Crack-face Traction Research Articles

Efficient technique for evaluation of three-dimensional elastic–plastic fracture mechanics parameters based on equivalent distributed stress concept

This study proposes an efficient technique for the evaluation of the elastic–plastic fracture mechanics (EPFM) parameters of three-dimensional (3D) cracks based on the modified crack cohesive force (CCF) model. In the current method, the 3D crack’s EPFM parameters are analyzed by applying the pseudo crack face traction (CFT) to a two-dimensional (2D) center crack in an infinite plate. This pseudo traction is called the equivalent distributed stress (EDS). The EDS to be applied on the 2D center crack is determined in a manner that reproduces the relationship between crack length and stress intensity factor (SIF) of the intended 3D crack. Once EDS is determined, EPFM parameters for 3D cracks can be obtained instantly by using the center crack’s analytical closed-form solutions. This approach can compute the 3D crack’s EPFM parameters in dramatically less computation time than 3D finite element (FE) analysis. The effectiveness of the proposed method is validated by comparing the EPFM parameters of a 3D penny-shape crack obtained from this method against the reference analytical solutions and numerical FE analysis results. The parameters determined by the present method show excellent agreement with the reference solutions.

Extrinsic/intrinsic cohesive zone modelling and experiments on interface failure of multi-walled carbon nanotube reinforced adhesively bonded joints under mode II loading

The present work is primarily concerned with determining mode II cohesive zone parameters for eliminating the crack tip stress-field singularity for constant, linear, and parabolic extrinsic cohesive zone models (CZMs). A semi-analytical approach is used to estimate the stress intensity factor (SIF) associated with the cohesive zone ahead of the physical crack tip. Simultaneously, the obtained SIF is compared with the popular Interaction integral technique results considering the influence of crack face traction. The influence of the order of the traction-separation law (TSL) on the global load–displacement responses is numerically investigated using a crack propagation methodology based on the nullification of SIF. The effectiveness of the proposed approach has been demonstrated through a series of experiments involving the failure of epoxy-based adhesively bonded modified compact tension specimens (CTS) subjected to pure mode II loading. The adhesives are reinforced with different multi-walled carbon nanotubes (MWCNTs) reinforcement of 0.1 wt%, 0.2 wt%, and 0.3 wt%, and its effect on the global load vs displacement responses are recorded. Specific cohesive zone parameters are obtained for the experimental problem to model the failure behaviour for a broad spectrum of cases considered using extrinsic and intrinsic TSLs.

Extrinsic cohesive zone modeling for interface crack growth: Numerical and experimental studies

The present work is concerned with the study of interface crack using the extrinsic cohesive zone model (CZM) that nullifies the crack tip stress singularity. A semi-analytical procedure combining the generalized crack opening displacement solution and the finite element (FE) result is shown to estimate the traction-separation law (TSL) parameters. The stress intensity factor (SIF), which symbolizes the strength of the singularity, is computed using the domain-independent interaction integral that considers crack-face traction. The SIF obtained from the FE simulations is plotted along the cohesive zone length to demonstrate the reduction in the strength of the crack tip singularity and found in good agreement with the analytical solutions. Finally, the effectiveness of the proposed procedure is validated for an interface crack propagation between isotropic parent materials.

Accurate and efficient method for analyzing mixed-mode SIFs for inclined surface cracks in semi-infinite bodies by using numerical influence function method

An effective technique to compute mixed-mode stress intensity factors (MM-SIFs) for inclined surface cracks in semi-infinite bodies under arbitrary stress fields is proposed and validated. The proposed technique in this study is accurate and handiness for calculating MM-SIFs of different crack angles by using only one non-inclined cracked model. The benefit of this technique is achieved by using the influence function method (IFM) to evaluate MM-SIFs. A fully-automated influence coefficient database (ICDB) calculation system is developed based on the IFM. The interaction integral method (IIM) including the crack face traction (CFT) integral, which can improve the accuracy of SIF solutions, is employed in the developed ICDB. Once the ICDB for unit distributed load (UDL) is established for a target finite element (FE) model, MM-SIFs under arbitrary stress distributions of different crack angles can be calculated accurately in a short time. The developed ICDB is validated by comparing mode-I and MM-SIF solutions obtained by IFM with well-established reference solutions for different crack angles and Poisson’s ratios. The effect of Poisson’s ratio on MM-SIFs is also discussed based on the SIF solutions.

