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1.
A closed-form solution is obtained for the problem of a mode-III interfacial edge crack between two bonded semi-infinite dissimilar elastic strips. A general out-of-plane displacement potential for the crack interacting with a screw dislocation or a line force is constructed using conformal mapping technique and existing dislocation solutions. Based on this displacement potential, the stress intensity factor (SIF, KIII) and the energy release rate (ERR, GIII) for the interfacial edge crack are obtained explicitly. It is shown that, in the limiting special cases, the obtained results coincide with the results available in the literature. The present solution can be used as the Green’s function to analyze interfacial edge cracks subjected to arbitrary anti-plane loadings. As an example, a formula is derived correcting the beam theory used in evaluation of SIF (KIII) and ERR (GIII) of bimaterials in the double cantilever beam (DCB) test configuration.  相似文献   

2.
For a central crack in a piezoelectric plate, the mode-I stress intensity factor (KI), electric displacement intensity factor (KD), energy release rates (GGM) and energy density factor (S) are obtained from the finite element results. For the impermeable crack, the numerical results of KI and KD are coupled; this error is contrary to the uncoupled analytical solutions. The error has little effect on the total energy release rate G and energy density factor S, but in some cases, large errors in the mechanical energy release rate GM are observed. G is global while SED is local. Also G is negative which defies physics where energy cannot be created while crack attempts to extend as implied by G. Computations should be made for the J-integral and also show that J becomes negative. What this shows is that the global fracture energy criterion is not suitable to address the local release of energy because it includes the overall energy which are irrelevant to fracture initiation being a local behavior. In addition, the case study shows that the energy density theory is the better fracture criterion for the piezoelectric material. According to the results of S, it retards the crack growth when the external electric field and piezoelectric poling are on opposite directions. This conclusion agrees with analytical and experimental evidence in the past references.  相似文献   

3.
The maximum energy release rate criterion, i.e., G max criterion, is commonly used for crack propagation analysis. This fracture criterion is based on the elastic macroscopic strength of materials. In the present investigation, however, the G max criterion has been modified in order to accommodate the consideration of plastic strain energy. This modified criterion is extended to study the fatigue crack growth characteristics of mixed-mode cracks. To predict crack propagation due to fatigue loads, a new elasto–plastic energy model is presented. This new model includes the effects of material properties such as strain hardening exponent n, yield strength σ y , and fracture toughness and stress intensity factor ranges. The results obtained are compared with those obtained using the commonly employed crack growth law and the experimental data.  相似文献   

4.
Strain energy density expressions are obtained from a field model that can qualitatively exhibit how the electrical and mechanical disturbances would affect the crack growth behavior in ferroelectric ceramics. Simplification is achieved by considering only three material constants to account for elastic, piezoelectric and dielectric effects. Cross interaction of electric field (or displacement) with mechanical stress (or strain) is identified with the piezoelectric effect; it occurs only when the pole is aligned normal to the crack. Switching of the pole axis by 90° and 180° is examined for possible connection with domain switching. Opposing crack growth behavior can be obtained when the specification of mechanical stress σ and electric field E or (σ,E) is replaced by strain ε and electric displacement D or (ε,D). Mixed conditions (σ,D) and (ε,E) are also considered. In general, crack growth is found to be larger when compared to that without the application of electric disturbances. This includes both the electric field and displacement. For the eight possible boundary conditions, crack growth retardation is identified only with (Eyy) for negative Ey and (Dyy) for positive Dy while the mechanical conditions σy or εy are not changed. Suitable combinations of the elastic, piezoelectric and dielectric material constants could also be made to suppress crack growth.  相似文献   

5.
Fatigue crack growth is caused primarily by shear decohesion due to dislocation motion in the crack tip region. The resolved shear stress, which drives dislocation in a crystal, is strongly orientation dependent, and therefore, the cyclic plastic deformation of the shear decohesion process is highly anisotropic.The crack planes are often inclined to the loading axis both in the inplane orientation and in the thickness direction. This inclination induces all three modes of the crack tip stress field, KI, KII, and KIII.Fatigue crack growth in large-grain Al 7029 aluminum alloy was studied. The crack tip stress fields of the test specimens are calculated with the finite element method. The values of KI, KII, and KIII are evaluated. The orientation of the crystal at a crack tip was determined with the Laue X-ray method. The crystal orientation and the calculated crack tip stress fields are used to compute the resolved shear stress intensity of each of the twelve slip systems of the crystal at the crack tip. The resolved shear stress field of a slip system is linearly proportional to the resolved shear stress intensity coefficient, RSSIC.The values of RSSIC thus evaluated are used to analyze the orientations of the crack plane and to correlate with the shear fatigue crack growth rate.  相似文献   

