Analysis Of Dynamic Crack Propagation Research Articles

Analysis of dynamic crack propagation in two-dimensional elastic bodies by coupling the boundary element method and the bond-based peridynamics

A novel method for predicting dynamic crack propagation based on coupling the boundary element method (BEM) and bond-based peridynamics (BBPD) is developed in this work. The special feature of this method is that it can take full advantages of both the BEM and PD to achieve a higher level of accuracy and efficiency. Based on the scale of the structure and the location of cracks, the considered domain can be divided into a non-cracked region and a cracked region. For the non-cracked region, a meshfree boundary-domain integral equation method (meshfree-BDIEM) is employed in the analysis to reduce the dimension by one and to increase the computational efficiency. The bond-based PD is applied to simulate the cracked region, which can model the initiation and propagation of the cracks automatically. The boundary nodes from the BEM on the interfaces can interact with the material points from the PD directly. By using the displacement continuity and force equilibrium conditions on the interfaces, a combined model is obtained by merging the mass, stiffness, and force matrices from each region of the domain. Both the implicit and explicit BEM-PD coupled solution methods can deliver accurate results without inducing the ghost forces. Several benchmark problems of dynamic crack propagation have been modeled by using the method, which demonstrate that the developed BEM-PD coupled approach can be an efficient numerical tool to model the dynamic crack propagation problems.

Dynamic crack propagation analysis combined the stable scheme and continuous-discontinuous cellular automaton

A continuous-discontinuous cellular automaton method (CDCA) is developed for dynamic crack propagation. First, a separated time integral scheme is built, in which time difference is divided into two separated time steps: one balances the change of the geometric discretization caused by crack growing, and the other balances the dynamic loading. Second, an adaptive energy conservation strategy is proposed for the CDCA that includes the change in the degree of nodal freedom for the crack tip element, and a new strategy for the inheritance of the degrees of nodal freedom is proposed. This method retains the enrichment scheme for the discontinuity, and the Shepard interpolation method is employed to transform the variables’ values, so as to keeps the energy conservation caused by crack tip location change. Then, the enriched degree of nodal freedom values are easily passed from the crack tip enrichment to the penetrated enrichment and crack tip local coordinate system changing with crack growing. Third, a dynamic crack propagation criterion is developed, which can be used for tensile fractures and compression shear fractures. Based on those theories, a new cellular automaton model is built for dynamic crack propagation. Compared to the extended finite element method (XFEM), the calculation efficiency has been greatly improved, and several numerical examples are given to illustrate accuracy and efficiency of the present method.

Dynamic crack propagation analysis based on the s-version of the finite element method

A strategy to efficiently analyse dynamic crack propagation based on the s-version of the finite element method (s-method) is proposed. This strategy superimposes a local mesh over the area that includes the propagating crack tip, which is made possible by the flexible definition of the local mesh. For a strictly accurate evaluation based on the local fracture stress criterion, we introduce the nodal force release technique to the local mesh to simulate dynamic crack propagation. Based on the numerical results, we identify the appropriate global and local mesh conditions required to achieve accurate and efficient local stress evaluations. Comparisons with the standard finite element method using equivalent accuracies show that the proposed strategy can successfully reduce numerical costs. Our results thus demonstrate that the proposed strategy for dynamic crack propagation analysis based on the s-method significantly improves the efficiency of dynamic crack propagation analysis.

Analysis of Fatigue Crack Propagation on Orthotropic Bridge Deck Based on Extended Finite Element Method