Critical investigation on the influence of welding heat input and welding residual stress on stress intensity factor and fatigue crack propagation

Abstract This paper investigates the influence of the change in welding heat input (HI) and welding residual stress (RS) on the behavior of stress intensity factor (SIF) and fatigue crack propagation (FCP) by means of finite element method. Three welding HI cases were examined using a bead-on-plate FE model. One of the applied welding HI cases represents welding conditions used in experiments. Furthermore, for the sake of comparison, a stress-relieved case that does not consider the influence of welding RS was employed. Experimental data used in the analyses and verification were taken from a Ph.D. dissertation conducted by Kusuba ( http://hdl.handle.net/10069/16925 ). A thermal-elastic-plastic analysis was firstly conducted to simulate welding process and to predict welding RS. A powerful fracture analysis technique named WARP3D interaction integral method that provides crack face traction integral was employed. WARP3D is an open research code for nonlinear FEA of large-scale, 3-D solids and structures subjected to static and dynamic loads. The employed technique was used to precisely calculate SIF with considering the influence of welding RS under different constant stress amplitude loadings. The results revealed that the ranges of welding RS induced by the simulated welding HI cases have a negligible influence on the behavior of SIF and FCP, whilst when increasing the magnitude of those welding RS a larger influence can be observed. The influence of welding RS induced by the simulated welding HI cases on FCP was manifested by comparing FCP obtained by the cases that consider the effect of welding RS with that given by the stress-relieved case. A large reduction of fatigue lives was obtained when welding RS is considered compared with that obtained by the stress-relieved case. A reduction percentage of 35.9–40.7% in fatigue lives was obtained when welding RS is considered compared with that calculated by the stress-relieved case for the applied stress loading conditions. The calculated fatigue lives were verified with experimental data taken from the literature. Facture behaviors of the studied cases were discussed, as well. Furthermore, a basic study was conducted to examine the influence of the change in the magnitude of RS on FCP behavior.

Evaluation of stress intensity factor for a surface cracked butt welded joint based on real welding residual stress

This paper examines the evaluation of stress intensity factor (SIF) for surface cracks in a non-uniform residual stress field. A technique that based on utilizing the crack face traction (CFT) integral implemented in the interaction integral method using an open source code for models with a particular crack-block mesh density was presented. 3-D flat plate models with different crack-block mesh densities were employed under different loading conditions to examine the accuracy, conditions and easiness to use of the present technique. The influence of the crack-block mesh density on the calculated SIF solutions due to the application of non-uniform tractions over the crack face was discussed. A considerable improvement of SIF solutions calculated by crack face tractions was observed when the crack-block mesh density becomes fine enough. The effectiveness of the present technique was then validated for different 3-D numerical examples of welded joints under different loading conditions. The present technique was thereafter employed to evaluate SIF for a surface crack in a butt welded joint using real welding residual stress. The SIF solution calculated due to the application of welding residual stress was verified with that given by mechanical loading (without welding residual stress).

T-Shaped Crack in a Piezoelectric Strip Under Thermo-Electro-Mechanical Loadings

The thermo-electro-mechanical fracture problem of a piezoelectric strip containing a T-shaped crack is considered in this study. The problem is solved for a piezoelectric strip that is under thermo-electro-mechanical loadings. The crack faces are supposed to be completely insulated thermally and electrically. By using both the principle of superposition and the Fourier transform techniques, the isothermal electromechanical problem is reduced to a system of singular integral equations, respectively. The outline of the procedure for obtaining the crack face traction is also presented. The singular integral equations are solved numerically. Numerical calculations are carried out, and detailed results are presented to illustrate the influence of the geometric parameters on the stress and electric displacement intensity factors.

