Ali O. Ayhan

Mixed mode stress intensity factors for deflected and inclined surface cracks in finite-thickness plates

Using three-dimensional enriched finite elements, mixed mode stress intensity factor solutions are presented for deflected and inclined surface cracks in finite-thickness plates under uniform tensile remote loading. It is demonstrated that the enriched finite element technique provides fracture solutions for these types of problems in a very direct and convenient manner without a need for post-processing the finite element solution. Mixed mode stress intensity factor solutions are generated for semi-circular surface cracks with various deflection and inclination angles ranging from 0° to 75°. The effect of plate thickness on the mixed mode fracture solution is also investigated. In the analyses presented, crack length/plate thickness (a/t) ratio ranges from 0.2 to 0.8. It is shown that decreasing the plate thickness results in magnification of mixed mode stress intensity factors along the crack front. Based on the computed mixed mode stress intensity factors, crack propagation angles along the deflected and inclined crack fronts are also determined.

Finite element analysis of interface cracking in semiconductor packages

The application of enriched crack tip finite elements for the prediction of interface fracture parameters, e.g., strain energy release rate and mixed mode stress intensity factors, is presented. Of particular interest, is the comparison between fracture results obtained from two-dimensional (2-D) models and related three-dimensional (3-D) (generalized plane strain) calculations. These results show that for thermal cycling problems, one cannot anticipate 3-D fracture results based on 2-D calculations alone, i.e., plane stress, plane strain, and axisymmetric models. On the other hand, it is shown that the 2-D models are quite adequate for modeling interface fracture in the case of pressure loading on the interface, e.g., pressure due to water vapor expansion during solder reflow. The fracture results presented in this paper were obtained using special enriched crack tip elements that contain the analytic asymptotic displacement and stress field. Enriched crack tip elements for 2-D and 3-D elements are shown to provide highly accurate results for simulating debonding in semiconductor packages subjected to thermal cycling and/or moisture absorption.

Modeling the mechanical behavior of underfill resins and predicting their performance in flip-chip assemblies

A number of analytical models exist that can predict the effect of filler content on the mechanical behavior of filled epoxy resins. Such models can predict increases in viscosity, strength, fracture toughness, and modulus as well as the decrease in the coefficient of thermal expansion with increasing filler content. In this paper we will couple these analytical models that predict the mechanical behavior of filled epoxy resins with our FEM analyses of the thermal cycling behavior for flip-chip assemblies. Such an exercise should identify the effect of filler content on flip-chip performance.

Fracture Analysis of Cracks in Anisotropic Materials Using 3DFAS and ANSYS

The analysis of two and three dimensional fracture mechanics problems in anisotropic materials using ANSYS finite element software and 3DFAS (Three Dimensional Fracture Analysis System) is examined in this study. The methodology uses analytically derived generalized plane strain crack tip fields in anisotropic materials and is implemented into an ANSYS Macro using ANSYS Parametric Design Language. It is shown that quarter-point finite element approach is still a very effective technique for general three dimensional crack problems in homogeneous anisotropic materials. The expressions of the crack tip asymptotic displacement field are summarized and numerical examples of two and three dimensional crack problems in orthotropic, directionally solidified, and single crystal materials are presented. The stress intensity factors are compared with two-dimensional analytical and numerical solutions available in the literature and with numerical solutions obtained from FRAC3D [1, 2], a three dimensional fracture analysis program using enriched finite elements. Very good agreement is obtained between the different numerical techniques or with the analytical solutions.Copyright

Investigation of mixed mode - I/II fracture problems - Part 1: computational and experimental analyses

In this study, to investigate and understand the nature of fracture behavior properly under in-plane mixed mode (Mode-I/II) loading, three-dimensional fracture analyses and experiments of compact tension shear (CTS) specimen are performed under different mixed mode loading conditions. Al 7075-T651 aluminum machined from rolled plates in the L-T rolling direction (crack plane is perpendicular to the rolling direction) is used in this study. Results from finite element analyses and fracture loads, crack deflection angles obtained from the experiments are presented. To simulate the real conditions in the experiments, contacts are defined between the contact surfaces of the loading devices, specimen and loading pins. Modeling, meshing and the solution of the problem involving the whole assembly, i.e., loading devices, pins and the specimen, with contact mechanics are performed using ANSYSTM. Then, CTS specimen is analyzed separately using a submodeling approach, in which three-dimensional enriched finite elements are used in FRAC3D solver to calculate the resulting stress intensity factors along the crack front. Having performed the detailed computational and experimental studies on the CTS specimen, a new specimen type together with its loading device is also proposed that has smaller dimensions compared to the regular CTS specimen. Experimental results for the new specimen are also presented.

