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This study aims to explain the characterization of cyclic behavior of a tube made of functionally graded material (FGM) under different combinations of internal pressure and cyclic through-thickness temperature gradients.

The normality rule, nonlinear kinematic hardening Chaboche model and Von Mises yield criterion were used to model the constitutive behavior of an FG tube in the incremental form. The material properties and hardening parameters of the Chaboche model vary according to the power-law function in the radial direction. The backward Euler integration scheme combined with return mapping algorithm which relies on the solution of a nonlinear equation performs the numerical procedure. The algorithm is implemented within the user subroutine UMAT in ABAQUS/standard.

The published works on FG components considering only the mechanical and physical properties as a function of spatial coordinate and nonlinear kinematic hardening parameters have not been considered to be changed continuously from one surface to another. Motivated by this, the present paper has deliberately been targeted to tackle this kind of problem to simulate the cyclic behavior of an FG tube as accurately as possible. In addition, to classify various behaviors the FG tube under cyclic thermomechanical loadings, Bree’s interaction diagram as an essential tool in designing of the FG pressure vessels in many engineering sectors is presented.

Provides a detailed description of the FG parameters of Chaboche kinematic hardening parameters in the adopted constitutive equations. In this paper, the significant effects of internal pressure values, kinematic hardening models and also FG inhomogeneity index related to the hardening rule parameters on plastic deformation of the FG tube are illustrated. Finally, the various cyclic behaviors of the FG tube under different combinations of thermomechanical loading are fully explored.

The primary purpose of this research was to expand the knowledge base regarding the behavior of steel columns during exposure to fire. This paper presents the numerical study of the effect of heat on the performance of parking steel column in a seven-story steel building under cyclic loading.

In this research, the forces and deformations developed during a fire are estimated by using detailed 3D finite-element models. The analyses are in the form of a coupled thermo-mechanical analysis in two types of loading: concurrent loading (fire and cyclic loading) and non-concurrent loading (first fire and then cyclically), and the analyses have been conducted in both states of the fire loading with cooling and without cooling using the ABAQUS software. Further, it was investigated whether, during the fire loading, the specimen was protected by a 3-cm-thick concrete coating and how much it changes the seismic performance. After verification of the specimen with the experimental test results, the column model was investigated under different loading conditions.

The result of analyses indicates that the effect of thermal damage on the performance of steel columns, when cooling is happening late, is more than the state in which cooling occurs immediately after the fire. In this paper, thermal–seismic performance of parking steel columns has been specified and the effect of the fire damage has been investigated for the protected steel by concrete coating and to the non-protected steel, under both cooling and non-cooling states.

This study led to recommendations based on the findings and suggestions for additional work to support performance-based fire engineering. It is clear that predicting force and deformation on steel column during fire is complex and it is affected by many variables. Here in this paper, those variables are examined and proper results have been achieved.

The problem of concurrent thermal and vibration loading has not been thoroughly studied even though it is common in electronic packaging applications. Here we attempt to address such a problem using a damage mechanics based constitutive model. Damage mechanics constitutive model for eutectic Pb/Sn solder alloys is used to simulate the damage effects of concurrent cyclic thermal loads and vibrations on Ball Grid Array (BGA) packages. The model is implemented into the commercial finite element code ABAQUS through its user defined material subroutine capability. For the integration algorithm we have used a return mapping scheme, which dramatically improves the convergency rate as compared to previous implementations of the same model. Results are examined in terms of accumulation of plastic strain within the solder connections. It is shown that the simplistic Miner’s rule can not accurately account for the combined effect of both loadings acting concurrently.

The purpose of this paper is to provide a systematic method to perform analysis and test for vibration‐thermal strain behavior of plastic ball grid array (PBGA) assembly by considering thermal and vibration loading mode. Also to investigate the dynamic behavior of PBGA assembly by considering loading modes for design and reliability evaluation of PBGA packaging.

A PBGA assembly prototype with different structure and material parameters is designed and manufactured. Based on investigation of the structural and physical parameters of PBGA sample, the vibration‐thermal strain test is developed to measure the strain distribution at the surface of the BT (bismaleimide triazine) substrates and PCB (printed circuit board) surface under vibration‐thermal cycling loading such as random vibration and the temperature is changed from 0°C to 100°C.

