The proper use of thermal expansion coefficients in finite element calculations

Niffenegger, Markus; Reichlin, K.

doi:10.1016/j.nucengdes.2011.12.006

Cited by 30 publications

(18 citation statements)

References 2 publications

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“…CTEs can be presented either in instantaneous or mean formats. Mean CTE refers to the average value of the CTE between a reference temperature and the current temperature whereas instantaneous CTE refers to the actual rate of the change of strain at each temperature [8]. Instantaneous CTEs of different materials are presented in Figure 1 as a function of temperature.…”

Section: Methodsmentioning

confidence: 99%

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Wide temperature range through silicon vias made of Invar and spin-on glass for interposers and MEMS

Laakso

Asiatici

Fischer

et al. 2016

2016 IEEE 29th International Conference on Micro Electro Mechanical Systems (MEMS)

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Through silicon vias (TSVs) are used e.g. to create electrical connections through MEMS wafers or through silicon interposers used in 2.5D packaging. Currently available technologies do not address situations in which TSVs through unthinned wafers have to withstand large temperature variations. We propose using ferromagnetic Invar metal alloy for this purpose due to its low mismatch in heat induced strain in comparison to silicon. We demonstrate the suitability of a magnetic assembly process for Invar TSV fabrication and the use of spin-on glass as a TSV insulator. We demonstrate TSVs, with contact pads, that tolerate temperature cycling between -50 °C and 190 °C and can withstand elevated temperatures of at least up to 365 °C.

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Section: Methodsmentioning

confidence: 99%

“…The resulting mean CTE curve has been converted [8] to instantaneous CTE. Both are plotted in Figure 1.…”

Section: Methodsmentioning

confidence: 99%

Wide temperature range through silicon vias made of Invar and spin-on glass for interposers and MEMS

Laakso

Asiatici

Fischer

et al. 2016

2016 IEEE 29th International Conference on Micro Electro Mechanical Systems (MEMS)

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“…where m = D(U) is the mechanical strain, and th = {α ab ∆T, α c ∆T, 0} is the thermal induced strain for a local increase in temperature, ∆T = T − T ref [23]. α ab and α c are the directional linear thermal expansion coefficients of the bulk in K −1 [24].…”

Section: Modeling Of the Problemmentioning

confidence: 99%

Distribution of Current Density, Temperature, and Mechanical Deformation in YBCO Bulks Under Field-Cooling Magnetization

Trillaud

Berger

Douine

et al. 2018

IEEE Trans. Appl. Supercond.

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Abstract-Most of the latest models of HTS bulk magnetization take into account the thermal and electromagnetic coupling, but, they still lack the implementation of the mechanical deformation under strong magnetic fields. The following work tries to fill up partly the gap by proposing a model of the dependence of the electrical conductivity upon mechanical deformation during Field-Cooling magnetization. This dependence is carried out by the critical current density as a function of induced thermal and mechanical strain in the bulk. As a first approximation and bearing in mind the obvious discrepancies, a simple model inferred from HTS thin films and generic knowledge on ceramics is proposed. This first approach allows drawing some generalities on the expected thermal, magnetic and mechanical response of disk-shaped YBCO pellets during magnetization. The utter goal is to assess design parameters to insert those pellets in electrical rotatory machines.

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“…In PTS analyses, it is common practice to start the calculation at operating conditions (17 MPa, 288°C) and to assume that the RPV is stress free at this temperature. Since the mean thermal expansion coefficients given in Table 3 are temperature dependent, special attention has to be paid to their proper use [5]. Figure 11 shows the ring models with the temperatures calculated by CFD and the resulting radial (σ rr ), angular (σ θθ ) and axial stresses (σ zz ) for a certain time, calculated by the FEM.…”

Section: Structural Mechanics Calculationmentioning

confidence: 99%

Analysis of a reactor pressure vessel subjected to pressurized thermal shocks

Niffenegger¹,

Qian²,

González-Albuixech³

et al. 2016

Int. J. CMEM

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The integrity of reactor pressure vessels (RPVs) of nuclear power plants is one of the most important topics in the field of nuclear energy production. Therefore, the integrity of RPVs has to be assessed for normal operation as well as for emergency transients. A critical transient concerning the RPV integrity is the emergency cooling of a pressurized water reactor, initiated by a leak in the hot leg. Such shock-like cooling in combination with the pressure, the so-called pressurized thermal shock (PTS), causes high thermal stresses in the RPV wall and stress intensities of pre-existing cracks which could exceed the remaining fracture toughness of the material, which is additionally embrittled due to neutron irradiation. This may result in a cleavage fracture of the most safety relevant reactor component.We present a PTS study of a reference reactor, starting with the calculation of the thermal-hydraulic system behaviour, followed by the simulation of the cold water temperature injection and mixing by means of computational fluid dynamics (CFD) method and the subsequent structural and fracture mechanics calculation. In the safety assessment, we compare the evolution of the stress intensity factors (SIF) during an emergency cooling transient with the fracture toughness at the tip of postulated cracks. Results and open questions will be discussed in the light of a realistic estimation of safety margins.

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The proper use of thermal expansion coefficients in finite element calculations

Cited by 30 publications

References 2 publications

Wide temperature range through silicon vias made of Invar and spin-on glass for interposers and MEMS

Wide temperature range through silicon vias made of Invar and spin-on glass for interposers and MEMS

Distribution of Current Density, Temperature, and Mechanical Deformation in YBCO Bulks Under Field-Cooling Magnetization

Analysis of a reactor pressure vessel subjected to pressurized thermal shocks

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