Numerical Simulation Of Crack Growth Research Articles

Экспериментальная оценка адекватности численного моделирования межслоевой трещиностойкости слоистого стеклоэпоксикомпозита при комбинированной моде нагружения I/II

The reliability of numerical simulation of crack growth in a laminate glass-epoxy composite under mixed-mode loading by opening (mode I) and shear (mode II) of an interlayer crack is verified. According to the experimentally determined standard (DCB and ENF) and nonstandard (SLB and OLB) methods, the values of the parameters of interlayer crack resistance under individual and mixed-mode loading modes I and II calculated the exponent in the Benzeggagh-Kenane equation as a material constant of the laminate epoxy glass composite. Using this parameter and the ANSYS software package, within the framework of linear elastic fracture mechanics and the method of virtual crack closure, numerical finite element modeling of the growth of interlayer cracks in samples of a laminate glass-epoxy composite of the SLB and OLB types was carried out under a mixed-mode loading with a different fraction of modes. With the optimal number of elements in the finite element mesh per given length of the crack growth trajectory, numerical simulation provides sufficient accuracy of calculations of the limit load of the beginning of crack growth with a minimum amount of calculations and good agreement between the experimentally determined and calculated crack resistance parameters.

Influence of hard phase size and spacing on the fatigue crack propagation in tool steels—Numerical simulation and experimental validation

AbstractIn this study, the fatigue crack growth rate in four different tool steel microstructures (hot rolled, powdermetallurgically processed, as‐cast, and carbide‐free) is experimentally measured and correlated with hard phase size and spacing, as well as with the roughness of the fracture surface that is created by crack kinking. Numerical simulations of crack growth in carbide‐containing microstructures are conducted and investigated. The results indicate a favorable influence of carbides with a larger size and higher degree of roundness, as they create the largest mean free path between the individual carbides at the same hard phase volume content. This facilitates the formation of a plastic zone in the matrix, which dissipates crack energy and reduces the effective stress intensity. In addition, the effect of crack kinking is increased at larger carbide sizes. Concerning practical application, the results suggest that a high degree of deformation is favorable regarding the fatigue growth resistance of tool steels, and that the use of powder metallurgically (PM) grades with small carbides is discouraged, if the lifetime of a tool is mainly controlled by the crack growth rate and not crack initiation.

Influence of plane mixed-mode loading on the kinking angle of clinchable metal sheets

The aim of the present paper is to investigate the influence of plane mixed-mode loading on the kinking angle of clinchable metal sheets. In many fields of product manufacturing, the structures consist of individual components and sheets. The sheets can be joined to form complex structures with the aid of the simple and auxiliary part-free joining process "clinching". The main area of application are sheet metals with a maximum total thickness of 4 mm. During operation, joined structures can experience multi-axial, out-of-phase mixed-mode loading, causing small defects or cracks to propagate through the structure and ultimately lead to the component failure. Beginning with investigations of the influence of plane mixed-mode loading on the kinking angle of clinchable metal sheets, CTS specimens are taken from the 1.5 mm thick metal sheets of the base material used in the clinching process. In these specimens a pre-crack is initiated by Mode I loading. Subsequently, the specimens are clamped at different loading angles with the help of a special loading device, which enables a superposition of normal and shear loading. Under different loading angles, the specimens are subjected to cyclic loading to cause a kinking of the crack path. The resulting kinking angle is measured and compared with an analytical criterion for determining the kinking angle. Furthermore, the criterion is verified with the help of numerical crack growth simulation.

Numerical simulation of “Hall 1 of the Belgrade Fair“

This paper involves the analytical and numerical calculations of the the largest pre-stressed concrete free-standing structure in the world – the Dome of the “Hall 1 of the Belgrade Fair”, designed by a well-known Serbian scientist and engineer Branko Žeželj, one of the founders of the Institute for testing of materials IMS in Belgrade, conveniently positioned just across the street, best known for coming up with a concrete pre-stressing system, which is still widely used today. As a part of this research, this large and unique structure will be analyzed from point of view of structural integrity, including numerical simulation of crack growth in one of its support columns. Presented analyses also include the calculation of forces and moments in the structure as a whole, while also taking into account foundation displacements in the columns.

