Resistance of materials: textbook

Volosukhin, Viktor; Evtushenko, Sergey; Logvinov, Viktor

doi:10.12737/16729

Cited by 7 publications

(3 citation statements)

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“…The degree of stress increase depends primarily on the type and shape of the auxiliary line. The greater the cross-sectional difference in the transition section and the sharper the transitions and undercuts, the higher the local maximum stress occurs [ 50 ]. We choose angular structure as the main shape because it provides up to 5 times higher maximum stress than the nominal one.…”

Section: Methodsmentioning

confidence: 99%

Self-Controlled Cleaving Method for Silicon DRIE Process Cross-Section Characterization

Andronic

Sorokina

et al. 2021

Micromachines

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Advanced microsystems widely used in integrated optoelectronic devices, energy harvesting components, and microfluidic lab-on-chips require high-aspect silicon microstructures with a precisely controlled profile. Such microstructures can be fabricated using the Bosch process, which is a key process for the mass production of micro-electro-mechanical systems (MEMS) devices. One can measure the etching profile at a cross-section to characterize the Bosch process quality by cleaving the substrate into two pieces. However, the cleaving process of several neighboring deeply etched microstructures is a very challenging and uncontrollable task. The cleaving method affects both the cleaving efficiency and the metrology quality of the resulting etched microstructures. The standard cleaving technique using a diamond scriber does not solve this issue. Herein, we suggest a highly controllable cross-section cleaving method, which minimizes the effect on the resulting deep etching profile. We experimentally compare two cleaving methods based on various auxiliary microstructures: (1) etched transverse auxiliary lines of various widths (from 5 to 100 μm) and positions; and (2) etched dashed auxiliary lines. The interplay between the auxiliary lines and the etching process is analyzed for dense periodic and isolated trenches sized from 2 to 50 μm with an aspect ratio of more than 10. We experimentally showed that an incorrect choice of auxiliary line parameters leads to silicon “build-up” defects at target microstructures intersections, which significantly affects the cross-section profile metrology. Finally, we suggest a highly controllable defect-free cross-section cleaving method utilizing dashed auxiliary lines with the stress concentrators.

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Section: Methodsmentioning

confidence: 99%

Self-Controlled Cleaving Method for Silicon DRIE Process Cross-Section Characterization

Andronic

Sorokina

et al. 2021

Micromachines

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“…According to the elasticity theory, the relationship between the elastic bending of the beam e and the force P, applied to the end of the rectangular beam with a cross-section of a×b, is determined by the well-known equation [8,9] (Fig. 2а):…”

Section: Analytical and Numerical Calculationsmentioning

confidence: 99%

Numerical calculation the fracture toughness of square section beam under three-point bending test

Deryugin,

Pazhin

2024

E3S Web Conf.

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A universal equation is proposed to determine specific fracture energy based on numerical calculations by finite element methods in the ANSYS system referring to the three-point bending of a square beam arranged edgewise on supports. Numerical dependences of the specimen compliance on the crack length were represented as the 5th and 6th degree polynomials on the relative value of Δl/h, where Δl is the crack length and h is the half length of the square diagonal. To calculate the specific fracture energy, we used the derivative of specimen compliance by the crack length. The analysis has shown that finite value of specific fracture energy at Δl→0 is obtained when the decomposition term at Δl/h is equal to 0. A satisfactory agreement between the specific fracture energy values for the 5th and 6th degree decompositions is observed only at Δl/h ≈ 1. As the values of Δl decrease, the difference becomes increasingly significant. The averaging of coefficients at corresponding Δl/h degrees of two considered decompositions allows us to find a power function that weakly depends on the Δl/h ratio and leads to a consistent dependence of the specific fracture energy on the crack length. Due to the performed calculations, a universal equation is obtained to determine the specific fracture energy according to the test data of square beams by three-point bending in a wide range of geometric dimensions.

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“…Выпуск 1 (22) распечатке приведены на немецком и дополнены переводом, комментариями и ссылками на нормативные документы (DIN) на русском языке. Затем рассмотрим расчет СНиП [7]. Расчетная схема фермы с нумерацией узлов и стержней показана на рис.…”

Section: Riorunclassified