M -Integral for Calculating Intensity Factors of Cracked Piezoelectric Materials Using the Exact Boundary Conditions

In this paper, the M-integral is extended for calculating intensity factors for cracked piezoelectric ceramics using the exact boundary conditions on the crack faces. The poling direction is taken at an angle to the crack faces within the plane. Since an analytical solution exists, the problem of a finite length crack in an infinite body subjected to crack face traction and electric flux density is examined. In this case, poling is taken parallel to the crack faces. Numerical difficulties resulting from multiplication of large and small numbers were treated by normalizing the variables. This problem was solved with the M-integral and displacement-potential extrapolation methods. With this example, the superiority of the conservative integral is observed. The values for the intensity factor obtained with the M-integral are found to be more accurate than those found by means of the extrapolation method. In addition, a crack parallel to the poling direction in a four-point bend specimen subjected to both an applied load and an electric field was analyzed and different electric permittivity values in the crack gap were assumed. It is seen that the electric permittivity greatly influences the stress intensity factor KII and the electric flux density intensity factor KIV. The absolute value of these intensity factors increases with an increase in the value of the electric permittivity in the crack. The influence of the permittivity on KI is rather small.

Finite Element Alternating Method for Interacting Surface Cracks

The finite element alternating method (FEAM), in conjunction with the finite element analysis (FEA) and the analytical solution for an elliptical crack in an infinite solid subject to arbitrary crack-face traction, can derive the stress intensity factor (SIF) of surface cracks by using the FEA results for an uncracked body. In the present study, the FEAM was applied to evaluations of SIF for noncoplanar multiple surface cracks. The SIF was evaluated for two surface cracks of dissimilar size, and three crack of the same size. The results suggested that the interaction is greatly affected by the relative crack size and negligible when the difference in the crack size is large enough, and the interaction can be evaluated by taking into account the adjacent cracks even if there are many cracks around them. Finally, the crack growth simulations were conducted and a possibility of the direct evaluation of influence of interaction between adjacent crack without using the combination rules was revealed.

Interaction integral procedures for 3-D curved cracks including surface tractions

This study examines a two-state interaction integral for the direct computation of mixed-mode stress intensity factors along curved cracks under remote mechanical loads and applied crack-face tractions. We investigate the accuracy of stress intensity factors computed along planar, curved cracks in homogeneous materials using a simplified interaction integral that omits terms to reflect specifically the effects of local crack-front curvature. We examine the significance of the crack-face traction term in the interaction integral, and demonstrate the benefit of a simple, exact numerical integration procedure to evaluate the integral for one class of three-dimensional elements. The work also discusses two approaches to compute auxiliary, interaction integral quantities along cracks discretized by linear and curved elements. Comparisons of numerical results with analytical solutions for stress intensity factors verify the accuracy of the proposed interaction integral procedures.

Analysis of Surface Crack in Cylinder by Finite Element Alternating Method

The finite element alternating method (FEAM), in conjunction with the finite element analysis (FEA) and the analytical solution for an elliptical crack in an infinite solid subject to arbitrary crack-face traction, is used for evaluating the stress intensity factor (SIF) of surface cracks in a cylinder. The major advantage of this method is that the SIF can be calculated by using the FEA results for an uncracked body. A newly developed system allows the FEAM to be performed by a simple method, which consists of the conventional FEA for an uncracked body and a subroutine for the FEAM alternating procedure. It is shown that the system can derive the precise SIF of circumferential, longitudinal, and inclined surface cracks in a cylinder. The crack growth predictions are performed for an inclined crack and projected longitudinal and circumferential crack in a cylinder. The results suggests that the crack characterizing procedure prescribed in Sec. XI may cause an unconservative evaluation in the crack growth prediction, and that the FEAM is valid for complex problems, to which the SIF evaluation by the FEA cannot be adopted easily.

