Simple Uniaxial Tensile Research Articles

Effective Macroscopic Thermomechanical Characterization of Multilayer Circuit Laminates for Advanced Electronic Packaging

Laminate substrates in advanced IC packages serve as not only the principal heat dissipation pathway but also the critical component governing the thermomechanical performance of advanced packaging technologies. A solid and profound grasp of their thermomechanical properties is of crucial importance to better understand IC packages’ thermomechanical behavior. This study attempts to introduce a subregion homogenization modeling framework for effectively and efficiently modeling and characterizing the equivalent thermomechanical behavior of large-scale and high-density laminate substrates comprising the non-uniform distribution and non-unidirectional orientation of tiny metal traces. This framework incorporates subregion modeling, trace mapping and modeling, and finite element analysis (FEA)-based effective modeling. In addition, the laminates are macroscopically described as elastic orthotropic or elastic anisotropic material. This framework is first validated with simple uniaxial tensile and thermomechanical test simulations, and the calculation results associated with these two effective material models are compared with each other, as well as with those of two existing mixture models, and direct the detailed FEA. This framework is further tested on the prediction of the process-induced warpage of a flip chip chip-scale package, and the results are compared against the measurement data and the results of the whole-domain modeling-based effective approach and two existing mixture models.

Unified periodic boundary condition for homogenizing the thermo-mechanical properties of composites

This work emphasizes on the Periodic Boundary Condition (PBC) utilized in the Finite Element Homogenization (FEH) method to numerically determine the Thermo-mechanical (T-M) properties of composites. The unified numerical implementation algorithms of the PBC used for accurately predicting the elastic properties, coefficients of thermal expansion and elasto-plastic behaviors of composites and available for representative volume elements with conformal and non-conformal surface meshes, respectively, are proposed and detailed. Regarding not only the thermo-elastic properties of composites, but also the elasto-plastic behaviors of composites under both simple uniaxial tensile, shear, uniaxial cycle loading paths and complex non-radial loading paths, the unified numerical implementation algorithms are verified to accurately predict the T-M properties of composites, through comparison with the results of the analytical models, the DIGIMAT-FE method, the experimental test and the results from the literature. The unified numerical implementation algorithms of the PBC can be extended to the predictions of other properties of various composites. This work provides a comprehensive insight into the PBC used for predicting the T-M properties of composites and benefits development of future FE codes implemented in commercial software packages.

Nonlinear Stress–Strain Characterization of Cast Iron Used to Manufacture Pipes for Water Supply

The stress–strain response of cast iron under tension or compression is nonlinear. This paper examines how the hyperbolic constitutive law can be applied to characterize nonlinear stress–strain behavior of cast iron used in water supply networks. Procedures are described to obtain parameters of the hyperbolic constitutive law from either the response (data) obtained from simple uniaxial tensile and compressive tests or from bending tests. To demonstrate its applicability, this hyperbolic constitutive law is first applied to data obtained from uniaxial tensile and compressive tests conducted by Schlick and Moore (1936, “Strength and Elastic Properties of Cast Iron in Tension, Compression, Flexure, and Combined Tension and Flexure,” Bulletin 127, Iowa Engineering Experiment Station, Ames, IA). In addition, an approach to extract parameters for the hyperbolic constitutive law from bending (beam and pipe rings) tests is proposed and subsequently applied to tests conducted by Talbot (1908, “Tests of Cast-Iron and Reinforced Concrete Culvert Pipe,” Bulletin No. 22, University of Illinois, Urbana, IL). This latter approach is attractive for practical purposes because the test set up is simple and the test coupons are very easy to prepare. The hyperbolic constitutive law in conjunction with maximum normal strain theory as proposed by St. Venant (Collins, J. A., 1993, Failure of Materials in Mechanical Design: Analysis, Prediction, Prevention, John Wiley, New York, NY) was also used to predict failure loads.