Mean-field homogenization of thermoelastic material properties of a long fiber-reinforced thermoset and experimental investigation

2020 ◽  
Vol 54 (25) ◽  
pp. 3777-3799
Author(s):  
Loredana Kehrer ◽  
Jeffrey T Wood ◽  
Thomas Böhlke
Keyword(s):  
Thermal Expansion ◽  
Coefficient Of Thermal Expansion ◽  
Mean Field ◽  
Material Behavior ◽  
Fiber Reinforced Polymers ◽  
Material System ◽  
Fiber Reinforced ◽  
Thermoset Resin ◽  
Thermoelastic Material ◽  
Fiber Orientation Distribution

Fiber-reinforced polymers contribute significantly to weight-reducing components for various industrial applications. A discontinuous glass fiber-reinforced thermoset resin is considered which is produced by the sheet molding compound (SMC) process. Related to the production process, the samples considered in this work exhibit an anisotropic fiber orientation distribution which highly affects the thermomechanical properties. The thermoviscoelastic material behavior of three selected samples is characterized by means of dynamic mechanical analysis. These tests show the temperature-dependent elastic modulus and the glass transition of the composite. Measurements of the thermal expansion of the SMC composite provide data on the coefficient of thermal expansion (CTE). These experimental investigations provide data for the thermoelastic material modeling. Aiming at the prediction of the effective thermal and mechanical properties, a Hashin–Shtrikman-based homogenization method is presented. Based on an eigenstrain formulation, the effective Young’s modulus and CTE are computed in two steps. Moreover, the mean-field method is given in dependence of a variable reference stiffness allowing to tailor the approach to the material system. The influence of this variable reference stiffness on the effective quantities as well as the predicted behavior is analyzed with respect to the experiments. The presented numerical results are in good agreement with the experimental data.

Role of Out-of-Plane Coefficient of Thermal Expansion in Electronic Packaging Modeling

1999 ◽  
Vol 122 (2) ◽  
pp. 121-127 ◽  
Author(s):  
Manjula N. Variyam ◽  
Weidong Xie ◽  
Suresh K. Sitaraman
Keyword(s):  
Thermal Expansion ◽  
Electronic Packaging ◽  
Thermal Loading ◽  
Coefficient Of Thermal Expansion ◽  
Plane Deformation ◽  
Three Dimensional ◽  
Dissimilar Materials ◽  
3D Models ◽  
Material Behavior ◽  
Element Analysis

Components in electronic packaging structures are of different dimensions and are made of dissimilar materials that typically have time, temperature, and direction-dependent thermo-mechanical properties. Due to the complexity in geometry, material behavior, and thermal loading patterns, finite-element analysis (FEA) is often used to study the thermo-mechanical behavior of electronic packaging structures. For computational reasons, researchers often use two-dimensional (2D) models instead of three-dimensional (3D) models. Although 2D models are computationally efficient, they could provide misleading results, particularly under thermal loading. The focus of this paper is to compare the results from various 2D, 3D, and generalized plane-deformation strip models and recommend a suitable modeling procedure. Particular emphasis is placed to understand how the third-direction coefficient of thermal expansion (CTE) influences the warpage and the stress results predicted by 2D models under thermal loading. It is seen that the generalized plane-deformation strip models are the best compromise between the 2D and 3D models. Suitable analytical formulations have also been developed to corroborate the findings from the study. [S1043-7398(00)01402-X]

Design of Discontinuous Fiber Reinforced Injection Molded Polymer Matrix Composite Parts

2014 ◽  
Vol 633-634 ◽  
pp. 266-269 ◽  
Author(s):  
Zoltan Major ◽  
Martin Reiter
Keyword(s):  
Mean Field ◽  
Orientation Distribution ◽  
Fiber Reinforced ◽  
Glass Fiber Reinforced ◽  
Fiber Orientation Distribution ◽  
Discontinuous Fiber ◽  
Homogenization Approach ◽  
Component Strength ◽  
Injection Molded ◽  
Phd Thesis

Injection molded discontinuous fiber reinforced components are widely used in many demanding engineering applications and are exposed to a complex combination of thermo-mechanical loads. Mean field homogenization approach was successfully applied for predicting the global stiffness behavior over wide part geometry complexity, fiber orientation distribution (FOD) and loading situations including loading rate and temperature dependence. The prediction of the component strength, however, is significantly more complicated and requires additional and theoretical considerations as well as the application of various numerical tools and sophisticated experiments. To overcome above difficulties the MFH technique was extended with the first pseudo grain failure or damage (FPGF or FPGD) approach proposed by the research group of Doghri [1] elaborated in detail using short glass fiber reinforced PP-GF in the PhD Thesis of Reiter [2] and shortly described in this study.

Effects of temperature on the behaviour of fiber reinforced polymer reinforced concrete members: experimental studies

2000 ◽  
Vol 27 (5) ◽  
pp. 993-1004 ◽  
Author(s):  
Mamdouh M Elbadry ◽  
Hany Abdalla ◽  
Amin Ghali
Keyword(s):  
Thermal Expansion ◽  
Reinforced Concrete ◽  
Thermal Stresses ◽  
Experimental Studies ◽  
Fiber Reinforced Polymer ◽  
Fiber Reinforced Polymers ◽  
Fiber Reinforced ◽  
Concrete Members ◽  
Reinforced Polymer ◽  
Effects Of Temperature

