Measurement and interpretation of stress in copper films as a function of thermal history

1991 ◽  
Vol 6 (7) ◽  
pp. 1498-1501 ◽  
Author(s):  
Paul A. Flinn
Keyword(s):  
Mechanical Properties ◽  
Thermal Expansion ◽  
Elastic Modulus ◽  
Thermal History ◽  
Copper Films ◽  
Thermally Induced ◽  
Aluminum Films ◽  
Interconnection Material ◽  
Interconnect Systems

Since copper has some advantages relative to aluminum as an interconnection material, it is appropriate to investigate its mechanical properties in order to be prepared in advance for possible problems, such as the cracks and voids that have plagued aluminum interconnect systems. A model previously used to interpret the behavior of aluminum films proves to be, with minor modification, also applicable to copper. Although the thermal expansion of copper is closer to that of silicon and, consequently, the thermally induced strains are smaller, the much larger elastic modulus of copper results in substantially higher stresses. This has implications for the interaction of copper lines with dielectrics.

Measuring the elastic modulus and residual stress of freestanding thin films using nanoindentation techniques

2009 ◽  
Vol 24 (9) ◽  
pp. 2974-2985 ◽  
Author(s):  
Erik G. Herbert ◽  
Warren C. Oliver ◽  
Maarten P. de Boer ◽  
George M. Pharr
Keyword(s):  
Thin Films ◽  
Mechanical Properties ◽  
Residual Stress ◽  
Thermal Expansion ◽  
Elastic Modulus ◽  
Dimensional Analysis ◽  
Experimental Verification ◽  
Cu Films ◽  
Proposed Model ◽  
The Difference

A new method is proposed to determine the elastic modulus and residual stress of freestanding thin films based on nanoindentation techniques. The experimentally measured stiffness-displacement response is applied to a simple membrane model that assumes the film deformation is dominated by stretching as opposed to bending. Dimensional analysis is used to identify appropriate limitations of the proposed model. Experimental verification of the method is demonstrated for Al/0.5 wt% Cu films nominally 22 µm wide, 0.55 µm thick, and 150, 300, and 500 µm long. The estimated modulus for the four freestanding films match the value measured by electrostatic techniques to within 2%, and the residual stress to within 19.1%. The difference in residual stress can be completely accounted for by thermal expansion and a modest change in temperature of 3 °C. Numerous experimental pitfalls are identified and discussed. Collectively, these data and the technique used to generate them should help future investigators make more accurate and precise measurements of the mechanical properties of freestanding thin films using nanoindentation.

scholarly journals Elastic Modulus, Thermal Expansion, and Pyrolysis Shrinkage of Norway Spruce Under High Temperature

2021 ◽  
Author(s):  
Tito Adibaskoro ◽  
Michalina Makowska ◽  
Aleksi Rinta-Paavola ◽  
Stefania Fortino ◽  
Simo Hostikka
Keyword(s):  
Mechanical Properties ◽  
Thermal Expansion ◽  
Elastic Modulus ◽  
Norway Spruce ◽  
Elastic Moduli ◽  
Elevated Temperatures ◽  
Ambient Air ◽  
Time Dependent ◽  
Temperature History ◽  
Direction Parallel

AbstractThe orthotropic and temperature-dependent nature of the mechanical properties of wood is well recognized. However, past studies of mechanical properties at elevated temperatures are either limited to temperatures below 200 °C or focus only on the direction parallel to grain. The effect of time-dependent pyrolysis during measurement is often neglected. This paper presents a novel method for determining elastic modulus at high temperatures and thermal expansion coefficient in different orthotropic directions via Dynamic Mechanical-Thermal Analyser (DMTA). The method allows for drying, drying verification, and measurement in one chamber, eliminating the possibility of moisture reabsorption from ambient air. The repeatable measurements can be carried out in temperatures up to 325°C, adequate for observing time-dependent pyrolysis during measurement. Results of the measurements of Norway Spruce provide data of its mechanical response at temperature range previously not explored widely, as well as in the orthotropic direction. Time-dependent behaviour was observed in the thermal expansion and shrinkage experiment, where above 250°C the amount of shrinkage depends on heating rate. At such temperature, elastic moduli measurement also shows time dependence, where longer heating at certain temperature slightly increases the measured elastic modulus. Additionally, bilinear regression of the relationship between elastic moduli and temperature shows quantitatively good fit. Numerical simulation of the DMTA temperature history and wood chemical components mass losses show the onset of shrinkage and onset of hemicellulose mass loss occurring at around the same time, while decomposition of cellulose correlate with the sudden loss of elastic moduli.

