Thermal Stresses in a Freezing Sphere and its Application to Cryobiology

1998 ◽  
Vol 65 (2) ◽  
pp. 328-333 ◽  
Author(s):  
Y. Rabin ◽  
P. S. Steif
Keyword(s):  
Phase Transition ◽  
Thermal Expansion ◽  
Thermal Stresses ◽  
Closed Form Solution ◽  
Form Solution ◽  
Volume Changes ◽  
Perfectly Plastic ◽  
Parametric Studies ◽  
Elastic Perfectly Plastic ◽  
Biological Solutions

Thermal stresses in an inwardly solidifying sphere are studied analytically. A closed-form solution is given which accounts for thermal expansion associated with temperature gradients and volume changes associated with phase transition. Consistent with the target application of cryopreservation of biological solutions and tissues, the material is modeled as elastic-perfectly plastic. Parametric studies using appropriate material properties and typical cryopreservation protocols suggest that strains associated with phase transition lead to far higher stresses than those associated with thermal expansion, with important implications for cryopreservation procedures.

Thermal Stress Measurement of Solder Joints in BGA Packages: Theoretical and Experimental

2008 ◽  
Author(s):  
H. X. Shang ◽  
J. X. Gao ◽  
P. I. Nicholson
Keyword(s):  
Thermal Stresses ◽  
Solder Joints ◽  
Stress Measurement ◽  
Closed Form Solution ◽  
Dissimilar Materials ◽  
Form Solution ◽  
Bga Packages ◽  
Reliability Characteristics ◽  
Bga Package ◽  
Graded Interlayer

In this study, an analytical model to obtain a closed-form solution for thermomechanical behaviours of BGA (Ball Grid Array) package was derived and experimentally validated. In the theoretical analysis, the BGA package was represented by a three-layer axisymmetrical model: two layers of dissimilar materials jointed by a graded interlayer. Based on the classical bending theory, the thermal stresses induced by temperature changes were calculated accurately. 2-D FE (Finite Element) meshes of BGA packages subjected to high temperature were used to verify the theoretical solutions. Furthermore, two types of BGA samples, each with eutectic (63wt%Sn/37wt%Pb) and Pb-free SAC387 (95.5wt%Sn/3.8wt%Ag/0.7wt%Cu) solder joints respectively, were experimentally investigated by high resolution Moire´ Interferometry (MI). Thermal cycling tests were performed on each package with temperature variation from 25°C to 125°C. It was found that the thermal deformation obtained from moire´ tests matched well with those from analytical solutions and FE analyses. Based on the shear strain values, the reliability characteristics of BGA assemblies were also assessed.

Thermal stresses in a rotating, nonhomogeneous, anisotropic disk of varying thickness and density

1975 ◽  
Vol 10 (3) ◽  
pp. 137-142 ◽  
Author(s):  
G V Gurushankar
Keyword(s):  
Thermal Loading ◽  
Thermal Stresses ◽  
Closed Form Solution ◽  
Rotating Disk ◽  
Form Solution ◽  
Annular Disk ◽  
Varying Thickness ◽  
Principal Axes ◽  
Rotationally Symmetric ◽  
Anisotropic Disk

Closed form solution is obtained for stresses in a rotationally symmetric, nonhomogeneous, anisotropic, annular disk of varying thickness and density, subjected to thermal loading. Analysis is presented for a particular type of anisotropy, namely Polar Orthotropy, in which axes of anisotropy coincide with the principal axes of stresses at each point in the disk. The variations of homogenity, density and thickness are assumed to be hyperbolic. Numerical results in the form of graphs presented show the effect of nonhomogenity, density and degree of orthotropy on the stress distribution in a disk subjected to constant and varying temperature gradients. Homogeneous, varying density anisotropic rotating disk of varying thickness forms a special case of the analysis.

Finite Deformations of a Rigid Perfectly Plastic Arch

1962 ◽  
Vol 29 (3) ◽  
pp. 549-553 ◽  
Author(s):  
E. T. Onat ◽  
L. S. Shu
Keyword(s):  
Closed Form ◽  
Yield Point ◽  
Finite Deformation ◽  
Closed Form Solution ◽  
Form Solution ◽  
Finite Deformations ◽  
Deformation History ◽  
Rigid Plastic ◽  
Perfectly Plastic ◽  
History Of

The quasi-static postyield deformation of a rigid-plastic arch in the presence of geometry changes is considered. The problem is formulated in terms of a series of boundary-value problems concerned with rates of stress and velocities. In the present simple case, the consideration of the rate problem associated with the yield-point state of the structure enables one to construct a closed-form solution which describes the entire deformation history of the arch. However, the principal aim of the present study is to stress the central role played by the rate problem in the investigation of the finite deformation of structures.

