Precise Integration Symplectic Analytical Singular Element for Cracks Analysis Under Transient Thermal Conduction

Numerical modeling of mechanical behavior of cracks under transient thermal conduction involves solving an initial value problem (IVP) and two boundary value problems (BVPs). Both of the BVPs have a singularity issue. Drawbacks such as numerical error accumulation and high computational expense of existing numerical approaches should be overcome. This contribution intends to build a unified framework with highly efficiency and accuracy for the numerical modeling of cracks under thermal shock. The precise integration method (PIM) and the symplectic analytical singular element (SASE) have been demonstrated to be favorable alternatives for each problem, i.e., the PIM for solving the IVP and SASE for the BVP. However, it is found that these two methods cannot be combined directly. In order to incorporate the SASEs into the PIM, the existing SASEs are reformulated for the thermal shock cracks analysis. Details of the mathematical derivations are provided. The validity of the proposed method is demonstrated through numerical examples.

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Transient thermal conduction with variable conductivity using the Meshless Local Petrov–Galerkin method

Applied Mathematics and Computation ◽

10.1016/j.amc.2015.02.084 ◽

2016 ◽

Vol 272 ◽

pp. 676-686 ◽

Cited By ~ 4

Author(s):

N.P. Karagiannakis ◽

G.C. Bourantas ◽

A.N. Kalarakis ◽

E.D. Skouras ◽

V.N. Burganos

Keyword(s):

Galerkin Method ◽

Thermal Conduction ◽

Transient Thermal ◽

Variable Conductivity

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Thermal shock weakening of granite rock under dynamic loading: 3D numerical modeling based on embedded discontinuity finite elements

International Journal for Numerical and Analytical Methods in Geomechanics ◽

10.1002/nag.3107 ◽

2020 ◽

Vol 44 (13) ◽

pp. 1788-1811

Author(s):

Timo Saksala ◽

Adnan Ibrahimbegovic

Keyword(s):

Numerical Modeling ◽

Finite Elements ◽

Thermal Shock ◽

Dynamic Loading ◽

3D Numerical Modeling ◽

Granite Rock

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Transient thermal shock behavior simulation of porous silicon nitride ceramics

Ceramics International ◽

10.1016/j.ceramint.2015.10.102 ◽

2016 ◽

Vol 42 (2) ◽

pp. 3130-3137 ◽

Cited By ~ 9

Author(s):

Meng Chen ◽

Hongjie Wang ◽

Haiyun Jin ◽

Xide Pan ◽

Zhihao Jin

Keyword(s):

Silicon Nitride ◽

Porous Silicon ◽

Thermal Shock ◽

Behavior Simulation ◽

Nitride Ceramics ◽

Thermal Shock Behavior ◽

Transient Thermal

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Integrated Thermal Conduction and Hardenability Laboratory Activity

Volume 5: Education and Globalization ◽

10.1115/imece2013-63211 ◽

2013 ◽

Author(s):

Natasha L. Smith ◽

Brandon S. Field

Keyword(s):

Heat Transfer ◽

Thermal Conduction ◽

Machine Design ◽

Engineering Curriculum ◽

Laboratory Activity ◽

One Dimensional ◽

Practical Applications ◽

Transformation Curve ◽

Transient Thermal ◽

Quench Test

This paper describes an integrated laboratory project between separate heat transfer and machine design courses. The project was structured around a Jominy end quench hardenability test. Most of the students participating were simultaneously enrolled in both classes. In the heat transfer class, students were required to model one-dimensional, transient thermal conduction for an end quench geometry of 4140 steel. In machine design, students applied their theoretical temperature profiles to a continuous cooling transformation curve (CCT) of 4140 steel to predict microstructure and matched the theoretical cooling rates with hardenability curves from literature to predict hardness. In laboratory, students then performed an end quench test in accordance with ASTM A255 on four steel rods. By combining activities across the two courses, students developed an appreciation for the interconnectivity of material within the engineering curriculum, and learned that practical applications typically require they employ knowledge from a variety of sources.

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Mechanical Performance Evaluation of the Al-Mg-Si-(Cu) Aluminum Alloys after Transient Thermal Shock through an Novel Equivalent Structure Design and Finite Element Modeling

Metals ◽

10.3390/met10040537 ◽

2020 ◽

Vol 10 (4) ◽

pp. 537

Author(s):

Congchang Xu ◽

Ke Liu ◽

Hong He ◽

Hanlin Xiang ◽

Xinxin Zhang ◽

...

Keyword(s):

Mechanical Properties ◽

Finite Element ◽

Thermal Shock ◽

Constitutive Relation ◽

Mechanical Performance ◽

Lap Joints ◽

Structure Design ◽

Equivalent Structure ◽

Material Constitutive Relation ◽

Transient Thermal

In this paper, the microstructure evolution and mechanical performance of the Al-Mg-Si-(Cu) aluminum alloy after transient thermal shock were investigated through experimental tests and finite element simulations. A novel equivalent structure was designed as a typical case in which one side of the plate was welded therefore the other side was thermally shocked with different temperature distribution and duration. The temperature gradient which influences most importantly the mechanical properties was simulated and experimentally verified. Through cutting layers and tensile testing, the mechanical response and material constitutive relation were obtained for each layer. Gurson-Tvergaard-Needlemen (GTN) damage parameters of these samples under large strains were then obtained by the Swift law inverse analysis approach. By sorting the whole welded joint into multi-material composed structure and introducing the obtained material constitutive relation and damage parameters, tensile properties were precisely predicted for typical types of weld joint such as butt, corner, and lap joints. The results show that precipitate coarsening, phase transformation from β″ phase to Q′ phase, and dissolving in the temperature range of 243.3–466.3 °C during the thermal shock induced a serious deterioration of the mechanical properties. The highest reduction of the ultimate tensile strength (UTS) and yield strength (YS) would be 38.6% and 57.4% respectively. By comparing the simulated and experimentally obtained force-displacement curves, the error for the above prediction method was evaluated to be less than 8.1%, indicating the proposed method being effective and reliable.

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