Experimental investigation of crack growth direction in multiple cracks

In this paper, the interaction between multiple cracks in crack growth direction is studied in an aluminium alloy under static and fatigue loading. Self similar as well as non‐self‐similar crack growth has been observed which depends on the relative crack positions defined by crack offset distance and crack tip distance. On the basis of experimental observations, the criterion for crack coalescence and crack growth direction are expressed in terms of the crack positions defined by crack offset and crack tip distances. The criterion presented in this study can be used to determine the limiting value of crack tip and crack offset distance and to determine the mode in which cracks coalesce during their growth process. Experimental results and crack interaction criterion presented under various crack positions and size conditions could be used to derive a new evaluation method of crack growth in multiple crack geometry.     

Numerical simulation of growth pattern of a fluid-filled subsurface crack under moving hertzian loading

Cracking of a fluid-filled subsurface crack is studied by means of the distributed dislocation technique within the framework of two-dimensional linear elastic fracture mechanics. The Griffith crack was initially opened by the application of hydrostatic pressure of an incompressible fluid within the crack. A moving Hertz line contact load distribution is applied at the surface of the half-plane in the presence of friction. The stress intensity factors at the tips of the fluid-filled crack are analyzed with the restriction that due to the fluid incompressibility there is no change of the crack-opening volume. When the crack starts to propagate/kink, numerical results show that the internal fluid pressure will be relieved, and as the ratio of the branched crack length to main crack length increases, the elastic strain energy release rate decreases. The crack growth is assumed to be arrested when the energy release rate is below a certain value. Based on the energy criterion, predictions are attempted for determining the load position where the crack propagation/kink commences as well as the growth increment of the branch crack before it is arrested. A step-by-step crack path is constructed to simulate the growth pattern of the fluid-filled crack under moving Hertzian loading.     

On the method of virtual crack extensions

The measurement of energy release rates using virtual crack extensions has been made using finite element techniques. An economic and accurate technique for calculating energy changes due to any number of virtual tip changes is presented. Mixed-mode situations can be dealt with by observing the direction of maximum energy release rate. Examples are given including various cracks in a plate in tension, a curving crack in a general two-dimensional shape, and a three-dimensional crack in a plate.     

Shape prediction and stability analysis of Mode-I planar cracks

This paper presents a numerical technique for simulating stable growth of Mode-I cracks in two and three dimensions, using energy release rate and its derivatives. The crack growth model used in the numerical simulation is based on the concept of maximizing potential energy of the system released as cracks evolve. Therefore, a series of quadratic programming (QP) problems with linear constraints and bounds are solved to simulate stable growth of Mode-I planar cracks. The derivative of energy release rate provides a stability condition for crack growth in structures and can be regarded as a discretized influence function that represents the strength of the interaction among crack extensions at different crack tips in 2-D and different locations along a crack front in 3-D. The energy release rate and its derivative are accurately calculated by the analytical virtual crack extension method [Engng. Fract. Mech. 59 (1998) 521; 68 (2001) 925] in a single analysis. Numerical examples are presented to demonstrate the capabilities of the proposed approach. Examples include a central crack subjected to wedge forces in a 2-D finite plate, a system of interacting thermally induced parallel cracks in a two-dimensional semi-infinite plane and a 3-D penny-shaped crack embedded in a large cylinder, pressurized in a central circular region.     

Computation analysis of interlaminar fracture of laminated composites

The interlaminar fracture behavior of laminated composites has been investigated. Contact and friction along the crack surfaces is taken into account in the finite element modeling of the delamination crack growth. Mode I, mode II and mixed mode loading conditions at the crack tip have been analyzed. For the cracks with contact and friction along the crack surfaces the virtual crack closure integral method is used in order to calculate separated energy release rates. Computational modeling and analysis of cross-ply laminates in three-point bending has been performed. Contact elements were used in order to prevent the material interpenetration along the crack surfaces. Comparison of the results obtained with and without using contact elements has been carried out and significant differences between the correlated values of the energy release rates have been found. The influence of the coefficient of friction on the energy release rates was found to be significant for short delamination crack lengths but insignificant for long cracks. Numerical analyses of experimental data obtained for unidirectionally reinforced glass fiber composites by double cantilever beam tests and by notched flexure tests have been carried out. For the double cantilever beam test geometric linear and nonlinear finite element analyses have been performed and critical energy release rates were calculated. For the end notched flexure test the contact problem has been solved taking into account that adjacent to the support contact and friction will occur. For the double cantilever beam test the critical energy release rates obtained by linear and nonlinear finite element solution has been compared with those from four different analytical data reduction methods (the area method, the Berry method, the modified beam analysis, the compliance method). For the end notched flexure test the critical energy release rates, calculated by the finite element analysis and taking into account contact and friction along the crack surfaces, have been compared with those obtained by conventional beam analysis. This revised version was published online in July 2006 with corrections to the Cover Date.     

