A new M-integral parameter for mixed-mode crack growth in orthotropic viscoelastic material

This paper deals with a new independent path integral which provides the mixed-mode during a creep crack growth process in viscoelastic orthotropic media. The developments are based on an energetic approach using conservative laws. The mixed-mode fracture separation is introduced according to the generalization of the virtual work principle. The fracture algorithm is implemented in a finite element software and coupled with an incremental viscoelastic formulation and an automatic crack growth simulation. This M-integral provides the computation of stress intensity factors and energy release rate for each fracture mode. A numerical validation, in terms of energy release rate and stress intensity factors, is carried out on a CTS specimen under mixed-mode loading for different crack growth speeds.     

A Finite Element Analysis of Creep-Crack Growth in Viscoelastic Media

In this paper, the effects of viscoelastic characteristics, on the creep-crack growth process are studied through a finite element approach. The general approach of an independent path integral is extended to crack propagation. Afterwards, fracture parameters are computed through a coupling process with an incremental viscoelastic formulation. Finally, numerical examples are presented in order to demonstrate the independence of the integration domain and the possibility of evaluating fracture characteristics which can be energetic (energy release rate) and local in the vicinity of the crack tip (stress and crack opening intensity factors).     

A nonlinear viscoelastic fracture analysis of concrete/FRP delamination in aggressive environments

In this paper, the durability of the bondline between concrete and FRP reinforcement was characterized at various temperature and humidity levels. The linear and nonlinear viscoelastic constitutive behavior of the epoxy bondline was characterized and used for a nonlinear viscoelastic fracture analysis of delamination. A hygrothermal nonlinear viscoelastic pseudo-stress model was developed and calibrated in order to compute a generalized J integral. Driven wedge tests were conducted for examining the fracture behavior of the interface. A finite element analysis was developed for determining the cohesive zone size and the generalized J integral at various temperature and humidity levels. The fracture energy obtained from these parameters greatly depended upon crack growth rate, temperature and humidity.     

The effect of facesheet/core delamination in sandwich structures under transverse loading

The present work is concerned with the problem of a delamination crack along the facesheet/core interface of a sandwich structure which is submitted to transverse loading. In contrast to a loading by compressive inplane forces or a bending loading the presumed transverse loading does not lead to buckling of the delaminated facesheet but it may provoke further delamination crack growth. As a kind of crack driving force the energy release rate is studied for a virtual crack growth by means of Irwin's crack closure integral within a finite element modelling. The resultant energy release rate is dependent on various geometrical and material parameters which is investigated in some detail.     

Non-Local Theory Solution for an Anti-Plane Shear Permeable Crack in Functionally Graded Piezoelectric Materials

In this paper, the non-local theory solution of a Griffith crack in functionally graded piezoelectric materials under the anti-plane shear loading is obtained for the permeable electric boundary conditions, in which the material properties vary exponentially with coordinate parallel to the crack. The present problem can be solved by using the Fourier transform and the technique of dual integral equation, in which the unknown variable is the jump of displacement across the crack surfaces, not the dislocation density function. To solve the dual integral equations, the jump of the displacement across the crack surfaces is directly expanded in a series of Jacobi polynomials. From the solution of the present paper, it is found that no stress and electric displacement singularities are present near the crack tips. The stress fields are finite near the crack tips, thus allows us to use the maximum stress as a fracture criterion. The finite stresses and the electric displacements at the crack tips depend on the crack length, the functionally graded parameter and the lattice parameter of the materials, respectively. On the other hand, the angular variations of the strain energy density function are examined to associate their stationary value with locations of possible fracture initiation.     

Dynamic crack propagation analysis of orthotropic media by the extended finite element method

Dynamic crack propagation of composites is investigated in this paper based on the recent advances and development of orthotropic enrichment functions within the framework of partition of unity and the extended finite element method (XFEM). The method allows for analysis of the whole crack propagation pattern on an unaltered finite element mesh, defined independent of the existence of any predefined crack or its propagation path. A relatively simple, though efficient formulation is implemented, which consists of using a dynamic crack initiation toughness, a crack orientation along the maximum circumferential stress, and a simple equation to presume the crack speed. Dynamic stress intensity factors (DSIFs) are evaluated by means of the domain separation integral method. The governing elastodynamics equation is first transformed into a standard weak formulation and is then discretized into an XFEM system of time dependent equations, to be solved by the unconditionally stable Newmark time integration scheme. A number of benchmark and test problems are simulated and the results are compared with available reference results.     

Simulation of crack growth in composite material shell structures

This paper implements a domain integral energy method for modelling crack growth in composite material shell structures using the finite element method. Volume integral expressions to evaluate the dynamic energy release rate in a through‐thickness three‐dimensional crack are derived. Using the domain integral, the energy release rate computation is implemented in the DYNA3D explicit non‐linear dynamic finite element analysis program wherein crack propagation is modelled by releasing the constraints between initially constrained node pairs. The implementation enables the program to either determine the energy resistance response for the material (provided experimental data is available) or predict the rate of crack propagation in shell structures. The numerical implementation was verified by simulating mode I and mode III slow crack growth problems in semi‐infinite transversely isotropic media, for which analytic solutions are available. Oscillations of energy following the release of nodal constraints as the crack propagates in discrete increments were suppressed using light mass proportional damping and a moving averaging scheme. Copyright © 2004 John Wiley & Sons, Ltd.     

