Steady-State Crack Velocity in a Viscoelastic Composite Material

The velocity of a semi-infinite crack slowly propagating in aninfinitely long strip made of a viscoelastic composite material isdetermined according to Christensen's fracture criterion. The edges ofthe strip are subjected to uniform opposite displacements normal to thecrack plane. The crack velocity is obtained from an energy balanceequation involving the energy dissipated in the whole strip; the latteris evaluated using an approximate, but sufficiently accurate, expressionof the stress field in the structure obtained by taking into account thestrong anisotropy of the long fibre composite material of interest. Thisnew version of Christensen's criterion compares favourably with theoriginal one and gives crack velocity predictions very close to thoseprovided by Schapery's criterion.     

Plane crack propagation in a hyperelastic incompressible material

We propose a crack propagation criterion for hyperelastic materials (rubber type material) within the framework of plane elasticity in finite deformation. The criterion is based on the examination of the asymptotic elastic field near the crack tip prior to propagation. According to this criterion, the propagation will take place for a critical value of the strain energy density intensity factor. The kink angle, obtained by applying the criterion of maximum opening stress, will depend on the fracture tensile stress of the actual material. We propose to use a local iterative finite element method to compute the asymptotic quantities involved in the criterion at a reasonable cost. Examples of computation for some hyperelastic laws simulating the behavior of vulcanized rubber are presented.     

Toughening by partial or full bridging of cracks in ceramics and fiber reinforced composites

A complete solution is given for a fully or partially bridged straight crack in transversely isotropic elastic materials which may correspond to unidirectionally fiber-reinforced ceramics or other brittle composites. The stiffness of the bridging materials may have an arbitrary variation along the crack, representing partially failed fibers or ligaments. The crack may have any orientation with respect to the axis of the material symmetry. The solution is explicit in terms of the Chebychev polynomials when the bridging-forces are linearly dependent on the crack-opening-displacement. In addition, uniformly valid asymptotic solutions are developed for fully or partially bridging cracks. For the case when the crack is short relative to a length scale which depends on the material properties, the method yields a complete asymptotic solution when the bridging forces are linearly or non-linearly dependent on the crack-opening-displacement (a square-root dependence, corresponding to continuous fibers, is used for illustration). For the case of long cracks, the proposed asymptotic is effective, but the results are not presented in this work.The mechanism of crack kinking is studied for an oblique partially or fully bridged, or unbridged crack in a macroscopically transversely isotropic elastic solid. The crack is assumed to grow in the matrix material (containing unbroken strong fibers) under local driving forces which are calculated on the basis of the overall anisotropic material response. The results of various fracture criteria are studied. It is illustrated that, under far-field tensile forces normal to the crack, the criterion of the maximum opening mode stress intensity factor in the homogenized anisotropic solid (i.e., the orientation for which the strength of the singularity associated with the tensile hoop stress is maximum) produces results which suggest crack growth more or less parallel to the fibers, whereas the results based on the maximum Mode I stress intensity factor in the isotropic matrix material and/or on the local symmetry criterion (again, for the isotropic matrix) predict crack extension more or less normal to the reinforcing fibers.     

Creep-fatigue crack initiation in 316L stainless steel: Comparison between stress and strain calculation methods

The French A16 guide developed at CEA Saclay proposes a methodology to estimate the stress and strain in the vicinity of the crack tip and a criterion to assess crack initiation by using these local parameters. A worked example for a CT specimen is developed and the results are compared with finite element analysis. Both calculation methods have their specific material behaviour models. In this text, the finite element constitutive model is presented. The material coefficients needed for the A16 guide are then determined by means of numerical simulation on smooth specimens.     