The test results show that the loading modes have different impact on PCB, EMC and substrate, respectively. In the meantime, it is shown that the characteristics of the compound mode is not the linear accumulative result by single vibration mode and single thermal loading mode as forecasted. The nonlinear mechanism for these modes application is the future work for progress.

It is very difficult to set up a numerical approach to illustrate the validity of the testing approach because the complex loading modes and the complex structure of PBGA assembly. The research on an accurate mathematical model of the PBGA assembly prototype is a future work.

It implies a potential design characteristic for future application of PBGA assembly. It also builds a basis for future work for design and reliability evaluation of BGA package.

This paper fulfils useful information about the thermal‐vibration coupling dynamic behavior of PBGA assembly with different structure characteristics, materials parameters.

Regeneratively cooled thrust chamber is a key component of reusable liquid rocket engines. Subjected to cyclic thermal-mechanical loadings, its failure can seriously affect the service life of engines. QCr0.8 copper alloy is widely used in thrust chamber walls due to its excellent thermal conductivity, and its mechanical and fatigue properties are essential for the evaluation of thrust chamber life. This paper contributes to the understanding of the damage mechanism and material selection of regeneratively cooled thrust chambers for reusable liquid rocket engines.

In this paper, tensile and low-cycle fatigue (LCF) tests were conducted for QCr0.8 alloy, and a Chaboche combined hardening model was established to describe the elastic-plastic behavior of QCr0.8 at different temperatures and strain levels. In addition, an LCF life prediction model was established based on the Manson–Coffin formula. The reliability and accuracy of models were then verified by simulations in ABAQUS. Finally, the service life was evaluated for a regenerative cooling thrust chamber, under the condition of cyclic startup and shutdown.

In this paper, a Chaboche combined hardening model was established to describe the elastoplastic behavior of QCr0.8 alloy at different temperatures and strain levels through LCF experiments. The parameters of the fitted Chaboche model were simulated in ABAQUS, and the simulation results were compared with the experimental results. The results show that the model has high reliability and accuracy in characterizing the viscoplastic behavior of QCr0.8 alloy.

(1)The parameters of a Chaboche combined hardening constitutive model and LCF life equation were optimized by tensile and strain-controlled fatigue tests of QCr0.8 copper alloy. (2) Based on the Manson–Coffin formula, the reliability and accuracy of constitutive model were then verified by simulations in ABAQUS. (3)Thermal-mechanical analysis was carried out for regeneratively cooled thrust chamber wall of a reusable liquid rocket engine, and the service life considering LCF, creep and ratcheting damage was analyzed.

A computational study is presented in this paper to investigate the effect of variation in material properties on the fatigue life prediction of solder joints subjected to cyclic thermal loading. The package under investigation was a plastic quad flat pack (PQFP) with gull‐wing leads. A commercial finite element code, ABAQUS, was employed to perform a two‐dimensional plane stress analysis. While all other constituents of the PQFP assembly were assumed to be linear elastic, the solder joint was considered to be elastic‐viscoplastic. The creep model was adopted from Norton’s equation and was implemented in the finite element analysis via a user‐defined subroutine. The maximum creep strain was evaluated and incorporated into the modified Coffin‐Manson equation to estimate the life cycles under thermal fatigue. It was found that the variation in material properties could have a significant influence on the fatigue life prediction of solder joints.

A formulation of non‐linear kinematic hardening in plasticity is given, with a short description of the model properties under cyclic loading. A resolution algorithm based on the initial stress method is implemented in a two‐dimensional finite element code (ZEBULON). The procedure is tested on examples including mechanical and thermal loading. Some remarks are made on the maximum increment size, the relative efficiency of ‘radial return’ and ‘secant stiffness method’ is discussed. Finally, the possibilities of the model concerning ratchetting, cyclic hardening and softening are shown.

The overall aim of this research work was the improvement of the failure behavior of printed circuit boards (PCBs). In order to describe the mechanical behavior of PCBs under cyclic thermal loads, thin copper layers were characterized. The mechanical properties of these copper layers were determined in cyclic four-point bend tests and in cyclic tensile-compression tests, as their behavior under changing tensile and compression loads needed to be evaluated.

