Creep Constitutive Models Suitable for Solder Alloys in Electronic Assemblies

2016 ◽  
Vol 138 (3) ◽  
Author(s):  
Subhasis Mukherjee ◽  
Mohammed Nuhi ◽  
Abhijit Dasgupta ◽  
Mohammad Modarres
Keyword(s):  
Creep Deformation ◽  
Constitutive Relations ◽  
Constitutive Models ◽  
Grain Boundary Sliding ◽  
Deformation Mechanisms ◽  
Coarse Grained ◽  
Mechanistic Models ◽  
Creep Response ◽  
Test Conditions ◽  
Sn37pb Solder

Most solders used in electronic systems have low-melting temperature and hence experience significant amount of creep deformation throughout their life-cycle because typical operational and test conditions represent high homologous temperature. Phenomenological and mechanistic models used in the literature for predicting creep response of both bulk and grain scale specimens are reviewed in this paper. The phenomenological models reviewed in this paper are based on purely empirical observations of the creep deformation behavior or derived from qualitative interpretation of the underlying microscale mechanisms. These models have some intrinsic disadvantages since they do not have explicit mechanistic dependence on microstructural features. Therefore, the constitutive relations derived using the above models are difficult to extrapolate beyond the test conditions. This paper also reviews how some of the above limitations can be mitigated by using mechanistic or microstructurally motivated models. Mechanistic models are capable of estimating the material creep response based on the detailed physics of the underlying mechanisms and microstructure. The microstructure and constitutive response of the most popular family of lead-free solders, namely, SnAgCu (SAC) solders, are significantly different from those of previously used eutectic Sn37Pb solder. The creep deformation in Sn37Pb solder occurs primarily through diffusion-assisted grain-boundary sliding. In SAC solder joints, dislocation-based creep deformation mechanisms such as glide, climb, detachment, and cross-slip appear to be the dominant mechanisms in coarse-grained joints. Mechanistic creep models are therefore based on the deformation mechanisms listed above.

Effects of Strain Rate and Grain Size on Behavior of Nano Crystalline Materials

2012 ◽  
Vol 17 ◽  
pp. 35-51 ◽  
Author(s):  
Reza Jafari Nedoushan ◽  
Mahmoud Farzin ◽  
Mohammad Mashayekhi
Keyword(s):  
Grain Size ◽  
Grain Boundary ◽  
Strain Rate ◽  
Strain Rate Sensitivity ◽  
Rate Sensitivity ◽  
Grain Boundary Sliding ◽  
Deformation Mechanisms ◽  
Coarse Grained ◽  
Crystalline Materials ◽  
Nano Crystalline

Recent Experiments on Nano-Crystalline Materials Show an Increase of Strain-Rate Sensitivity in Contrast to the Conventional Coarse-Grained Materials. these Materials Also Show a Different Grain Size Dependency as Compared to Coarse-Grained Materials. to Explain these Issues, a Constitutive Equation Is Proposed which Considers Dominant Deformation Mechanisms Including Grain Interior Plasticity, Grain Boundary Diffusion and Grain Boundary Sliding. the Stresses Obtained from these Constitutive Equations Match Well with the Experimental Data for Nanocrystalline Copper at Different Strains and Strain Rates. the Model Also Well Predicts Variation of Strain Rate Sensitivity Parameter. this Variation Can Be Explained with Regard to the above Mentioned Effective Deformation Mechanisms. Deviation from the Hall-Petch Law and Inverse Hall-Petch Effect Are Also Well Illustrated by the Model.

scholarly journals Creep Deformation Mechanisms in Coarse-Grained Solid Solution Mg Alloys

2004 ◽  
Vol 45 (4) ◽  
pp. 1266-1271 ◽  
Author(s):  
Sung Wook Chung ◽  
Hiroyuki Watanabe ◽  
Woo-Jin Kim ◽  
Kenji Higashi
Keyword(s):  
Solid Solution ◽  
Creep Deformation ◽  
Mg Alloys ◽  
Deformation Mechanisms ◽  
Coarse Grained

scholarly journals Friction of Metals: A Review of Microstructural Evolution and Nanoscale Phenomena in Shearing Contacts

2021 ◽  
Vol 69 (4) ◽  
Author(s):  
Michael Chandross ◽  
Nicolas Argibay
Keyword(s):  
Shear Strength ◽  
Grain Boundary Sliding ◽  
Deformation Mechanisms ◽  
Low Friction ◽  
Friction Behavior ◽  
Important Conclusion ◽  
Fundamental Properties ◽  
Wide Range ◽  
Boundary Sliding ◽  
Metal Interfaces

AbstractThe friction behavior of metals is directly linked to the mechanisms that accommodate deformation. We examine the links between mechanisms of strengthening, deformation, and the wide range of friction behaviors that are exhibited by shearing metal interfaces. Specifically, the focus is on understanding the shear strength of nanocrystalline and nanostructured metals, and conditions that lead to low friction coefficients. Grain boundary sliding and the breakdown of Hall–Petch strengthening at the shearing interface are found to generally and predictably explain the low friction of these materials. While the following is meant to serve as a general discussion of the strength of metals in the context of tribological applications, one important conclusion is that tribological research methods also provide opportunities for probing the fundamental properties and deformation mechanisms of metals.