Welded joint geometry effect on fatigue crack growth resistance in different metallic materials

Fatigue crack growth through different welded joint regions was investigated, in terms of welded joint geometry and fatigue crack position. In the first phase of investigation, numerical simulation of crack growth in a welded joint made of steel P460NL1 was performed using extended Finite Element Methods (xFEM). Numerical models employed Paris law, using experimentally determined coefficients for each welded joint zone. Weld geometry was varied by using different heat affected zone (HAZ) widths, i.e. fatigue crack lengths. The second stage involved similar numerical models with different material (Protac 500). Fatigue lives for regions in both models were then compared.

Numerical simulation of crack growth in a welded joint with defects

Research presented in this paper involves the numerical simulation of crack growth in a welded joint made of common structural steel S235JR2, but with the presence of a number of different welding defects, which represents a scenario that is not covered by relevant standards, in this case EN ISO 5817. After analysing several defect combinations, which could occur in reality, the one with the least favourable combination of stress concentration and plastic strain was selected as the relevant model. A crack was then introduced in the location where the stresses, caused by tensile loading of the welded joint model, were above the yield stress. The numerical analysis performed in this case involved different combinations of load magnitudes and crack length, in order to determine at which point the initial crack will start propagating.

Fracture Modeling Of Cracked Pipe Under Monotonic And Cyclic Loading

ABSTRACT The present work presents experiment and numerical modelling to quantify the effect of the loading type on ductile crack growth in circumferential through-wall cracked SA508 Gr.1a pipes. In tests, three types of loading conditions are considered; monotonic, displacement-controlled and load-controlled large-amplitude cyclic loading. Experimental data are compared with numerical crack growth simulation results based on the multiaxial fracture strain energy model. Simulated results show overall good agreements with experimental data for all loading types. Based on FE results, the effects of the loading type and cyclic hardening model on ductile crack growth are discussed.

Lifetime Calculation of Soil-Loaded Non-Pressure Polymer Pipes

Outstanding durability of plastic pressure and non-pressure pipes can cause difficulties, when a reasonable lifetime estimation is needed. It is impossible to prove the lifetime by testing, but there is a method of calculation that can provide a certain idea about the expected lifetime. The lifetime estimation is based on the assumption that the failure occurs as a result of the slow crack growth mechanism and it is calculated using the linear elastic fracture mechanics approach. Numerical simulations of crack growth in the pipe are necessary for this calculation. These simulations must consider various effects that can play a role in the lifetime. This paper deals with the lifetime calculations of a pressure and a non-pressure corrugated pipe considering the soil loads acting on pipes when they are buried. In the simulation of the pressure pipe, a combination of loads is applied that consists of internal pressure, residual stress and the soil loads. The influence of the loads is discussed. The non-pressure corrugated pipe is loaded by the soil loads only.

Numerical simulation of crack growth in piezoelectric structures by BEM

In this paper, a dual boundary element computer program is developed for numerical simulation of a crack propagating in piezoelectric plates under a combined quasi-static electric and mechanical loading. To determine the crack growth path, two fracture criteria are taken into account: the maximum of hoop stress intensity factor (HSIF) and hoop mechanical strain energy release rate (HMERR). By using the displacement extrapolation method, these fracture parameters of any small kinked crack branch are obtained and validated by comparing with the available analytical results. The critical fracture loads for some test specimens are numerically analyzed based on the maximum HMERR fracture criterion. Different electrical boundary conditions on the crack faces are considered and checked with the experimental data. Finally, one crack or a pair of cracks propagating in infinite or finite piezoelectric plates is numerically simulated. The influences of the loading conditions, the anisotropic fracture toughness and the interaction between the cracks on the crack growth paths are also studied. The comparisons with the exiting finite element results show the accuracy and efficiency of the present BEM program for numerical simulation of crack growth in piezoelectric materials.

A simplified evaluation of the mechanical energy release rate of kinked cracks in piezoelectric materials using the boundary element method

Based on the concept of the hoop field intensity factors of an initial crack prior to any kink, an apparent hoop mechanical (strain) energy release rate (MERR) is defined to approximate the MERR of a piezoelectric crack with an infinitesimal kink at any arbitrary angle. The validity and the efficiency of the simplified approximation are examined by numerical examples using the boundary element method (BEM). The generalized crack-opening-displacements or displacement jumps are computed by the traction boundary integral equations (BIEs). By using the displacement extrapolation method, the crack-tip field intensity factors of any arbitrarily kinked crack in linear piezoelectric materials are obtained and the BEM results are validated by comparing them with the available reference analytical results. Then, the differences between the conventional field intensity factors and MERR of an infinitesimally kinked crack and the hoop field intensity factors and hoop MERR of the main crack prior to any kink are numerically analyzed. Finally, the crack propagation in an infinite linear piezoelectric material is numerically simulated. The paths of the crack growth are predicted by adopting four different fracture criteria, namely, the maximum hoop stress intensity factor (SIF) and MERR fracture criteria for the main crack-tip before the next propagation, and the maximum KI and MERR fracture criteria for the kinked tip of the main crack with an infinitesimal branch at an arbitrary kinking angle evaluated by using a trial crack extension technique. The comparisons among these results show that the present simplified approximation can efficiently provide a sufficient accuracy for numerical simulation of crack growth in linear piezoelectric materials.

