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1.
Based on the mechanics of anisotropic materials,the dynamic propagation problem of a mode Ⅲ crack in an infinite anisotropic body is investigated.Stress,strain and displacement around the crack tip are expressed as an analytical complex function,which can be represented in power series.Constant coefficients of series are determined by boundary conditions.Expressions of dynamic stress intensity factors for a mode Ⅲ crack are obtained.Components of dynamic stress,dynamic strain and dynamic displacement around the crack tip are derived.Crack propagation characteristics are represented by the mechanical properties of the anisotropic materials,i.e.,crack propagation velocity M and the parameter α.The faster the crack velocity is,the greater the maximums of stress components and dynamic displacement components around the crack tip are.In particular,the parameter α affects stress and dynamic displacement around the crack tip. 相似文献
2.
Based on mechanics of anisotropic material, the dynamic crack propagation problem of I/II mixed mode crack in an infinite anisotropic body is investigated. Expressions of dynamic stress intensity factors for modes I and II crack are obtained. Components of dynamic stress and dynamic displacements around the crack tip are derived. The strain energy density theory is used to predict the dynamic crack extension angle. The critical strain energy density is determined by the strength parameters of anisotropic materials. The obtained dynamic crack tip fields are unified and applicable to the analysis of the crack tip fields of anisotropic material, orthotropic material and isotropic material under dynamic or static load. The obtained results show Crack propagation characteristics are represented by the mechanical properties of anisotropic material, i.e., crack propagation velocity M and fiber direction α. In particular, the fiber direction α and the crack propagation velocity M give greater influence on the variations of the stress fields and displacement fields. Fracture angle is found to depend not only on the crack propagation but also on the anisotropic character of the material. 相似文献
3.
The Laplace transform, Wiener-Hopf technique and Cagniard-de Hoop method are used to solve the problem of a mode III semi-infinite crack which propagates suddenly at constant velocity in an anisotropic medium. The transient displacement field and the dynamic stress intensity factor at the moving crack tip are obtained.This research is supported by the Seismological United Foundation. 相似文献
4.
A novel experimental technique for measuring crack tipT-stress, and hence in-plane crack tip constraint, in elastic materials has been developed. The method exploits optimal positioning
of stacked strain gage rosette near a mode I crack tip such that the influence of dominant singular strains is negated in
order to determineT-stress accurately. The method is demonstrated for quasi-static and low-velocity impact loading conditions and two values
of crack length to plate width ratios (a/W). By coupling this new method with the Dally-Sanford single strain gage method for measuring the mode I stress intensity
factorK
I
, the crack tip biaxiality parameter
is also measured experimentally. Complementary small strain, static and dynamic finite element simulations are carried out
under plane stress conditions. Time histories ofK
I
andT-stress are computed by regression analysis of the displacement and stress fields, respectively. The experimental results
are in good agreement with those obtained from numerical simulations. Preliminary data for critical values ofK
I
and β for dynamic experiments involving epoxy specimens are reported. Dynamic crack initiation toughness shows an increasing
trend as β becomes more negative at higher impact velocities. 相似文献
5.
In this paper, an improved plate impact experimental technique is presented for studying dynamic fracture mechanism of materials,
under the conditions that the impacting loading is provided by a single pulse and the loading time is in the sub-microsecond
range. The impacting tests are carried out on the pressure-shear gas gun. The loading rate achieved is dK/dt∼108 MPa m1/2s−1. With the elimination of influence of the specimen boundary, the plane strain state of a semi-infinite crack in an infinite
elastic plate is used to simulate the deformation fields of crack tip. The single pulses are obtained by using the “momentum
trap” technique. Therefore, the one-time actions of the single pulse are achieved by eradicating the stress waves reflected
from the specimen boundary or diffracted from the crack surfaces. In the current study, some important phenomena have been
observed. The special loading of the single pulse can bring about material damage around crack tip, and affect the material
behavior, such as kinking and branching of the crack propagation. Failure mode transitions from mode I to mode II crack are
observed under asymmetrical impact conditions. The mechanisms of the dynamic crack propagation are consistent with the damage
failure model.
