths 6.35, 43.9 and 305 mm, are tested under tension. The results are shown to agree with Bažant’s law for type I energetic (deterministic) size effect derived by asymptotic matching of a solution by equivalent linear elastic fracture mechanics for large sizes and plastic crack solution for small sizes (in the derivation, the statically indeterminate size-dependent lateral shift of the axial load resultant due to rotational end restrain is taken into account). Fitting this law, previously verified for many quasibrittle materials, to the test results furnishes the values of the fracture energy of the foam as well as the characteristic size of the fracture process zone of foam. The size effect method of measuring the fracture characteristics of foam is further supported by analysis of recent notched beam tests of Zenkert and Bäcklund. Furthermore, it is shown that compressed V-notched specimens exhibit no size effect. Subsequently, the size effect of Type II is studied using previous test data of Fleck, Olurin and co-workers for dissimilar long holed panels having different width and different diameter-width ratios. An asymptotic matching formula for this type of size effect (similar to a previously derived formula for kink band failure of fiber composites) is set up and is shown capable of matching the test data well. But its verification as a predictive tool cannot yet be claimed because of inaccurate asymptotic properties of the available energy release function. Finally, the size effect of Type I is analyzed using the eigenvalue method for the cohesive crack model and the numerical results are shown to agree again with both Bažant’s size effect law and the test results. |
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