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1.
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. 相似文献
2.
Taking into account the marked anisotropic character of carbon fibre composite materials, a small parameter related to material properties is introduced. The stress field in a semi-infinite strip with a semi-infinite crack whose tip is close to the strip free end is investigated through a singular perturbation method. For slow crack propagation, the quasi-static character of the stress field is established. An accurate asymptotic solution is derived, which allows the interaction between the strip free end and the stress field around the crack tip to be studied. For the carbon–epoxy material investigated, this interaction becomes negligible when the distance between the crack tip and the strip free end is greater than 1.5h, where h is the strip half-height. 相似文献
3.
H. K. Mueller 《International Journal of Fracture》1971,7(2):129-141
The stress-intensity factor and the size of the crack opening have been calculated for a linearly viscoelastic strip with a slowly propagating central crack. The edges of the infinitely long strip are displaced normal to the crack and both clamped and shear-free strip edges have been investigated. The results are based on the solution to the problem of a suddenly loaded strip with a stationary crack. The resulting integral equation has been solved numerically for arbitrary crack length and analytical solutions in form of asymptotic series are given for crack length up to about half the strip width. The response to a propagating crack is found by superposition.This work represents part of a Ph.D. Thesis submitted to the California Institute of Technology. The author gratefully acknowledges the support of this work by the National Aeronautics and Space Administration under Research Grant NGL-05-002-005, GALCIT 120. 相似文献
4.
Deformations such as crack opening and sliding displacements in a cracked viscoelastic body are numerically investigated by the extended finite element method (XFEM). The solution is carried out directly in time domain with a mesh not conforming to the crack geometry. The generalized Heaviside function is used to reflect the displacement discontinuity across a crack surface while the basis functions extracted from the viscoelastic asymptotic fields are used to manifest the gradient singularity at a crack tip. With these treatments, the XFEM formulations are derived in an incremental form. In evaluating the stiffness matrix, a selective integration scheme is suggested for problems with high Poisson ratios often encountered in viscoelastic materials over different element types in the XFEM. Numerical examples show that the crack opening displacement and crack sliding displacement are satisfactory. 相似文献
5.
提出了一种用于解决线粘弹性断裂问题的增量加料有限元法。为了反映裂纹尖端的应力奇异性,在裂尖附近的应力奇异区采用若干四边形加料单元和过渡单元,非奇异区采用常规四边形单元,三种单元分区混合使用形成求解域网格划分。加料单元通过引入裂尖渐近位移场,构造出可以较好反映裂尖奇异性的单元位移模式,过渡单元在加料单元基础上引入调整函数构造单元位移模式,用于连接加料单元和常规单元,以消除加料单元和常规单元间位移不协调。基于Boltzmann叠加原理,推导了粘弹性材料的增量型本构关系,进而获得了增量加料有限元列式,并基于节点位移外推法计算粘弹性介质中裂纹应变能释放率。数值算例验证了该文方法的正确性和有效性。 相似文献
6.
R. A. Schapery 《International Journal of Fracture》1975,11(3):369-388
Starting with equations developed in Part I for the opening mode of displacement, simple, approximate relations are derived for predicting the time of fracture initiation and crack tip velocity in linearly viscoelastic media. First we use the assumption that the second derivative of the logarithm of creep compliance with respect to logarithm of time is small (which is normally valid for viscoelastic materials); we next derive a relation between instantaneous values of tip velocity and stress intensity factor. This result is then used to examine some characteristics of crack growth behavior. Finally, some results are obtained for the separate problem of predicting the time at which propagation initiates. 相似文献
7.
With the view of comparing local and global viscoelastic fracture criteria, an extension of Christensen's criterion to composite materials with stiff elastic fibers is proposed. Several versions of this criterion are compared with Schapery's local approach of the same phenomenon. The asymptotic version of Christensen's criterion for rapid crack propagation is found suitable for the material investigated, at room temperature. Dissipation in the specimen has two main sources: the undamaged material on one hand, and the damaged material inside the `failure zone' close to the crack tip on the other. The respective roles of these two kinds of dissipation are assessed. 相似文献
8.
E. Béchet M. Scherzer M. Kuna 《International journal for numerical methods in engineering》2009,77(11):1535-1565
This paper presents an application of the extended finite element method (X‐FEM) to the analysis of fracture in piezoelectric materials. These materials are increasingly used in actuators and sensors. New applications can be found as constituents of smart composites for adaptive electromechanical structures. Under in service loading, phenomena of crack initiation and propagation may occur due to high electromechanical field concentrations. In the past few years, the X‐FEM has been applied mostly to model cracks in structural materials. The present paper focuses at first on the definition of new enrichment functions suitable for cracks in piezoelectric structures. At second, generalized domain integrals are used for the determination of crack tip parameters. The approach is based on specific asymptotic crack tip solutions, derived for piezoelectric materials. We present convergence results in the energy norm and for the stress intensity factors, in various settings. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
9.
