Maximum Circumferential Stress Criterion Research Articles

Crack growth modeling in elastic solids by the extended meshfree Galerkin radial point interpolation method

We present a new approach based on local partition of unity extended meshfree Galerkin method for modeling quasi-static crack growth in two-dimensional (2D) elastic solids. The approach utilizing the local partition of unity as a priori knowledge on the solutions of the boundary value problems that can be added into the approximation spaces of the numerical solutions. It thus allows for extending the standard basis functions by enriching the asymptotic near crack-tip fields to accurately capture the singularities at crack-tips, and using a jump step function for the displacement discontinuity along the crack-faces. The radial point interpolation method is used here for generating the shape functions. The representation of the crack topology is treated by the aid of the vector level set technique, which handles only the nodal data to describe the crack. We employ the domain-form of the interaction integral in conjunction with the asymptotic near crack-tip field to extract the fracture parameters, while crack growth is controlled by utilizing the maximum circumferential stress criterion for the determination of its propagating direction. The proposed method is accurate and efficient in modeling crack growths, which is demonstrated by several numerical examples with mixed-mode crack propagation and complex configurations.

Theoretical modeling and analysis of thermal fracture of semi-infinite functionally graded materials with edge cracks

The present investigation is devoted to a problem of the interaction of two edge cracks inclined arbitrary to the boundary of a non-homogeneous half-plane, which is a functionally graded layer on a homogeneous substrate. The functionally graded properties vary exponentially in thickness direction. One cycle of cooling from sintering temperature is considered. An approach based on integral equations is used and a solution is obtained, then the stress intensity factors are calculated and direction of the initial crack propagation is evaluated by using the maximum circumferential stress criterion. Influence of geometrical and material (inhomogeneity) parameters on the fracture characteristics is investigated. This study can serve as a part of the modeling of the fracture process in FGM coatings under cyclic heating–cooling thermal loading.

FGM/homogeneous bimaterials with systems of cracks under thermo-mechanical loading: Analysis by fracture criteria

Fracture criteria for prediction of extension of the interface crack and of the crack growth direction in a bimaterial consisting of a homogeneous and a functionally graded material (FGM) with systems of internal defects are studied. The bimaterial is subjected to a heat flux and a tensile load applied at infinity. It is assumed that the thermal properties of the FGM have exponential form. The Young’s modulus and Poisson’s ratio are assumed to be constant. In the previous papers (Petrova and Schmauder, 2011a,b, 2012a,b) asymptotic analytical formulas for the stress intensity factors (SIFs) at the interface crack tips were obtained as a series of a small parameter (the ratio between sizes of the internal and interface cracks). These SIFs are used in fracture criteria to obtain the possible direction of crack propagation and critical loads. The maximum circumferential stress criterion is used and some results for the fracture angles is obtained by the minimum strain energy density in order to compare the predictions for the fracture angles by two fracture criteria. The influence of geometry of the problem (location and orientation of cracks) and the parameters of non-homogeneity of FGMs on the main fracture characteristics is investigated.

A Mixed-Mode Fracture Criterion for Brittle Materials

The inclined surface cracks are under the mixed mode I,II,III loading conditions. Direct tension experiments of brittle materials with surface crack have been carried out. The crack growth process, fracture pattern and the initiation angle of the surface crack were attained. In order to analyze the mixed-mode fracture criterion of the surface crack in brittle materials stress intensity factor of the crack front of the surface crack was calculated based on the FRANC3d firstly. And then the minimum strain energy density criterion, the maximum circumferential stress criterion and the revised maximum circumferential stress criterion were used to calculate the initiation angle. The revised maximum circumferential stress criterion proved to be fit for the attained experimental results.

Eddy Current Sensor Modeling for the Nondestructive Evaluation of Stress Intensity Factor

In this paper, a nondestructive evaluation by sensor Eddy current is used as a tool to control cracks and microcracks in materials. A simulation by a numerical approach such as the finite element method is employed to detect cracks in materials and eventually to study their propagation using a crucial parameter such as a Stress Intensity Factor (SIF). This method has emerged as one of the most efficient techniques for prospectin cracks in materials, evaluating SIFs and analyzing crack's growth in the context of linear elastic fracture mechanics (LEFM). This technique uses extrapolation of displacements from results compared with those obtained by the integral interaction. On the other hand, crack'sgrowth is analyzed as a model by combining the maximum circumferential stress criteria with the critical plane for predicting the direction of crack growth. In this research, a constant crack growth increment is determined using the classical Paris's model, or the so-called modified Paris's model. It is also shown herein that stress intensity factors needed for these models are calculated using the domain form of the J-integral interactions.

