Crack Opening Model Research Articles

A new framework based on XFEM to study the role of electrostatic tractions in semipermeable piezoelectric material

In this work, a crack opening model is proposed to study the role of electrostatic tractions in a cracked semipermeable piezoelectric material. The extended finite element method (XFEM) is used in conjunction with six-fold electro-mechanical enrichment functions to capture the singularity and the discontinuous surface independent of the background mesh. The electric displacement intensity factor (EDIF) is evaluated using an electromechanical interaction integral approach in the presence of a dielectric medium inside the crack cavity. The accuracy of the proposed XFEM based approach is verified by comparing the numerical results with available analytical solutions. Further, a systematic numerical study is done to study the influence of electrostatic tractions on the EDIF using different crack configurations under far-field loading.

Crack opening model for unidirectional ceramic matrix composites at elevated temperature

Crack opening displacement (COD) is a key parameter determining the gas diffusion regime and the associated oxidation kinetics of ceramic matrix composites (CMCs) in high temperature oxidative atmosphere. In this paper, COD of an isolated tunneling crack in unidirectional CMCs is formulated based on shear-lag theory. The model simultaneously considers the coupling effects of applied stress, environmental temperature and interface degradation. Both the elastic constants of the constituents and the interface slipping stress are regarded as temperature-dependent parameters. And, interface recession length was introduced to quantify oxidation effect on crack opening behavior of CMCs. Reasonability of the model was validated by comparing the predictions with experimental data of single tow SiC/BN/SiC composites. Besides, parametric analysis was performed with C/SiC composites, revealing that tension stress contributes to open matrix crack, while temperature acts the opposite. But, temperature effect on crack healing is weakened by interfacial friction. With aggravated interface oxidation, matrix crack closure can hardly be achieved for new interface debonding generates, resulting in linear increase of crack opening.

Empirical model for plasticity‐induced crack closure based on Kmax and ΔK

AbstractThe mean stress has a significant effect on crack propagation life and must be included in prediction models. However, there is no consensus in the fatigue community regarding the dominant mechanism explaining the mean stress effect. The concept of crack closure has been widely used and several empirical models can be found in literature. The stress ratio, R, is usually the main parameter of these models, but present numerical results showed a significant influence of Kmax. A new empirical model is therefore proposed here, dependent on Kmax and ΔK, with four empirical constants. The model also includes the effect of material's yield stress, and two additional parameters were defined to account for stress state and crack closure parameter. A comparison was made with Kujawski's and Glinka's parameters, for a wide range of loading conditions. ΔKeff lies between Kujawski's and Glinka's parameters, and some agreement is evident, although the concepts are quite different. The crack opening model was applied to literature results and was able to collapse da/dN–ΔK curves for different stress ratios to a single master curve.

A multiscale damage and crack opening model for the prediction of flow path in laminated composite

Laminated composites are increasingly used for fluid storage or transportation. The composite structure generally includes a metallic or polymer liner in order to prevent leakage which can generate a significant increase in cost and mass. The development of a linerless solution thus represents a promising improvement. Nevertheless, composite laminates are subjected to damage which can generate leakage paths at a load level significantly lower than strength load. In this paper, a multiscale approach is used to model the damage state by two physical variables representing the crack density and the delamination length at crack tips. The effect of damage and load on crack opening is evaluated using a batch of finite element simulations on elementary damaged cells. The ply scale model resulting from this work can be used to predict the flow path in any composite laminate subject to any in-plane loading.

About on Low-Alloy Coupled Steel Bars Concretes Rigidity and Crack Opening Model Formula Establishment

Coupled steel bars have already more than 30 year historical development. But, it was made by HPB235, Plasticity and ductility were very poor, so, only use in planking component. Now, we made coupled steel bars by Low-alloy steels. According to tentative data, model building formula that’s rigidity and crack Opening. Provide the basis for the project construction.