A New Incremental Formulation in the Time Domain for Crack Initiation in an Orthotropic Linearly Viscoelastic Solid

The problem of predicting the crack growth initiation in a linearlyviscoelastic material is investigated. A new incremental fractureequations relating viscoelastic stress intensity factors (VSIFs) toviscoelastic opening displacement intensity factors (VODIFs) areestablished. Crack growth initiation is studied in detail by means of acomputational approach based on a modified path independent integral. Itis found that the mechanical and kinematical fields around the crack tipcan be determined using an incremental formulation based on a discretespectrum representation of the viscoelastic compliance functions; thusthe difficulty of computer storage requirements is avoided. Numericalresults are obtained for predicting the time at which propagationinitiates and these are compared with the analytical solution.     

Influence of residual stresses on stable crack growth

Abstract

The influence of residual stresses resulting from thermal shock and pressure loading on the initiation and stable growth of cracks in pressure vessels and pipes is considered and preliminary calculations have been made. The residual stresses of a precracked vessel of a 0·22Cr–0·75Ni–0·7Mo–Cr steel at an arbitrarily chosen temperature transient have been analysed using the finite element method. After reheating to normal operating temperature, the influence of the remaining residual stresses on the initiation of the assumed crack is considered. The results provide the initial conditions for stable crack growth analysis based on the J–integral method, which is implemented into the non–linear finite element program ADINA.

MST/27     

Interfacial crack propagation in a thin viscoelastic film bonded to an elastic substrate

Edge decohesion along the interface of a thin viscoelastic film bonded to an elastic substrate under tensile residual stresses is considered. The tensile residual stress in the film is replaced by a combination of edge loads, and an explicit relation of strain energy with respect to time is obtained through simple beam analysis. The strain energy function is discretized into time steps which are assumed to be very small so that the dissipation effects over the time steps can be neglected. The energy release rate is then calculated using a Griffith type energy balance. An analytical model is developed to predict the crack growth and its velocity. Extent of crack growth along the interface is prediced based on a fracture criteria. The analytical predictions are compared with results from a viscoelastic finite element analysis.     

Viscoelastic crack growth process in wood timbers: An approach by the finite element method for mode I fracture

In this paper the effects of viscoelastic characteristics in wood timbers, on the creep crack growth process are studied through a new finite element approach in the time domain. In order to take into account the linear viscoelastic orthotropic behavior, we present an incremental formulation based on a rheological representation of creep tensor components. By using a relationship between stress and crack opening intensity factors, the general approach of path independent integrals is extended in order to calculate energy release rate and local fracture characteristics. Afterwards, fracture parameters are computed through a coupling process with the incremental viscoelastic behavior. The numerical algorithm is presented and validated through numerical as well as experimental examples.     

On The Use Of Vector J-Integral In Crack Growth Criteria For Brittle Solids

In this paper the criterion for crack-growth in solids is investigated on the basis of the concept of potential energy release rate. The expressions for path-independent vector integral J_i (i = 1,2) are derived for brittle crack growth. The relationship is then established between the value of the path-independent vector integral J_i and the potential energy release rate for crack growth in an arbitrary orientation. This allows the prediction of crack re-orientation angles on the basis of the maximum energy release rate (MERR) criterion. The crack growth angle is determined analytically as a function of (). This result is compared with other theoretical formulations of crack growth criteria, as well as with experimental results reported in the literature, and good agreement is found. The formulation provides a rigorous basis for numerical modelling of the processes of crack initiation and propagation.     

A viscoelastic Unitary Crack-Opening strain tensor for crack width assessment in fractured concrete structures

A post-processing technique which allows computing crack width in concrete is proposed for a viscoelastic damage model. Concrete creep is modeled by means of a Kelvin–Voight cell while the damage model is that of Mazars in its local form. Due to the local damage approach, the constitutive model is regularized with respect to finite element mesh to avoid mesh dependency in the computed solution (regularization is based on fracture energy).The presented method is an extension to viscoelasticity of the approach proposed by Matallah et al. (Int. J. Numer. Anal. Methods Geomech. 34(15):1615–1633, 2010) for a purely elastic damage model. The viscoelastic Unitary Crack-Opening (UCO) strain tensor is computed accounting for evolution with time of surplus of stress related to damage; this stress is obtained from decomposition of the effective stress tensor. From UCO the normal crack width is then derived accounting for finite element characteristic length in the direction orthogonal to crack. This extension is quite natural and allows for accounting of creep impact on opening/closing of cracks in time dependent problems. A graphical interpretation of the viscoelastic UCO using Mohr’s circles is proposed and application cases together with a theoretical validation are presented to show physical consistency of computed viscoelastic UCO.     