A general solution method for an anti-plane shear crack dynamically accelerating along a bimaterial interface

We develop a general solution method for a dynamically accelerating crack under anti-plane shear conditions along the interface between two different homogeneous isotropic elastic materials. The crack is initially at rest, and after loading is applied the crack-tip speed which may accelerate up to the shear wave speed of the more compliant material. The analysis includes an exact, closed-form expression for the stress intensity factor for an arbitrary time-dependent crack-face traction, as well as expressions for computing the crack-face displacements and the stress in front of the crack. We also present some numerical examples for fixed loads and for loads moving with the crack tip, using a stress intensity factor fracture criterion, in order to examine the predicted effect of material mismatch on interfacial fracture.

A Method for Solving Dynamically Accelerating Crack Problems in Linear Viscoelasticity

We develop a general solution technique for a dynamically accelerating crack in a linear viscoelastic material, based on a transform method developed by Slepyan (see [Models and Phenomena in Fracture Mechanics, Springer-Verlag, New York, 2002]) for solution of dynamic elastic fracture problems. We review the elastic fracture solution method and then treat the viscoelastic mode III fracture problem for crack tip speeds less than the short-time shear wave speed. The analysis includes an exact, closed-form expression for the stress intensity factor for an arbitrary time dependent crack face traction. As examples, we apply this solution method to the Achenbach--Chao and standard linear solid viscoelastic models.

Sudden deceleration or acceleration of an intersonic shear crack

Sudden jumps in the crack tip velocity were revealed by numerical simulation (in both continuum/cohesive element and molecular dynamics approaches) and experiments for rapid shear cracking. The cracking velocity may accelerate from a sub-Rayleigh speed to the intersonic range, or from an intersonic speed to a higher one, when the reflected impact wave reloads the crack tip. On the other hand, the cracking velocity may decelerate from an intersonic speed to a lower one or recede to the sub-Rayleigh range when the fracture driving force declines. The velocity change encountered during intersonic cracking plays a different role from that in the acceleration or deceleration of a subsonic crack. A crack propagating at an intersonic speed would leave a shear wave trailing behind. When the crack decelerates or accelerates, the effect of the trailing wave will lead to a transition period from one steady-state solution of crack tip singularity to another. This investigation aims at quantifying these processes. The full field solution of an intersonic mode II crack whose speed changed suddenly from one velocity (intersonic or subsonic) to another (intersonic or subsonic) is given in closed form. The solution is facilitated via superposing a series of propagating crack problems that are loaded by dislocations to seal the unwanted crack-face sliding or by concentrated forces moving at various speeds to negate the crack-face traction. In contrast to the subsonic solution, the results in the intersonic case indicate that the elastic fields around the crack tip depend on the deceleration or acceleration history that is traced back over a long time. Singularity matching dictates the jump that may actually take place.

A Shape Design Sensitivity Approach for Two-Dimensional Mixed-Mode Fracture Analysis Under General Loading

Under general loadings including body forces and crack-face traction, the energy release rate equation for a two-dimensional cracked body is derived by a shape design sensitivity approach. Defining the virtual crack extension (VCE) as the variation of the geometry, the virtual work principle and the material derivative concept are used to obtain the final analytical equation for the energy release rate. In contrast to the results of other researchers, the functionals which appear in the derived energy release rate equation do not involve the derivative of the displacement field on the crack surface, thereby improving the numerical accuracy in the computation of the energy release rate. Although the finite element method (FEM) is applied to crack problems in this paper, any numerical analysis method can be applied to the resulting equation. In addition, if body forces and crack-face traction are constant with respect to VCE, i.e., their material derivatives are identically zero, then the energy release rate equation is domain independent for domains which exclude the crack-tip region. Three example problems are treated which demonstrate the generality, accuracy, and domain-independent nature of the derived energy release rate equation.