Analysis method of planar cracks of arbitrary shape in the isotropic plane of a three-dimensional transversely isotropic magnetoelectroelastic medium

The hyper-singular boundary integral equation method of crack analysis in three-dimensional transversely isotropic magnetoelectroelastic media is proposed. Based on the fundamental solutions or Green’s functions of three-dimensional transversely isotropic magnetoelectroelastic media and the corresponding Somigliana identity, the boundary integral equations for a planar crack of arbitrary shape in the plane of isotropy are obtained in terms of the extended displacement discontinuities across crack faces. The extended displacement discontinuities include the displacement discontinuities, the electric potential discontinuity and the magnetic potential discontinuity, and correspondingly the extended tractions on crack face represent the conventional tractions, the electric displacement and the magnetic induction boundary values. The near crack tip fields and the intensity factors in terms of the extended displacement discontinuities are derived by boundary integral equation approach. A solution method is proposed by use of the analogy between the boundary integral equations of the magnetoelectroelastic media and the purely elastic materials. The influence of different electric and magnetic boundary conditions, i.e., electrically and magnetically impermeable and permeable conditions, electrically impermeable and magnetically permeable condition, and electrically permeable and magnetically impermeable condition, on the solutions is studied. The crack opening model is proposed to consider the real crack opening and the electric and magnetic fields in the crack cavity under combined mechanical-electric-magnetic loadings. An iteration approach is presented for the solution of the non-linear model. The exact solution is obtained for the case of uniformly applied loadings on the crack faces. Numerical results for a square crack under different electric and magnetic boundary conditions are displayed to demonstrate the proposed method.

Surface displacement characteristics of line crack trespassing the Rayleigh wave speed barrier as influenced by velocity and applied stress dependent local zone of restrain

Surface displacement characteristics of line crack trespassing the Rayleigh wave speed barrier as influenced by velocity and applied stress dependent local zone of restrain

Re-examination of crack opening model of interface fracture

The complex singularity associated with a crack at the interface between two dissimilar, isotropic and homogeneous materials leads to mathematical artefacts, such as stress oscillations and crack face interpenetrations in the vicinity of the crack tip. To avoid these unrealistic features, Sinclair (Sinclair GB. On the stress singularity at an interface crack. International Journal of Fracture 1980;16(2):111–9) assumed a finite crack opening angle (COA) such that the singularity λ became real equal to 1/2. This paper extends the COA model by considering real singularities not necessarily equal to 1/2. When COA is 0°, the interface crack singularity is complex with a real part equal to 1/2. On increasing COA, the imaginary part of the singularity decreases and becomes zero at a threshold value of COA; at this point, the singularity is a real, repeated value. A further increase in COA results in a pair of real singularities. Different crack opening configurations and material combinations are studied, and results presented for threshold COAs and associated values of singularity. Stress analyses for these three regimes: (a) complex, (b) real pair and (c) real repeated singularities, are reported. It is seen that additional complexities are present in the last case. Typical results for stress fields are also included for comparing with standard fields.

Single and two-phase discharge from a pressurized vessel

The objective of this work was to establish models for the blowdown process of partially filled pressure liquefied vessels and to validate the models by comparison with experimental pressure measurements. On the basis of experiments using small 400 mL steel pressure vessels with creep and knife induced cracks, a crack opening model was developed using the Crack Opening Displacement theory and plastic displacement assumptions. For a single-phase discharge, an expression for the unsteady compressible choked flow through openings of varying areas was developed. The results of this blowdown model were compared with experimental pressure measurements obtained for nine small vessels filled with argon and water - at different fill levels (70, 80 and 90%) with different initial pressures. The influence of the speed of crack propagation and discharge coefficient were evaluated. The simulations of the single-phase model were found to be in reasonable agreement with the experiments. The work also presents a comparison of several available two-phase blowdown models applicable to the discharge of a pressure liquefied gas (simulated here by refrigerants R11, R22 and R123). Some modifications to these models were also examined. The two-phase models did not seem to adequately describe the experimental results even when the model parameters were adjusted to suit the experiments.