A micromechanical model for a viscoelastic cohesive zone

A micromechanical model for a viscoelastic cohesive zone is formulated herein. Care has been taken in the construction of a physically-based continuum mechanics model of the damaged region ahead of the crack tip. The homogenization of the cohesive forces encountered in this region results in a damage dependent traction-displacement law which is both single integral and internal variable-type. An incrementalized form of this traction-displacement law has been integrated numerically and placed within an implicit finite element program designed to predict crack propagation in viscoelastic media. This research concludes with several example problems on the response of this model for various displacement boundary conditions.     

A proposed mixed-mode fracture specimen for wood under creep loadings

A mixed-mode fracture specimen was designed in this paper. This geometry is a judicious compromise between a modified Double Cantilever Beam specimen and Compact Tension Shear specimens. The main objective is to propose a specimen which traduces a stable crack growth during creep loading taking into account viscoelastic behaviour under mixed-mode loadings. The numerical design is based on the instantaneous response traduced by a crack growth stability zone. This zone is characterized by a decrease of the instantaneous energy release rate versus the crack length. In order to obtain a mixed-mode separation, the paper deals with the use of the M-integral approach implemented in finite element software, according to energetic fracture criterions. In these considerations, a numerical geometric optimization is operated for different mixed-mode ratios. Finally, a common specimen which provides to obtain fracture parameters, viscoelastic properties and creep crack growth process for different mixed-mode configurations is proposed.     

A virtual crack closure-integral method (VCCM) to compute the energy release rates and stress intensity factors based on quadratic tetrahedral finite elements

This paper proposes a new virtual crack closure-integral method (VCCM) for quadratic tetrahedral finite element to compute the energy release rates/stress intensity factors. The formulations, numerical implementations and some numerical results of proposed VCCM are presented in this paper. Proposed VCCM enables us to adopt the tetrahedral finite element in 3D crack problems and us to use automatic mesh generation programs. Therefore process time to perform 3D crack analysis drastically reduces compared with the case of hexahedral elements.     

Fatigue crack initiation and propagation under cyclic contact loading

A computational model for contact fatigue damage analysis of gear teeth flanks is presented in this paper. The model considers the conditions required for the surface fatigue crack initiation and then allows for proper simulation of the fatigue crack propagation that leads to the appearance of small pits on the contact surface. The fatigue process leading to pitting is divided into crack initiation and a crack propagation period.The model for prediction of identification of critical material areas and the number of loading cycles, required for the initial fatigue crack to appear, is based on Coffin-Manson relations between deformations and loading cycles, and comprises characteristic material fatigue parameters. The computational approach is based on continuum mechanics, where a homogenous and elastic material model is assumed and results of cyclic loading conditions are obtained using the finite element method analysis.The short crack theory together with the finite element method is then used for simulation of the fatigue crack growth. The virtual crack extension (VCE) method, implemented in the finite element method, is used for simulating the fatigue crack growth from the initial crack up to the formation of the surface pit. The relationship between the stress intensity factor K and crack length a, which is needed for determination of the required number of loading cycles N_p for a crack propagation from the initial to the critical length, is shown.     

梯度复合材料裂纹扩展路径和起裂载荷的有限元分析

为了模拟功能梯度材料(FGM)在工程应用中可能会出现的断裂问题并计算相应的开裂载荷,通过编写用户自定义UEL子程序将梯度扩展单元嵌入到ABAQUS软件中模拟功能梯度材料的物理场,并编写交互能量积分后处理子程序计算裂纹尖端的混合模式应力强度因子(SIF),采用最大周向应力准则编写子程序计算裂纹的偏转角,并模拟了裂纹扩展路径,计算了裂纹的起裂载荷。讨论了材料梯度参数对裂纹扩展路径以及起裂载荷的影响规律。通过与均匀材料的对比,验证了功能梯度材料断裂性能的优越性。研究表明:外载平行于梯度方向时,垂直梯度方向的初始裂纹朝着等效弹性模量小的方向扩展,且偏转角在梯度指数线性时出现峰值,并随着组分弹性模量比的增加而变大;当外载和初始裂纹均平行于梯度方向时,材料等效弹性模量和断裂韧性的增加或者梯度指数的减小都导致起裂载荷变大。     

Fracture analyses and experimental results of crack growth under general mixed mode loading conditions

In this paper detailed results of 3D finite element (FE) and mixed mode analyses of different fracture specimens are presented and discussed. Special interest is taken in 3D and mode coupling effects to be found in strain energy release rate (SERR) results along crack fronts, in particular adjacent to corners, where a crack front intersects a free surface of a specimen. It will be shown that these effects stay small if they are related to Poisson’s ratio but that they can also be considerably pronounced if they are related to the global deformation behaviour of the specimen. The computational fracture analysis is based on the calculation of separated energy release rates (SERRs) by the aid of the modified virtual crack closure integral (MVCCI)-method in order to calculate the local SERR-distributions along the crack front. Furthermore some qualitative experimental results will show the influence of these variable mixed mode I, II and III loading conditions along the crack front on crack initiation and on the further development of 3D crack growth in the specimens.