• Title/Summary/Keyword: Strain Energy Release Rate

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Analysis of mixed mode crack problems for anisotropic composite laminates using the $J_k$ integral ($J_k$ 적분을 이용한 이방성 복합적층판에 대한 혼합 모우드 파괴문제의 해석)

  • 주석재;홍창선
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.13 no.3
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    • pp.479-489
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    • 1989
  • The $J_{k}$ integral method for determining mixed mode stress intensity factors separately in the cracked anisotropic plate is developed. Stress intensity factors are indirectly determined from the values of $J_{1}$ and $J_{2}$. The $J_{2}$ integral can be evaluated efficiently from a finite element solution, neglecting the contribution from the portion of the integration contour along the crack faces, by selecting the integration contour in the vicinity of the crack tip. Using functions of a complex variable, the complete relations between $J_{1}$, $J_{2}$ and $K_{I}$ , $K_{II}$ for anisotropic materials are derived conveniently by selecting narrow rectangular contours shrinking to the crack tip. Compared to the existing path independent integral methods, the present method does not involve calculating the auxiliary solution and hence numerical procedures become quite simple. Numerical results to various problems are given and demonstrate the accuracy, stability and versatility of the method.

A Study on Surface Properties of Mechanical Interfacial Behavior of DGEBA/PMR-15 Blends (DGEBA/PMR-15 블렌드계의 표면특성 변화가 기계적 계면특성에 미지는 영향)

  • Park, Soo-Jin;Lee, Hwa-Young;Han, Mijeong;Hong, Sung-Kwon
    • Journal of Adhesion and Interface
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    • v.4 no.1
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    • pp.1-8
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    • 2003
  • In this work, the effect of PMR-15 content on the variation of surface free energy of the DGEBA/PMR-15 blend system was investigated in terms of contact angles and mechanical interfacial tests. Based on FT-IR result of the blend system. C=O (1,772, $1,778cm^{-1}$) and C-N ($1,372cm^{-1}$) peaks appeared with imidization of PMR-15 and -OH ($3,500cm^{-1}$) peak showed broadly at 10 phr of PMR-15 by ring-opening of epoxy. Contact angle measurements were performed by using deionized water and diiodomethane as testing liquids. As a result, the surface free energy of the blends gave a maximum value at 10 phr of PMR-15, due to the significant increasing of specific component. The mechanical interfacial properties measured from the critical stress intensity factor ($K_{IC}$) and the critical strain energy release rate ($G_{IC}$) showed a similar behavior with the results of surface energetics. This behavior was probably attributed to The improving of the interfacial adhesion between intermolecules, resulting from increasing the hydrogen bondings of the blends.

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Bond Strength of Wafer Stack Including Inorganic and Organic Thin Films (무기 및 유기 박막을 포함하는 웨이퍼 적층 구조의 본딩 결합력)

  • Kwon, Yongchai;Seok, Jongwon
    • Korean Chemical Engineering Research
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    • v.46 no.3
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    • pp.619-625
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    • 2008
  • The effects of thermal cycling on residual stresses in both inorganic passivation/insulating layer that is deposited by plasma enhanced chemical vapor deposition (PECVD) and organic thin film that is used as a bonding adhesive are evaluated by 4 point bending method and wafer curvature method. $SiO_2/SiN_x$ and BCB (Benzocyclobutene) are used as inorganic and organic layers, respectively. A model about the effect of thermal cycling on residual stress and bond strength (Strain energy release rate), $G_c$, at the interface between inorganic thin film and organic adhesive is developed. In thermal cycling experiments conducted between $25^{\circ}C$ and either $350^{\circ}C$ or $400^{\circ}C$, $G_c$ at the interface between BCB and PECVD $ SiN_x $ decreases after the first cycle. This trend in $G_c$ agreed well with the prediction based on our model that the increase in residual tensile stress within the $SiN_x$ layer after thermal cycling leads to the decrease in $G_c$. This result is compared with that obtained for the interface between BCB and PECVD $SiO_2$, where the relaxation in residual compressive stress within the $SiO_2$ induces an increase in $G_c$. These opposite trends in $G_cs$ of the structures including either PECVD $ SiN_x $ or PECVD $SiO_2$ are caused by reactions in the hydrogen-bonded chemical structure of the PECVD layers, followed by desorption of water.

