Pei Gu

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.

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.

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.

Strengthening at nanoscaled coherent twin boundary in f.c.c. metals

This paper analyses slip transfer at the boundary of nanoscaled growth twins in face-centred cubic (f.c.c.) metals for strengthening mechanism. The required stress for slip transfer, i.e. inter-twin flow stress, is obtained in a simple expression in terms of stacking fault energy and/or twin boundary (TB) energy, constriction energy and activation volume. For nanotwinned Al, Cu and Ni, inter-twin flow stress versus twin thickness remarkably shows Hall–Petch relationship. The Hall–Petch slope is rationalized for various reactions of screw and non-screw dislocations at the TB. Additionally, strengthening at the boundary of nanoscaled deformation twins in f.c.c. metals is analysed by evaluating required twinning stress. At small nanograin size, the prediction of deformation twin growth stress shows inverse grain-size effect on twinning, in agreement with recent experimental finding.

Size-dependent deformation in nanograins and nanotwins

This paper discusses three aspects that have not been looked into within mechanistic model for rationalizing observed behavior of nanocrystalline materials. (1) For the nano-materials with low energy barrier to emit the trailing partial after the leading partial, such as nanocrystalline Al (nc-Al), both partials extend intra-granularly in strengthening effect. (2) In the transition grain-size region between strengthening and softening, the coupled effect of intra-granular dislocation extension and grain boundary deformation contributes to flow stress. (3) Reformulating the non-homogeneous nucleation model, the activation volume is further examined.

Revisiting the intra-granular dislocation extension model for flow stress in nanocrystalline metals

In our previous work (R.J. Asaro, P. Krysl and B. Kad, Philos. Mag. Lett. 83 (2003) p.733; P. Gu, B. Kad and M. Dao, Scr. Mater. 62 (2010) p.361), the intra-granular partial dislocation extension model was shown to be consistent with the experimental data of flow stress in nanocrystalline FCC materials. However, since the averaged extension was taken for a non-uniform loop, the model predicted small dislocation extension across the grain. In this article, extending our previous work, we reformulate the intra-granular partial dislocation model for FCC nanocrystalline materials using a more realistic loop. The flow stress obtained from the reformulated model shows good agreement with experimental data for various nanocrystalline FCC materials and expectedly large dislocation extension across the grain. In the second portion of this article, the mechanistic model for partial dislocation extension is extended to develop an intra-granular perfect dislocation extension model. The perfect dislocation model is examined by comparing its prediction of flow stress with experimental data of nanocrystalline Fe. Additionally, activation volume and strain-rate sensitivity are discussed within the mechanistic model in the light of available experimental data on nanocrystalline Fe.

Failure of a thin film due to inclusions on the interface

Abstract This paper addresses failures near irregularities on the interface between a film and a substrate. Several boundary value problems, including two-dimensional and three-dimensional problems, involving inclusions of various shapes placed on the interface, are considered. The loading is induced by the lattice parameter mismatch between the film and substrate. Stresses near the interface and the inclusion boundary are of particular interest. The solutions show stress concentration around the inclusion boundary; in fact, a logarithmic singularity exists at the intersection of the inclusion, film and substrate. Emphasis is placed on identifying failures associated with high stresses near the inclusion. A theoretical prediction of the misfit strain to cause adhesion failure is obtained. The driving force for dislocation emission from the inclusion is calculated, and it is shown that dislocation emission from inclusions is favoured under a sufficiently large misfit strain.