Development of a dynamic model for crack propagation in glazing system under thermal loading

The present study reports on the development and validation of a finite element program, GLAZ-CRACK, for predicting crack initiation and propagation of glass in fire or under other thermal loadings. The model is based on three crack modes to calculate the stress intensity factors (SIFs) and strain energy release rates. The crack initiation is predicted from the stress distribution using either probabilistic or deterministic method. The crack growth can be predicted by one of the three criterions, which are SIFs based mixed-mode criterion, energy release rates based mixed-mode criterion and SIFs based maximum circumferential stress criterion. The crack spread rate and crack direction are calculated based on first principles of fracture mechanics. A moving crack tip mesh topology is proposed to locally refine the grid resolution in the tip region. Predictions for the SIFs of a central horizontal crack in a square plate, a central horizontal crack in a long plate and a single edge cracked plate under plane stress condition show good agreement with either the previous predictions of ANSYS or the theoretical values. Exploratory calculations of a single crack under thermal loading have shown that the crack initiation and crack propagation pattern agree with the experimental observations.

Modelling of crack propagation of gravity dams by scaled boundary polygons and cohesive crack model

Crack propagation in concrete gravity dams is investigated using scaled boundary polygons coupled with interface elements. The concrete bulk is assumed to be linear elastic and is modelled by the scaled boundary polygons. The interface elements model the fracture process zone between the crack faces. The cohesive tractions are modelled as side-face tractions in the scaled boundary polygons. The solution of the stress field around the crack tip is expressed semi-analytically as a power series. It reproduces the singular and higher-order terms in an asymptotic solution, such as the William’s eigenfunction expansion when the cohesive tractions vanish. Accurate results can be obtained without asymptotic enrichment or local mesh refinement. The stress intensity factors are obtained directly from their definition and provide a convenient and accurate means to assess the zero-K condition, which determines the stability of a cohesive crack. The direction of crack propagation is determined from the maximum circumferential stress criterion. To accommodate crack propagation, a local remeshing algorithm that is applicable to any polygon mesh is augmented by inserting cohesive interface elements between the crack surfaces as the cracks propagate. Three numerical benchmarks involving crack propagation in concrete gravity dams are modelled. The results are compared to the experimental and other numerical simulations reported in the literature.

Modelling of Crack Propagation in Anisotropic Material Using Single-Domain Boundary Element Method

This paper evaluates the stress intensity factors (SIFs) at the crack tips, predicts the crack initiation angles and simulates the crack propagation path in the two-dimensional cracked anisotropic materials using the single-domain boundary element method (SDBEM) combined with maximum circumferential stress criterion. Numerical examples of the application of the formulation for different crack inclination angles, crack lengths, degree of material anisotropy, and crack types are presented. Furthermore, the propagation path in Cracked Straight Through Brazilian Disc (CSTBD) specimen is numerically predicted and the results of numerical and experimental data compared with the actual laboratory observations. Good agreement is found between the two approaches. The proposed BEM formulation is therefore suitable to simulate the process of crack propagation. Additionally, the anisotropic rock slope failure initiated by the tensile crack can also be analyzed by the proposed crack propagation simulation technique.

扩展有限元法在准脆性混凝土结构断裂中的数值模拟

扩展有限元法是基于自适应离散裂纹方法进行的混凝土裂纹扩展仿真模拟。并采用接触边界模型，接触边界模型包括正向位移和切向位移，允许通过界面进行剪切应力的传递，在扩展有限元法的框架中，对一个有凝聚力的裂纹扩展的延伸方向的研究有不同准则。通过两个例子，对最大周向应力理论，最大能量释放率理论和最小势能理论的实验数据进行了比较并形成规范。采用XFEM方法在一般加载模式I型和混合型加载条件下进行的混凝土断裂扩展数值模拟的灵活性和有效性已经得到了证实。 In this paper, the extended finite element method (XFEM) is used for a discrete crack simulation of concrete using an adaptive crack growth algorithm. An interface model is proposed which includes normal and tangential displacements and allows the transfer of shear stresses through the interface. Different criteria for predicting the direction of the extension of a cohesive crack are conducted in the framework of the XFEM. On the basis of two examples, a comparison between the maximum circumferential stress criterion, the maximum energy release rate and the minimum potential energy criterion with experimental data has been carried out. The considered numerical simulations have confirmed the flexibility and effectiveness of the XFEM for the modelling of crack growth under general mode I and mixed-mode loading conditions.