A Technique for Deducing In-Plane Modulus and Coefficient of Thermal Expansion of a Supported Thin Film

2002 ◽  
Vol 124 (2) ◽  
pp. 274-277 ◽  
Author(s):  
Martin Y. M. Chiang ◽  
Chwan K. Chiang ◽  
Wen-li Wu
Keyword(s):  
Thin Film ◽  
Thin Films ◽  
Mechanical Properties ◽  
Thermal Expansion ◽  
Thermal Stress ◽  
Elastic Modulus ◽  
Coefficient Of Thermal Expansion ◽  
Thermal And Mechanical Properties ◽  
Reduction Scheme ◽  
Coupled Equations

A technique for determining the in-plane modulus and the coefficient of thermal expansion (CTE) of supported thin films has been developed. The modulus and CTE are calculated by solving two coupled equations that relate the curvature of film samples deposited on two different substrates to the thermal and mechanical properties of the constituents. In contrast with the conventional method used to calculate modulus and CTE, which involves differentiation of the thermal stress in the film, this new technique does not require the differentiation of the thermal stress, and can also provide the temperature-dependence of the in-plane CTE and elastic modulus of supported thin films. The data reduction scheme used for deducing CTE and elastic modulus is direct and reliable.

scholarly journals INFLUENCE OF ELEVATED TEMPERATURES ON MECHANICAL PROPERTIES OF CONCRETE

2018 ◽  
Vol 14 (1) ◽  
pp. 178-184 ◽  
Author(s):  
Vladimir I. Andreev ◽  
Lyudmila S. Polyakova
Keyword(s):  
Mechanical Properties ◽  
Thermal Expansion ◽  
Elastic Modulus ◽  
Shear Deformation ◽  
Mechanical Characteristics ◽  
Elevated Temperatures ◽  
Strength Functions ◽  
Deformation Coefficient

he paper considers the influence of elevated temperatures in the range from 20°C to 800°C in the mechanical properties of the concrete the thermal expansion, elastic modulus, shear deformation coefficient, strength. Functions describing the dependences of the mechanical characteristics of concrete on temperature as well as functions approximating the nonlinear diagram deformation of concrete at elevated temperatures are pro-posed.

Evaluation of Procera/Porcelain Interface in Metal-Free Prosthesis

2005 ◽  
Vol 498-499 ◽  
pp. 606-611
Author(s):  
S.H. Yasuda ◽  
Antonio C. Guastaldi ◽  
E. Vedovato
Keyword(s):  
Mechanical Properties ◽  
Thermal Expansion ◽  
Elastic Modulus ◽  
Residual Stresses ◽  
Crack Propagation ◽  
Metal Free ◽  
Thermal Expansion Coefficients ◽  
Dental Application ◽  
Expansion Coefficients

Prosthetic substructures for dental application are veneered by porcelain comprising a structure with different elastic modulus and thermal expansion coefficients layers. This structure may present residual stresses in different layers leading to crack propagation and delamination. Although veneering porcelain remains basically on same strength than standard feldspathic porcelains, new ceramic cores have been developed with higher mechanical properties overcoming metal substructures, improving esthetics and biocompatibility. The interface between the Procera dense sintered alumina core and the manufacturer recommended veneering porcelain (AllCeram-Degussa) were evaluated using SEM in coping shaped specimen simulating the standard dental preparation. There were neither crack presences at the interface nor porcelain delamination.

