N. Chandra

Some issues in the application of cohesive zone models for metal–ceramic interfaces

Abstract Cohesive zone models (CZMs) are being increasingly used to simulate discrete fracture processes in a number of homogeneous and inhomogeneous material systems. The models are typically expressed as a function of normal and tangential tractions in terms of separation distances. The forms of the functions and parameters vary from model to model. In this work, two different forms of CZMs (exponential and bilinear) are used to evaluate the response of interfaces in titanium matrix composites reinforced by silicon carbide (SCS-6) fibers. The computational results are then compared to thin slice push-out experimental data. It is observed that the bilinear CZM reproduces the macroscopic mechanical response and the failure process while the exponential form fails to do so. From the numerical simulations, the parameters that describe the bilinear CZM are determined. The sensitivity of the various cohesive zone parameters in predicting the overall interfacial mechanical response (as observed in the thin-slice push out test) is carefully examined. Many researchers have suggested that two independent parameters (the cohesive energy, and either of the cohesive strength or the separation displacement) are sufficient to model cohesive zones implying that the form ( shape ) of the traction–separation equations is unimportant. However, it is shown in this work that in addition to the two independent parameters, the form of the traction–separation equations for CZMs plays a very critical role in determining the macroscopic mechanical response of the composite system.

Atomistic simulation of grain boundary sliding in pure and magnesium doped aluminum bicrystals

Abstract Molecular dynamics and statics simulations are used to study grain boundary sliding and energy in bicrystals with symmetric tilt grain boundaries of Al and Mg doped Al. There is an increase in grain boundary energy in Al bicrystals with the presence of Mg depending on the position of Mg atom. Simulations of sliding show a clear dependence of magnitude of sliding on grain boundary energy.

Effect of the Shape of T–δ Cohesive Zone Curves on the Fracture Response

ABSTRACT Cohesive Zone Models (CZMs) are increasingly being used to simulate fracture and fragmentation processes in metallic, polymeric, ceramic materials, and composites thereof. A key feature of this approach is to represent the micromechanics of the fracture processes through a unique load-displacement relation. Most researchers consider magnitude of the energy, in addition to one of the two parameters (cohesive strength or critical displacement), to define the cohesive zone characteristics, ignoring the actual form (shape) of the relationship. Some of our recent work [1–3] and the work of others [17] has clearly shown that the energetics of the fracture process not only depends on the inelastic constitutive equation of the bounding material, but also on the choice of the cohesive zone model. CZM represents the embodiment of different inelastic micromechanisms active in the fracture process zone (FPZ). Since the micromechanisms are fundamental material characteristics, the choice of the CZM should depend on the specific material. The form (shape) of CZM represents the net effect of the processes and, hence, depends on the material system. In general, the shape of CZM is comprised of a rising, peak, and falling segment, and each segment exhibits a different influence on the energy dissipation, not only in the FPZ, but also (indirectly) on the bounding material. The commonly used exponential, bilinear, and trapezoidal models are analyzed to establish the relationships between the form (rise, peak value, and fall) characteristics of the T–δ curve and thermomechanical energy dissipation, plastic zone size, crack initiation load, and local stiffness behavior. By doing so, we provide specific guidelines to the CZM developers and users as to the criteria for the selection of appropriate CZM for a range of material system.

Micromechanical Modeling of Process-Induced Residual Stresses in Ti-24Al-11Nb/SCS-6 Composite

A crucial problem in the application of Metallic and Intermetallic Matrix Composites (MMCs and IMCs) is the presence of high levels of residual stresses induced during the fabrication process. This process-induced stress is essentially thermal in nature, and is caused by a significant difference in the coefficients of thermal expansion (CTE) of the fiber and the matrix and the large temperature differential of the cooling process. Residual stresses may lead to the development of matrix cracking, and may also have an adverse effect on the thermomechanical properties of the composites, e.g., stress-strain behavior, fracture toughness, fatigue, and creep. A micromechanical analysis is needed to study the effects of residual stresses, since phenomena like damage are local in nature even though they affect the macro properties. An elastic-plastic finite element analysis is performed to model the thermal stresses induced during fabrication of Ti-24Al-11Nb/SCS-6 unidirectional composite and the effect of these stresses on subsequent transverse loading. The state of residual stress induced in this intermetallic composite is found to be quite different from that in Ti-6Al-4V/SCS-6 metal matrix composite which is extensively discussed in the literature. The influence of fiber-matrix interfacial bonding and fiber arrangement on the thermomechanical behavior of Ti-24Al-11Nb/SCS-6 composite is also studied.

