Robert J. Asaro

Cracks in functionally graded materials

A semi-infinite crack in a strip of an isotropic, functionally graded material under edge loading and in-plane deformation conditions is analyzed. Mixed mode stress intensity factors are analytically solved for up to a numerically determined parameter. The effects of material gradients on the mode I and mode II stress intensity factors and the phase angle used to measure mode mixity are determined. The solution is extended to the case where the strip is made of an orthotropic, functionally graded material. These results are applied to solve a four-point bending specimen configuration that may be used to test the fracture behavior of functionally graded materials. The nature of the crack tip fields and possible fracture criterion for functionally graded materials are discussed.

Deformation mechanism transitions in nanoscale fcc metals

We consider possible mechanisms that lead to transitions in the mechanisms of deformation in fcc metals and alloys. In particular, we propose that, when grain sizes are below a critical size (i.e. below 100 nm), deformation can occur via the emission of stacking faults from grain boundaries into the intragranular space. A model is developed that accounts for observed experimental data and which, in turn, shows how stacking-fault energy together with shear modulus determines achievable strength. A mechanism is proposed based on this model for transitions at both high and quasistatic strain rates, including grain-boundary sliding.

A Simplified Method for Calculating the Crack-Tip Field of Functionally Graded Materials Using the Domain Integral

A finite element based method is proposed for calculating stress intensity factors of functionally graded materials (FGMs). We show that the standard domain integral is sufficiently accurate when applied to FGMs; the nonhomogeneous term in the domain integral for nonhomogeneous materials is very small compared to the first term (the standard domain integral). In order to obtain it, the domain integral is evaluated around the crack tip using sufficiently fine mesh. We have estimated the error in neglecting the second term in terms of the radius of the domain for the domain integration, the material properties and their gradients. The advantage of the proposed method is that, besides its accuracy, it does not require the input of material gradients, derivatives of material properties; and existing finite element codes can be used for FGMs without much additional work. The numerical examples show that it is accurate and efficient. Also, a discussion on the fracture of the FGM interlayer structure is given.

Development of repetitive corrugation and straightening

In this paper, we present recent developments in repetitive corrugation and straightening (RCS), a new severe plastic deformation (SPD) technique. Two refinements of the original RCS method are presented and results are shown for commercial purity copper that illustrate the associated improvements in the effectiveness of nanostructuring. Second-generation tooling was implemented using a bench scale rolling mill for continuous processing of sheet and bar. We have found that this design does not produce enough plastic strain per RCS cycle for effective grain refinement prior to the formation and growth of fatigue cracks. Third-generation tooling was designed to process sheet and increase the amount of shear deformation per iteration. The third-generation tooling design introduced significant shear strain and was found to be effective in grain refinement.

Crack deflection in functionally graded materials

Abstract Small crack deflection in brittle functionally graded materials (FGMs) is studied. The FGMs are modeled as simply nonhomogeneous materials, i.e., the effect of microstructure is neglected and the material property variation is considered to be continuous. Considering local homogeneity and the small scale inelasticity of brittle materials, the toughness is taken to be independent of direction; therefore, the crack propagates along the direction of maximum energy release rate, or the direction which gives a vanished mode II stress intensity factor. Kink directions for several specimens which may be used to experimentally study fracture behavior of FGMs are calculated. It is shown that material gradients have a strong effect on the kink direction when the crack is at the central region of a FGM, whereas they have little effect when the crack is close to the boundaries of the FGM.

A micromechanical study of residual stresses in functionally graded materials

A physically based computational micromechanics model is developed to study random and discrete microstructures in functionally graded materials (FGMs). The influences of discrete microstructure on residual stress distributions at grain size level are examined with respect to material gradient and FGM volume percentage (within a ceramic-FGM-metal three-layer structure). Both thermoelastic and thermoplastic deformation are considered, and the plastic behavior of metal grains is modeled at the single crystal level using crystal plasticity theory. The results are compared with those obtained using a continuous model which does not consider the microstructural randomness and discreteness. In an averaged sense both the micromechanics model and the continuous model give practically the same macroscopic stresses; whereas the discrete micromechanics model predicts fairly high residual stress concentrations at the grain size level (i.e. higher than 700 MPa in 5–6 vol% FGM grains) with only a 300°C temperature drop in a NiAl2O3 FGM system. Statistical analysis shows that the residual stress concentrations are insensitive to material gradient and FGM volume percentage. The need to consider microstructural details in FGM microstructures is evident. The results obtained provide some insights for improving the reliability of FGMs against fracture and delamination.