Effects of Encapsulation Layer on Center Crack and Fracture of Thin Silicon Chip using Numerical Analysis (봉지막이 박형 실리콘 칩의 파괴에 미치는 영향에 대한 수치해석 연구)

  • Choa, Sung-Hoon;Jang, Young-Moon;Lee, Haeng-Soo
    • Journal of the Microelectronics and Packaging Society
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    • v.25 no.1
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    • pp.1-10
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    • 2018
  • Recently, there has been rapid development in the field of flexible electronic devices, such as organic light emitting diodes (OLEDs), organic solar cells and flexible sensors. Encapsulation process is added to protect the flexible electronic devices from exposure to oxygen and moisture in the air. Using numerical simulation, we investigated the effects of the encapsulation layer on mechanical stability of the silicon chip, especially the fracture performance of center crack in multi-layer package for various loading condition. The multi-layer package is categorized in two type - a wide chip model in which the chip has a large width and encapsulation layer covers only the chip, and a narrow chip model in which the chip covers both the substrate and the chip with smaller width than the substrate. In the wide chip model where the external load acts directly on the chip, the encapsulation layer with high stiffness enhanced the crack resistance of the film chip as the thickness of the encapsulation layer increased regardless of loading conditions. In contrast, the encapsulation layer with high stiffness reduced the crack resistance of the film chip in the narrow chip model for the case of external tensile strain loading. This is because the external load is transferred to the chip through the encapsulation layer and the small load acts on the chip for the weak encapsulation layer in the narrow chip model. When the bending moment acts on the narrow model, thin encapsulation layer and thick encapsulation layer show the opposite results since the neutral axis is moving toward the chip with a crack and load acting on chip decreases consequently as the thickness of encapsulation layer increases. The present study is expected to provide practical design guidance to enhance the durability and fracture performance of the silicon chip in the multilayer package with encapsulation layer.

Effects of Boliing, Steaming, and Chemical Treatment on Solid Wood Bending of Quercus acutissima Carr. and Pinus densiflora S. et. Z. (자비(煮沸), 증자(蒸煮) 및 약제처리(藥劑處理)가 상수리나무와 소나무의 휨가공성(加工性)에 미치는 영향(影響))