Tailorable Thermal Expansion of Lightweight and Robust Dual-Constituent Triangular Lattice Material

2017 ◽  
Vol 84 (10) ◽  
Author(s):  
Kai Wei ◽  
Yong Peng ◽  
Weibin Wen ◽  
Yongmao Pei ◽  
Daining Fang
Keyword(s):  
Mechanical Properties ◽  
Thermal Expansion ◽  
Triangular Lattice ◽  
Coefficient Of Thermal Expansion ◽  
Bulk Material ◽  
Structure Design ◽  
Thermally Induced ◽  
Precise Control ◽  
Wide Range ◽  
Lattice Material

Current studies on tailoring the coefficient of thermal expansion (CTE) of materials focused on either exploring the composition of the bulk material or the design of composites which strongly depend on a few negative CTE materials or fibers. In this work, an approach to achieve a wide range of tailorable CTEs through a dual-constituent triangular lattice material is studied. Theoretical analyses explicitly reveal that through rational arrangement of commonly available positive CTE constituents, tailorable CTEs, including negative, zero, and large positive CTEs can be easily achieved. We experimentally demonstrate this approach through CTE measurements of the specimens, which were exclusively fabricated from common alloys. The triangular lattice material fabricated from positive CTE alloys is shown to yield large positive (41.6 ppm/°C), near-zero (1.9 ppm/°C), and negative (−32.9 ppm/°C) CTEs. An analysis of the collapse strength and stiffness ensures the robust mechanical properties. Moreover, hierarchal triangular lattice material is proposed, and with certain constituents, wide range of tailorable CTEs can be easily obtained through the rationally hierarchal structure design. The triangular lattice material presented here integrates tailorable CTEs, lightweight characteristic, and robust mechanical properties, and is very promising for engineering applications where precise control of thermally induced expansion is in urgently needed.

scholarly journals Experimental Analysis of the Mechanical Properties and Resistivity of Tectonic Coal Samples with Different Particle Sizes

Energies ◽  
2021 ◽  
Vol 14 (8) ◽  
pp. 2303
Author(s):  
Congyu Zhong ◽  
Liwen Cao ◽  
Jishi Geng ◽  
Zhihao Jiang ◽  
Shuai Zhang
Keyword(s):  
Mechanical Properties ◽  
Particle Size ◽  
Compressive Strength ◽  
Elastic Modulus ◽  
Uniaxial Compressive Strength ◽  
Coalbed Methane ◽  
Coal Sample ◽  
Fine Particles ◽  
Particle Sizes ◽  
Tectonic Coal

Because of its weak cementation and abundant pores and cracks, it is difficult to obtain suitable samples of tectonic coal to test its mechanical properties. Therefore, the research and development of coalbed methane drilling and mining technology are restricted. In this study, tectonic coal samples are remodeled with different particle sizes to test the mechanical parameters and loading resistivity. The research results show that the particle size and gradation of tectonic coal significantly impact its uniaxial compressive strength and elastic modulus and affect changes in resistivity. As the converted particle size increases, the uniaxial compressive strength and elastic modulus decrease first and then tend to remain unchanged. The strength of the single-particle gradation coal sample decreases from 0.867 to 0.433 MPa and the elastic modulus decreases from 59.28 to 41.63 MPa with increasing particle size. The change in resistivity of the coal sample increases with increasing particle size, and the degree of resistivity variation decreases during the coal sample failure stage. In composite-particle gradation, the proportion of fine particles in the tectonic coal sample increases from 33% to 80%. Its strength and elastic modulus increase from 0.996 to 1.31 MPa and 83.96 to 125.4 MPa, respectively, and the resistivity change degree decreases. The proportion of medium particles or coarse particles increases, and the sample strength, elastic modulus, and resistivity changes all decrease.

scholarly journals Experimental and Numerical Analysis of the Mechanical Properties of a Pretreated Shape Memory Alloy Wire in a Self-Centering Steel Brace

