Crack In Homogeneous Material Research Articles

Interface crack analysis in 2D bounded dissimilar materials using an enriched physics-informed neural networks

This study explores the application of physics-informed neural networks (PINNs) to analyze interface crack problems within the context of elastic bimaterial fracture mechanics. Bimaterial interface cracks exhibit a distinct behavior compared to cracks in homogeneous materials, and this behavior often involves oscillatory phenomena that can pose challenges in numerical modeling. By employing neural networks for solution approximation, PINNs are meshless and are trained using batches of collocation points, which may be randomly or strategically sampled across the computational domain. To effectively capture the oscillatory singular behavior in the crack-tip regions, this paper introduces an enhanced PINNs formulation that enables the modeling of interface cracks without requiring any refinement near the crack-tip. The trainable parameters of the current PINNs are dynamically optimized throughout the training process to fulfill both the underlying differential equations and the associated initial/boundary conditions. One of the significant advantages of the present PINNs is that it uses enrichment functions to capture the behavior around the crack region, allowing for greater flexibility in handling irregular or complex crack paths. The method's accuracy and stability are validated across several benchmark examples.

On energy release rate for an electrically permeable interface crack between two different 1D hexagonal piezoelectric QCs

A bi-material composed of two 1D piezoelectric hexagonal quasicrystals with a crack along the material interface was considered. Phonon and phason remote loading providing plane strain conditions were applied at infinity and an open crack model was adopted. Because electromechanical fields have an oscillating singularity at the crack tip, the energy release rate (ERR) is the most important fracture parameter in this case. The main purpose of this study is to define ERR in an analytical form. Using the obtained earlier asymptotic presentations of the phonon and phason fields at the crack tip and the crack closure integral approach, the desired formula is obtained in a simple form. The eligibility of the formula is verified by means of a crack in the bi-material composed of two 1D piezoelectric hexagonal quasicrystals and by considering a crack in homogeneous materials of this type. An additional comparison of the results obtained for a particular case of an isotropic material with known values confirmed the validity of the obtained formula.

Cohesive-zone models and singularities at corners and cracks in homogeneous materials

The stress singularities at corners in elastic bodies are not strong enough to provide a driving force for fracture, except in the limit of a crack. Here, we re-examine these elastic stresses from the perspective of cohesive-zone models. We present a general framework to understand fracture at corners, and define the magnitude of a stress-intensity factor and its phase angle, showing how these reduce to the familiar concepts of linear-elastic fracture mechanics (LEFM), in the special case of a crack. We discuss how the cohesive length, ξ, which is inherent to cohesive-zone models, is responsible for permitting fracture (and slip) at a corner. The work done against the tractions at a corner scales with ξ1−2n and ξ1−2m, where n and m are the strengths of the two elastic stress singularities. Therefore, except in the case of a crack, for which n=m=0.5 and the dependency on the cohesive length disappears, the work goes to zero in the classical elasticity limit of ξ=0, and neither fracture nor slip can occur.Using simple, uncoupled traction–separation laws, we show that the normal and shear deformations across the interface at a corner are generally coupled, despite the lack of explicit coupling in the laws. The crack-tip phase angle is shifted from the applied phase angle, and the properties of each traction–separation law affects the deformation in the other mode. These features lead to a very rich behavior that would be further complicated by consideration of more complex laws.

Analysis of bimaterial interface cracks using the localized method of fundamental solutions

This short communication makes the first attempt to apply the localized method of fundamental solutions (LMFS), a newly-developed meshless collocation method, for fracture mechanics analysis of bimaterial interface crack problems. The asymptotic crack-tip field for bimaterial interface cracks exhibits an oscillatory behavior which is quite different from that for in-plane cracks in homogeneous materials. This paper describes an enriched LMFS approach whereby a set of enrichment functions are embedded in the classical LMFS approximation to account for the presence of interface cracks. This method automatically incorporates the oscillatory behavior of the near-tip fields and thus the complex stress intensity factors (SIFs) can be solved accurately with no or very little remeshing. The results presented show excellent accuracy for a range of two-dimensional (2D) bimaterial with interface cracks, where the complex SIFs for interface cracks are computed with relatively errors less than 0.6 per cent.