Global-local analysis of large-scale composite structures using finite element methods

Abstract Large domain design problems using finite element methods (FEM) require special techniques to achieve solutions within reasonable computational time. Global-local FEM refers to a set of numerical techniques designed to reduce the total solution time (and therefore the computational effort) for a given level of solution accuracy. In this paper we address the solution to large-scale periodic structures made up of multi-material composite systems, using two different global-local techniques. An error analysis is performed where the spatial distribution of errors due to material discontinuities and numerical solution procedures are evaluated for both of the methods. A simple illustrative example is used in which the error is quantified in relation to the savings in computational time. The two methods are then applied to the design of a high-field hybrid magnet, an axi-symmetric composite structure made up of a periodic array of “unit cells”.

Effect of residual stresses on the interfacial fracture behavior of metal-matrix composites

Abstract The fiber/matrix interface plays a critical role in the mechanical behavior of the composites. The fiber pushout test is increasingly being used to characterize the interfacial behavior of metal-matrix composites (MMCs). A fracture mechanics approach is used to examine the interfacial debonding process in MMCs and ceramic-matrix composites (CMCs) during a fiber push-out test. The equivalent domain integral (EDI) method is implemented in a finite element code and is used to compute the strain-energy release rates for the interface crack. The cooling process from the composite consolidation temperature, specimen preparation for the push-out test and the actual testing are included in the finite element simulation. A strain-energy-based debonding criterion is used to predict the interfacial behavior. The experimentally observed phenomenon of bottom debonding in MMCs is explained from the energy release rate variation for the loading and support end cracks. It is shown that processing-induced residual stresses significantly affect the initiation and propagation of interface cracks. The advantage of the EDI method over conventional methods for modeling interface crack propagation, by eliminating the need for singular elements and thus remeshing with crack advance is demonstrated through the simulation of the push-out test.

Superplastic process modeling of plane strain components with complex shapes

Computational process models using membrane element method are developed in this paper for the superplastic forming of plane strain boxes with complex cross-sectional details. Many practical superplastic components manufactured in industry have sloping sidewalk with die bottoms either corrugated and/or at angles to the sides. The new method is used to develop process models for such configurations and the resulting software can be used interactively in a computer. The method is useful to a designer in the parametric study of die geometry, die wall friction, initial thickness, and material property, or to determine if a specific geometry is suitable for superplastic forming. The kinematics of deformation are illustrated, and the numerical results of the model are compared with continuum finite element solutions and also with experimental data.

Evaluation of fracture toughness of MMC interfaces using thin-slice push-out tests

A fracture mechanics based approach is used to compute residual and interfacial fracture energies of some MMC and CMC systems during push-out tests. The phenomenon of bottom debonding in MMC thin slice specimens is examined using experimental results and strain energy computations. Residual stress predictions are correlated with experimentally reported values. The main contribution to the interfacial fracture toughness in MMCs is found to be from the residual stresses and thus the values of G{sub ic}. This factor is also demonstrated in the push-out test simulations for pre-strained specimens, where in the absence of residual stresses, a far higher push-out load is necessary for the same critical strain energy release rate; consequently no fiber push-out is observed at lower loads. Interface fracture toughnesses for certain typical MMC and CMC systems are predicted using the developed methodology.

Effects of interface chemistry on the fracture properties of titanium matrix composites

Abstract The fiber–matrix interface plays a critical role in the performance of titanium matrix composites (TMCs). In this work, the effect of fiber–matrix interfacial reactions on the fracture properties of the interface is studied using experimental characterization and computational modeling techniques. The objective of this study is to establish a link between the evolution of the interfacial chemistry and the resulting mechanical properties. SCS-6/Timetal21s composite is chosen as the candidate material system. The composite specimens are exposed to temperatures as high as 927°C for extended periods. The diffusion of elements across the interface is investigated through metallurgical techniques. Fiber push-out is used to characterize the mechanical properties of the interface. A novel computational method is used to simulate the propagation of interfacial cracks during the tests. The fracture toughness of the interface is evaluated from the experimental data using this method.

Effect of fiber fracture and interfacial debonding on the evolution of damage in metal matrix composites

Abstract A new approach for modeling the behavior of laminated composite structures using computational methods is presented, considering damage evolution at the micromechanical level. Micromechanical models are developed to predict the stress–strain response of a composite lamina explicitly accounting for the local damage mechanisms such as fiber fracture and interfacial bonding. The model is applied to metal matrix composites and hence the inelastic constitutive behavior of the matrix phase is included. The stochastic variation of the fiber properties is incorporated in this simulation using the two-parameter Weibull model. The effect of fiber volume fraction and the properties of the fiber, matrix and interface on the damage evolution is studied using this approach. A constitutive damage tensor for the composite lamina is developed from the micromechanical models which can be input into laminate structural analysis codes.