The project supported by the National Natural Science Foundation of China (No. 19672066 and 18981180-4) and the Key Project
of Chinese Academy of Sciences (No. KJ951-1-20) 相似文献
6.
A detailed analytical and experimental investigation is presented to understand the dynamic fracture behavior of functionally
graded materials (FGMs) under mode I and mixed mode loading conditions. Crack-tip stress, strain and displacement fields for
a mixed mode crack propagating at an angle from the direction of property gradation were obtained through an asymptotic analysis
coupled with a displacement potential approach. This was followed by a comprehensive series of experiments to gain further
insight into the behavior of propagating cracks in FGMs. Dynamic photoelasticity coupled with high-speed photography was used
to obtain crack tip velocities and dynamic stress fields around the propagating cracks. Birefringent coatings were used to
conduct the photoelastic study due to the opaqueness of the FGMs. Dynamic fracture experiments were performed using different
specimen geometries to develop a dynamic constitutive fracture relationship between the mode I dynamic stress intensity factor
(K
ID
) and crack-tip velocity (
) for FGMs with the crack moving in the direction of increasing fracture toughness. A similar
-K
ID
relation was also obtained for matrix material (polyester) for comparison purposes. The results obtained show that crack
propagation velocities in FGMs were about 80% higher than the polyester matrix. Crack arrest toughness was found to be about
10% lower than the value of local fracture toughness in FGMs. 相似文献
7.
In this paper, the steady crack growth of mode III under small scale yielding conditions is investigated for anisotropic hardening materials by the finite element method. The elastic-plastic stiffness matrix for anisotropic materials is given. The results show the significant influences of anisotropic hardening behaviour on the shape and size of plastic zone and deformation field near the crack tip. With a COD fracture criterion, the ratio of stress intensity factorsk
ss/kc varies appreciably with the anisotropic hardening parameterM and the hardening exponentN. 相似文献
8.
The influence of inertia on the stress and deformation fields near the tip of a crack growing in an elastic-plastic material is studied. The material is characterized by the von Mises yield criterion and J2 flow theory of plasticity. The crack grows steadily under plane strain conditions in the tensile opening mode. Features of the stress and deformation state at points near the moving crack tip are described for elastic-perfectly plastic response and for several crack propagation speeds. It is found that inertia has a significant effect on the elastic-plastic response of material particles near the crack tip, and that elastic unloading may occur behind the crack tip for higher speeds. The relationship between the applied crack driving force, represented by a remote stress intensity factor, and the crack tip speed is examined on the basis of a critical crack tip opening angle growth criterion. The calculated result is compared with dynamic fracture toughness versus crack speed data for a 4340 steel. 相似文献
9.
Discrete dipoles located near the crack tip play an important role in nonlinear electric field induced fracture of piezoelectric
ceramics. A physico-mathematical model of dipole is constructed of two generalized concentrated piezoelectric forces with
equal density and opposite sign. The interaction between crack and electric dipole in piezoelectricity is analyzed. The closed
form solutions, including those for stress and electric displacement, crack opening displacement and electric potential, are
obtained. The function of piezoelectric anisotropic direction,p
a
(θ)=cosθ+p
a
sinθ, can be used to express the influence of a dipole's direction. In the case that a dipole locates near crack tip, the
piezoelectric stress intensity factor is a power function with −3/2 index of the distance between dipole and crack tip.
Supported by National Natural Science Foundation of China(No. 10072033) 相似文献
10.
《International Journal of Solids and Structures》2006,43(10):2989-3005
This paper considers an interfacial crack with a cohesive zone ahead of the crack tip in a linearly elastic isotropic bi-material and derives the mixed-mode asymptotic stress and displacement fields around the crack and cohesive zone under plane deformation conditions (plane stress or plane strain). The field solution is obtained using elliptic coordinates and complex functions and can be represented in terms of a complete set of complex eigenfunction terms. The imaginary portion of the eigenvalues is characterized by a bi-material mismatch parameter ε = arctanh(β)/π, where β is a Dundurs parameter, and the resulting fields do not contain stress singularity. The behaviors of “Mode I” type and “Mode II” type fields based on dominant eigenfunction terms are discussed in detail. For completeness, the counterpart for the Mode III solution is included in an appendix. 相似文献
11.