Crack propagation at the interface between viscoelastic and elastic materials

Crack propagation in viscoelastic materials has been understood with the use of Barenblatt cohesive models by many authors since the 1970’s. In polymers and metal creep, it is customary to assume that the relaxed modulus is zero, so that we have typically a crack speed which depends on some power of the stress intensity factor. Generally, when there is a finite relaxed modulus, it has been shown that the “apparent” toughness in a semi-infinite crack increases between a value at very low speeds at a threshold toughness w0, to a very fast fracture value at w∞, and that the enhancement factor in infinite systems (where the classical singular fracture mechanics field dominates) simply corresponds to the ratio of instantaneous to relaxed elastic moduli.Here, we apply a cohesive model for the case of a bimaterial interface between an elastic and a viscoelastic material, assuming the crack remains at the interface, and neglect the details of bimaterial singularity. For the case of a Maxwell material at low speeds the crack propagates with a speed which depends only on viscosity, and the fourth power of the stress intensity factor, and not on the elastic moduli of either material. For the Schapery type of power law material with no relaxation modulus, there are more general results. For arbitrary viscoelastic materials with nonzero relaxed modulus, we show that the maximum “effective” toughness enhancement will be reduced with respect to that of a classical viscoelastic crack in homogeneous material.

Numerical Investigation on Fracture Initiation Properties of Interface Crack in Dissimilar Steel Welded Joints

Fracture toughness property is of significant importance when evaluating structural safety. The current research of fracture toughness mainly focused on crack in homogeneous material and experimental results. When the crack is located in a welded joint with high-gradient microstructure and mechanical property distribution, it becomes difficult to evaluate the fracture toughness behavior since the stress distribution may be affected by various factors. In recent years, numerical method has become an ideal approach to reveal the essence and mechanism of fracture toughness behavior. This study focuses on the crack initiation behavior and driving force at different interfaces in dissimilar steel welded joints. The stress and strain fields around the crack tip lying at the interfaces of ductile-ductile, ductile-brittle and brittle-brittle materials are analyzed by the numerical simulation. For the interface of ductile-ductile materials, the strain concentration on the softer material side is responsible for ductile fracture initiation. For the ductile-brittle interface, the shielding effect of the ductile material plays an important role in decreasing the fracture driving force on the brittle material side. In the case of brittle-brittle interface, a careful matching is required, because the strength mismatch decreases the fracture driving force in one side, whereas the driving force in another side is increased. The results are deemed to offer support for the safety assessment of welded structures.

Stress Intensity Factors of Interfacial Crack with Arbitrary Crack Tractions

Interfacial crack is much more complicated than a crack in homogeneous material. The crack is always in mixed-mode even for symmetrical geometry and symmetrical load, and the stress intensity factor has a complex value, which poses great challenges to numerical modelling. In some cases, there is surface traction on the crack faces, which can be crucial to the stability of the crack. In the presented research, a procedure is brought forward for analysis of interfacial crack with arbitrary surface traction based on the Scaled boundary finite element method(SBFEM). The surface traction on the crack is firstly divided into two parts, one in the direction normal to the crack face and the other in the tangential direction. Then each part is further divided into a series of power function of the radial coordinate. The solution for each can be solved semi-analytically by the SBFEM and is then superimposed to get the total solution. With this procedure, the stress and displacement are solved analytically in the radial direction, and the stress singularity at crack tip is obtained with high precision without refined mesh. Both anisotropic and isotropic materials can be considered. For validation of the procedure, a plate containing an interfacial crack and assuming different material propertes and different surface traction is investigated. Sensitivity analysis is also performed concerning the plate geometry and material properties. Finally the model is applied to solving the stress intensity factors of an interfacial crack of a gravity dam filled with water.