A study on failure prediction and design criteria for fiber composites under fire degradation

Abstract Polymer matrix composites can be severely degraded/damaged under thermal loading caused by fire. Fire degradation of fiber composites is a serious concern in large load-bearing structural applications such as ship, piers and bridges. This paper describes results from combined experimental and theoretical studies of compressive failures of polymer-matrix glass-reinforced composites which have undergone fire degradation. The focus of the present paper is on single skin composites. Experimental studies have included structural collapse under combined thermal (i.e. fire) and mechanical loading. Detailed analytical and numerical simulations of panel deformation and collapse show good agreement with the experimental observations. A quantitative methodology for developing the design approach is proposed and discussed with respect to the experimental results and thermal boundary conditions.

A study of void nucleation, growth, and coalescence in spheroidized 1518 steel

The ductile fracture of a spheroidized 1518 steel has been investigated using three types of tensile specimens — smooth tensile, notched tensile, and plane-strain tensile. It was found that void nucleation has two different modes (Type I and Type II) depending on local conditions, the most important of which are the size, shape, and distribution of the particles. By identifying the low-strain-range nucleation behavior (Type I), it was possible to determine the value of plastic strain, εN, after which void nucleation at average-sized carbide particles (Type II) begins; εN is 0.45 for the smooth tensile case, 0.30 for the notched, and 0.25 for the plane strain. The critical stress for Type II void nucleation, σc, is of the order of 1200 MPa. Void growth depends on the macroscopic stress-strain state: longitudinal growth is given by a linear function of applied plastic strain, εp, whereas lateral growth shows a linear dependence on the triaxial stress, σT. When the local value ofVf reaches a critical volume fraction of voids (Vfcri = 5 ± 0.5 pct), void coalescence occurs in a catastrophic manner, leading to final separation within a highly localized zone. The stress concentration caused by the notched tensile specimen geometry and the localized mode of plastic flow caused by the constraint of the plane-strain state in a Clausing-type specimen were found to affect the substeps of void nucleation, growth, and coalescence.

Non-Schmid effects and localized plastic flow in intermetallic alloys

Abstract A general strain rate dependent crystallographic slip theory which incorporates both non-Schmid effects and thermal deformation is presented. The theory is applied to the description of deformation in intermetallic alloys such as Ni 3 Al. For Ni 3 Al, as an example, it is shown that the approach embodies descriptions of stress state dependent yielding as observed experimentally as well as described by existing models such as that of Paidar, Pope and Vitek ( Acta Metall., 32 (1984)435). Finite element calculations of crystals deforming on only one slip system demonstrate that Asaro and Rices ( J. Mech. Phys. Solids, 25 (1977) 309) criterion for bifurcation is a necessary condition for the formation of shear bands in crystals undergoing slip on only one slip system. Geometric effects are shown, however, to play an important role in the development of such localized shear bands. Strain rate sensitivity can delay significantly the formation of the localization, and lattice rotations relative to the surrounding lattice inside the shear bands are found to be quite small. This is in contrast to the case in multiple slip where lattice rotations play an important role in the localization process. In multiple slip the criteria for localized plastic flow are found to be of the sort described by Asaro ( Acta Metall., 27 (1979) 445; Mech. Mater., 4 (1985) 343), although localization generally occurs much sooner in the deformation process as a result of deviations from Schmids rule.

Elastic-plastic crystal mechanics for low symmetry crystals

Abstract A method of averaging the elastic-viscoplastic aggregate behavior of low symmetry materials is developed. The single crystal constitutive model includes both elasticity and rate dependent crystallographic slip. The constraint conditions imposed on the local deformations are discussed and developed in a form that allows elastic deformation without crystallographic slip in the constrained directions. The interaction law between the macroscopic and local deformations is achieved by a modified Taylor type model in which macroscopic equilibrium and compatibility are maintained, but local compatibility is not considered. Deformations in the constrained directions are posed as Lagrange multipliers rigorously enforcing a minimum work rate throughout the aggregate. The constitutive model is used to predict deformation response and texture evolution in a broad class of low symmetry materials lacking the five independent slip systems required to accommodate a general deformation. The predictions are compared to experimental data for the various materials. By including elasticity into the new model, predictive capabilities are now expanded to include a broad range of phenomena critical to the processing of such low symmetry crystals (i.e. yield surfaces, residual stresses, etc.).