Thermal characteristics of fiber reinforced polymer (FRP) reinforcement can be substantially different from those of concrete and conventional steel reinforcement. The influence of this difference on the behaviour of FRP reinforced concrete members is studied in this paper. Concrete beams reinforced with different types of FRP rebars are tested under the effects of temperature gradient while the rotation at the two ends of the beam are restrained. The bending moments and cracking developed by the thermal gradient are monitored. The results are compared with those obtained from tests on beams of the same dimensions but reinforced with steel bars. The behaviour of thermally cracked members is also investigated under mechanical load effects at both service and ultimate load levels. The potential cracking of the concrete cover caused by the transverse thermal expansion of FRP bars is examined by testing concrete cylinders. The experiments show the difference in thermal behaviour of glass and carbon FRP and steel bars.Key words: bond, concrete, cracking (fracturing), fiber reinforced polymers, loads (forces), reinforcement, temperature, tensile strength, thermal expansion, thermal stresses.

scholarly journals Thermal expansion and crystal structure of cementite, Fe3C, between 4 and 600 K determined by time-of-flight neutron powder diffraction

2004 ◽  
Vol 37 (1) ◽  
pp. 82-90 ◽  
Author(s):  
I. G. Wood ◽  
Lidunka Vočadlo ◽  
K. S. Knight ◽  
David P. Dobson ◽  
W. G. Marshall ◽  
...  
Keyword(s):  
Crystal Structure ◽  
Thermal Expansion ◽  
Powder Diffraction ◽  
Coefficient Of Thermal Expansion ◽  
Mean Field Theory ◽  
Mean Field ◽  
Neutron Powder Diffraction ◽  
Ferromagnetic Phase ◽  
Ferromagnetic Phase Transition ◽  
Full Temperature

The cementite phase of Fe3C has been studied by high-resolution neutron powder diffraction at 4.2 K and at 20 K intervals between 20 and 600 K. The crystal structure remains orthorhombic (Pnma) throughout, with the fractional coordinates of all atoms varying only slightly (the magnetic structure of the ferromagnetic phase could not be determined). The ferromagnetic phase transition, withTc≃ 480 K, greatly affects the thermal expansion coefficient of the material. The average volumetric coefficient of thermal expansion aboveTcwas found to be 4.1 (1) × 10−5 K−1; belowTcit is considerably lower (< 1.8 × 10−5 K−1) and varies greatly with temperature. The behaviour of the volume over the full temperature range of the experiment may be modelled by a third-order Grüneisen approximation to the zero-pressure equation of state, combined with a magnetostrictive correction based on mean-field theory.

Hydrophobic sealing materials for harsh environmental electrical connector package applications

2019 ◽  
Vol 2019 (1) ◽  
pp. 000078-000084
Author(s):  
Hua Xia ◽  
Nelson Settles ◽  
David DeWire
Keyword(s):  
Thermal Expansion ◽  
Coefficient Of Thermal Expansion ◽  
Electrical Power ◽  
Covalent Bond ◽  
Material System ◽  
Inconel Alloys ◽  
Electrical Connector ◽  
Sealing Material ◽  
Amorphous Glass ◽  
Highly Hydrophobic

Abstract A highly hydrophobic sealing material system has been developed using high-temperature melt-quenching and sintering technologies for harsh environmental electrical connector package sealing applications. The sealing material properties can be varied by its phase structures, such as amorphous glass, crystalline monoclinic and tetragonal mixed phase, and covalent bond tetragonal phase, which are determined by a two-stage synthesizing process. The dilatometer measurements have found that the ambient coefficient of thermal expansion varies from ~5.8 to 7.1 ppm/°C while the coefficient of thermal expansion at its glass transition temperatures varies from ~7.0 to 9.0 ppm/°C. These coefficients of thermal expansion could provide not only wide options for integrating metal materials, such as Ti-alloy, Kovar, Inconel alloys, and Stainless Steels for making reliable electrical connector packages, but also enable the design of electrical connector packages with a safety factor of 3 performance, operable at 30KSI (30,000 PSI) pressure, and −100 −300°C harsh conditions while maintaining at least 5,000MΩ insulation resistances, for reliable signal, data, and electrical power transmissions.

Processing of ZrW2O8-ZrO2 Continuous Functionally Graded Materials by Co-Sintering ZrO2 and ZrO2+WO3 Multi-Layer Compacts

2008 ◽  
Author(s):  
Li Sun ◽  
Sam Baldauf ◽  
Patrick Kwon
Keyword(s):  
Thermal Expansion ◽  
Functionally Graded Materials ◽  
Powder Mixture ◽  
Coefficient Of Thermal Expansion ◽  
Functionally Graded ◽  
Material System ◽  
Cross Sectional ◽  
Graded Materials ◽  
Powder Mixtures ◽  
Processing Steps

A powder mixture of ZrO2+WO3 and ZrO2 powder were stacked, co-compacted and co-sintered in the processing steps commonly used to fabricate multi-layer materials. However, the observation of the cross-sectional microstructures as well as the measurement of the radial thermal expansion provided the evidence that the sintered samples are continuous Functionally Graded Materials (FGMs) made of ZrW2O8 and ZrO2, Because of the discrepancy in the sintering potentials between two materials, the sintered samples do not retain the original cylindrical shapes of the green compacts. This problem has been resolved by choosing the appropriate powder mixture for each layer of the compacts. The formation of the continuous FGM structure is due to three factors: 1) the diffusion of WO3, 2) the sublimation of WO3 and 3) the reaction between ZrO2 and WO3. The continuous variation in the radial coefficient of thermal expansion can be utilized to reduce the thermal stress induced from a thermal gradient loading within a material system. This study shows that the processing steps typically used in processing stepwise FGMs can also be used to create continuous FGMs for some special powder mixtures.

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