  • So, Won-Tek
    • Journal of the Korean Wood Science and Technology
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    • v.13 no.1
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    • pp.19-62
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    • 1985
  • This study was performed to investigate: (i) the bending processing properties of silk worm oak (Quercus acutissima Carr.) and Korean red pine (Pinus densiflora S. et Z.) by boiling and steaming treatments; (ii) the effects of interrelated factors - sapwood and heartwood, annual ring placement, softening temperature and time, moisture content. and wood defects on bending processing properties; (iii) the changing rates of bending radii after release from a tension strap, and (iv) the improving methods of bending process by treatment with chemicals. The size of specimens tested was $15{\times}15{\times}350mm$ for boiling and steaming treatments and $5{\times}10{\times}200mm$ for treatments with chemicals. The specimens were green for boiling treatments and dried to 15 percent for steaming treatments. The specimens for treatments with chemicals were soaked in saturated urea solution, 35 percent formaldehyde solution, 25 percent polyethylene glycol -400 solution, and 25 percent ammonium hydroxide solution for 5 days and immediately followed the bending process, respectively. The results obtained were as follows: 1. The internal temperature of silk worm oak and Korean red pine by boiling and steaming time was raised slowly to $30^{\circ}C$ but rapidly from $30^{\circ}C$ to $80-90^{\circ}C$ and then slowly from $80-90^{\circ}C$ to $100^{\circ}C$. 2. The softening time required to the final temperature was directly proportional to the thickness of specimen. The time required from $25^{\circ}C$ to $100^{\circ}C$ for 15mm-squared specimen was 9.6-11.2 minutes in silk worm oak and 7.6-8.1 minutes in Korean red pine. 3. The moisture content (M.C.) of specimen by steaming time was increased rapidly first 4 minutes in the both species, and moderately from 4 to 20 minutes and then slowly and constantly in silk worm oak, and moderately from 4 to 15 minutes and then slowly and constantly in Korean red pine. The M.C. of 15mm-squared specimen in 50 minutes of steaming was increased to 18.0 percent in the oak and 22.4 percent in the pine from the initial conditioned M.C. of 15 percent The rate of moisture adsorption measured was therefore faster in the pine than in the oak. 4. The mechanical properties of the both species were decreased significantly with the increase of boiling rime. The decrement by the boiling treatment for 60 minutes was measured to 36.6-45.0 percent in compressive strength, 12.5-17.5 percent in tensile strength, 31.6-40.9 percent in modulus of rupture, and 23.3-34.6 percent in modulus of elasticity. 5. The minimum bending radius (M.B.R.) of sapwood and heartwood was 60-80 mm and 90 mm in silk worm oak, and 260 - 300 mm and 280 - 300 mm in Korean red pine, respectively. Therefore, the both species showed better bending processing properties in sapwood than in heartwood. 6. The M.B.R. of edge-grained and flat-grained specimen in suk worm oak was 60-80 mm, but the M.B.R. in Korean red pine was 240-280 mm and 260-360 mm, respectively. Comparing the M.B.R. of edge-grained with flat-grained specimen, in the pine the edge-grained showed better bending processing property than the flat-grained. 7. The bending processing properties of the both species were improved by the rising of softening temperature from $40^{\circ}C$ to $100^{\circ}C$. The minimum softening temperature for bending was $90^{\circ}C$ in silk worm oak and $80^{\circ}C$ in Korean red pine, and the dependency of softening temperature for bending was therefore higher in the oak than in the pine. 8. The bending processing properties of the both species were improved by the increase of softening time as well as temperature, but even after the internal temperature of specimen reaching to the final temperature, somewhat prolonged softening was required to obtain the best plastic conditions. The minimum softening time for bending of 15 mm-squared silk worm oak and Korean red pine specimen was 15 and 10 minutes in the boiling treatment, and 30 and 20 minutes in the steaming treatment, respectively. 9. The optimum M.C. for bending of silk worm oak was 20 percent, and the M.C. above fiber saturation point rather degraded the bending processing property, whereas the optimum M.C. of Korean red pine needed to be above 30 percent. 10. The bending works in the optimum conditions obtained as seen in Table 24 showed that the M.B.R. of silk worm oak and Korean red pine was 80 mm and 240 mm in the boiling treatment, and 50 mm and 280 mm in the steaming treatment, respectively. Therefore, the bending processing property of the oak was better in the steaming than in the boiling treatment, but that of the pine better in the boiling than in the steaming treatment. 11. In the bending without a tension strap, the radio r/t of the minimum bending radius t to the thickness t of silk worm oak and Korean red pine specimen amounted to 16.0 and 21.3 in the boiling treatment, and 17.3 and 24.0 in the steaming treatment, respectively. But in the bending with a tension strap, the r/t of the oak and the pine specimen decreased to 5.3 and 16.0 in t he boiling treatment, and 3.3 and 18.7 in the steaming treatment, respectively. Therefore, the bending processing properties of the both species were significantly improved by the strap. 12. The effect of pin knot on the degradation of bending processing property was very severe in silk worm oak by side, e.g. 90 percent of the oak specimens with pin knot on the concave side were ruptured when bent to a 100 mm radius but only 10 percent of the other specimens with pin knot on the convex side were ruptured. 13. The changing rate in the bending radius of specimen bent to a 300 mm radius after 30 days of exposure to room temperature conditions was measured to 4.0-10.3 percent in the boiling treatment and 13,0-15.0 percent in the steaming treatment. Therefore, the degree of spring back after release was higher in the steaming than in the boiling treatment. And the changing rate of moisture-proofing treated specimen by expoxy resin coating was only -1.0.0 percent. 14. Formaldehyde, 35 percent solution, and 25 percent polyethylene glycol-400 solution found no effect on the plasticization of the both species, but saturated urea solution and 25 percent ammonium hydroxide solution found significant effect in comparison to non-treated specimen. But the effect of the treatment with chemicals alone was inferior to that of the steaming treatment, and the steaming treatment after the treatment with chemicals improved 10-24 percent over the bending processing property of steam-bent specimen. 15. Three plasticity coefficients - load-strain coefficient, strain coefficient, and energy coefficient - were evaluated to be appropriate for the index of bending processing property because the coefficients had highly significant correlation with the bending radius. The fitness of the coefficients as the index was good at load-strain coefficient, energy coefficient, and strain coefficient, in order.

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