Asymptotic solution for interface crack between two materials governed by dipolar gradient elasticity

An asymptotic solution for interface crack between mismatched materials that obey a special form of linear isotropic strain gradient elasticity under conditions of plane strain is developed. It is shown that the asymptotic solution depends in a complicated manner both on a mismatch of elastic properties and a mismatch of the internal length scale parameter. Numerical analysis shows that the mismatch of elastic moduli and the gradient coefficient c respectively lift the degeneracy of the exponent p that is characteristic for a crack in homogeneous material. The total energy release rate Gint due to a crack extension along the interface is derived generalizing the classical virtual crack closure method. The reciprocal work contour integral method for the evaluation of amplitude factors in the asymptotic expansion is extended to interface crack in the linear isotropic strain gradient elasticity.

Nonlocal criterion of bridged cracks growth: analytical analysis

A nonlocal fracture criterion with accounting of the work during bonds deformation at the fracture process zone has been implemented analytically for analysis of bridged cracks growth. This criterion consists of two conditions: (1) the necessary energy condition of the crack tip limit equilibrium, which takes into account the energy release rate to the crack tip and the rate of deformation energy consumed by bonds in the crack bridged zone; (2) the sufficient condition is the equality of the crack opening at the bridged zone trailing edge to the bond limit stretching. Subcritical and quasi-statical regimes of bridged cracks growth have been formulated on these fracture conditions. Regimes of bridged cracks growth are analyzed in detail for the case of an internal straight bridged crack in homogeneous material with bonds traction, which is constant and independent of the external loading. Analytical expressions are obtained for the deformation energy release rate and for the rate of deformation energy consumed by bonds. The main fracture parameters, the critical external load and the crack bridged zone size in the limit equilibrium state are determined and analyzed. The limit cases of a crack which is filled with bonds and a crack with a small-scale bridged zone are considered. A comparative study with the well-known force fracture criterion for bridged crack growth is performed.

Energy dissipation in the mixed mode growth of cracks at the interface between brittle materials

In the present paper we compare the propagation of a crack in a homogeneous linear elastic material and the propagation of a geometrically identical crack located at the interface between two ideally brittle materials. Whereas the former crack is free to kink, the evolution of an interface crack results in a competition among the relative toughnesses of the surrounding layers and of the interface. By constraining cracks in homogeneous materials to propagate straight, as along an imaginary interface in a continuum, significant insights on the mixed mode growth of cracks at the interface between brittle materials are provided. It is shown that the collinear elongation in homogeneous materials under mixed mode conditions requires a higher amount of energy, which turns out to be dependent on the mode mixity. Such a surplus of energy has the same mathematical form of the expression widely used to model the increment of the fracture energy in layered materials. One can thus argue about which roles are played by thermodynamics constitutive prescriptions and which roles are played by geometrical constraints.

Investigation of the stress intensity factors for interface corners

From the viewpoint of linear elastic fracture mechanics, the stress intensity factor is an important parameter denoting the magnitude of stress singularity. If the singular order is a single real value, no ambiguity or inconsistency occurs about the definitions of the stress intensity factors such as the singular order 0.5 for a crack in homogeneous materials. Since the singular order of general interface corners may be real or complex, distinct or repeated, the definitions proposed in the literature may not be consistent with each other. Due to the inconsistency of the definitions and units, a direct comparison of the magnitude of the stress intensity factors for different interface corners is meaningless. Thus, the fracture toughness or fracture criterion established for a certain interface corners (e.g. a crack specimen) cannot be applied directly to the other interface corners. In order to build a direct connection among all general interface corners (including cracks and interface cracks), some unified definitions of stress intensity factors were proposed in the literature. Based upon the analytical near tip solutions of singular stresses, a new unified definition valid for almost all possible interface corners is proposed in this paper. To calculate this newly defined stress intensity factor accurately and efficiently, the path-independent H-integral is used and a relation between the H-integral and the stress intensity factors is also derived. The comparison and discussion between the present definition and those proposed in the literature are then presented through some analytical relations and numerical examples.