Local approach to fracture for cleavage crack arrest prediction

Crack arrest can complement the crack initiation concept to assess integrity of structures. This paper deals with the application of a local approach model derived from the RKR model to predict cleavage crack propagation and arrest in thermal shock experiments performed on pre-cracked discs made of a low alloy bainitic steel. The numerical procedure takes into account dynamic effects and an accurate behavior law for the material. Simulations with a crack speed criterion help the identification of the critical stress criterion. The results show a good prediction of the crack jump when a 3D modeling is used.     

Asymptotic stress field in a cracked orthotropic strip

Christensen's theory of viscoelastic fracture allows the crack propagation velocity to be determined in terms of dissipation whose calculation requires the knowledge of the stress field in the vicinity of the crack tip: the simplest configuration leading to a constant velocity is that of a straight semi-infinite crack contained in an infinitely long strip whose clamped edges are displaced normal to the crack; although experimental data pertaining to this problem have been obtained for a number of materials, no analytical solution is available. When the material is highly anisotropic, an asymptotic solution involving a small parameter related to the ratio of shear modulus to the larger Young's modulus can be attempted. As the corresponding perturbation problem is singular, a matched asymptotic expansion has to be used: it is the sum of outer and inner approximations; both of these are solutions to simple boundary-value problems which can be solved in closed form. The so-constructed asymptotic solution is shown to agree with finite element results, even when the small parameter is as large as 0.2.     

A three-dimensional meshfree method for continuous multiple-crack initiation,propagation and junction in statics and dynamics

This paper proposes a three-dimensional meshfree method for arbitrary crack initiation and propagation that ensures crack path continuity for non-linear material models and cohesive laws. The method is based on a local partition of unity. An extrinsic enrichment of the meshfree shape functions is used with discontinuous and near-front branch functions to close the crack front and improve accuracy. The crack is hereby modeled as a jump in the displacement field. The initiation and propagation of a crack is determined by the loss of hyperbolicity or the loss of material stability criterion. The method is applied to several static, quasi-static and dynamic crack problems. The numerical results very precisely replicate available experimental and analytical results.     

The scattering of harmonic elastic anti-plane shear waves by a Griffith crack in a piezoelectric material plane by using the non-local theory

In this paper, the dynamic behavior of a Griffith crack in a piezoelectric material plane under anti-plane shear waves is investigated by using the non-local theory for impermeable crack face conditions. For overcoming the mathematical difficulties, a one-dimensional non-local kernel is used instead of a two-dimensional one for the anti-plane dynamic problem to obtain the stress and the electric displacement near the crack tips. By using the Fourier transform, the problem can be solved with the help of two pairs of dual integral equations. These equations are solved using the Schmidt method. Contrary to the classical elasticity solution, it is found that no stress and electric displacement singularity is present near the crack tip. The non-local dynamic elastic solutions yield a finite hoop stress near the crack tip, thus allowing for a fracture criterion based on the maximum dynamic stress hypothesis. The finite hoop stress at the crack tip depends on the crack length, the circular frequency of incident wave and the lattice parameter. For comparison results between the non-local theory and the local theory for this problem, the same problem in the piezoelectric materials is also solved by using local theory.     

冲击压缩下准脆性材料含微裂纹损伤的本构模型

基于准脆性材料中翼型拉伸裂纹的成核准则,运用细观损伤理论推导了翼型裂纹损伤对材料弹性模量的弱化作用.考虑裂纹扩展对材料动态断裂的滞后效应,建立了动态裂纹扩展准则,并给出损伤演化方程,在此基础上建立了准脆性材料单轴冲击压缩下的动态损伤本构模型.结合氧化铝陶瓷材料独特的力学响应和破坏特性,讨论了模型中微裂纹成核参数、微裂纹尺寸对动态断裂强度的影响,并用该模型计算了单轴压缩下氧化铝陶瓷的应力应变曲线,数值结果与实验结果吻合良好.     

