A Statistics-Based Cracking Criterion of Resin-Bonded Silica Sand for Casting Process Simulation
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VEINING is a casting defect formed during filling and solidification due to the crack of sand molds/cores. In order to control the veining defect, many studies have been done focusing on the improvement of sand properties by adding sand additives to reduce the thermal expansion.[1] In addition to the sand property improvement, the design, mechanical support, and thermal history of the molds/cores should also be considered to lower the tensile stress of the sand during filling and solidification of the casting alloy. A robust cracking criterion, relating sand properties and stress/ thermal conditions, is needed in predicting/controlling veining defect during the casting design and development stages. Resin-bonded silica sand is generally a ‘‘brittle’’ material. The failure strength of brittle materials varies in a much wider range as compared to ductile materials due to the different cracking mechanisms. A ductile material yields locally around microscopic flaws to prevent rapid fracture, and it is, thus, bulk property dependent. For a brittle material, cracking propagates rapidly after initiated from one of the microscopic flaws, HUIMIN WANG and YAN LU are with the Department of Materials Science & Engineering, The Ohio State University, 137 Fontana Labs, 116 W. 19th Ave., Columbus, OH, 43210. KEITH RIPPLINGER is with Honda Engineering North America, Anna, OH, 45302. DUANE DETWILER is with Honda R&D Americas, Raymond, OH, 43067. ALAN A. LUO is with the Department of Materials Science & Engineering, The Ohio State University, and also with the Department of Integrated Systems Engineering, The Ohio State University, Columbus, OH 43210. Contact e-mail: [email protected] Manuscript submitted August 25, 2016. METALLURGICAL AND MATERIALS TRANSACTIONS B
and it is microscopic property dependent. Therefore, it is necessary to employ statistics methods to set up the cracking criterion of a brittle material due to the fact that each specimen has a unique flaw distribution and each specimen has a unique strength.[2] Weibull statistics was proposed by Weibull[3] in 1939 for brittle material strength distribution.[3] It is based on the weakest link in the material. The material fails if its weakest volume fails. It assumes that flaws are likely to be evenly distributed in the specimen and that the probability of having the weakest link depends on the material volume under stress, which is called ‘‘effective volume.’’ Therefore, in Weibull’s statistics, the failure probability of the material is not only related to the applied stress, but also to the effective volume. The probability of failure under stress r is expressed in Eq. [1], where Pf is the failure probability, m is Weibull modulus which relates to stress distribution or data scatter and is material property related, r0 is nominal strength and does not have physical meaning. Both m and r0 can be derived from a least-square fit of a batch of experimental data.[4] Another format of Eq. [1] with the term of effective volume is expressed in Eq. [2], where rmax is the maximum fractur
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