Cellular Automata to Simulate Crack Propagation of Quasi-Brittle Materials

Crack propagation in quasi-brittle material such as rock and concrete is studied by a new numerical method, lattice cellular automata. Cellular automaton method is an efficient method that simulates the process of self-organization of the complex system by constructing some simple local rules. It is of the advantage of localization and parallelization. Lattice model can transform a complex triaxial problem into a simpler uniaxial problem as well as consider the heterogeneity of the materials. Lattice cellular automata integrate advantages of both cellular automata and lattice model. In this paper the importance of the study of crack propagation, fundamentals and applications of cellular automata are briefly introduced firstly. Then the cellular automata model is presented, and in order to verify lattice cellular automata, the propagation of mode-I crack in homogeneous material is studied. Results of the numerical simulation are in good accordance with the experimental results and theoretical results of classical fracture mechanics. Furthermore, based on lattice cellular automata, the crack propagation of single crack under uniaxial compression was simulated. During the crack growth the wing crack and secondary cracks were found. The simulation results were consistent with the experimental results.

An improved numerical method for computation of stress intensity factors along 3D curved non-planar cracks in FGMs

A simplified strategy based on the interaction energy integral is implemented in the finite element framework to evaluate mixed mode Stress Intensity Factors (SIFs) in 3D non-planar cracks. The proposed approach does not require any a priori information about crack front and crack surface curvatures, therefore different arbitrary non-planar cracks can be easily investigated. In particular, both conical and lens-shaped cracks in homogeneous materials are considered as case studies in order to demonstrate the accuracy of the present approach. Finally, the computational strategy is extended to Functionally Graded Materials (FGMs) and the effect of graded material properties (Young’s modulus and Poisson’s ratio) on the SIFs is studied in detail.

Crack paths in composite materials

Composites are often exposed to harsh loading conditions. This may lead to crack formation and propagation. In this paper, an algorithm is described to predict the path of pre-existing cracks in homogeneous materials, based on an incremental approach. The approach is shown to also deal with the highly heterogeneous behaviour of periodically distributed composites.

Plastic dissipation energy at a bimaterial crack tip under cyclic loading

A theory has been introduced that relates the fatigue crack growth rate to the total plastic energy dissipated ahead of a crack tip under cyclic loading. Due to advances in computational efficiency, the reversed plastic zone can now be resolved adequately using the finite element method. The authors have previously published results for the plastic dissipation energy for cracks in homogeneous materials under mixed mode I and II loading. The purpose of the current research is to expand that set of results to include interface cracks in a general layered material. Applications of crack growth along a bimaterial interface include soldering, layered manufacturing, thermal spray coating, welding, brazing, or any other process that deposits a material onto a substrate where often it is more energetically favorable for a crack to grow along the interface than to propagate into either of the contiguous materials. Results of the plastic dissipation energy are obtained using 2-D elastic–plastic plane strain finite element analysis of a sharp crack along a bimaterial interface. Results show the plastic dissipation energy is proportional to the square of the strain energy release rate. By normalizing the results for the plastic dissipation with respect to the loads and material properties, it can be seen that the plastic dissipation energy has the greatest dependence on the mode mix ratio, followed by elastic and plastic property mismatches, respectively. Furthermore, a definition of the mode mix ratio based on dissipated energy is presented, which provides physical motivation for the characteristic length parameter needed to quantify the mode mix along a bimaterial interface.

ANALYSIS OF APPROXIMATED CURVED CRACKS IN HOMOGENEOUS AND GRADED MATERIALS

In this paper two stages of analysis are studied. In stage I, the influence of crack shape on thecrack-tip stresses, critical loads and subsequent propagation direction is investigated via a simpleanalytical model for cracks in homogeneous materials. This model is verified through finite elementsimulations using ANSYS. It is demonstrated that accurate predictions of mechanical energy releaserate and crack deflection angle may be obtained from a smaller number of crack shape parameters.In stage II, this concept is extended to curved cracks in functionally graded materials (FGMs).It iscommon that analytical and computational models of fracture in FGMs have focused almostextensively on straight cracks. If it can be demonstrated that straight cracks give an adequateapproximation of curved cracks in graded materials, then the existing solutions for straight cracksprovide a sufficient foundation for fracture analysis of FGMs. On the other hand, if straight cracksdo not adequately approximate curved cracks in FGMs, then the development of solutions for nonstraight cracks in graded materials is priority. Three cracks shapes approximations are performed tocompare with the actual crack in isotropic and graded materials. The crack propagation and the SIFswere simulated using finite element method. It was concluded that piecewise linear crack shapesprovide a significantly better approximation than straight crack shapes. Accordingly, analyticalsolutions for piecewise linear cracks in graded materials would be very useful, and should be afocus of future work in this area.