Displacement control crack-growth instability in an elastic-softening material

The criterion for crack growth instability in an elastic-softening material that is subjected to displacement control loading conditions is examined. A theoretical analysis of the model of a solid containing two symmetrically situated deep cracks and with tensile loading of the remaining ligament, defines the criterion for crack growth instability. The criterion is expressed in terms of the material's softening characteristics and the solid's geometrical parameters. The analysis covers the complete spectrum of material behaviour from the case where the softening zone is very small to the case where instability does not occur until the softening zone traverses the ligament between the crack tips.     

Crack path tracking from full field measurements: A novel empirical methodology

The identification of crack growth models requires the knowledge of the crack path geometry and, in particular, of the crack tip position. The objective of the present paper is to provide a criterion for the detection of the crack tip position regardless of the loading conditions or the material behavior. The novelty of the proposed approach is its ability to provide a good estimation of the crack tip even when large plastic deformations occur. The proposed empirical criterion uses the evolution of the displacement gradient standard deviation along a potential crack path to locate the crack tip. It thus relies on full field measures that are relatively smooth while providing accurate displacement vectors even close to the lips. We successfully apply the proposed criterion in two cases of fatigue crack growth: A straight crack at high temperature and a curved crack at room temperature involving large plastic deformations.     

Finite element modelling of multiple cohesive discrete crack propagation in reinforced concrete beams

This paper presents a finite element (FE) model for fully automatic simulation of multiple discrete crack propagation in reinforced concrete (RC) beams. The discrete cracks are modelled based on the cohesive/fictitious crack concept using nonlinear interface elements with a bilinear tensile softening constitutive law. The model comprises an energy-based crack propagation criterion, a simple remeshing procedure to accommodate crack propagations, two state variable mapping methods to transfer structural responses from one FE mesh to another, and a local arc-length algorithm to solve system equations characterised by material softening. The bond-slip behaviour between reinforcing bars and surrounding concrete is modelled by a tension-softening element. An example RC beam with well-documented test data is simulated. The model is found capable of automatically modelling multiple crack propagation. The predicted cracking process and distributed crack pattern are in close agreement with experimental observations. The load-deflection relations are accurately predicted up to a point when compressive cracking becomes dominant. The effects of bond-slip modelling and the efficiency and effectiveness of the numerical algorithms, together with the limitations of the current model, are also discussed.     

Ultimate plasticity—the universal local fracture criterion for lifetime prediction of welded structures

A method is presented of the modeling of material fatigue destruction on the basis of a ductile fracture criterion—ultimate plasticity as a function of stress 3-axity. The criterion enables one both to determine the number of cycles until the fatigue crack initiation from the stress concentrator and to predict the character of its growth. The condition of reliability of results is high accuracy of finite element modeling with geometric and physical nonlinearity taken into account. The criterion is applicable for stress concentrators of different sharpness. The local character of the criterion makes it suitable for inhomogeneous material properties, as well as for thermally loaded structures.     

Correction to the Crack Extension Direction in Numerical Modelling of Mixed Mode Crack Paths

In order to avoid introduction of an error when a local crack growth criterion is used in an incremental crack growth formulation, each straight crack extension would have to be infinitesimal or have its direction corrected. In this paper a new procedure to correct the crack extension direction is proposed in connection with crack growth analyzed by the Dual Boundary Element Method (DBEM). The proposed correction procedure and a reference correction procedure already described in the literature are evaluated by solving two different computational crack growth examples. In the two examples it is found that analyses of the crack paths performed with the proposed crack correction procedure using big increments of crack extension are in excellent agreement with analyses of the crack paths performed by using very small increments of crack extension. Furthermore, it is shown that the reference correction procedure has a tendency to overcorrect the crack growth direction if the stop criterion for the iterative correction procedure is not calibrated in each new crack growth analysis.     