Processes ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 80
Author(s):  
Bo Zhang ◽  
Sizhi Zeng ◽  
Fenghua Tang ◽  
Shujun Hu ◽  
Qiang Zhou ◽  
...  
Keyword(s):  
Mechanical Properties ◽  
Elastic Modulus ◽  
Energy Dissipation ◽  
Shape Memory Alloy ◽  
Shape Memory ◽  
Loading Rate ◽  
Effective Elastic Modulus ◽  
Maximum Energy ◽  
Numerical Results ◽  
Energy Dissipation Capacity

As a stimulus-sensitive material, the difference in composition, fabrication process, and influencing factors will have a great effect on the mechanical properties of a superelastic Ni-Ti shape memory alloy (SMA) wire, so the seismic performance of the self-centering steel brace with SMA wires may not be accurately obtained. In this paper, the cyclic tensile tests of a kind of SMA wire with a 1 mm diameter and special element composition were tested under multi-working conditions, which were pretreated by first tensioning to the 0.06 strain amplitude for 40 cycles, so the mechanical properties of the pretreated SMA wires can be simulated in detail. The accuracy of the numerical results with the improved model of Graesser’s theory was verified by a comparison to the experimental results. The experimental results show that the number of cycles has no significant effect on the mechanical properties of SMA wires after a certain number of cyclic tensile training. With the loading rate increasing, the pinch effect of the hysteresis curves will be enlarged, while the effective elastic modulus and slope of the transformation stresses in the process of loading and unloading are also increased, and the maximum energy dissipation capacity of the SMA wires appears at a loading rate of 0.675 mm/s. Moreover, with the initial strain increasing, the slope of the transformation stresses in the process of loading is increased, while the effective elastic modulus and slope of the transformation stresses in the process of unloading are decreased, and the maximum energy dissipation capacity appears at the initial strain of 0.0075. In addition, a good agreement between the test and numerical results is obtained by comparing with the hysteresis curves and energy dissipation values, so the numerical model is useful to predict the stress–strain relations at different stages. The test and numerical results will also provide a basis for the design of corresponding self-centering steel dampers.

Mechanical Properties of Secondary Wall and Compound Corner Middle Lamella near the Phenol-Formaldehyde (PF) Adhesive Bond Line Measured by Nanoindentation

2011 ◽  
Vol 236-238 ◽  
pp. 1746-1751 ◽  
Author(s):  
Kun Liang ◽  
Guan Ben Du ◽  
Omid Hosseinaei ◽  
Si Qun Wang ◽  
Hui Wang
Keyword(s):  
Mechanical Properties ◽  
Elastic Modulus ◽  
Secondary Wall ◽  
Phenol Formaldehyde ◽  
Middle Lamella ◽  
Adhesive Bond ◽  
Cellular Level ◽  
Bond Line ◽  
Line Region ◽  
Penetration Behavior

To find out the penetration of PF into the wood cell wall and its effects onthe mechanical properties in the cellular level, the elastic modulus and hardness of secondary wall (S2layer) and compound corner middle lamella (CCML) near PF bond line region were determined by nanoindentation. Compare to the reference cell walls (unaffected by PF), PF penetration into the wood tissues showed improved elastic modulus and hardness. And the mechanical properties decreased slowly with the increasing the distance from the bond line, which are attributed to the effects of PF penetration into S2layer and CCML. The reduced elastic modulus variations were from18.8 to 14.4 GPa for S2layer, and from10.1 to 7.65 GPa for CCML. The hardness was from 0.67 to 0.52 GPa for S2layer, and from 0.65 to 0.52 GPa for CCML. In each test viewpoint place, the average hardness of CCML was almost as high as that of S2layer, but the reduced elastic modulus was about 50% less than that of S2layer. But the increase ratio of mechanical properties was close. All the results showed PF penetrates into the CCML. The penetration behavior and penetration depth from bond line were similar in both S2layer and CCML.

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