Analyse the role of the non‐singular stress in brittle fracture by BEM coupled with eigen‐analysis

ABSTRACTA coupled model resulting from the boundary element method and eigen‐analysis is proposed in this paper to analyse the stress field at crack tip. This new combine method can yield several terms of the non‐singular stress in the Williams asymptotic expansion. Then the maximum circumferential stress (MCS) criterion taken the non‐singular stress into account is introduced to predict the brittle fracture of cracked structures. Two earlier experiments are re‐examined by the present numerical method and the role of the non‐singular stress in the brittle fracture is investigated. Results show that if more terms of non‐singular stress are taken into account, the predicted crack propagation direction and the critical loading by MCS criterion are much closer to the existing experimental results, especially for dominating mode II loading conditions. Moreover, numerical results manifest that Williams series expansion can describe the stress field further from the crack tip if more non‐singular stress terms are adopted.

Crack propagation criteria in three dimensions using the XFEM and an explicit–implicit crack description

This paper studies propagation criteria in three-dimensional fracture mechanics within the extended finite element framework (XFEM). The crack in this paper is described by a hybrid explicit–implicit approach as proposed in Fries and Baydoun (Int J Numer Methods Eng, 2011). In this approach, the crack update is realized based on an explicit crack surface mesh which allows an investigation of different propagation criteria. In contrast, for the computation of the displacements, stresses and strains by means of the XFEM, an implicit description by level set functions is employed. The maximum circumferential stress criterion, the maximum strain energy release rate criterion, the minimal strain energy density criterion and the material forces criterion are realized. The propagation paths from different criteria are studied and compared for asymmetric bending, torsion, and combined bending and torsion test cases. It is found that the maximum strain energy release rate and maximum circumferential stress criterion show the most favorable results.

Typical Calculation Method of Stress Intensity Factors and Crack Growth Criterions on Infinite Plate Containing Hole-Edge Cracks

This paper introduces a finite element analysis software FRANC2D/L to calculate the stress intensity factor (SIF) and simulate the crack growth. Samples with infinite plate containing center crack, one hole-edge crack and two symmetrical hole-edge cracks were analyzed by this software. Comparing the SIF calculation results of the three samples based on displacement correlation method, J-integral method and virtual crack closure integral method, the results show that the three methods are all suitable for calculating the SIF problems, and the calculation precision of J-integral method and virtual crack closure integral method are better. Comparing the three crack growth criterion of maximum circumferential stress, maximum strain energy release rate and minimum strain energy density, the calculation velocity and precision of maximum circumferential stress criterion and minimum strain energy density criterion are prior to maximum strain energy release rate criterion. The calculating time and angle error of maximum strain energy release rate criterion is larger than that of the other two criterions．

XFEM fracture analysis of orthotropic functionally graded materials

In the present study, the extended finite element method (XFEM) has been used for fracture analysis of orthotropic functionally graded materials. Orthotropic crack tip enrichments have been used to reproduce the singular stress field near a crack tip. Moreover, the incompatible interaction integral method has been employed to extract the stress intensity factor components. Accuracy and convergence of the proposed method have been evaluated by numerical examples and quality results have been obtained by far fewer DOFs. Also, crack propagation in isotropic and orthotropic FGMs in the presence of crack tip enrichments has been investigated and various propagation criteria have been compared, and verified, if available, by experimental and numerical data in the literature. Application of XFEM in combination of the maximum circumferential tensile stress criterion for investigation of crack propagation in orthotropic FGM problems is performed for the first time.

ANALYTICAL SOLUTIONS OF THE TENSILE STRENGTH AND PREPONDERANT CRACK ANGLE FOR THE I-II MIXED CRACK IN BRITTLE MATERIAL

The I-II mixed crack is one of the most common cracks contained in the engineering materials. In this study, the theoretical solutions of the brittle tensile failure capability K J , the tensile strength σ c , and the initial fracture angle θ 0 are developed for the engineering materials containing the mode I-II mixed cracks (the crack angle is β ) under uniaxial tensile stress loading based on the maximum circumferential stress criterion. Additionally, under the same frame and boundary conditions, it is concluded that the preponderant crack angle β is 68.09 which making the cracks are most easy to fail and propagate; the corresponding brittle tensile capability K J is 0.97 K I C , and the tensile strength σ c is σ c =0.97K IC /√pa . Based on the results stated above, it is further concluded that, in the engineering structure design, if the tensile strength of materials σ c is given, the allowed maximum length of cracks a 0 is limited to 0.94 K 2 IC / pσ c 2 , which would provide the theoretical foundations for limiting the maximum length of cracks, and detecting cracks in engineering design. DOI: http://dx.doi.org/10.5755/j01.mech.18.1.1275

Dynamic crack propagation in matrix involving inclusions by a time-domain BEM

The dynamic crack propagation in composites with inclusions is analyzed by a time-domain boundary element method (BEM) in conjunction with the sub-region technique. The crack-growth direction and the crack-tip instantaneous velocity are determined by the maximum circumferential stress criterion. The instantaneous velocity is well smoothed by a bisection technique. New crack-tip elements of inconstant length are added to the active crack-tip to simulate the fast crack growth. Square root shape functions are adopted as to describe the proper asymptotic behavior in the vicinity of the crack-tips. The computation time for the dynamic fracture problems in composites with multiple inclusions is reduced by a numerical method. The influences of the inclusions on the shielding ratio, the crack growing path and the crack-tip instantaneous speed are well investigated.

