Elastoplastic analysis of layered materials under thermal loading: Edge cracks parallel to the interface

The present study is a fracture mechanics analysis of a layered bimaterial with sharp interface having a stationary edge crack parallel to the interface and subjected to monotonic variation in temperature. Elastic and incremental elastoplastic analyses are carried out to evaluate the energy release rate. Closed-form solutions are derived, as functions of the thermomechanical properties and the geometry of the layers, for different critical temperatures at which distinct transitions occur in the deformation due to thermal loading. Finite-element simulations are used to examine the influence of variation in thermo- mechanical properties of the layers with temperature, as well as the effects of finite geometry. The evolution and path dependency of the J-integral with variation in temperature is examined. Detailed finite-element results are presented for the technologically important Ni-Al₂O₃ bimaterial system. The effect of crack propagation is considered. This revised version was published online in August 2006 with corrections to the Cover Date.     

Rapid propagation of cracks in orthotropic materials

Translated from Fiziko-Khimicheskaya Mekhanika Materialov, No. 5, pp. 70–71, September–October, 1989.     

Contact model of cracks in orthotropic materials

We consider a plane strain problem for an orthotropic half plane loaded at infinity and containing a crack along its fixed edge. To remove a singularity near the right crack tip, we introduce an artificial contact zone. The problem under consideration is reduced to the mixed Dirichlet-Riemann boundaryvalue problem. We present the exact solution of this problem and deduce formulas for stresses in the contact zone and on the continuation of the crack and for the stress intensity factors. By using both analytic and numerical methods, we prove that the energy-release rate is quasiinvariant in the process of crack propagation relative to the size of the contact zone. On the basis of these results, we propose an algorithm for the evaluation of the paramenters of fracture of composites of finite dimensions with interface cracks. As a special case, we develop a model of interface cracks with actual contact zone and establish the dependences of the length of this zone on the external load and elasticity moduli of the material. Dnepropetrovsk State University, Dnepropetrovsk. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 35, No. 5, pp. 59–66, September–October, 1999     

An interaction integral method for analysis of cracks in orthotropic functionally graded materials

This paper presents two new interaction integrals for calculating stress-intensity factors (SIFs) for a stationary crack in two-dimensional orthotropic functionally graded materials of arbitrary geometry. The method involves the finite element discretization, where the material properties are smooth functions of spatial co-ordinates and two newly developed interaction integrals for mixed-mode fracture analysis. These integrals can also be implemented in conjunction with other numerical methods, such as meshless method, boundary element method, and others. Three numerical examples including both mode-I and mixed-mode problems are presented to evaluate the accuracy of SIFs calculated by the proposed interaction integrals. Comparisons have been made between the SIFs predicted by the proposed interaction integrals and available reference solutions in the literature, generated either analytically or by finite element method using various other fracture integrals or analyses. An excellent agreement is obtained between the results of the proposed interaction integrals and the reference solutions. The authors would like to acknowledge the financial support of the U.S. National Science Foundation (NSF) under Award No. CMS-9900196. The NSF program director was Dr. Ken Chong.     

Cyclic cracking resistance of brittle materials under compressive loading

Fatigue behavior of brittle materials under compression is considered. The findings should be taken into account in the failure probability assessment of components made of materials with limited plasticity, which are used in various stress states. __________ Translated from Problemy Prochnosti, No. 1, pp. 83–87, January–February, 2009.     

On modelling cracks in orthotropic plates under biaxial loading: synthesis and summary

The model of a crack with a process zone is considered and generalized to orthotropic materials. It is assumed that a material in the process zone satisfies a strength condition of arbitrary form. Based on the crack model, the fracture of an orthotropic cracked plate under biaxial loading is studied. The crack is directed along one of the anisotropy axes with external loads being applied in parallel and perpendicularly to it. The influence of the biaxiality of external loading on the critical state of the cracked plate is analysed within the framework of the critical crack opening displacement and critical J ‐integral criteria. Numerical solution is obtained using the Mises‐Hill and Gol’denblat‐Kopnov strength criteria. Theoretical results are compared with experimental data obtained by testing specimens made of structural metals.     