Specimens for the four-point bend tests were manufactured by bonding 18-μm-thick copper layers on both sides of 10-mm-thick silicone plates. The silicone was characterized in tensile, shear and blow-up tests to provide input data for a hyperelastic material model. Specimens for the cyclic tensile-compression tests were produced in a compression molding process. Four layers of glass fiber-reinforced epoxy resin (thickness 90 μm) and five layers of copper (thickness 60 μm) were applied.

The results showed that, due to the hyperelastic material behavior of silicone, the four-point bend tests were applicable only for small strains, while the cyclic tensile-compression tests could successfully be applied to characterize thin copper foils in tensile and compression up to 1 percent strain.

Thin copper layers (foils) could be characterized successfully under cyclic tensile and compression loads.

The purpose of this paper is to assess the thermo-mechanical reliability of a solder bump with different underfills, with the evaluation of different underfill materials. As there is more demand in higher input/output, smaller package size and lower cost, a flip chip mounted at the module level of a board is considered. However, bonding large chips (die) to organic module means a larger differential thermal expansion mismatch between the module and the chip. To reduce the thermal stresses and strains at solder joints, a polymer underfill is added to fill the cavity between the chip and the module. This procedure has typically, at least, resulted in an increase of the thermal fatigue life by a factor of ten, as compared to the non-underfilled case. Yet, this particular case is to deal with a flip chip mounted on both sides of a printed circuit board (PCB) module symmetrically (solder bump interconnection with Cu-Pillar). Note that Cu-Pillar bumping is known to possess good electrical properties and better electromigration performance. The drawback is that the Cu-Pillar bump can introduce high stress due to the higher stiffness of Cu compared to the solder material.

As a reliability assessment, thermal cyclic loading condition was considered in this case. Thermal life prediction was conducted by using finite element analysis (FEA) and modified Darveaux’s model, considering microsize of the solder bump. In addition, thermo-mechanical properties of four different underfill materials were characterized, such as Young’s modulus at various temperatures, coefficient of temperature expansion and glass transition temperature. By implementing these properties into FEA, life prediction was accurately achieved and verified with experimental results.

The modified life prediction method was successfully adopted for the case of Cu-Pillar bump interconnection in flip chip on the module package. Using this method, four different underfill materials were evaluated in terms of material property and affection to the fatigue life. Both predicted life and experimental results are obtained.

This study introduces the technique to accurately predict thermal fatigue life for such a small scale of solder interconnection in a newly designed flip chip package. In addition, a guideline of underfill material selection was established by understanding its affection to thermo-mechanical reliability of this particular flip chip package structure.

The high heat induced by fire can substantially decrease the load-bearing capacity, which is more critical in unprotected steel structures than concrete reinforced structures. One of the conventional steel structures is a steel-plate shear wall (SPSW) in which thin infill steel plates are used to resist against the lateral loads. Due to the small thickness of infill plates, high heat seems to dramatically influence the lateral load-bearing capacity of this type of structures. Therefore, this study aims to provide an investigation into the performance of SPSW with reduced beam section at high temperature.

In the present paper, to examine the seismic performance of SPSW at high temperature, 48 single-span single-story steel frames equipped with steel plates with the thicknesses of 2.64 mm, 5 mm and 7 mm and yield stresses of 85 MPa, 165 MPa, 256 MPa and 300 MPa were numerically modeled. Furthermore, their behavioral indices, namely, strength, stiffness, ductility and hysteresis behavior, were studied at the temperatures of 20, 458, 642 and 917? The simulated models in the present paper are based on the experimental specimen presented by Vian and Bruneau (2004).

The obtained results revealed that the high heat harshly diminishes the seismic performance of SPSW so that the lateral strength is reduced even by 95% at substantially high temperatures. Therefore, SPSW starts losing its strength and stiffness at high temperature such that it completely loses its capacity of strength, stiffness and energy dissipation at the temperature of 917? Moreover, it was proved that by separating the percentage of their participations variations of the infill plate in SPSW, their behavior and the bare frame can be examined even at high temperatures.

To the best of the authors’ knowledge, the seismic performance of SPSW at different temperatures has not been evaluated and compared yet.