Due to stress concentration as well as welding residual stress, fracture due to vehicle fatigue loads is easy to occur in the weld and its adjacent position of long-span bridge, especially at the toe of weld between the U-rib and orthotropic steel bridge deck. In order to investigate the fatigue crack propagation mechanism of the toe of weld in long-span bridge, a multi-scale finite element model including the whole bridge, local components, the welding details and cracks was established firstly. And then, based on birth and death element technology, the welding heat and structural coupling process simulation was carried out in order to investigate the effect of welding residual stress on fatigue performance. Finally, based on the extended finite element method, the static analysis and the dynamic crack propagation analysis for the semi-elliptical crack in the established multi-scale finite element model were conducted. The welding process shows that the peak value of residual tensile stress in weld zone between the U-rib and top deck could reach the material yield strength, while the regions far away from the weld are in the state of compression. A 32ton standard fatigue vehicle specified in British Standard BS5400 was applied for the fatigue crack static analysis. The results show that when the vehicle is acting on different lanes, the fatigue crack initiating from the toe of weld between U-rib and top deck is mainly under compression in most cases. Only in several cases the fatigue crack is in the state of tension, however, the tensile stress required by the fatigue crack propagation has not be reached. Under the 50ton vehicle, the fatigue stress only at the toe of weld of U-rib can meet the requirements of the fatigue crack propagation. The dynamic analysis on fatigue crack reveals that the crack in the toe of weld of U-rib is in tensile stress state, and the fatigue crack is the mixed mode crack of Mode I, II and III. When the residual stress field was introduced, the stress state at the region where fatigue crack initiates will change and the angle of fatigue crack propagation will increase. The crack at the toes of weld of top deck under the 32ton and 50ton fatigue vehicles is mainly under compression. When the residual stress field was introduced, the crack will be subjected to be a tensile state. It will become mixed mode crack of Mode I, II and III and be dominated by Mode I.

Parametric analysis of dynamic crack propagation of concrete bending beam based on the extended finite element method

The fracture properties of concrete are affected by various factors, including material parameters and crack geometry parameters. In the paper, pure mode I fracture and mixed mode fracture of concrete bending beams under impact load were studied experimentally and numerically. Numerical models by applying extended finite element method based on the cohesive crack model were employed to simulate pure mode I fracture and mixed mode fracture of concrete bending beams, an experimental program was conducted to validate the numerical models. The effects of material parameters as well as crack geometry parameters on the fracture properties of concrete bending beams were discussed and the most sensitive parameter to affect the fracture properties of concrete bending beams was determined based on the numerical simulations. The results show that the simulation results match reasonably well with the experimental results. For pure mode I fracture, concrete strength grade is proved to have less influence on the fracture properties of concrete bending beams under relative high strength grade condition; Elastic modulus was determined to have the greatest impact on the fracture properties of concrete bending beams, followed by tensile stress, initial crack length and fracture energy; however, Poisson ratio have almost no effect on the fracture properties of concrete bending beams. For mixed mode fracture problem, the influences of initial notch position on crack propagation path can be expressed as a competition between mode I fracture and mixed mode fracture, with offset parameter increasing from 0.0 to 1.0, the fracture failure mode of concrete bending beams changes from pure mode I fracture to mixed mode fracture, followed by both mode I and mixed mode fractures, and finally translates to mode I fracture.

Numerical analysis of dynamic crack propagation in biaxially strained rubber sheets

This paper proposes a computational framework for dynamic crack propagation in rubber in which a nonlinear finite element analysis using cohesive zone modeling approach is used. A suddenly initiated crack at the center of biaxially stretched sheet problem is studied under plane stress conditions. A transient dynamic analysis using implicit time integration scheme is performed. In the constitutive modeling, the continuum is characterized by finite-viscoelasticity theory and coupled with the fracture processes using a cohesive zone model. This computational framework was introduced previously by the present authors (Elmukashfi and Kroon, 2012). In the current work, the use of a rate-dependent cohesive model is examined in addition to investigation of generalized biaxial loading cases. A Kelvin–Voigt element is used to describe the rate-dependent cohesive model wherein the spring is described by a bilinear law and dashpot with a constant viscosity is adopted. An explicit integration is used to incorporate the rate-dependent cohesive model in the finite element environment. A parametric study over the cohesive viscosity is performed and the steady crack propagation velocity is evaluated and compared with experimental data. It appears that the viscosity varies with the crack speed. Further, the total work of fracture is estimated using rate-independent cohesive law such that the strength of the cohesive zone is assumed to be constant and the separation work per unit area is determined form the experimental data. The results show that fracture-related processes, i.e. creation of new surfaces, cavitation and crystallization; contribute to the total work of fracture in a contradictory manner.

