Displacement Intensity Factors Research Articles

Interfacial dynamic impermeable crack analysis in dissimilar piezoelectric materials by a new interaction integral

Dynamic intensity factors (IFs) provide an important parameter for assessing the failure risk of an interfacial crack for piezoelectric composites exposed to electromechanical impact loadings. In the present research, a new dynamic interaction integral (I-integral) is built for computing the dynamic stress IFs (SIFs) and electric displacement IF (EDIF) of an interfacial crack located in dissimilar inhomogeneous piezoelectric media. Through proper selection of auxiliary variables, the domain expression of I-integral for the inhomogeneous piezoelectric bi-materials does not need to take into account any derivative term for any piezoelectric material property. Further, after rigorous theoretical derivation, the resulting I-integral is still valid for complex models where the integration domain contains other multiple interfaces, regardless of whether the extra materials are straight or curved. Incorporating the modified extended finite element method, the accuracy is confirmed by checking the dynamic IFs extracted from the I-integral with referenced results. The domain-independence is tested by varying ranges of integration domains for inhomogeneous piezoelectric bi-materials and multi-interface piezoelectric composites. Finally, typical examples are employed to discuss the influences of the direction and magnitude of electric impact loading, combination of polarizations, inhomogeneous degree of piezoelectric bi-materials and complex distribution of diverse material properties on the dynamic IFs.

A Numerical Algorithm for Arbitrary Real-Order Hankel Transform

The Hankel transform is widely used to solve various engineering and physics problems, such as the representation of electromagnetic field components in the medium, the representation of dynamic stress intensity factors, vibration of axisymmetric infinite membrane and displacement intensity factors which all involve this type of integration. However, traditional numerical integration algorithms cannot be used due to the high oscillation characteristics of the Bessel function, so it is particularly important to propose a high precision and efficient numerical algorithm for calculating the integral of high oscillation. In this paper, the improved Gaver-Stehfest (G-S) inverse Laplace transform method for arbitrary real-order Bessel function integration is presented by using the asymptotic characteristics of the Bessel function and the accumulation of integration, and the optimized G-S coefficients are given. The effectiveness of the algorithm is verified by numerical examples. Compared with the linear transformation accelerated convergence algorithm, it shows that the G-S inverse Laplace transform method is suitable for arbitrary real order Hankel transform, and the time consumption is relatively stable and short, which provides a reliable calculation method for the study of electromagnetic mechanics, wave propagation, and fracture dynamics.

Study on Crack Propagation of the Tunnel Model under Dynamic Loading

Crack defects make it difficult to predict the dynamic fracture of tunnel specimens under an impact load. To study the impact of the velocity and crack location on a roadway under dynamic load, specimens with tunnel‐type voids were made using polymethyl methacrylate. The split‐Hopkinson bar was used as the loading method, and a digital laser dynamic caustics system was used to observe the fracture process of the specimens. The dynamic fracture process was evaluated by the crack propagation velocity, displacement, and dynamic stress intensity factor. To predict and verify the test results, ABAQUS was used to simulate the test process. It was found that the results of the simulated combinations of the crack propagation path and initial fracture toughness change law are consistent with the test results. The initial fracture toughness and the peak value of the crack propagation velocity increased with the increase of the impact velocity. The crack propagation law and trajectory were affected by the location of the prefabricated cracks.

Stress and Displacement Intensity Factors of Cracks in Anisotropic Media

A relation connecting stress intensity factors (SIF) with displacement intensity factors (DIF) at the crack front is derived by solving a pseudodifferential equation connecting stress and displacement discontinuity fields for a plane crack in an elastic anisotropic medium with arbitrary anisotropy. It is found that at a particular point on the crack front, the vector valued SIF is uniquely determined by the corresponding DIF evaluated at the same point.

On asymptotes of surface tractions and displacement discontinuities at the crack front

Analytical expression between the stress intensity factor and displacement intensity factor is derived for an arbitrary shaped plane crack with a smooth crack front. The crack is placed in a medium with an arbitrary elastic anisotropy. The analysis is based on constructing the outer and inner asymptotes for the corresponding surface tractions and displacement discontinuity fields at the crack front. The closed-form pseudodifferential operator of the crack theory along with the associated amplitudes and symbols is constructed.