Rice et al. (Journal of Mechanics and Physics of Solids42, 813–843) analyze the propagation of a planar crack with a nominally straight front in a model elastic solid with a single displacement component. Using the form of Willis et al. (Journal of the Mechanics and Physics of Solids43, 319–341), of dynamic mode I weight functions for a moving crack, we address that problem solved by Rice et al. in the 3D context of elastodynamic theory. Oscillatory crack tip motion results from constructive-destructive interference of stress intensity waves. Those waves, including system of the dilatational, shear and Rayleigh waves, interact on each other and with moving edge of crack, can lead to continuing fluctuations of the crack front and propagation velocity. 相似文献
12.
Lin Bai-song 《应用数学和力学(英文版)》1989,10(8):759-765
Under the condition that any perfectly plastic stress components at a crack tip are nothing but the functions of 0 only making use of equilibrium equations. Hill anisotropic yield condition and unloading stress-strain relations, in this paper, we derive the general analytical expressions of anisotropic plastic stress fields at the slowly steady propagating tips of plane and anti-plane strain. Applying these general analytical expressions to the concrete cracks, the analytical expressions of anisotropic plastic stress fields at the-slowly steady propagating tips of Mode I and Mode III cracks are obtained. For the isotropic plastic material, the anisotropic plastic stress fields at a slowly propagating crack tip become the perfectly plastic stress fields. 相似文献
13.
Dynamic extension of Sih's fracture criterion based on strain energy density factor, rc (dW/dV), is used to analyze dynamic crack propagation and branching. Influence of the nonsingular components, which are known as the higher order terms (HOT) in the crack tip stress field, on the strain energy density distribution at a critical distance surrounding the crack tip moving at constant crack velocity is examined. This rc (dW/dV) fracture criterion is then used to analyze available dynamic photoelastic results of crack branching and of engineering materials. 相似文献
14.
A simple model was proposed for the interpretation of the non-circular form of the Rayleigh wavefronts emitted by a fast running crack in a plate. The surface deformation around the crack tip, due to the high stress concentration there, propagated as a surface wave after fracture of this zone. On the other hand, the moving singularity of the crack tip created a dynamic stress field of varying intensity with time all over the specimen. This dynamic stress field resulted in a significant change of the mechanical properties of a strain-rate dependent material and therefore it influenced the velocity of propagation of fracture-Rayleigh wavefronts. An analysis of this varying dynamic strain field explained the non-circular form of Rayleigh waves, accompanying the propagating crack. For the experimental evaluation of the K1-factor the method of dynamic caustics was used in conjunction with the high-speed photography technique. 相似文献
15.
R.M. McMeeking 《Journal of the mechanics and physics of solids》1977,25(5):357-381
Analyses of the stress and strain fields around smoothly-blunting crack tips in both non-hardening and hardening elastic-plastic materials, under contained plane-strain yielding and subject to mode I opening loads, have been carried out by use of a finite element method suitably formulated to admit large geometry changes. The results include the crack-tip shape and near-tip deformation field, and the crack-tip opening displacement has been related to a parameter of the applied load, the J-integral. The hydrostatic stresses near the crack tip are limited due to the lack of constraint on the blunted tip, limiting achievable stress levels except in a very small region around the crack tip in power-law hardening materials. The J-integral is found to be path-independent except very close to the crack tip in the region affected by the blunted tip. Models for fracture are discussed in the light of these results including one based on the growth of voids. The rate of void-growth near the tip in hardening materials seems to be little different from the rate in non-hardening ones when measured in terms of crack-tip opening displacement, which leads to a prediction of higher toughness in hardening materials. It is suggested that improvement of this model would follow from better understanding of void-void and void-crack coalescence and void nucleation, and some criteria and models for these effects are discussed. The implications of the finite element results for fracture criteria based on critical stress or strain, or both, is discussed with respect to transition of fracture mode and the angle of initial crack-growth. Localization of flow is discussed as a possible fracture model and as a model for void-crack coalescence. 相似文献
16.
