No description available.

A phenomenological cohesive term is proposed and added to an existing cohesive constitutive law (by Roy and Dodds) to model the crack tip high inertia region proposed by Gao. The new term is attributed to fracture mechanisms that result in high energy dissipation around the crack tip and is assumed to be a function of external energy per volume input into the system. Finite element analysis is performed on PMMA with constant velocity boundary conditions and mesh discretization based on the work of Xu and Needleman. The cohesive model with the proposed dissipative term is only applied in the high inertia zone i.e., to cohesive elements very close to the crack tip and the traditional Roy and Dodds model is applied on cohesive elements in the rest of the domain. It was observed that crack propagated in three phases with a speed of 0.35cR before branching, which are in good agreement with experimental observations. Thus, modeling of high inertia zone is one of the key aspects to understanding brittle fracture.

No description available.

No description available.

Brazing, as a type of joining process, is widely used in manufacturing industries to join individual components of a structure. Structural reliability of a brazed assembly is strongly dependent on the joint mechanical properties. In the present work, mechanical reliability of low carbon steel brazed joints with copper filler metal is investigated and a methodology for failure analysis of brazed joints using the cohesive zone model (CZM) is presented. Mechanical reliability of the brazed joints is characterized by strength and toughness. Uniaxial and biaxial strengths of the joints are evaluated experimentally and estimated by finite element method using the ABAQUS software. Microstructural analysis of the joint fracture surfaces reveals different failure mechanisms of dimple rupture and dendritic failure. Resistance of the brazed joints against crack propagation, evaluated by the single-parameter fracture toughness criterion, shows dependency on the specimen geometry and loading configuration. Fracture of the brazed joints and the subsequent ductile tearing process are investigated using a two-parameter CZM. The characterizing model parameters of the cohesive strength and cohesive energy are identified by a four-point bend fracture test accompanied with corresponding FE simulation. Using the characterized CZM, the joint fracture behavior under tensile loading is well estimated. Predictability of the developed cohesive zone FE model for fracture analysis of brazed joints independent of geometry and loading configuration is validated. The developed cohesive zone FE model is extended to fatigue crack growth analysis in brazed joints. A cyclic damage evolution law is implemented into the cohesive zone constitutive model to irreversibly account for the joint stiffness degradation over the number of cycles. Fatigue failure behavior of the brazed joints is characterized by performing fully reversed strain controlled cyclic tests. The damage law parameters are calibrated based on the analytical solutions and the experimental fatigue crack growth data. The characterized irreversible CZM shows applicability to fatigue crack growth life prediction of brazed joints.

Brazing, as a type of joining process, is widely used in manufacturing industries to join individual components of a structure. Structural reliability of a brazed assembly is strongly dependent on the joint mechanical properties. In the present work, mechanical reliability of low carbon steel brazed joints with copper filler metal is investigated and a methodology for failure analysis of brazed joints using the cohesive zone model (CZM) is presented. Mechanical reliability of the brazed joints is characterized by strength and toughness. Uniaxial and biaxial strengths of the joints are evaluated experimentally and estimated by finite element method using the ABAQUS software. Microstructural analysis of the joint fracture surfaces reveals different failure mechanisms of dimple rupture and dendritic failure. Resistance of the brazed joints against crack propagation, evaluated by the single-parameter fracture toughness criterion, shows dependency on the specimen geometry and loading configuration. Fracture of the brazed joints and the subsequent ductile tearing process are investigated using a two-parameter CZM. The characterizing model parameters of the cohesive strength and cohesive energy are identified by a four-point bend fracture test accompanied with corresponding FE simulation. Using the characterized CZM, the joint fracture behavior under tensile loading is well estimated. Predictability of the developed cohesive zone FE model for fracture analysis of brazed joints independent of geometry and loading configuration is validated. The developed cohesive zone FE model is extended to fatigue crack growth analysis in brazed joints. A cyclic damage evolution law is implemented into the cohesive zone constitutive model to irreversibly account for the joint stiffness degradation over the number of cycles. Fatigue failure behavior of the brazed joints is characterized by performing fully reversed strain controlled cyclic tests. The damage law parameters are calibrated based on the analytical solutions and the experimental fatigue crack growth data. The characterized irreversible CZM shows applicability to fatigue crack growth life prediction of brazed joints.