Two‐Dimensional Fracture Mechanics Analysis Using a Single‐Domain Boundary Element Method

This work calculates the stress intensity factors (SIFs) at the crack tips, predicts the crack initiation angles, and simulates the crack propagation path in the two‐dimensional cracked anisotropic materials using the single‐domain boundary element method (BEM) combined with maximum circumferential stress criterion. The BEM formulation, based on the relative displacements of the crack tip, is used to determine the mixed‐mode SIFs and simulate the crack propagation behavior. Numerical examples of the application of the formulation for different crack inclination angles, crack lengths, degree of material anisotropy, and crack types are presented. Furthermore, the propagation path in Cracked Straight Through Brazilian Disc (CSTBD) specimen is numerically predicted and the results of numerical and experimental data compared with the actual laboratory observations. Good agreement is found between the two approaches. The proposed BEM formulation is therefore suitable to simulate the process of crack propagation. Additionally, the anisotropic rock slope failure initiated by the tensile crack can also be analyzed by the proposed crack propagation simulation technique.

Development of X-FEM methodology and study on mixed-mode crack propagation

The extended finite element method (X-FEM) is a novel numerical methodology with a great potential for using in multi-scale computation and multi-phase coupling problems. The algorithm is discussed and a program is developed based on X-FEM for simulating mixed-mode crack propagation. The maximum circumferential stress criterion and interaction integral are deduced. Some numerical results are compared with the experimental data to prove the capability and efficiency of the algorithm and the program. Numerical analyses of sub-interfacial crack growth in bi-materials give a clear description of the effect on fracture made by interface and loading condition.

Fatigue life prediction under cyclic thermal loads using the boundary elements method for two-dimensional problems

This study describes a sub-domain boundary element procedure for predicting the fatigue life of elastic media under cyclic transient thermal loads. The procedure assumes an initial crack in a two-dimensional medium, and evaluates the crack extension along a path defined by the maximum circumferential stress criterion. Partial closure may occur on the growing crack faces due to thermal loading. Appropriate thermal and mechanical boundary conditions are imposed on the numerical model to account for the contact state. The analysis requires solutions to the equations of quasi-static thermo-elasticity, and uses an iterative procedure to detect the contact region. We investigate cases of pure opening or mixed mode fracture, demonstrating the effects of crack closure on the predicted fatigue life. We compare the obtained results with those of other publications.

Numerical Simulation of Quasi-Brittle Fracture in Concrete Structures with Extended Finite Element Method

In this paper, the extended finite element method (XFEM) is used for a discrete crack simulation of concrete using an adaptive crack growth algorithm. An interface model is proposed which includes normal and tangential displacements and allows the transfer of shear stresses through the interface. Different criteria for predicting the direction of the extension of a cohesive crack are conducted in the framework of the XFEM. On the basis of two examples, a comparison between the maximum circumferential stress criterion, the maximum energy release rate and the minimum potential energy criterion with experimental data has been carried out. The considered numerical simulations have confirmed the flexibility and effectiveness of the XFEM for the modelling of crack growth under general mode I and mixed-mode loading conditions.

Mixed-mode dynamic crack propagation in graded materials under thermo-mechanical loading

Mixed-mode dynamic crack growth behavior in functionally graded materials (FGMs) under thermo-mechanical loading is studied. Asymptotic analysis in conjunction with displacement potentials has been used to develop thermo-mechanical stress fields for a mixed mode propagating crack in a FGM. The shear modulus, mass density, thermal conductivity and coefficient of thermal expansion of the FGM are assumed to vary exponentially along the gradation direction. First, asymptotic temperature fields are derived for an exponential variation of thermal conductivity and later these temperature fields are used in deriving stress fields. Using asymptotic thermo-mechanical stress fields the variation of maximum shear stress, circumferential stress and strain-energy density as a function of temperature around the crack tip are generated. Finally, utilizing the minimum strain-energy density criterion and the maximum circumferential stress criterion, the crack growth direction for various crack-tip speeds, non-homogeneity coefficients and temperature fields are determined.