In this paper, the S-theory is applied to determine crack initiation and direction for cracked T-beams and circumferentially cracked pipes. It makes use of a parameter called strain energy density factor, S, which is a function of the stress intensity factors. The strain energy density theory provides a more general treatment of fracture mechanics problems by virtue of its ability in describing the multiscale feature of material damage and in dealing with mixed mode crack propagation problem. A simple method for obtaining approximate stress intensity factors is also applied. It takes into account the elastic crack tip stress singularity while using the elementary beam theory. Some basic loading conditions in beams and pipes are studied. 相似文献
17.
Steady state crack propagation problems of elastic-plastic materials in Mode I, plane strain under small scale yielding conditions were investigated with the aid of the finite element method. The elastic-perfectly plastic solution shows that elastic unloading wedges subtended by the crack tip in the plastic wake region do exist and that the stress state around the crack tip is similar to the modified Prandtl fan solution. To demonstrate the effects of a vertex on the yield surface, the small strain version of a phenomenological J2, corner theory of plasticity (Christoffersen, J. and Hutchinson, J. W. J. Mech. Phys. Solids,27, 465 C 1979) with a power law stress strain relation was used to govern the strain hardening of the material. The results are compared with the conventional J2 incremental plasticity solution. To take account of Bauschinger like effects caused by the stress history near the crack tip, a simple kinematic hardening rule with a bilinear stress strain relation was also studied. The results are again compared with the smooth yield surface isotropic hardening solution for the same stress strain curve. There appears to be more potential for steady state crack growth in the conventional J2 incremental plasticity material than in the other two plasticity laws considered here if a crack opening displacement fracture criterion is used. However, a fracture criterion dependent on both stress and strain could lead to a contrary prediction. 相似文献
18.
Effects of fractal crack 总被引:1,自引:0,他引:1
Experimental results indicate that propagation paths of cracks in geomaterials are often irregular, producing rough fracture surfaces which are fractal. In this paper, crack tip motion along a fractal crack trace is discussed. A fractal kinking model of the crack extension path is established to describe irregular crack growth. The length, velocity and kinking effects of the fractal crack are analysed. A formula is derived to describe the effects of fractal crack propagation on the dynamic stress intensity factor and on crack velocity. Finally, expressions of stress and displacement fields near the fractal crack tip are given. 相似文献
19.
裂纹扩展速度对焦散线的影响和动态应力光学常数的测定 总被引:5,自引:0,他引:5
本文从焦散线形成原理的数学描述出发,用扩展裂纹尖端附近的应力分量表达式,在前人工作的基础上,作了详细的数值计算。特别分析了裂纹扩展速度对焦散斑和初始曲线的形状、大小的影响,为测量扩展裂纹尖端的动态应力强度因子K_1~d提供了依据,并通过拟合得到了以裂纹扩展速度为参量的修正因子表达式。本文还提出了一种测定透明材料动态应力光学常数的方法,并用这一方法测定了有机玻璃的动态应力光学常数。 相似文献
20.
An elastic-viscoplastic mechanics model is used to investigate asymptotically the mode Ⅲ dynamically propagating crack tip field in elastic-viscoplastic materials. The stress and strain fields at the crack tip possess the same power-law singularity under a linear-hardening condition. The singularity exponent is uniquely determined by the viscosity coefficient of the material. Numerical results indicate that the motion parameter of the crack propagating speed has little effect on the zone structure at the crack tip. The hardening coefficient dominates the structure of the crack-tip field. However, the secondary plastic zone has little influence on the field. The viscosity of the material dominates the strength of stress and strain fields at the crack tip while it does have certain influence on the crack-tip field structure. The dynamic crack-tip field degenerates into the relevant quasi-static solution when the crack moving speed is zero. The corresponding perfectly-plastic solution is recovered from the linear-hardening solution when the hardening coefficient becomes zero. 相似文献