Fracture analysis of a surface through-thickness crack in PZT thin film under a continuous laser irradiation

In this paper, the surface crack problem in PZT thin films under a continuous laser irradiation has been investigated by the superposition principle. Using commercial (FEM) software ANSYS 9.0, the piezoelectric fields near the crack tip were solved for surface crack in the finite PZT thin film. The SIFs for crack-tip fields were obtained by using the limited stress extrapolation technique (LSET) and then the energy release rates were calculated by the relation to the intensity factors. When the irradiation time and crack location were changed, the energy release rates G, G_I, and G_e for total, mechanical terms (mode I) and electric contribution were investigated. The results show that the mechanical opening mode I is the main mode for the surface crack under a continuous laser irradiation. However, electric mode IV has inhibiting effect on crack growth. At the beginning of laser irradiation, the surface tiny crack which is close to the centre of film will propagate more easily. During the laser irradiation, the crack which is far from the centre of film will propagate more easily.     

MODIFIED CRACK CLOSURE INTEGRAL (MCCI) FOR 3-d PROBLEMS USING 20-NODED BRICK ELEMENTS

Abstract— The Modified Crack Closure Integral (MCCI) technique based on Irwin's crack closure integral concept is very effective for estimation of strain energy release rates G in individual as well as mixed-mode configurations in linear elastic fracture mechanics problems. In a finite element approach, MCCI can be evaluated in the post-processing stage in terms of nodal forces and displacements near the crack tip. The MCCI expressions are however, element dependent and require a systematic derivation using stress and displacement distributions in the crack tip elements.
Earlier a general procedure was proposed by the present authors for the derivation of MCCI expressions for 3-dimensional (3-d) crack problems modelled with 8-noded brick elements. A concept of sub-area integration was proposed to estimate strain energy release rates at a large number of points along the crack front. In the present paper a similar procedure is adopted for the derivation of MCCI expressions for 3-d cracks modelled with 20-noded brick elements. Numerical results are presented for center crack tension and edge crack shear specimens in thick slabs, showing a comparison between present results and those available in the literature.     

TEM observations of dislocation emission at crack tips in aluminium

Direct observations were made of the propagation of ductile cracks and associated dislocation behaviour at crack tips in aluminium during tensile deformation in an electron microscope. In the electropolished area, the cracks propagated as a Mode III shear-type by emitting screw dislocations on a plane coplanar to the crack plane. A zone free of dislocations was observed between the crack tip and the plastic zone. As the cracks propagated into thicker areas, the fracture mode changed from Mode III to predominantly Mode I. The crack top of the Mode I cracks was blunted by emitting edge dislocations on planes inclined to the crack plane. The blunted cracks did not propagate until the area ahead of the crack tip was sufficiently thinned by plastic deformation. The cracks then propagated abruptly, apparently without emitting dislocations. The stress intensity factor was measured from the crack tip geometry of Mode III cracks and it was found to be in good agreement with the critical value of the stress intensity factor required for dislocation generation.     

Fatigue growth prediction of center slant crack in rectangular plate

This paper presents a numerical prediction model of mixed‐mode crack fatigue growth in a plane elastic plate. It involves a formulations of fatigue growth of multiple crack tips under mixed‐mode loading and a displacement discontinuity method with crack‐tip elements (a boundary element method) proposed recently by Yan is extended to analyse the fatigue growth process of multiple crack tips. Due to an intrinsic feature of the boundary element method, a general growth problem of multiple cracks can be solved in a single‐region formulation. In the numerical simulation, for each increment of crack extension, remeshing of existing boundaries is not necessary. Crack extension is conveniently modelled by adding new boundary elements on the incremental crack extension to the previous crack boundaries. At the same time, the element characters of some related elements are adjusted according to the manner in which the boundary element method is implemented. As an example, the present numerical approach is used to analyse the fatigue growth of a centre slant crack in a rectangular plate. The numerical results illustrate the validation of the numerical prediction model and can reveal the effect of the geometry of the cracked plate on the fatigue growth.     

Determination of Critical Tearing Energy of Tyre Rubber

Abstract:  An experimental investigation was conducted to determine the crack growth characteristics and critical tearing energy of pure tyre rubber under mode-I and -III loading. Constrained tension and trousers specimens were used, respectively. In the trousers test it was observed that the crack does not propagate at a steady rate, but in a stick–slip way, i.e., it is arrested and re-initiated at fairly regular intervals. Thus, the force necessary to propagate the crack varies widely from a maximum value at crack initiation to a minimum value at crack arrest. In the constrained tension tests, no stable crack growth was observed and crack initiation coincides with catastrophic fracture. The critical tearing energies corresponding to crack initiation and arrest under mode-III and to unstable crack growth under mode-I loading were determined from the load–displacement records by an approximate analysis of the trousers and the constrained tension tests.     