Basalt columns: Large scale constitutional supercooling?

The conventional interpretation of basalt column formation in terms of cracking of a homogeneous magma during cooling is questionable because cooling cracks in homogeneous materials do not tend to form quasi-hexagonal patterns. It is proposed that basalts develop inhomogeneous patterned compositions during cooling as a result of “constitutional supercooling”. The latter is observed in metallic alloys, and its mechanism is briefly described. It is expected to produce a quasi-hexagonal pattern of glassy interfaces. These interfaces crack preferentially during uniaxial cooling.

Elastic–plastic fracture mechanics analyses of circumferential through-wall cracks between elbows and pipes

The present work proposes a method for elastic–plastic fracture mechanics analysis of the circumferential through-wall crack in weldment joining elbows and attached straight pipes, subject to in-plane bending. Heterogeneous nature of weldment is not explicitly considered and thus, the proposed method assumes cracks in homogeneous materials. Based on small strain finite element limit analyses using elastic–perfectly plastic materials, closed-form limit loads for circumferential through-wall cracks between elbows and straight pipes under bending are given. Then applicability of the reference stress-based method to approximately estimate J and crack opening displacement (COD) is evaluated. It was found that the limit moments for circumferential cracks between elbows and attached straight pipes can be much lower than those for cracks in straight pipes, particularly for a crack length of less than 30% of the circumference; this result is of great interest in practical cases. This result implies that, if one assumes that the crack locates in the straight pipe, limit moments could be overestimated significantly, and accordingly, reference stress-based J and COD could be significantly overestimated. For the leak-before-break analysis, accurate J and COD estimation equations based on the reference stress approach are proposed.

J-INTEGRAL FOR A 3-D INTERFACE CRACK CONFIGURATION IN WELDS OF DISSIMILAR STEELS

In this study, path-independent values of the J-integral in the finite element context for an arbitrary three-dimensional interface crack configuration in welds of dissimilar steels are presented. For the fracture mechanics analysis of an interface crack in welds of dissimilar steels, residual stress analysis and fracture analysis must be performed sequentially. In the analysis of cracked bodies containing residual stress, the usual domain integral formation results in path-dependent values of the J-integral. And unlike cracks in homogeneous materials, an interface crack in welds of dissimilar steels always induces both opening and shearing modes of stress in the vicinity of the crack tip. Therefore, this paper discusses modifications of the conventional J-integral that yield path independence in the presence of residual stress and the total J values which can characterize the severity of an interface crack tip in welds of dissimilar steels. A finite element method which can evaluate the J-integral for an interface crack in three-dimensional residual stress bearing bodies is developed using the modified J-integral definition and total J values. The situation when residual stresses only are present is studied as is the case when mechanical stresses are applied in conjunction with a residual stress field.

Improvement of measurement error for modified coherent gradient sensing

Recently, a novel optical method, coherent gradient sensing (CGS), has been widely used in the study of deformation near crack tips under quasi-static and dynamic conditions, which can produce high contrast fringes and provide some degree of control on the sensitivity of measurement during experiment. It involves a simple optical set-up and is relatively insensitive to vibrations and rigid body motions. Like other interferometries, such as electronic speckle pattern interferometry, moiré method, etc, the accuracy of the fringe order in the CGS interference image will deeply influence the precision of experimental study. But because of the different optical principle, the fringe order of CGS cannot be obtained through the phase-shift technology. In this paper, a modified CGS method is introduced and analysed, which can accurately obtain the fringe order of a random position in the CGS interference image. The modified CGS method needs two original CGS optical set-ups, and can be used in static and dynamic conditions, which requires no complicated image processing techniques. Static fracture experiments on mode-I crack in homogeneous materials show that this modified method can evidently improve the measurement precision of the CGS method.