Licheng Guo

The interface crack problem under a concentrated load for a functionally graded coating–substrate composite system

Abstract The plane crack problem for a functionally graded coating–substrate system under a concentrated load is studied in this paper. The medium consists of a functionally graded coating bonded to a homogeneous substrate of finite thickness, containing an interface crack of finite length. With use of the integration transform and differential factor methods, the displacement form can be obtained. By introducing auxiliary functions, the present problem can be turned into solving a group of singular integral equations. The mixed-mode stress intensity factors (SIFs) and strain energy release rates (SERRs) are obtained. The influences of the parameters such as the load location, nonhomogeneity constants and the geometry parameters on the SIFs and SERRs are studied.

Investigation Methods for Thermal Shock Crack Problems of Functionally Graded Materials–Part I: Analytical Method

In most published papers, in order to obtain the analytical solution of the crack problems in functionally graded materials (FGMs), the thermomechanical properties of FGMs are usually assumed to be very particular functions and, hence, may not be physically realizable for many actual material combinations. Very few analytical methods can be used to solve the thermal shock crack problem of an FGM cylindrical shell or plate with general thermomechanical properties. In this article, a set of analytical methods is proposed for the thermal shock crack problem of an FGM plate or cylindrical shell with general thermomechanical properties. The crack problem of a cylindrical shell is modeled by a plate on an elastic foundation. Greatly different from previous studies, a set of analytical methods using both the perturbation method and a piecewise model are developed to obtain the transient temperature field and thermal stress intensity factor (TSIF). The perturbation method is applied to deal with the general thermal properties and the piecewise model is used to deal with the general mechanical properties. In the analytical procedure, integral transform, the residue theorem, and the theory of singular integral equation are used. Several representative examples are considered to check the capability of the present method. The transient thermal shock behavior of a ZrO2/Ti-6Al-4 V FGM plate with a surface crack and a Rene 41-Zirconia FGM cylindrical shell with a circumferential crack are analyzed.

A damage model for 3D braided composites with transverse cracking

Abstract A simplified model of three-dimensional (3D) braided composites with the transverse cracking is presented. By using the principle of minimum complementary energy, the stress components are obtained in closed-form expressions in terms of a perturbation function, which is governed by two fourth-order inhomogeneous ordinary differential equations. All possible expressions of this perturbation function are obtained in closed forms. The effective Young’s modulus and Poisson ratio of 3D damaged braided composites are calculated using the determined minimum complementary energy. To demonstrate the solution, some examples are analyzed.

A fracture mechanics model for a crack problem of functionally graded materials with stochastic mechanical properties

This study aimed to develop a method to build a ‘bridge’ between the macro fracture mechanics model and stochastic micromechanics-based properties so that the macro fracture mechanics model can be expanded to the fracture mechanics problem of functionally graded materials (FGMs) with stochastic mechanical properties. An analytical fracture mechanics model is developed to predict the stress intensity factors (SIFs) in FGMs with stochastic uncertainties in phase volume fractions. Considering the stochastic description of the phase volume fractions, a micromechanics-based method is developed to derive the explicit probabilistic characteristics of the effective properties of the FGMs so that the stochastic mechanical properties can be combined with the macro fracture mechanics model. A thought for choosing the samples efficiently is proposed so that the stable probabilistic characteristic of SIFs can be obtained with a very small sample size. The probability density function of SIFs can be determined by developing a histogram from the generated samples. The present method may provide a thought to establish an analytical model for the crack problems of FGMs with stochastic properties.

Thermal Stress Intensity Factors for a Normal Surface Crack in a Functionally Graded Coating Structure

The thermal fracture behavior for a functionally graded coating structure (FGCS) with a normal surface crack is studied. The thermomechanical properties are continuous across the interface. The surface crack may intersect the interface. In the analytical procedure, integral transforms and residue theory are used. Some samples with some representative thermomechanical parameters are analyzed and the corresponding thermal stress intensity factors (TSIFs) are calculated. It is found that the TSIF is greatly affected by the temperature conditions and thermomechanical properties. Moreover, the possibility for a surface crack to expand across the interface is discussed.