Interpretation of effects at the static fatigue limit of soda-lime-silicate glass

Crack growth in soda-lime-silicate glass near the static fatigue limit is rationalized by a fracture mechanics model of the crack tip, in which a stressed layer is built up on the crack surface as a consequence of ion exchange at the crack tip. This model extends the one presented earlier by Bunker and Michalske. Ion exchange, between hydronium (H₃O⁺) ions in the solution and sodium (Na⁺) ions in the glass, gives rise to compressive stresses at the tips of cracks in soda-lime-silicate glasses. These compressive stresses are responsible for (1) the occurrence of a fatigue limit in glass, (2) for the fact that crack tips remain sharp at the fatigue limit even though the walls of the crack are corroded by the basic solutions that form as a consequence of ion exchange, (3) for the crack tip bifurcation often observed when cracks are held at the fatigue limit for a while and then restarted at higher loads, and (4) for the fact that a delay time to restart the crack is often observed after the crack is held under load at the static fatigue limit. Most of the predictions are in quantitative agreement with experimental observations on crack growth and crack tip structure for soda-lime-silicate glass. The prediction of the time required to restart the crack is, however, only qualitatively correct, as experimental data report a sharp peak centered at the fatigue limit in the plot of restart time versus hold stress intensity factor, whereas the model gives a broad maximum on such a plot. Clearly, further development of the model will be needed for a better representation of the experimental data.     

Closed-form solution for an eccentric anti-plane shear crack normal to the edges of a magnetoelectroelastic strip

Summary The problem of an anti-plane shear crack embedded in a magnetoelectroelastic strip is investigated. The crack is assumed to be normal to the strip edges. By using the finite Fourier transform, the associated mixed boundary-value problem is reduced to triple series equations, then to singular integral equations. Solving the resulting equations analytically, the field intensity factors and energy release rates at the crack tips can be determined in explicit form. The influences of applied electric and magnetic loadings on the normalized energy release rate and mechanical strain energy release rate are presented graphically. Obtained results reveal that applied electric and magnetic loadings affect crack growth, depending on their directions and adopted fracture criteria. The derived solution is applicable to other cases including two collinear cracks distributed symmetrically in a magnetoelectroelastic strip, and a periodic array of collinear cracks in a magnetoelectroelastic plane.     

Evaluation of the stress intensity factors and the T-stress in periodic crack problem

This paper investigates the T-stress at crack tips in the periodic crack problem. Remote tension in the y-direction is applied to cracks with an arbitrary inclined angle. The original stress field can be considered a superposition of a uniform stress field and a perturbation stress field. The problem of evaluating the stresses in the perturbation field can be considered a superposition of many single crack problems. A Fredholm integral equation is suggested for the solution of the perturbation stress field. In the equation, the loading on the crack face is chosen as unknown quantity. Once the integral equation is solved, the stress intensity factors and the T-stress at the crack tip can be evaluated immediately. For solving the integral equation and evaluating stresses in the perturbation field, the remainder estimation technique is suggested for evaluating the influences on the central crack from infinite cracks. The technique can considerably improve convergence in computation. Many results for the stress intensity factors and the T-stresses in periodic cracks are presented. It is shown that the interaction is significant for the closer cracks.     

Fatigue growth of short cracks in Ti-17: Experiments and simulations

The fatigue behaviour of through thickness short cracks was investigated in Ti-17. Experiments were performed on a symmetric four-point bend set-up. An initial through thickness crack was produced by cyclic compressive load on a sharp notch. The notch and part of the crack were removed leaving an approximately 50 μm short crack. The short crack was subjected to fatigue loading in tension. The experiments were conducted in load control with constant force amplitude and mean values. Fatigue growth of the short cracks was monitored with direct current potential drop measurements. Fatigue growth continued at constant R-ratio into the long crack regime. It was found that linear elastic fracture mechanics (LEFM) was applicable if closure-free long crack growth data from constant K_Imax test were used. Then, the standard Paris’ relation provided an upper bound for the growth rates of both short and long crack.The short crack experiments were numerically reproduced in two ways by finite element computations. The first analysis type comprised all three phases of the experimental procedure: precracking, notch removal and fatigue growth. The second analysis type only reproduced the growth of short cracks during fatigue loading in tension. In both cases the material model was elastic-plastic with combined isotropic and kinematic hardening. The agreement between crack tip opening displacement range, cyclic J-integral and cyclic plastic zone at the crack tip with ΔK_I verified that LEFM could be extended to the present short cracks in Ti-17. Also, the crack size limits described in the literature for LEFM with regards to plastic zone size hold for the present short cracks and cyclic softening material.     