A peridynamic material model for the analysis of dynamic crack propagation in orthotropic media

A new material model for the dynamic fracture analysis of anisotropic materials has been proposed within the framework of the bond-based peridynamic theory. This model enables predicting complex fracture phenomena such as spontaneous crack nucleation and crack branching, curving and arrest, a capability inherited from the bond-based peridynamic theory. An important feature of the model is that the bond properties, i.e. the stiffness constant and critical stretch, are continuous functions of bond orientation in the principal material axes. This facilitates fracture analysis of anisotropic materials with random orientations, such as polycrystalline microstructures. Elastic and fracture behaviour of the model has been verified through simulating uniaxial tension of a composite plate and fracture of a cortical bone compact tension specimen, and making quantitative comparisons to analytical and experimental data. To further demonstrate the capabilities of the proposed model, dynamic fracture of a polycrystalline microstructure (alumina ceramic) has been simulated. The influence of the grain boundary and grain interior fracture energies on the interacting and competing fracture modes of polycrystalline materials, i.e. intergranular and transgranular fracture, has been studied.

Dynamic crack propagation analysis using scaled boundary finite element method

The prediction of dynamic crack propagation in brittle materials is still an important issue in many engineering fields. The remeshing technique based on scaled boundary finite element method (SBFEM) is extended to predict the dynamic crack propagation in brittle materials. The structure is firstly divided into a number of superelements, only the boundaries of which need to be discretized with line elements. In the SBFEM formulation, the stiffness and mass matrices of the super-elements can be coupled seamlessly with standard finite elements, thus the advantages of versatility and flexibility of the FEM are well maintained. The transient response of the structure can be calculated directly in the time domain using a standard time-integration scheme. Then the dynamic stress intensity factor (DSIF) during crack propagation can be solved analytically due to the semi-analytical nature of SBFEM. Only the fine mesh discretization for the crack-tip super-element is needed to ensure the required accuracy for the determination of stress intensity factor (SIF). According to the predicted crack-tip position, a simple remeshing algorithm with the minimum mesh changes is suggested to simulate the dynamic crack propagation. Numerical examples indicate that the proposed method can be effectively used to deal with the dynamic crack propagation in a finite sized rectangular plate including a central crack. Comparison is made with the results available in the literature, which shows good agreement between each other.

Numerical analysis of dynamic crack propagation in rubber

In the present paper, dynamic crack propagation in rubber is analyzed numerically using the finite element method. The problem of a suddenly initiated crack at the center of stretched sheet is studied under plane stress conditions. A nonlinear finite element analysis using implicit time integration scheme is used. The bulk material behavior is described by finite-viscoelasticity theory and the fracture separation process is characterized using a cohesive zone model with a bilinear traction-separation law. Hence, the numerical model is able to model and predict the different contributions to the fracture toughness, i.e. the surface energy, viscoelastic dissipation, and inertia effects. The separation work per unit area and the strength of the cohesive zone have been parameterized, and their influence on the separation process has been investigated. A steadily propagating crack is obtained and the corresponding crack tip position and velocity history as well as the steady crack propagation velocity are evaluated and compared with experimental data. A minimum threshold stretch of 3.0 is required for crack propagation. The numerical model is able to predict the dynamic crack growth. It appears that the strength and the surface energy vary with the crack speed. Finally, the maximum principal stretch and stress distribution around steadily propagation crack tip suggest that crystallization and cavity formation may take place.

612 拡張個別要素法による脆性高分子材料の動的き裂伝ぱ解析(材料・構造部材の動的特性(2),ものづくりにおける基礎研究と先端技術の融合)

612 拡張個別要素法による脆性高分子材料の動的き裂伝ぱ解析(材料・構造部材の動的特性(2),ものづくりにおける基礎研究と先端技術の融合)

Dynamic crack propagation analysis of orthotropic media by the extended finite element method

Dynamic crack propagation of composites is investigated in this paper based on the recent advances and development of orthotropic enrichment functions within the framework of partition of unity and the extended finite element method (XFEM). The method allows for analysis of the whole crack propagation pattern on an unaltered finite element mesh, defined independent of the existence of any predefined crack or its propagation path. A relatively simple, though efficient formulation is implemented, which consists of using a dynamic crack initiation toughness, a crack orientation along the maximum circumferential stress, and a simple equation to presume the crack speed. Dynamic stress intensity factors (DSIFs) are evaluated by means of the domain separation integral method. The governing elastodynamics equation is first transformed into a standard weak formulation and is then discretized into an XFEM system of time dependent equations, to be solved by the unconditionally stable Newmark time integration scheme. A number of benchmark and test problems are simulated and the results are compared with available reference results.