Material Selection Issues for a Nozzle Guide Vane Against Service-Induced Failure

2017 ◽  
Vol 139 (5) ◽  
Author(s):  
Xijia Wu ◽  
Zhong Zhang ◽  
Leiyong Jiang ◽  
Prakash Patnaik
Keyword(s):  
Gas Turbine ◽  
Material Selection ◽  
Guide Vane ◽  
Failure Process ◽  
Inelastic Strain ◽  
Grain Boundary Sliding ◽  
Deformation Mechanisms ◽  
Strain Component ◽  
Combustion Gas ◽  
Nozzle Guide

Nozzle guide vanes (NGV) of gas turbine engines are the first components to withstand the impingement of hot combustion gas and therefore often suffer thermal fatigue failures in service. A lifting analysis is performed for the NGV of a gas turbine engine using the integrated creep–fatigue theory (ICFT). With the constitutive formulation of inelastic strain in terms of mechanism-strain components such as rate-independent plasticity, dislocation glide-plus-climb, and grain boundary sliding (GBS), the dominant deformation mechanisms at the critical locations are thus identified quantitatively with the corresponding mechanism-strain component. The material selection scenarios are discussed with regards to damage accumulated during take-off and cruise. The interplay of those deformation mechanisms in the failure process is elucidated such that an “optimum” material selection solution may be achieved.

scholarly journals Mechanical Properties and Deformation Mechanisms of Graphene Foams with Bi-Modal Sheet Thickness by Coarse-Grained Molecular Dynamics Simulations

Materials ◽  
2021 ◽  
Vol 14 (19) ◽  
pp. 5622
Author(s):  
Shenggui Liu ◽  
Mindong Lyu ◽  
Chao Wang
Keyword(s):  
Mechanical Properties ◽  
Elastic Recovery ◽  
Structural Connectivity ◽  
High Stress ◽  
Sheet Thickness ◽  
Functional Materials ◽  
Deformation Mechanisms ◽  
Coarse Grained ◽  
Graphene Sheets ◽  
Graphene Foams

Graphene foams (GrFs) have been widely used as structural and/or functional materials in many practical applications. They are always assembled by thin and thick graphene sheets with multiple thicknesses; however, the effect of this basic structural feature has been poorly understood by existing theoretical models. Here, we propose a coarse-grained bi-modal GrF model composed of a mixture of 1-layer flexible and 8-layer stiff sheets to study the mechanical properties and deformation mechanisms based on the mesoscopic model of graphene sheets (Model. Simul. Mater. Sci. Eng. 2011, 19, 54003). It is found that the modulus increases almost linearly with an increased proportion of 8-layer sheets, which is well explained by the mixture rule; the strength decreases first and reaches the minimum value at a critical proportion of stiff sheets ~30%, which is well explained by the analysis of structural connectivity and deformation energy of bi-modal GrFs. Furthermore, high-stress regions are mainly dispersed in thick sheets, while large-strain areas mainly locate in thin ones. Both of them have a highly uneven distribution in GrFs due to the intrinsic heterogeneity in both structures and the mechanical properties of sheets. Moreover, the elastic recovery ability of GrFs can be enhanced by adding more thick sheets. These results should be helpful for us to understand and further guide the design of advanced GrF-based materials.

Analysis of gas flow over a cylinder at all Knudsen numbers based on non-newtonian constitutive models

2020 ◽  
Vol 34 (14n16) ◽  
pp. 2040076
Author(s):  
Zhen-Yu Yuan ◽  
Zhong-Zheng Jiang ◽  
Wen-Wen Zhao ◽  
Wei-Fang Chen
Keyword(s):  
Constitutive Model ◽  
Gas Flow ◽  
Constitutive Relations ◽  
Constitutive Models ◽  
Direct Simulation Monte Carlo ◽  
Navier Stokes ◽  
Dsmc Simulation ◽  
Nonequilibrium Flows ◽  
Simulation Results ◽  
Better Than

This paper is focused on the gas properties over a cylinder from continuum to rarefied regimes based on the non-Newtonian constitutive model. This new constitutive model is first derived from Eu’s nonequilibrium ensemble method, which is intended for accurate description of nonequilibrium flows. Some assumptions and simplifications are made during the establishing progress of the new constitutive model by both Eu and Myong. To verify its accuracy, temperature contours and skin frictions around the cylinder are simulated by this new model. The inflow Mach number is equal to 10 and the Knudsen number ranges from 0.002 to 0.05. All simulation results are compared with Navier–Stokes (NS) and the direct simulation Monte Carlo (DSMC) methods in detail. The comparisons of friction around the surface show that the non-Newtonian constitutive models are better than the linear constitutive relations of NS equations for the prediction of nonequilibrium flow and much more close to DSMC simulation results.