Analytical Puncture Study of Circular Metal Plates

1980 ◽  
Vol 102 (3) ◽  
pp. 242-248 ◽  
Author(s):  
R. C. Shieh
Keyword(s):  
Large Deflection ◽  
Plate Thickness ◽  
Closed Form Solution ◽  
Analytical Techniques ◽  
Correlation Study ◽  
Form Solution ◽  
Punch Force ◽  
Perfectly Plastic ◽  
Static Responses ◽  
Metal Plates

An existing closed-form solution for large-deflection static responses of centrally loaded, rigid, perfectly plastic circular metal plates (with emphasis on steel plate cases) that are clamped (built-in) or simply supported at the edges is first modified to take into account the effects of elastic deformation and material strainhardening in an approximate manner. The modified theoretical solution is first shown to correlate very well with experimental results. Then it is applied in solving the quasi-static plate puncture problem in which the punch bar penetrates slowly into the plate. An analytical/experimental correlation study on punch force-deflection relationship and incipient plate puncture energy is made on newly obtained experimental data. Effects of variation of strainhardening parameter, boundary conditions and shear deformation on incipient puncture energy are studied, and plate puncture design curves are developed in the form of nondimensional incipient plate puncture energy as a function of punch diameter/plate thickness ratio for various values of punch diameter/plate diameter ratio. Application of these analytical techniques/design curves to the design of nuclear shipping cask plate components subject to regulatory puncture drop loading is also discussed.

scholarly journals Thermo-Mechanical Modeling of Distortions Promoted during Cooling of Ti-6Al-4V Part Produced by Superplastic Forming

2016 ◽  
Vol 838-839 ◽  
pp. 196-201
Author(s):  
Maxime Rollin ◽  
Vincent Velay ◽  
Luc Penazzi ◽  
Thomas Pottier ◽  
Thierry Sentenac ◽  
...  
Keyword(s):  
Finite Element ◽  
Thermal Stresses ◽  
Superplastic Forming ◽  
Model Material ◽  
Material Behavior ◽  
Mechanical Modeling ◽  
Temperature Dependent ◽  
Finite Element Software ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic

In AIRBUS, most of the complex shaped titanium fairing parts of pylon and air inlets are produced by superplastic forming (SPF). These parts are cooled down after forming to ease their extraction and increase the production rate, but AIRBUS wastes a lot of time to go back over the geometric defects generated by the cooling step. This paper investigates the simulations of the SPF, cooling and clipping operations of a part on Abaqus® Finite element software. The different steps of the global process impact the final distortions. SPF impacts the thickness and the microstructure/behavior of material, cooling impacts also the microstructure/behavior of material and promotes distortions through thermal stresses and finally, clipping relaxes the residual stresses of the cut part. An elastic-viscoplastic power law is used to model material behavior during SPF and a temperature dependent elastic perfectly plastic model for the cooling and clipping operations.

A closed-form solution for thermal stresses of structures using generalized variational principles

2018 ◽  
Vol 41 (6) ◽  
pp. 748-757 ◽  
Author(s):  
Zou-Qing Tan ◽  
Xue-Dong Jiang ◽  
Yun-Song He ◽  
Shu-Hao Ban ◽  
Ren-Qiang Xi ◽  
...  
Keyword(s):  
Closed Form ◽  
Thermal Stresses ◽  
Variational Principles ◽  
Closed Form Solution ◽  
Form Solution ◽  
Generalized Variational Principles

Green’s functions for soft materials containing a hard line inhomogeneity

2019 ◽  
Vol 24 (11) ◽  
pp. 3614-3631 ◽  
Author(s):  
Pengyu Pei ◽  
Guang Yang ◽  
Cun-Fa Gao
Keyword(s):  
Thermal Expansion ◽  
Heat Source ◽  
Closed Form ◽  
Hilbert Problem ◽  
Closed Form Solution ◽  
Soft Materials ◽  
Form Solution ◽  
Soft Material ◽  
Elastic Plane ◽  
Rigid Line

The linear elastic plane deformation of a soft material containing a rigid line inhomogeneity subjected to a concentrated force, a concentrated moment, and a point heat source was studied. Distinct from the existing rigid line inhomogeneity model which neglects the deformation of the inhomogeneity induced by both the mechanical stresses and thermal expansion, the current model allows for the thermal expansion-induced stretch and rotation of the inhomogeneity. In this context, we derive the closed-form solution for the full stress field in the soft material by solving the corresponding Riemann–Hilbert problem. In particular, our solution can serve as the Green’s function to establish other analytical solutions for more practical and complicated problems in this area. Several numerical examples are presented to illustrate our closed-form solution corresponding to the thermal loading. It is found that the presence of the heat source contributes significantly to the rigid rotation of inhomogeneity, and the thermal expansion-induced stretch of the inhomogeneity has a great impact on the stress intensity factors at the inhomogeneity tips.

Elastic, Plastic Stresses in Free Plate With Periodically Varying Surface Temperature

1958 ◽  
Vol 25 (4) ◽  
pp. 603-606
Author(s):  
Halil Yüksel
Keyword(s):  
Steady State ◽  
Surface Temperature ◽  
Constant Temperature ◽  
Thermal Stresses ◽  
Plastic Material ◽  
The Other ◽  
Perfectly Plastic ◽  
Temperature Oscillations ◽  
Steady State Temperature ◽  
Elastic Perfectly Plastic

Abstract The paper is concerned with a free plate that consists of an elastic, perfectly plastic material and is subjected to a harmonically varying temperature at one face, while the other face is kept at a constant temperature and the edge is perfectly insulated. The thermal stresses associated with the steady-state temperature oscillations are analyzed, and the development of plastic regions is discussed.

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