3D dynamic crack propagation analysis with PDS-FEM

This paper briefly explains a recently developed numerical technique called PDS-FEM and its dynamic extension. PDS-FEM is a simple and efficient numerical technique for modeling propagation crack in brittle materials. The discretization scheme used in this new numerical technique is called particle discretization scheme (PDS). PDS uses characteristic functions of Voronoi and Delaunay tessellations to discretize function and its derivatives, respectively. The uses of non-overlapping shape functions facilitate simple and numerically efficient failure treatment. We considered the dynamic extension of PDS-FEM and simulated several real life experiments, to illustrate the potential of simulating dynamic crack propagation of problems requiring fine domain discretizations.

Finite element analysis of dynamic crack propagation using remeshing technique

This paper presents a finite element analysis based on the remeshing technique to predict the dynamic crack propagation and crack arrest in a brittle material, namely Araldite-B. The dynamic fracture toughness criterion is used to form the crack tip equation of motion. Plane stress condition is invoked in the present two-dimensional fracture analysis of the RDCB (rectangular double cantilever beam) specimens and the unknown crack tip position, and velocity is computed during the analysis by the dynamic fracture criterion. According to the new crack tip position, a remeshing algorithm has been used to simulate the dynamic crack growth and arrest. The obtained results including kinetic energy and strain energy, crack tip velocity, dynamic stress intensity factor during crack growth and also crack arrest length have been presented. Comparison of the results with those cited in the literature has shown a good agreement.

Dynamic Crack Propagation Analysis by Node-Based FEM

Due to a very short time span of dynamic fracture event, it is quite difficult to experimentally measure dynamic stress field near the crack tip. Node-based finite element method (NBFEM) developed by Yagawa et al was extended to solve dynamic crack propagation problems by modifying the original NBFEM and three schemes of crack tip node separation during crack propagation are examined. A dynamic stress intensity factor in mode I, KdynI, is calculated for fast propagating crack at a constant speed. Three different schemes of the crack tip node separation were considered. Comparing the numerical results with those analytically obtained by Freund showed that the condition of zero initial velocity and nonzero acceleration gives the highest accuracy of three conditions with only 0.91% error.

730 脆性材料の動的き裂伝ぱ解析(OS11(3) 材料の動的破壊靭性とき裂伝播)

730 脆性材料の動的き裂伝ぱ解析(OS11(3) 材料の動的破壊靭性とき裂伝播)

160 粒子離散化にもとづく有限要素法による動的破壊進展解析(種々のメッシュフリー/粒子法,OSO9 メッシュフリー/粒子法と関連技術)

160 粒子離散化にもとづく有限要素法による動的破壊進展解析(種々のメッシュフリー/粒子法,OSO9 メッシュフリー/粒子法と関連技術)

熱衝撃による傾斜機能材料中の動的き裂進展解析(き裂・複合材料の計算力学,計算力学関連の理論・応用技術 OS.2)

熱衝撃による傾斜機能材料中の動的き裂進展解析(き裂・複合材料の計算力学,計算力学関連の理論・応用技術 OS.2)

Crack blunting and the strength of soft elastic solids

When a material is so soft that the cohesive strength (or adhesive strength, in the case of interfacial fracture) exceeds the elastic modulus of the material, we show that a crack will blunt instead of propagating. Large–deformation finite–element model (FEM) simulations of crack initiation, in which the debonding processes are quantified using a cohesive zone model, are used to support this hypothesis. An approximate analytic solution, which agrees well with the FEM simulation, gives additional insight into the blunting process. The consequence of this result on the strength of soft, rubbery materials is the main topic of this paper. We propose two mechanisms by which crack growth can occur in such blunted regions. We have also performed experiments on two different elastomers to demonstrate elastic blunting. In one system, we present some details on a void growth mechanism for ultimate failure, post–blunting. Finally, we demonstrate how crack blunting can shed light on some long–standing problems in the area of adhesion and fracture of elastomers.

131 熱衝撃を受ける傾斜機能材料の動的き裂進展解析

131 熱衝撃を受ける傾斜機能材料の動的き裂進展解析

639 拡張個別要素法による動的き裂伝ぱ解析

639 拡張個別要素法による動的き裂伝ぱ解析