10.
This paper presents a finite element study of cohesive crack growth in a thin infinite viscoelastic strip to investigate the
effects of viscoelastic properties, strip height, and cohesive model parameters on the crack growth resistance. The results
of the study show that the dependence of the fracture energy on the viscoelastic properties for the strip problem is similar
to that obtained for the infinite body problem even when the cohesive zone length is large compared to the height of the strip.
The fracture energy also depends on the crack speed v through the dimensionless parameter v
τ/L
∞ where L
∞ is the characteristic length of the cohesive zone and τ is the characteristic relaxation time of the bulk material. This relationship confirms that at least two properties of the
fracture process must be prescribed accurately to model viscoelastic crack growth. In contrast, the fracture energy and crack
speed are insensitive to the strip height even in situations where the growth of the dissipation zone is severely constrained
by the strip boundaries. We observe that at high speeds, where the fracture energy asymptotically approaches the maximum value,
the material surrounding the cohesive zone is in the rubbery (equilibrium) state and not the glassy state. 相似文献
11.
Xiaohong Chen 《International Journal of Fracture》2007,148(1):47-55
A coupled hygro-thermo-viscoelastic fracture theory is developed for quasi-static and dynamic crack propagation in viscoelastic
materials subject to combined mechanical loading and hygrothermal environmental exposure based on fundamental principles of
thermodynamics. The Helmholtz free energy is taken to be a functional of the histories of strain, temperature and fluid concentration
with the crack parameter being introduced as an internal state variable. A thermodynamically consistent time-dependent fracture
criterion for crack propagation in the presence of thermally and mechanically assisted fluid transport is obtained from the
global energy balance equation and the requirement of non-negativity of the global energy dissipation rate, which is generally
applicable to both quasi-static and dynamic loading and both isothermal/isohumidity and non-isothermal/non-isohumidity conditions
with classic fracture criteria as special cases. On the basis of the developed theory, the generalized energy release rate
method, the generalized contour integral method and the extended essential work of fracture method are proposed for fracture
characterization of load-carrying viscoelastic materials in hygrothermal environments, and the interrelation of these methods
and their correlation with conventional methods and existing models, simulations and experiments are discussed. 相似文献
12.
Experimental analysis of viscoelastic criteria for crack initiation and growth in polymers 总被引:1,自引:0,他引:1
Different viscoelastic theories have been applied to characterize the resistance to crack initiation and propagation in the fracture of two poly-diethyleneglicol-bis-allyl-carbonate grades that have different crosslinking densities.Tensile creep compliance curves have been obtained on unnotched specimens, and fracture tests have been conducted on single edge notched specimens loaded in tension at different temperatures and displacement rates.A theory developed by Schapery for linearly viscoelastic materials has been found to be fairly adequate to describe the experimental results obtained, provided that the hypothesis of the yield stress being constant with time is removed. The time-temperature equivalence has also been found to satisfactorily account for the temperature dependence of the fracture resistance at initiation; however, the same did not hold as good for propagation. A simple scheme to analyse fracture data obtained from viscoelastic materials is also proposed. 相似文献
13.
The principle of the conservation of energy is used to derive a solution for the velocity of crack growth in viscoelastic materials. This work generalizes earlier work by the same method that yielded only asymptotic solutions for crack velocity. 相似文献
14.
K. Sakaue Y. Uchiyama H. Tanaka S. Yoneyama M. Takashi 《Engineering Fracture Mechanics》2008,75(14):4140-4150
The crack tip strain and stress fields in a viscoelastic material under nonproportional loading conditions are evaluated. In order to evaluate the strain field, the crack tip displacement field is measured by using the digital image correlation (DIC) technique. This displacement field is then approximated by using the theoretically obtained crack tip displacement field in viscoelastic materials. The result shows that the approximation method can smoothly reconstruct the experimentally obtained displacement field. From the approximated displacement field, the crack tip strain field can be precisely obtained by using the differential form of the theoretical displacement. On the other hand, the crack tip stress field is analyzed by using the stress function. This suggests that the strain and stress fields can be independently evaluated. In addition, different time dependencies between stress and strain fields near the crack tip are observed. Based on this experiment, we can discuss the several criteria for the crack propagation directions in viscoelastic materials. 相似文献
15.