Random trajectories of crack growth caused by spatial stress fluctuations

The results of 2D computer simulations of crack trajectories in an elastic material under a superposition of external uniaxial or biaxial tension and spatially random stress fluctuations are presented. The initial crack is straight. The criterion of maximum tensile stress near the crack tip is used to determine the crack trajectory. It is assumed that crack propagates in linear segments, step by step from either left or right tip depending on where the local circumferential stress is higher. Each segment is subjected to randomly-generated uniform tractions whose values are normally distributed with zero mean, independent of loads on previous segments. It is shown that the deflection of the actual crack paths from the trend increases with the crack length; its standard deviation grows stronger than predicted by the `random walk' model.     

Random trajectories of crack growth caused by spatial stress fluctuations

The results of 2D computer simulations of crack trajectories in an elastic material under a superposition of external uniaxial or biaxial tension and spatially random stress fluctuations are presented. The initial crack is straight. The criterion of maximum tensile stress near the crack tip is used to determine the crack trajectory. It is assumed that crack propagates in linear segments, step by step from either left or right tip depending on where the local circumferential stress is higher. Each segment is subjected to randomly-generated uniform tractions whose values are normally distributed with zero mean, independent of loads on previous segments. It is shown that the deflection of the actual crack paths from the trend increases with the crack length; its standard deviation grows stronger than predicted by the `random walk' model.     

A criterion for low-stress brittle fracture of notched specimens based on combined micro- and macro fracture mechanics—1

Based on the combined micro- and macro fracture mechanics, the two requisites necessary for the crack propagation, that is, the energy unstable requisite and the critical local stress requisite, are derived for the low-stress brittle fracture of notched specimens. Thus the fracture criterion was obtained. The criterion is compared with the experimental data, such as on the relationships between the fracture stress or the fracture toughness and the grain size diameter, the crack length, the notch tip radius or the yield stress. The good agreement is obtained.     

Numerical simulations of dynamic crack growth along an interface

Dynamic crack growth is analyzed numerically for a plane strain bimaterial block with an initial central crack. The material on each side of the bond line is characterized by an isotropic hyperelastic constitutive relation. A cohesive surface constitutive relation is also specified that relates the tractions and displacement jumps across the bond line and that allows for the creation of new free surface. The resistance to crack initiation and the crack speed history are predicted without invoking any ad hoc failure criterion. Full finite strain transient analyses are carried out, with two types of loading considered; tensile loading on one side of the specimen and crack face loading. The crack speed history and the evolution of the crack tip stress state are investigated for parameters characterizing a PMMA/Al bimaterial. Additionally, the separate effects of elastic modulus mismatch and elastic wave speed mismatch on interface crack growth are explored for various PMMA-artificial material combinations. The mode mixity of the near tip fields is found to increase with increasing crack speed and in some cases large scale contact occurs in the vicinity of the crack tip. Crack speeds that exceed the smaller of the two Rayleigh wave speeds are also found.     

倾斜应力作用下垂直于功能梯度材料夹层的币型裂纹扩展问题

分析了功能梯度材料中币型裂纹扩展问题。该裂纹体受有与裂纹面成任意角度的张应力或压应力,裂纹垂直于无限域中功能梯度材料夹层。假定非均匀介质的功能梯度材料夹层与两个半无限域完全结合,其弹性模量沿厚度方向变化。利用已发表的裂纹应力强度因子数据和线弹性断裂力学的叠加原理,将应力强度因子耦合于最小应变能密度因子断裂判据,讨论了裂纹扩展的临界荷载;并讨论了荷载方向和材料性质对临界荷载的影响。     

How cracks propagate in a vitreous dense biopolymer material

Crack propagation in vitreous biopolymer material is studied considering numerical and experimental aspects. Finite Element computation is performed to predict crack propagation in starch material. Maximum dilatational strain energy criterion is used as a criterion for crack propagation. Model validation is undertaken considering notched specimens with a hole under tensile loading. The experimental results show that the crack path is affected by the presence of the defect, which allows adequate testing of the crack propagation criterion under a mixed mode. The predicted results show that the selected criterion anticipates adequately the crack propagation in vitreous starch under linear elastic conditions.