6.
In this paper, the classical solution of the opening mode crack in the 90° layer of 0/90/0 laminates has been determined by means of Fourier transformations and the procedure of Copson for a pair of dual integral equations. The fracture behavior and the in situ transverse strength of the 90° layer have been quantitatively studied in graphite/epoxy laminates, based on the solution obtained above. The results show that the stress intensity factor of this kind of laminates, which is different from that of a single unidirectional 90° layer, decreases with the increase in thicknessb, or modulusE L orG LT of the 0° layer and also decreases with the decrease in the thickness of the 90° layer. So the lamination effect manifests itself and thein situ transverse strength of the 90° layer is thereby enchanced. The theoretical calculations agree with the experimental data presented by D.L. Flaggs. Supported by National Natural Science Fundation of China.  相似文献   

7.
A numerical/analytical approach is proposed to determine the stress intensity factors KI, KII, and KIII of a 3D internal crack. The main point of this approach is the meshing technique that can model very sharp crack fronts. The meshing technique is based on an elliptical coordinate transformation that starts from a circular crack. It allows the obtainment of a curved crack front with elements normal to the crack front. Remarkable accuracy can be obtained for elliptical crack fronts with axes ratio smaller that 0.01. Accuracy demonstration is provided for cylindrical element with an inclined internal crack subjected to uni-axial tension. This case corresponds to crack propagation for all three modes of loading, the solution of which can checked with references’ results.  相似文献   

8.
Measuring Fracture Energy in a Brittle Polymeric Material   总被引:1,自引:0,他引:1  
The dynamic fracture behavior of a brittle polymer, polymethyl methacrylate (PMMA), was studied using single-edge-cracked tensile specimens and the method of caustics in combination with high-speed photography. The dynamic response of the specimen and the state of local stress near the crack tip, i.e., the stress intensity factor K, were measured. To analyze the dynamic response, the external work, Uex, applied to the specimen was partitioned into three components: the elastic energy, Ee; non-elastic energy, En, due to viscoelastic and plastic deformation; and fracture energy, Ef, for creating a new fracture surface, As. The results showed that Ee, En, and Ef increased with Uex, and the ratio Ef/Uex was about 46% over a wide range of Uex. Energy release rates were estimated using Gt = Uex/As and Gf = Ef/As. The mean energy release rate, Gm, during dynamic crack propagation was also determined using the value of K. A good correlation between Gf and Gm was found.  相似文献   

9.
For a crack subjected to combined mode I and III loading the influence of a T-stress is analyzed, with focus on crack growth. The solid is a ductile metal modelled as elastic–plastic, and the fracture process is represented in terms of a cohesive zone model. The analyzes are carried out for conditions of small scale yielding, with the elastic solution applied as boundary conditions on the outer edge of the region analyzed. For several combinations of the stress intensity factors KI and KIII and the T-stress crack growth resistance curves are calculated numerically in order to determine the fracture toughness. In all situations it is found that a negative T-stress adds to the fracture toughness, whereas a positive T-stress has rather little effect. For given values of KI and T the minimum fracture toughness corresponds to KIII = 0.  相似文献   

10.
The paper gives explicit expressions of the elastic T-stress components T I, T II, and T III for an elliptic crack in an unbounded body under uniform pressure and bending and expressions of all the T-stress components for parabolic and tunnel cracks under uniform loading. These formulas are derived by analyzing the asymptotic behavior of the stress components near the crack front using special harmonic functions. The dependence of the T-stresses on Poisson’s ratio, semiaxes and parametric angle of the elliptic crack is studied. The expressions of T I, T II, and T III for a penny-shaped crack under arbitrary uniform pressure and bending follow as a special case from the respective expressions for an elliptic crack __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 8, pp. 57–70, August 2007.  相似文献   

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