Investigation of mixed mode-I/II fracture problems - Part 2: evaluation and development of mixed mode-I/II fracture criteria

In this study, experimental and numerical results of compact tension shear (CTS) specimen and a new specimen type under in-plane mixed mode (Mode-I/II) loading conditions are compared with existing inplane mixed mode fracture criteria to investigate and understand the nature of fracture behavior properly. The material used in numerical and experimental analyses is Al 7075-T651 aluminum machined from rolled plates in the L-T rolling direction (crack plane is perpendicular to the rolling direction). In Part 1 of the study, results from numerical and experimental analyses are given. Having computed the mixed mode stress intensity factors from the numerical analyses, fracture loads are predicted and compared with different mixed mode-I/II fracture criteria. The experimental and numerical results show that many criteria are in good agreement with each other for predominately mode I to moderate mixed mode conditions. However, existing criteria increasingly differ from the experimental measurements for highly mode-II conditions. Using the computational and experimental results obtained, improved empirical mixed mode I/II fracture criteria for fracture condition and angle are also proposed.

Multiple and non-planar crack propagation analyses in thin structures using FCPAS

In this study, multiple and non-planar crack propagation analyses are performed using Fracture and Crack Propagation Analysis System (FCPAS). In an effort to apply and validate FCPAS procedures for multiple and non-planar crack propagation analyses, various problems are solved and the results are compared with data available in the literature. The method makes use of finite elements, specifically three-dimensional enriched elements to compute stress intensity factors (SIFs) without special meshing requirements. A fatigue crack propagation criterion, such as Paris-Erdo?an equation, is also used along with stress intensity factors to conduct the simulation. Finite element models are generated within ANSYS™ software, converted into and solved in FRAC3D program, which employs enriched crack tip elements. Having computed the SIFs for a given crack growth increment and using a growth criterion, the next incremental crack path is predicted and the fracture model is updated to reflect the non-planar crack growth. This procedure is repeated until cracks reach a desired length or when SIFs exceed the fracture toughness of the material. It is shown that FCPAS results are in good agreement with literature data in terms of SIFs, crack paths and crack growth life of the structure. Thus, accuracy and reliability of FCPAS software for multiple and non-planar crack propagation in thin structures is proven.

Finite element modeling and experimental studies on mixed mode-I/III fracture specimens

In this study, finite element modeling and experimental studies on a mode-I/III specimen similar to the compact tension specimen are presented. By using bolts, the specimen is attached to two loading apparatus that allow different levels of mode-I/III loading by changing the loading holes. Specimens having two different thicknesses are analyzed and tested. Modeling, meshing and the solution of the problem involving the whole assembly, i.e., loading devices, bolts and the specimen, with contact mechanics are performed using ANSYSTM. Then, the mode-I/III specimen is analyzed separately using a submodeling approach, in which threedimensional enriched finite elements are used in FRAC3D solver to calculate the resulting stress intensity factors along the crack front. In all of the analyses, it is clearly shown that although the loading is in the mode-I and III directions, mode-II stress intensity factors coupled with mode-III are also generated due to rotational relative deformations of crack surfaces. The results show that the mode-II stress intensity factors change sign along the crack front and their magnitudes are close to the mode-III stress intensity factors. It is also seen that magnitudes of the mode-III stress intensity factors do not vary much along the crack front. Fracture experiments also performed and, using the stress intensity factors from the analyses and crack paths and surfaces are shown.

Sensitivities of Two-Dimensional Fracture Problems to the Near-tip Mesh Parameters

Using the displacement correlation technique, near-tip mesh-parameter sensitivity studies are performed for cracks that cover most basic two-dimensional load-controlled problems. Stress intensity factors computed from two different mesh models for different settings of mesh parameters are compared with other solutions. The corresponding sensitivity graphs are plotted to visually see the parameters which affect results the most. Conclusions are drawn and settings of mesh parameter values are recommended.