Stack of non-uniformly loaded shear cracks in magnetoelectroelastic materials

Detailed expressions are derived in closed-form for the field components at a general point in the deformation of magnetoelectroelastic media by a stack of parallel, antiplane shear cracks to which non-uniform mechanical, electric, and magnetic loads are applied, by exploiting a generalized technique of continuous distributions of dislocations. Their angular variations around a crack tip are deduced; from which comprehensive, novel representations for the appropriate stress, electric displacement, and magnetic induction intensity factors follow. Representative numerical results are illustrated graphically. The phenomenon of the so-called crack shielding effect is exhibited. Limiting special cases are considered as validation of this analysis.

Moving row of antiplane shear cracks within one-dimensional piezoelectric quasicrystals

Closed-form expressions are deduced and discussed, using an extended form of the classical dislocation layer method, for the phonon and phason stress and electric displacement components and intensity factors generated in one-dimensional piezoelectric quasicrystals by a collinear row of moving shear cracks. Representative numerical results are presented graphically. Additionally, this analysis yields the fields of a single crack moving in a finite piezoelectric quasicrystalline plate and also of a moving edge crack in a plate

A rigorous solution for the piezoelectric materials containing elliptic cavity or crack with surface effect

A theoretical study on the problem of piezoelectric materials with a nano elliptic cavity considering surface effect subjected to far‐field antiplane mechanical load and inplane electric load is reported. Surface effect is introduced based on the theory of Gurtin‐Murdoch surface/interface model. A rigorous whole‐field solution is presented by using the complex variable elasticity theory and the conformal mapping method, in terms of which closed‐form solution of the stress/electric displacement fields and the stress/electric displacement intensity factors is obtained. The results reveal that the stress/electric displacement fields and the stress/electric displacement intensity factors are size dependent when the size of the cavity/crack is on the order of nanometer. The present solution approaches to the classical electroelastic results with the increase of the size of the nano elliptic cavity and crack. The influences of the elliptic cavity shape ratio on the stress and electric displacement concentration factors are discussed.

DYNAMIC PROPAGATION PROBLEMS OF MODE III SEMI-INFINITE CRACK

By means of the theory of complex functions, dynamic propagation problems of mode III semi- infinite crack were researched. The problems studied can be facilely transformed into riemann-hilbert problems and the universal expression of analytical solutions of stress, displacement and dynamic stress intensity factor under the conditions of moving increasing loads Px/t and Pt2/x, respectively, are very facilely obtained using the measures of self-similar functions. In view of corresponding material properties, the mutative rule of dynamic stress intensity factor was illuminated very well.

Original Crack and Adhesion Development of Nano Diamond Coating

A theoretical original microvoid model which describes the micro structural aspects of tiny original crack was developed based on fracture mechanics to explain the interface strength between nano diamond coating (NDC) and its substrate. The expression of stress fields, displacement and stress intensity factor ( SIF ) K at interface crack tip were deduced. Based on the original microvoid model, the technique to improve the adhesion strength between the NDC and its substrate was obtained by improving the diamond nucleation density and adjusting the coating residue stress.

Dynamic Extension Problems Concerning Symmetrical Mode III Crack

By means of the theory of complex variable functions, dynamic extension problems concerning symmetrical mode Ⅲ crack were researched. The problems considered can be very facilely translated into Riemann-Hilbert problem by the measures of self-similar functions, and the general expressions of analytical solutions of the stress, the displacement and dynamic stress intensity factor under the conditions of motive variable loads Px2/t and Pt2/x2 which were applied the surfaces of mode Ⅲ crack, respectively, were gained.

Dynamic Propagation of Mode Ⅲ Interfacial Crack Subjected to Variable Moving Concentrated Loads

Dynamic propagation of mode Ⅲ crack under variable moving loads on the crack surface is investigated using the theory of complex functions. Using the approaches of self-similar functions, the problems are readily transformed into Riemann-Hilbert problems. The paper presents a new mechanical model for dynamic crack propagation, in which the crack is under the conditions that the variable concentrated loads Pt3/x2 and Px/t move along x-axial with velocity β. At last, analytical solutions of stress, displacement and stress intensity factor are attained, respectively.