Matías Braun Vicente Francisco Gonzlez Albuixech 《Fatigue & Fracture of Engineering Materials & Structures》2019,42(5):1075-1084
In this work, the influence of crack propagation velocity in the stress intensity factor has been studied. The analysis is performed with a lattice method and a linear elastic constitutive model. Numerous researchers determined the relationship between the dynamic stress intensity factor and crack propagation velocity with experimental and analytical results. They showed that toughness increases asymptotically when the crack tip velocity is near to a critical. However, these methods are very complex and computationally expensive; furthermore, the model requires the use of several parameters that are not easily obtained. Moreover, its practical implementation is not always feasible. Hence, it is usually omitted. This paper aims to capture the physics of this complex problem with a simple fracture criterion. The selected criterion is based on the maximum principal strain implemented in a lattice model. The method used to calculate the stress intensity factor is validated with other numerical methods. The selected example is a finite 2D notched under mode I fracture and different loads rates. Results show that the proposed model captures the asymptotic behaviour of the SIF in function of crack speed, as reported in the aforementioned models. 相似文献
16.
《Computational Materials Science》2011,50(1):83-91
In the case of a brittle viscoelastic medium, the existence of a viscous dissipation affects the propagation of cracks. The paper first revisits the thermodynamic framework of Griffith’s theory extended to viscoelastic media. A criterion for propagation is derived in the form of a threshold for the driving force of the phenomenon. Analytical and numerical implementations are presented. The driving force of propagation and the evolution of the crack length are found to be very sensitive to the loading rate. 相似文献
17.
A discrete two-dimensional square-cell lattice with a steady propagating crack is considered. The lattice particles are connected
by massless bonds, which obey a piecewise-linear double- humped stress–strain relation. Initially, Hooke’s law is valid as
the first stable branch of the force–elongation diagram; then, as the elongation becomes critical, the transition to the other
branch occurs. Further, when the strain reaches the next critical value, the bond breaks. This transition is assumed to occur
only in a line of the breaking bonds; the bonds outside the crack line are assumed to be in the initial branch all the time.
The formulation relates to the crack propagation with a ‘damage zone’ in front of the crack. An analytical solution is presented
that allows to determine the crack speed as a function of the far-field energy release rate, to find the total speed-dependent
dissipation, and to estimate the role of the damage zone. The analytical formulation and the solution present a development
of the previous ones for the crack and localized phase transition dynamics in linear and bistable-bond lattices. 相似文献
18.
Prof. L. M. Brock 《Acta Mechanica》1995,112(1-4):95-106
Summary The displacement-controlled rapid tearing of a thermoelastic strip is modeled as steady-state propagation of a quasi-brittle crack. The strip satisfies the fully-coupled equations of thermoelasticity, and the small-scale plastic effects are represented by a Dugdale inelastic zone which also serves as a heat flux source. An asymptotic analysis gives expressions for the zone length, COD and dynamic fracture toughness. These expressions show, upon comparison with non-thermal results, the importance of fully-coupled thermoelastic effects, and that all the problem characteristic lengths, which range over several orders of magnitude, are prominent features. Zone heat flux values, based on experimental results for near-crack temperature gradients, are then used for calculation purposes. The calculations show that, independent of a particular fracture criterion, thermal effects noticeably increase inelastic zone size and dynamic fracture toughness. 相似文献
19.
Eric Lorentz Sam Cuvilliez Kyrylo Kazymyrenko 《International Journal of Fracture》2012,178(1-2):85-95
Continuum Damage Mechanics and cohesive zone models are both prone to model large crack propagation inside quasi-brittle materials. Comparing the advantages of the formulations, the latter could be advantageously applied in cases where the crack path is known a priori while the former implicitly encompasses crack path prediction but requires more complex computations involving nonlocal interactions. In order to assess the acceptability of such a hierarchy for industrial studies, it is necessary that the predictions coincide quantitatively. Starting from a gradient damage model in a one-dimensional context, a cohesive law is derived as the asymptotic response of the damage model for vanishing nonlocal length scale. The cohesive law is hence independent of the nonlocal length scale, which is consistent with the fact that it ignores details characteristic of the ??best-estimate?? damage approach. Besides, the existence of such a limit ensures that the damage model is not much sensitive to a small nonlocal length scale, which then appears rather as a numerical regularisation parameter. A numerical comparison between the damage model and its asymptotic cohesive law is then carried out for large bi-dimensional crack propagation. The computed responses remain close to each other although some small discrepancies arise probably related to the damage spread resulting from the stress distribution in the vicinity of the crack tip: the hierarchy strategy is thus validated. 相似文献