Sung Yi

The significance of (an)isotropic viscoelastic Poisson ratio stress and time dependencies

Abstract Although viscoelastic moduli may be linear, Poisson ratios (PR) are always nonlinear functions of pairs of normal strains. This is equally true for physical PR defined in the real time space and for pseudo PR differently derived in the Fourier transform (FT) domain. It is shown analytically that only if anisotropic or isotropic viscoelastic moduli and relaxation or creep functions are characterized by identical time functions in all ditections and stresses are constants or at most temporal and spatial separable functions, then corresponding PR must be time independent. Under all other conditions PR are proven to be time, stress and thermal expansion dependent through time integrals, although physical and pseudo PR are shown to be functionally unrelated. The consequences of PR nonlinearities are that their uniaxially determined values are not applicable to other uniaxial loadings with different time histories or to multiaxial loadings and thermal expansions, if the latter are present. Similarly, isotropic PR cannot generally be determined solely from viscoelastic Youngs and shear moduli, even for linear materials. Consequently, viscoelastic material property characterization in terms of PR is not unique and viscoelastic responses are best described in terms of creep or relaxation functions. Anisotropic and isotropic viscoelastic PR time effects are investigated analytically and evaluated numerically.

Fracture toughening mechanism of shape memory alloys due to martensite transformation

The fracture toughening mechanism of shape memory alloys is studied analytically. The asymptotic stress analysis of shape memory alloys under mode I loads is carried out using the Eshelby inclusion method and the weight function method. The toughening mechanism due to martensite transformation of shape memory alloys is investigated on the basis of the crack shielding theory of fracture mechanics. The transformation boundaries for static and steady advanced cracks are also determined. The analytic results show that the martensite transformation reduces the crack tip stress intensity factor and increases the toughness. The toughness of shape memory alloys is enhanced by the transformed strain fields which tend to limit or prevent crack opening and advancing.

A hybrid stress ANS solid‐shell element and its generalization for smart structure modelling. Part II—smart structure modelling

In Part I of the paper, a hybrid-stress-assumed natural strain eight-node solid-shell element immune to shear, membrane, trapezoidal, thickness and dilatational lockings has been developed. Moreover, the element computational cost is reduced by enforcing admissible sparsity in the flexibility matrix. In this part of the paper, the solid-shell element is generalized to a piezoelectric solid-shell element. Using the two solid-shell elements, smart structures with segmented piezoelectric sensors and actuators can be conveniently modelled. A number of problems are studied and comparisons with other ad hoc element models for smart structure modelling are presented. Copyright

A finite element approach for cure simulation of thermosetting matrix composites

Abstract A nonlinear transient heat transfer finite element model is developed to simulate the curing process of polymer matrix composites. Temperature distributions inside laminates can be evaluated by solving the nonlinear anisotropic heat conduction equations including internal heat generation produced by exothermic chemical reactions. Thermal properties are assumed to be both temperature and degree of cure dependent. Thermal properties, degree of cure and internal heat generation due to the exothermic reaction are permitted to vary within an element. Numerical examples are presented to verify accuracy and convergence and to demonstrate use of the present finite element procedure for analyzing composite curing processes. Glass-polyester and Hercules AS4/3501-6 graphite-epoxy composites are considered. Good agreement between experimentally measured and predicted temperature distributions is obtained for various cure cycle histories.

Prediction and verification of process induced warpage of electronic packages

Abstract During the manufacturing, testing and service, thermally induced deformations and stresses will occur in IC devices and packages, which may cause various kinds of product failures. FEM techniques are widely used to predict the thermal deformations and stresses and their evolutions. However, due to the complexity of the real engineering problems, various assumptions and simplifications have to be made in conducting FEM modelling. Therefore, the applicability of the predicted results depend strongly on the reliability and accuracy of the developed FEM-based prediction models which should be verified before applications. In this paper, FEM models are developed to predict the thermal deformations of certain electronic packages and naked die samples under packaging and testing loading. For all the package constituents, appropriate material properties and models are used, including temperature-dependent visco-elasticity, anisotropy, and temperature-dependent elasticity and plasticity. To verify the developed FE models, a series of optical metrology tests are performed. A compact 3D interferometry testing system that can measure simultaneously out-of plane and in-plane deformations has been developed. Thermal deformation measurements are performed on samples of both real electronic packages and naked dies attached on a leadframe. Identical deformation patterns were found for the measured fringe patterns in the U -, V -, and W -fields and the simulated ones. Also, quantitatively, the maximum deformation mismatch between the predicted and tested results is within 15%. It is concluded that the thermally induced deformations predicted by the non-linear FEM models match well with measured deformations for both the naked die and the real packages.