Mechanics of transonic debonding of a bimaterial interface: The anti-plane shear case

The recent experiment reported by Liu, Lambros and Rosakis (1993) (Highly transient elastodynamic crack growth in a bimaterial interface : higher order asymptotic analysis and optical experiments. J. Mech. Phys. Solids41, 1887–1954) raised the issue of transonic debonding. As a preliminary study, the present paper focuses on transonic debonding under anti-plane shear. The interfacial crack advances at a velocity higher than the shear wave speed of the compliant component but lower than that of the stiff component of the bimaterial. The governing equation for a steady state growing crack is elliptical in the stiff material and hyperbolic in the compliant material. We obtain a closed-form analytical solution that describes the transmission of the mechanics fields from the elliptical region to the hyperbolic region. The interface data travel along the inclined characteristic lines in the compliant material to the crack wake. The stress singularity at the crack tip depends on the crack propagation speed and varies from being constant-like when passing the lower shear wave speed to being square root singular when approaching the higher shear wave speed. The stress intensity coefficient measuring the strength of this singularity is determined for the case of a semi-infinite debonding crack subject to a steady state crack-face traction. The total energy release rate for transonic debonding vanishes and the energy flows from the stiff material to the compliant one along the characteristic lines, without deposition at the crack tip. We also conclude that the debonding speed cannot exceed the higher shear wave speed provided the energy flow through the interface is bounded.

破壊力学 微小だ円き裂群干渉解析のための交代操返し法

An alternating method is developed for the interaction analysis of arbitrary distributed multiple elliptical cracks. The completely analytical solutions (VNA solutions) for a single elliptical crack in an infinite solid, subject to arbitrary crack-face traction, are implemented in the present alternating method, together with the coordinate transformations for stress tensor. Since only the VNA solutions of individual cracks are used as a basic solution of the Schwartz-Neumann alternating technique, the present method leads to a highly accurate and efficient numerical tool for routine evaluation of the stress intensity factors for interacting multiple cracks. Numerical demonstrations are also given for interaction problems of several types.

On a dynamically accelerating crack in an achenbach-chao viscoelastic solid

A closed form solution is presented for a dynamically accelerating, semi-infinite, anti-plane shear crack in a Achenbach-Chao linear viscoelastic solid in the limiting case of a vanishing equilibrium shear modulus. Simple expressions for the crack-face displacement and the stress intensity factor are constructed for arbitrary time dependent crack-face traction and crack-tip velocity, ( t), subject only to the restriction that 0 $ ̌ = (t) < c , where c is the short time (glassy) shear wave speed. The extent of material memory in the stress intensity factor and crack-face relative displacement during the transition from an initial accelerating crack growth phase to a constant crack speed regime are compared for loads travelling with the crack-tip and for stationary loads. The viscoelastic and elastic stress intensity factors are shown to exhibit the same degree of limited dependence upon the initial acceleration phase whereas the viscoelastic and elastic crack-face displacements behave quite differently with the former exhibiting a persistent and the latter a limited memory of the initial acceleration phase.

Three-dimensional analysis of cracks in layered transversely isotropic media

A general mathematical formulation to analyse cracks in layered transversely isotropic media is developed in this paper. By constructing the Green’s functions, an integral equation is obtained to determine crack opening displacements when an applied crack face traction is specified. For the infinite body, the Green’s functions have solutions in a closed form. For layered media, a flexibility matrix in the integral transformed domain is formed that establishes the relation between the traction and the displacement for a single layer; the global matrix is formed by assembling all of the flexibility matrices constructed for each layer. The Green’s functions in the spatial domain are obtained by inversion of the Hankel transform. Finally, the crack opening displacement and the crack-tip opening displacement for a vertical planar crack in a layered transversely isotropic medium are obtained numerically by the boundary integral equation method.