Discussion on a tectonic model for the emplacement of the Main Donegal Granite, NW Ireland

Mr M. J. Arthur writes: Hutton (1982) suggested that the Main Donegal Granite (MDG) was accommodated in a NE–SW zone of tension ('elongate hole'), contemporaneously with NE–SW sinistral shearing around that zone about 400 Ma ago (end Silurian–early Devonian times). Calculations from strain studies suggested that the sinistral displacement was about 20 km at its maximum, across the NW boundary of the MDG, but only about 5 km where the NW and SE boundaries united and continued to the SW (Hutton 1982). No figure was given for the offset across the SE boundary, though it was considered to be a major sinistral shear zone (Hutton 1982). However, Hutton (1982) proposed an unorthodox ‘crack opening model’ for the emplacement, which is adequately explained by the well established pull-apart model. The MDG has the rhomboidal/elliptical shape (Fig. 1) typical of a pull-apart produced at a releasing bend (cf. Crowell 1974, fig. 3), resulting from the intersection of the two throughgoing parts of a left-stepping sinistral wrench fault (cf. Ramsay 1980, fig. 18). The MDG is about 50 km long and 11 km wide and thus has a length/width ratio of about 4.5, whilst the ratio for pull-aparts is commonly between 2 and 5 with an average of about 3 (Aydin & Nur 1982). Emplacement into an ‘elongate hole’ contemporaneously with shearing around it, is precisely a characteristic expected of a pull-apart. Although pull-aparts are perhaps best known for their occupation by sedimentary deposits they also often contain contemporaneous igneous

疲労亀裂開閉口に及ぼす応力比と応力拡大係数範囲の影響について

The effective stress intensity factor range based on the measurements of crack opening loads gives the same crack propagation behavior for various stress ratios. Many authors have reported that the crack opening ratio U depends only on the stress ratio R. It is observed in experiment, however, that U depends also on stress intensity factor range ΔK.In this study, fatigue crack propagation tests were carried out on a high strength steel with yield strength of 450 MPa class under various stress ratios. And a crack opening model, that contains the both effects of R and ΔK was investigated based on the cyclic elasto-plastic finite element analysis (FEA) and the fracture mechanics approach with the small scale yielding concept. The FEA can simulate well the plasticity-induced closure even under the plane strain condition. Generally, it is difficult to apply the FEA for oxide- and roughness- induced closures that play an important role in the near threshold region. On the other hand, in the small scale yielding model with the assumption of the existence of the residual deformation on the wake of a crack, the crack opening stress intensity factor can be calculated as the value at which the fatigue crack opening displacement becomes zero.The resultant formula of U contains two parameters, one is for the plastic deformation at a crack tip and the other is for the oxide and the roughness in a fatigue crack. This model can explain successfully the experimental results. As a result, the fatigue crack propagation behavior under various stress ratios is described by the equation with five parameters which can be obtained with only one specimen. The predicted crack propagation rates showed good agreement with empirical results. Therefore, the formula derived in this study may be applied well to the evaluation of fatigue crack extension.

溶接残留応力場における疲労き裂の部分開口モデルによる応力拡大係数範囲算定法の提案とそのき裂伝播挙動の推定

Generally, fatigue crack propagation rate is well put in order by stress intensity range ΔKeff by considering crack closure period in crack opening process. But, in weld residual stress field, it seems that crack propagation behavior can not be exactly expressed in ΔKeff. This would be caused that ΔKeff was calculated by detecting crack full opening point which was able to be well measured experimentally. On the other hand, partially crack opening phenomena, which was presumed theoretically by considering the residual stress distribution in the case of crack laying over the tension and compression stress transition region, has not reflected in ΔK calculation process by this time.In this paper, as mentioned above consideration, calculation method of stress intensity factor in partially crack opening condition was proposed and its model was based on superpose principle of elastic stress. As a result of applying our calculation of stress intensity range ΔKact to evaluate the fatigue crack propagation rate in welded plate, it was made clear that the crack propagation behavior could be put in order well by ΔKact than by ΔKeff.Namely, ΔKact concept would not be only modification of KΔeff, because of applying new calculation technique for partially crack opening model.