SOLDER JOINT RELIABILITY OF PLASTIC BALL GRID ARRAY PACKAGES

Presents the results of a study of the effects of solder ball pad metallurgy, intermetallic compound (IMC) thickness and thermal cycling on the shear strengths of PBGA package solder balls. The study of the microstructures of solder balls revealed that only a very thin layer of intermetallic compound existed between solder balls and Ni or Ni alloy barrier layers immediately after ball placement and reflow. The protective Au layer was dissolved completely and a needle like AuSn4 intermetallic compound was then formed and dispersed evenly in the solder balls. The overall thickness of the IMC layers was thicker than 15μm after storage at 150°C for 1,000 hours. During the shear tests failure occurred at the interface of the two IMC layers. The fracture surfaces of solder balls with electrolytic Ni and thick Au layers were smooth and brittle fracture was observed. The ball shear strength decreased dramatically with the formation of IMC layers. For the solder balls with electroless Ni and thin Au layers, only a single IMC layer was formed at the interface and its thickness was only 2.5 μm after storage at 150°C for 1,000 hours.

Fracture toughening mechanism of shape memory alloys under mixed-mode loading due to martensite transformation

This paper is devoted to the fracture toughening analysis of shape memory alloys (SMAs) with a macrocrack under mixed mode loads. The asymptotic analysis of the stress field and the derivation of the two-dimensional weight function for the semi-infinite crack in isotropic SMAs are investigated. The transformation boundaries for static crack and steady advanced crack are determined. The toughening mechanism due to martensite transformation of SMAs is also studied on the basis of the Eshelby inclusion method and weight function method. The results show that, for the mixed mode problem, the boundaries of the transformation zone is not symmetric and depend on the applied remote load field phase angle. Instead of stress intensity factors, the energy release rate and load phase angle are used for the analysis. It is found that the crack flanks may be closed owing to the martensite transformation near the crack tip when the remote load phase angle is small. The analytical results also show that the martensite transformation reduces the crack tip energy release rate and increases the toughness. The toughness of SMAs is enhanced by the transformation strain, which tends to limit or prevents crack advancing.

Large deformation finite element analyses of composite structures integrated with piezoelectric sensors and actuators

Nonlinear dynamic responses of structures integrated with piezoelectric materials are studied. Finite element formulations are derived on the basis of the updated Lagrangian formulation and the principle of virtual work. Twenty-node solid elements including electrical degrees of freedom are developed to analyze structures with piezoelectric sensors and actuators and multipoint constraints for electrical degrees of freedom are utilized to simulate electrodes. A limited number of numerical examples are presented in order to verify the accuracy and convergence of the present formulation and to demonstrate its usefulness for and applicability to solutions of large deformation dynamic responses of piezoelectric structures.

Anisotropic viscoelastic finite element analysis of mechanically and hygrothermally loaded composites

Abstract Quasi-static linear anisotropic viscoelastic responses of composite structures subjected to mechanical and hygrothermal loads are formulated in terms of finite element algorithms. Laplace and/or Fourier transforms rather than direct time integrations are used in this formulation, in order to improve the accuracy of results and save extensive computational time and storage. The present viscoelastic analyses require the same computer memory as is needed for corresponding elastic eigenvalue problems. Bending and stretching of composite plates for which analytical solutions exist are examined in order to evaluate the accuracy and effectiveness of the present approach. The time-dependent displacement fields in the transverse direction for the cross-ply and angle-ply laminates are calculated, and the stacking sequence effects of the laminates are discussed in detail. Creep responses for GY70 339 composite laminates with or without a circular hole are also studied. The numerical results compare favorably with analytical solutions, i.e. within 1.8% for bending and 10 −3 % for tension.

Stochastic Viscoelastic Delamination Onset Failure Analysis of Composites

The previously formulated deterministic viscoelastic quadratic time de pendent delamination onset criterion is generalized to complete three-dimensional stochastic environments. The analysis includes stochastic processes due to combined ran dom loads and random delamination failure stresses as well as random anisotropic vis coelastic material properties including the influence of stochastic temperature fields, mois ture contents and boundary conditions. It is shown that times for delamination onset occurrences in composites can be predicted probabilistically depending on any one or all of the above conditions. Illustrative examples are presented showing the relationship in terms of parametric variations between times to delamination and corresponding probabil ities that such events will occur. Since uniaxial tension, compression and shear vis coelastic delamination failure stresses decrease in time, the loading history is of significant importance. For cases where deterministic criteria predict no delamination failures, the present stochastic failure theory indicates high probabilities of failure at either early or long times depending on the load-time relations. The early time high probabilities of delamination onset predict short lifetimes and occur in conditions where the composite in ternal stresses relax at faster rates than the failure stresses are degrading. The effects of fiber orientation and of number of plies on delamination probabilities are also examined.