Multi-layered electronic packages increase in complexity with demands for functionality. Interfacial delamination remains a prominent failure mechanism due to mismatch of coefficient of thermal expansion (CTE). Numerous studies have investigated interfacial cracking in microelectronic packages using fracture mechanics, which requires knowledge of starter crack locations and crack propagation paths. Cohesive zone theory has been identified as an alternative method for modeling crack propagation and delamination without the need for a pre-existing crack. In a cohesive zone approach, traction forces between surfaces are related to the crack tip opening displacement and are governed by a traction-separation law. Unlike traditional fracture mechanics approaches, cohesive zone analyses can predict starter crack locations and directions or simulate complex geometries with more than one type of interface. In a cohesive zone model, cohesive zone elements are placed along material interfaces. Parameters that define cohesive zone behavior must be experimentally determined to be able to predict delamination propagation in a microelectronic package. The objective of this work is to study delamination propagation in a copper/mold compound interface through cohesive zone modeling. Mold compound and copper samples are fabricated, and such samples are used in experiments such as four-point bend test and double cantilever beam test to obtain the cohesive zone model parameters for a range of mode mixity. The developed cohesive zone elements are then placed in a small-outline integrated circuit package model at the interface between an epoxy mold compound and a copper lead frame. The package is simulated to go through thermal profiles associated with the fabrication of the package, and the potential locations for delamination are determined. Design guidelines are developed to reduce mold compound/copper lead frame interfacial delamination.

abstract: Polymer matrix composites (PMCs) are attractive structural materials due to their high stiffness to low weight ratio. However, unidirectional PMCs have low shear strength and failure can occur along kink bands that develop on compression due to plastic microbuckling that carry strains large enough to induce nonlinear matrix deformation. Reviewing the literature, a large fraction of the existing work is for uniaxial compression, and the effects of stress gradients, such as those present during bending, have not been as well explored, and these effects are bound to make difference in terms of kink band nucleation and growth. Furthermore, reports on experimental measurements of strain fields leading to and developing inside these bands in the presence of stress gradients are also scarce and need to be addressed to gain a full understanding of their behavior when UDCs are used under bending and other spatially complex stress states. In a light to bridge the aforementioned gaps, the primary focus of this work is to understand mechanisms for kink band evolution under an influence of stress-gradients induced during bending. Digital image correlation (DIC) is used to measure strains inside and around the kink bands during 3-point bending of samples with 0°/90° stacking made of Ultra-High Molecular Weight Polyethylene Fibers. Measurements indicate bands nucleate at the compression side and propagate into the sample carrying a mixture of large shear and normal strains (~33%), while also decreasing its bending stiffness. Failure was produced by a combination of plastic microbuckling and axial splitting. The microstructure of the kink bands was studied and used in a microstructurally explicit finite element model (FEM) to analyze stresses and strains at ply level in the samples during kink band evolution, using cohesive zone elements to represent the interfaces between plies. Cohesive element properties were deduced by a combination of delamination, fracture and three-point bending tests used to calibrate the FEMs. Modeling results show that the band morphology is sensitive to the shear and opening properties of the interfaces between the plies. / Dissertation/Thesis / Doctoral Dissertation Mechanical Engineering 2016

No description available.

Composite materials and hybrid materials such as fiber-metal laminates, and functionally graded materials are increasingly common in application in aerospace structures. However, adhesive bonding of dissimilar materials makes these materials susceptible to delamination. The use of integrated Sinc methods for predicting interlaminar failure in laminated composites and hybrid material systems was examined. Because the Sinc methods first approximate the highest-order derivative in the governing equation, the in-plane derivatives of in-plane strain needed to obtain interlaminar stresses by integration of the equilibrium equations of 3D elasticity are known without post-processing. Interlaminar stresses obtained with the Sinc method based on Interpolation of Highest derivative were compared for the first-order and third-order shear deformable theories, the refined zigzag beam theory and the higher-order shear and normal deformable beam theory. The results indicate that the interlaminar stresses by the zigzag theory compare well with those obtained by a 3D finite element analysis, while the traditional equivalent single layer theories perform well for some laminates. The philosophy of the Sinc method based on Interpolation of Highest Derivative was extended to create a novel weak form based approach called the Integrated Local Petrov-Galerkin Sinc Method. The Integrated Local Petrov-Galerkin Sinc Method is easily utilized for boundary-value problem on non-rectangular domains as demonstrated for analysis of elastic and elastic-plastic plane-stress panels with elliptical notches. The numerical results showed excellent accuracy compared to similar results obtained with the finite element method. The Integrated Local Petrov-Galerkin Sinc Method was used to analyze interlaminar debonding of composite and fiber-metal laminated beams. A double-cantilever beam and a fixed-ratio mixed mode beam were analyzed using the Integrated Local Petrov-Galerkin Sinc Method and the results were shown to correlate well with those by the finite element method. An adaptive Sinc point distribution technique was implemented for the delamination analysis which significantly improved the methods accuracy for the present problem. Delamination of a GLARE, plane-strain specimen was also analyzed using the Integrated Local Petrov-Galerkin Sinc Method. The results correlate well with 2D, plane-strain analysis by the finite element method, including interlaminar stresses obtained by through-the-thickness integration of the equilibrium equations of 3D elasticity. / Ph. D.