A general modelling method for functionally graded materials with an arbitrarily oriented crack

In order to analytically solve crack problems regarding functionally graded materials (FGMs), some ideal assumptions are often made. They are: (1) the properties of FGMs are usually assumed to be described by very particular functions; (2) the crack is assumed to be vertical to (or parallel to) the gradient of FGMs. However, these assumptions may not be practical for actual FGMs. Since the controlling differential equations with general mechanical properties are very difficult to solve and the arbitrarily oriented crack causes great trouble in the analytical procedure, a general piecewise-exponential model (GPE model) is proposed to investigate the fracture behaviour of FGMs with general mechanical properties and an arbitrarily oriented crack. “General mechanical properties” means that the mechanical properties in the GPE model are not required to be very particularly pre-defined functions but arbitrary functions determined by fitting the experimental results of FGMs. The studied FGMs are divided into some sub-layers with each layer’s properties varying exponentially so that the general mechanical properties can be approximated by a series of exponential functions and hence the stresses and displacements of each layer which may contain a mixed-mode crack can be solved analytically. By use of integral transform methods, principle of superposition, residual theorem and theory of singular integral equations, the mixed-mode crack problem can be turned into solving a group of singular integral equations from which mixed-mode stress intensity factors (SIFs) can be obtained. Finally, the influences of the nonhomogeneous and geometric parameters on the mixed-mode SIFs are analysed.

Investigation Methods for Thermal Shock Crack Problems of Functionally Graded Materials–Part II: Combined Analytical-Numerical Method

Fractures phenomena can be often found in functionally graded materials (FGMs) subjected to thermal shock loadings. This paper aims to develop a set of analytical-numerical methods for analyzing the mixed-mode thermal shock crack problems of a functionally graded plate (FGP). First, a domain-independent interaction energy integral method is developed for obtaining the mixed-mode transient thermal stress intensity factors (TSIFs). A perturbation method is adopted to obtain the transient temperature field. Then an analytical-numerical method combining the interaction energy integral method, a perturbation method, and the finite element method is developed to solve the present crack problem. Particularly, the influences of the materials parameters, crack length, and crack angle on the TSIFs and the crack growth angle are investigated. The results show that the present analytical-numerical method can be used to solve the thermal shock crack problem with high efficiency. The present work will be significant for the fracture mechanics analysis and design of FGM structures.

Investigation of Stress Intensity Factors for an Interface Crack in Multi-Interface Materials Using an Interaction Integral Method

A new interaction integral formulation is derived for obtaining mixed-mode stress intensity factors (SIFs) of an interface crack with the tip close to complicated material interfaces. The method is a conservation integral that relies on two admissible mechanical states (actual and auxiliary fields). By a suitable selection of the auxiliary fields, the domain formulation does not contain any integral related to the material interfaces, which makes it quite convenient to deal with complicated interface problems. The numerical implementation of the derived expression is combined with the extended finite element method (XFEM). According to the numerical calculations, the interaction integral shows good accuracy for straight and curved interface crack problems and exhibits domain-independence for material interfaces. Finally, an interfacial fracture problem is investigated for the representative centrosymmetric structure formed by two constituent materials.

A Mechanical Model of 3D Braided Composites with Internal Transverse Crack

A laminated mechanical model has been developed that can predict the mechanical properties of 3D braided composites with internal transverse crack. By using the principle of minimum complementary energy, the stress components are obtained in closed-form expressions in terms of a perturbation function, which is governed by two fourth-order inhomogeneous ordinary differential equations. The effective Young’s modulus and Poisson’s ratio of 3D braided composites with internal crack are calculated using the homogenization theorem. To demonstrate the solution, some examples are analyzed. Good agreement is obtained between the presented results and the values predicted by the modified finite element method.

Thermal Fracture Analysis Of Nonhomogeneous Plate with Interfaces Under Uniform Heat Flow

The mixed-mode thermomechanical fracture problem in a nonhomogeneous material plate with two interfaces is studied in this research. Uniform heat flow conditions are considered. The interaction energy integral method for the thermal fracture problem is developed to calculate the thermal stress intensity factors (TSIFs) in nonhomogeneous materials. This method is proved to be domain independent for nonhomogeneous materials even when the integral domain is cut by one interface or many interfaces. Combining the interaction energy integral method with the extended Finite Element Method (XFEM), the temperature fields, the displacement fields, the thermal stress fields, and the TSIFs are calculated. In this article, both the edge crack and the internal crack are considered. Some examples are presented to study the influence of the material properties on the TSIFs. It can be found that the mismatch of the elastic modulus and thermal expansion coefficient can affect the TSIFs dramatically; however, the thermal conductivity interface will not arouse a kinking behavior of the TSIFs. It can be concluded that the existence of an interface (especially for elastic modulus and thermal expansion coefficient) affects the TSIFs greatly.