A Comparative Study of the Response of Double Shearing and Hypoplastic Models

2002 ◽  
Author(s):  
Huaning Zhu ◽  
Morteza M. Mehrabadi ◽  
Mehrdad Massoudi
Keyword(s):  
Cyclic Loading ◽  
Mechanical Response ◽  
Constitutive Relations ◽  
Constitutive Models ◽  
Shear Loading ◽  
Biaxial Compression ◽  
Finite Element Program ◽  
Cyclic Shear ◽  
Hypoplastic Model ◽  
Element Program

The principal objective of this paper is to compare the mechanical response of a double shearing model with that of a hypoplastic model under biaxial compression and under cyclic shear loading. As the origins and nature of these two models are completely different, it is interesting to compare the predictions of these two models. The constitutive relations of the double shearing and the hypoplastic models are implemented in the finite element program ABACUS/Explicit. It is found that the hypoplastic and the double shearing constitutive models both show strong capability in capturing the essential behavior of granular materials. In particular, under the condition of non-cyclic loading, the stress ratio and void ratio predictions of the double shearing and the hypoplastic models are relatively close, while under the condition of cyclic loading, the predictions of these models are quite different. It is important to note that in the double shearing model employed in this comparison the shear rates on the two slip systems are assumed to be equal. Hence, the conclusions derived in this comparison pertain only to this particular double shearing model. Similarly, the hypoplasticity model considered here is that proposed by Wu, et al. [30] and the conclusions reached here pertain only to this particular hypoplasticity model.

scholarly journals Creep deformation behavior during densification of ZrB2-SiBCN ceramics with ZrO2 additive

2020 ◽  
Vol 9 (5) ◽  
pp. 544-557
Author(s):  
Bo Feng ◽  
Zhenhang Wang ◽  
Yunhao Fan ◽  
Jinghua Gu ◽  
Yue Zhang
Keyword(s):  
Grain Boundary ◽  
Creep Deformation ◽  
Applied Pressure ◽  
Grain Boundary Sliding ◽  
Diffusion Creep ◽  
Atom Diffusion ◽  
Grain Boundary Mobility ◽  
Controlling Mechanism ◽  
Temperature Ranges ◽  
Lower Temperature

Abstract ZrB2-SiBCN ceramics with ZrO2 additive are hot-pressed under a constant applied pressure. The densification behavior of the composites is studied in a view of creep deformation by means of the Bernard-Granger and Guizard model. With determination of the stress exponent (n) and the apparent activation energy (Qd), the specific deformation mechanisms controlling densification are supposed. Within lower temperature ranges of 1300–1400 °C, the operative mechanism is considered to be grain boundary sliding accommodated by atom diffusion of the polymer-derived SiBCN (n = 1, Qd = 123±5 kJ/mol) and by viscous flow of the amorphous SiBCN (n = 2, Qd = 249±5 kJ/mol). At higher temperatures, the controlling mechanism transforms to lattice or intra-granular diffusion creep (n = 3–5) due to gradual consumption of the amorphous phase. It is suggested that diffusion of oxygen ions inside ZrO2 into the amorphous SiBCN decreases the viscosity, modifies the fluidity, and contributes to the grain boundary mobility.

On instability of constitutive models for isotropic elastic-perfectly plastic material behaviour at finite deformations

2020 ◽  
pp. 095440622092068
Author(s):  
Marina Trajković-Milenković ◽  
Otto T Bruhns ◽  
Andrija Zorić
Keyword(s):  
Plastic Material ◽  
Constitutive Relations ◽  
Relevant Literature ◽  
Constitutive Models ◽  
Constitutive Law ◽  
Elastoplastic Deformations ◽  
Perfectly Plastic ◽  
User Subroutine ◽  
Shear Problem ◽  
Elastic Perfectly Plastic

The main goal of this work is to test the possibility of a newly introduced constitutive law to model the behaviour of the isotropic elastic-perfectly plastic material which is exposed to large elastoplastic deformations. The proposed constitutive relation is based on the hypo-elastic relation and the inelastic INTERATOM model. The verification of the model is done by its implementation into the commercial software ABAQUS/Standard via the user subroutine UMAT. For that purpose, the large simple shear problem is studied where selected objective corotational rates, i.e. the logarithmic rate, the Jaumann rate and the Green-Naghdi rate, are individually implemented in the aforementioned constitutive relations. The obtained results are compared mutually and with the relevant literature. The proposed constitutive model is also used to test the behaviour of the part of a real engineering structure, i.e. a seismic isolator, in order to obtain the correct input data for further analysis of superstructure behaviour due to seismic excitation.

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