313 平板試験片中の分岐切欠の開口変位と応力拡大係数の測定(OS3.計算力学に貢献する実験的アプローチ(4),OS・一般セッション講演)

313 平板試験片中の分岐切欠の開口変位と応力拡大係数の測定(OS3.計算力学に貢献する実験的アプローチ(4),OS・一般セッション講演)

Investigation on the Effect of Crack Length on Mechanical Properties of Functionally Graded Materials

In this article, the thermo-mechanical responses of ceramic/metal functionally graded thermal barrier coating(TBC) in work environment are analyzed by a finite element method. Both the crack-tip field and the stress intensity factor of functionally graded TBC are analyzed and calculated. It is discussed that the effect of crack length on mechanical properties of functionally graded TBC in the condition creep and no creep of pure metal. The numerical results indicate that the effect of crack length(a/t) is negligible to temperature distributions and the maximum displacements of whole model but remarkable to the 1st principal stress and stress intensity factor of crack region. Moreover, creep phenomenon of pure metal can relax the value of displacement, stress and stress intensity factor but do not alter their distribution.

Two Dynamic Propagation Problems of Symmetrical Mode III Crack

By the approaches of the theory of complex functions, two dynamic propagation problems of symmetrical mode Ⅲ crack were researched. The problems considered can be very facilely changed into Riemann-Hilbert problem by means of self-similar functions, and the general representations of analytical solutions of the stress, the displacement and dynamic stress intensity factor under the conditions of moving variable loads Pt and Px2/t2 which were applied the edges of mode Ⅲ crack, respectively, were readily acquired.

Fracture dynamics problem on mode I semi-infinite crack

By means of the theory of complex functions, fracture dynamics problems concerning mode I semi-infinite crack were studied. Analytical solutions of stress, displacement and dynamic stress intensity factor under the action of moving increasing loads Pt3/x3, Px3/t2, respectively, are very easily obtained using the ways of self-similar functions. The correlative closed solutions are attained based on the Riemann–Hilbert problems.

Fracture dynamics problems of orthotropic solids under anti-plane shear loading

By application of the approaches of the theory of complex functions, fracture dynamics problems of orthotropic solids under anti-plane shear loading were researched. Universal representation of analytical solutions was obtained by means of self-similar functions. The problems dealt with can be facilely transformed into Riemann–Hilbert problems by this technique, and analytical solutions of the stress, the displacement and dynamic stress intensity factor under the actions of moving increasing loads Px2/t2 and Pt3/x2 for the edges of asymmetrical mode III crack, respectively, were acquired. In the light of corresponding material properties, the variable rule of dynamic stress intensity factor was illustrated very well.

Dynamic Propagation of Mode III: Crack Concerning Surfaces Subjected to Variable Moving Concentrated Loads

Asymmetric dynamic propagation of mode III: crack under variable moving loads on the crack surface is investigated using the theory of complex functions. Using the approach of self-similar function, the problems are readily transformed into Riemann-Hilbert problems. The paper presents a new mechanical model for dynamic crack propagation, in which the crack is under the conditions that the variable concentrated loads Pt3/x2 and Pt/x move along x-axial with velocity β. And then, analytical solutions of stress, displacement and stress intensity factors are attained, respectively. These solutions are utilizable to attain solutions of arbitrarily complex problems, using the superposition theorem

Dynamic Fracture of Orthotropic Solids Under Anti-Plane Shear Loading

By application of the approaches of the theory of complex functions, dynamic fracture of orthotropic solids under anti-plane shear loading were researched. Universal expression of analytical solutions was attained by the measures of self-similar functions. The problems dealt with can be facilely transformed into Riemann-Hilbert problems by this technique, and analytical solutions of the stress, the displacement and dynamic stress intensity factor under the actions of moving increasing loads Pt/x and Pt2/x for the edges of asymmetrical mode III crack, respectively, were acquired. In light of corresponding material properties, the variable rule of dynamic stress intensity factor was depicted very well.

(3) Measurement of Opening Displacement and Stress Intensity Factor of Bifurcated Notch by Moire Interferometry

(3) Measurement of Opening Displacement and Stress Intensity Factor of Bifurcated Notch by Moire Interferometry