Mixed mode fatigue crack growth: A literature survey

The applications of fracture mechanics have traditionally concentrated on crack growth problems under an opening or mode I mechanism. However, many service failures occur from growth of cracks subjected to mixed mode loadings. This paper reviews the various criteria and parameters proposed in the literature for predictions of mixed mode crack growth directions and rates. The physical basis and limitations for each criterion are briefly reviewed, and the corresponding experimental supports are discussed. Results from experimental studies using different specimen geometries and loading conditions are presented and discussed. The loading conditions discussed consist of crack growth under mode II, mode III, mixed mode I and II, and mixed mode I and III loads. The effects of important variables such as load magnitudes, material strength, initial crack tip condition, mean stress, load non-proportionality, overloads and crack closure on mixed mode crack growth directions and/or rates are also discussed.     

Stress intensity factors and energy release rates of delaminations in composite laminates

Due to the oscillatory characteristics of stresses near interface crack tips, the stress intensity factor K_i, i = I, II, III, should be modified and the energy release rate G_i, i = 1, 2, 3, of each fracture mode calculated by the virtual crack closure method may not exist. Based upon a near-tip solution for interface cracks between dissimilar anisotropic media, a proper definition for the stress intensity factors and energy release rates for general anisotropic bimaterial interface cracks is provided in this paper, which is applicable for the delaminated composites. Moreover, this definition can be reduced to the classical definition for a crack tip in homogeneous media when the two materials become the same. A simple quadratic relation between K_i and _Gi is derived, which is further reduced explicitly for orthotropic bimaterials. The influence of fiber orientation and the coupling among opening, shearing and tearing mode fracture are studied numerically. The results show that the classical stress intensity factors and energy release rates are still the dominant stress intensity and energy release rate of the mixed mode condition induced by the interface.     

Viscoelastic Creep Crack Growth: A Review of Fracture Mechanical Analyses

The study of time dependent crack growth in polymers using a fracture mechanics approach has been reviewed. The time dependence of crack growth in polymers is seen to be the result of the viscoelastic deformation in the process zone, which causes the supply of energy to drive the crack to occur over time rather than instantaneously, as it does in metals. Additional time dependence in the crack growth process can be due to process zone behavior, where both the flow stress and the critical crack tip opening displacement may be dependent on the crack growth rate. Instability leading to slip-stick crack growth has been seen to be the consequence of a decrease in the critical energy release rate with increasing crack growth rate due to adiabatic heating causing are duction in the process zone flow stress, a decrease in the crack tip opening displacement due to a ductile to brittle transition at higher crack growth rates, or an increase in the rate of fracture work due to more rapid viscoelastic deformation. Finally, various techniques to experimentally characterize the crack growth rate as a function of stress intensity have been critiqued. This revised version was published online in July 2006 with corrections to the Cover Date.     

定向断裂控制爆破爆生裂纹扩展机理的实验研究

采用新型数字激光动态焦散线实验系统,对缺陷介质双孔定向断裂控制爆破裂纹扩展的动态行为进行了研究。结果表明,预制斜裂纹阻断了爆生主裂纹的扩展,最终两条主裂纹分别与翼裂纹形成相互勾连的形状。爆生主裂纹尖端以张拉应力场为主,其断裂为近似I型断裂。当爆生主裂纹运动到预制裂纹附近时,主裂纹端部应力场与预制裂纹尖端奇异应力场相互叠加,在预制裂纹尖端形成较强的拉剪应力场,且受已有主裂纹面的影响,预制裂纹扩展表现为弯向主裂纹面的弯曲断裂。研究结果可为含节理岩体定向断裂控制爆破提供理论依据。     

Comparison of cohesive zone parameters and crack tip stress states between two different specimen types

The cohesive zone parameters (separation energy and cohesive strength) and the crack tip triaxialities are compared between a compact tension (CT) and a double edge notched tension (DENT) specimen with smooth side-surfaces. The material is a pressure vessel steel 20MnMoNi55. The cohesive zone parameters are determined by fitting the simulated crack extensions near the midsection to the experimental data. The purpose of the study is to understand the relationship between the cohesive zone parameters and the crack tip stress triaxiality. The results show that for the same cohesive zone parameters the crack tip triaxiality near the midsection is lower in DENT specimens than in CT specimens. When the separation energy is set constant for CT and DENT specimens, the cohesive strength for the DENT specimens should be significantly lower than that for the CT specimens in order to make the simulated crack extensions near the midsection fit to the experimental data. Near the midsection, the cohesive strength and crack tip triaxiality influence each other: the specimen with a higher stress triaxiality has a higher cohesive strength; an increase of cohesive strength results in an increase of the crack tip triaxiality.