Close interaction of coplanar circular cracks under shear loading

A new method is proposed for the stress analysis of an elastic space weakened by several arbitrarily located coplanar circular cracks subjected to an arbitrary shear loading. The method is based on a new type of integral equation and has definite advantages over the existing methods: equations are non-singular, the iteration procedure is rapidly convergent even for very close interactions. The method allows us to obtain a practically exact numerical solution to the problem of very close interactions. An accurate analytical solution is obtained for the case of two cracks, which are separated by a half of their radius or more. The stress intensity factors and the crack energy increase due to the interaction are computed for various distances between the cracks.The reported research was supported by a grant from the Natural Sciences and Engineering Research Council of Canada     

Transient dynamic analysis of interface cracks in layered anisotropic solids under impact loading

Transient elastodynamic crack analysis in two-dimensional (2D), layered, anisotropic and linear elastic solids is presented in this paper. A time-domain boundary element method (BEM) in conjunction with a multi-domain technique is developed for this purpose. Time-domain elastodynamic fundamental solutions for homogenous, anisotropic and linear elastic solids are applied in the present time-domain BEM. The spatial discretization of the boundary integral equations is performed by a Galerkin-method, while a collocation method is adopted for the temporal discretization of the arising convolution integrals. An explicit time-stepping scheme is developed to compute the unknown boundary data and the crack-opening-displacements (CODs). To show the effects of the crack configuration, the material anisotropy, the layer combination and the dynamic loading on the dynamic stress intensity factors and the scattered elastic wave fields, several numerical examples are presented and discussed.     

A model for interface cracks in layered orthotropic solids: Convergence of modal decomposition using the interaction integral method

The mode‐partitioning problem for bimaterial interfaces is still not resolved by the classical fracture mechanics approach in a satisfactory manner. Stress oscillations and overlapping crack faces are a direct consequence of the rigorous solution of the elastic boundary value problem, if the constitutive law changes discontinuously across the interface. Conversely, continuously varying material properties, also referred to as functionally graded materials (FGM), avoid these physically not admissible drawbacks. In this case the crack tip fields are of the same nature as those known from homogeneous materials. Therefore, the well‐established stress intensity factor concept can be used without any changes. Following this motivation an FGM‐interface model for delaminated composite beam structures was developed and its characteristics with respect to the modal decomposition of the crack tip fields were investigated. The considered beam structures consisted of two orthotropic layers, each of a different material. The spatial variation of the material properties in the interface region was modeled by a tanh ‐function introducing one transition parameter that controlled the FGM‐gradient. Four load cases were analyzed for each structural configuration: either a unit normal force or a unit bending moment was imposed on each end of the split beam. Thus, any load case can be simply reconstructed from the presented results by means of superposition. The stress intensity factors for modes I and II were then evaluated using an interaction integral method along with the finite element method. The corresponding results are given depending on the mesh density of the interface region, the integration domain and the transition parameter. In this manner, the influence of the transition parameter on the mode ratio and on the convergence behavior of the modal decomposition scheme with respect to its integration domain was identified. Finally, the ability of the FGM‐interface model to represent bimaterial interfaces while still maintaining the advantages of crack analysis in homogeneous materials was highlighted. Copyright © 2008 John Wiley & Sons, Ltd.     

Evaluation of the strength of structural materials with cracks under complex loading

We develop an experimental procedure and geometry of the specimens for the evaluation of the characteristics of crack growth resistance of structural materials for various macromechanisms of fracture (modes I, II, and III). We plotted diagrams of the limiting-equilibrium state of a body containing a crack (its strength) under complex proportionally increasing loading.     

Finite layer analysis of layered viscoelastic materials under three-dimensional loading conditions

A method is presented which enables the calculation of the settlement behaviour of circular or general loadings on horizontally layered soils which undergo secondary or ‘creep’ consolidation. The method of analysis involves the use of Hankel or double Fourier transforms to simplify the equations governing the consolidation process. This leads to great savings in the preparation of data and the amount of computer storage needed to solve problems involving three-dimensional loadings since such problems are essentially reduced to that of one spatial dimension: Solutions are then obtained by a ‘forward marching’ process where solutions at a particular time are found from those at a previous time. A method is presented which eliminates the need to store the solutions at all previous time steps, and is therefore very efficient. The theory is illustrated by examples of the behaviour of rectangular and circular loadings on layered soil profiles.     

Tunneling radial cracks in layered structures from contact loading

Glass/epoxy laminates glued onto a compliant substrate are indented with a hard ball. The damage is characterized by a set of transverse cracks which pop out from the subsurface of the glass layers due to flexure and propagate stably in the radial direction with load in a bell-shape front under a diminishing stress field. Compliant interlayers, even extremely thin ones, are effective in inhibiting crossover fracture. This leads to crack tunneling and crack multiplication in the hard layers, which enhances energy dissipation and reduces the spread of damage relative to the basic bilayer configuration. The experiments show that the fracture in a given layer is well approximated by a power-law relation of the form c^3/2K_C/P = δ, where P, c, and K_C are the indentation load, crack length and fracture toughness, in that order, and δ an implicit function of the layer position and material and geometric variables, derived with the aid of available tunnel crack solutions.The model specimen studied provides a useful insight into the fracture behavior of natural, biological and synthetic layered structures from concentrated loading. The analysis shows that the crack arrest capability of a thin interlayer increases in proportion to the modulus misfit ratio between the layer and interlayer, and that the spread of radial cracks in a laminate of given thickness reduces in proportion to n^1/3, where n is the number layers in the laminate.     

Crack interaction study in piezoelectric materials under thermo-electro-mechanical loading environment

Multiple voids and cracks were generated during material processing techniques, which interact with each other and affects the service performance of piezoelectric components. This work aims to study the behavior of piezoelectric components in presence of multiple cracks under thermo-electro-mechanical loading environment. Extended finite element method has been implemented to model geometrical discontinuities with crack interaction phenomenon. In this work, thermo-electro- mechanical problem has been decoupled into thermal and electro-elastic problems. Temperature distribution has been obtained by solving heat conduction equation and then used as an input to the electro-elastic problem. In post processing phase, interaction integral method and generalized Stroh formalism were used to predict the stress intensity factors. The methodology has been implemented with in-house developed MATLAB code. Set of cases for crack interaction studies were presented using the proposed approach.

     

Crack extension under compressive loading

Non-planar extension (kinking) of a crack subjected to remote biaxial compression is studied to gain insight into compressive failure of brittle solids. Approximate expressions are developed for the stress intensity factors at the tips of the resulting wing cracks. Assuming the wing crack propagates at a constant value of $\text{K}{}_{\mathrm{Ic}}$, one can calculate wing crack extension vs load. The significance of the dependence on various parameters is discussed.     

Effective transverse conductivity of layered materials with through cracks in the layers

The problem of the transverse conductivity of a multilayered packet when loaded in the same plane as the layers, which are mechanically independent, in the presence of or on the generation of a number of through cracks in the layers under load is analyzed.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 30, No. 5, pp. 868–875, May, 1976.     

Disintegration of ice under fast compressive loading

During the interaction of ice with ships or other offshore structures, a compressive zone develops in the ice. This is the focus of the present work. An interpretation of field measurements shows that the compressive ice load is far from uniform; indeed, most of the load is transmitted through small areas of intense pressure characterized by a highly damaged layer. The processes leading to the formation of these zones include fractures, and in particular spalls near the edges of the zones, as well as a separate process of damage and microstructural change within the layer itself. In order to capture the essential points for deducing design requirements, we have formulated a probabilistic model of high-pressure zones. The mechanics of failure of ice in these zones is explored. Triaxial tests have been conducted. Mechanisms discussed include microcracking (shear banding), recrystallization and grain boundary melting. As pressures increase, the microcracking and recrystallization are suppressed and the strain rates decrease. At even higher pressures, the results show pressure softening with enhanced strain rates. Two state variables are used to model the ice deformation, corresponding to the hardening at lower pressures, and to the softening at higher pressures. Finite element analyses of the ice response incorporating these variables, corresponding to a medium scale indentation test have yielded promising results, showing the decline in load and the layer formation. This revised version was published online in July 2006 with corrections to the Cover Date.