Modeling and numerical simulation of crack growth and damage with a phase field approach

AbstractPhase field methods allow for convenient and efficient moving interface simulations. In this paper phase field approaches of different order are presented, and applied to simulate damage in solids of temperature dependent and non‐linear elastic materials. The numerical framework provides a NURBS based finite element method which minimizes the numerical and computational effort without impairing the smoothness required by the problem.In order to demonstrate the possibilities of such general phase field approaches a series of different models from material science and fracture mechanics is investigated. Specifically, a priori unknown crack propagation in different fracture modes is studied, simulations of thermomigration in a technical alloy and of void growth are presented and an inverse analysis of a dynamic fracture experiment is performed. The examples show the versatility of the presented low‐order and high‐order phase field approaches. (© 2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Theoretical, experimental and numerical investigations on crack growth in fracture mechanical graded structures

Crack propagation is not only influenced by the loading situation but also by a material gradation within the structure. Therefore, it has to be examined how the crack propagation behavior changes when a crack grows through regions which are characterized by different fracture mechanical material properties. Within the scope of this paper, especially the influence of a fracture mechanical material gradation on the beginning of stable crack propagation, the crack velocity, the crack propagation direction as well as on the occurrence of unstable crack growth for statically and cyclically loaded components is discussed. In this context, a developed concept for the prediction of crack propagation in fracture mechanical graded structures, experimental investigations as well as numerical simulations of crack growth are presented. The experimental considerations clarify the influence of the material gradation and confirm the predictions of the new concept. The numerical simulations of crack growth indicate the influence of the material gradation especially on the lifetime of graded components.

Fatigue crack growth near regions with differing stiffness

The choice of suitable process parameters can influence Young´s modulus of additively manufactured materials. Thereby regions with different stiffness can be generated to achieve a material gradation adapted to the loading of a component. Similar components can be produced with graded materials that are the topic of the Collaborative Research Centre TRR 30 of the Deutsche Forschungsgemeinschaft (DFG). If cracks grow near regions with differing stiffness, curved crack paths occur. In order to establish basic rules about the propagation behaviour of fatigue cracks in regions with differing stiffness the crack paths and the stress intensity factors for such cracks are numerically determined with the specially designed numerical crack growth simulation program ADAPCRACK3D. Hereby the orientation angle of the region boundaries and Young´s modulus of these regions are varied.

Crack propagation in fracture mechanical graded structures

The focus of manufacturing is more and more on innovative and application-oriented products considering lightweight construction. Hence, especially functional graded materials come to the fore. Due to the application-matched functional material gradation different local demands such as absorbability, abrasion and fatigue of structures are met. However, the material gradation can also have a remarkable influence on the crack propagation behavior. Therefore, this paper examines how the crack propagation behavior changes when a crack grows through regions which are characterized by different fracture mechanical material properties (e.g. different threshold values ?KI,th, different fracture toughness ?KIC). In particular, the emphasis of this paper is on the beginning of stable crack propagation, the crack velocity, the crack propagation direction as well as on the occurrence of unstable crack growth under static as well as cyclic loading. In this context, the developed TSSR-concept is presented which allows the prediction of crack propagation in fracture mechanical graded structures considering the loading situation (Mode I, Mode II and plane Mixed Mode) and the material gradation. In addition, results of experimental investigations for a mode I loading situation and numerical simulations of crack growth in such graded structures confirm the theoretical findings and clarify the influence of the material gradation on the crack propagation behavior. KEYWORDS. Functional fracture mechanical gradation; Crack propagation direction; TSSR-concept; Experimental investigations; Numerical simulations.

Investigation of crack paths in natural fibre-reinforced composites

Nowadays, fibre-reinforced composite materials are widely used in many fields, e.g. automotive and aerospace. Natural fibres such as flax and hemp provide good density specific mechanical properties. Additionally, the embodied production energy in natural fibres is much smaller than in synthetic ones. Within this paper the fracture mechanical behaviour of flax fibre-reinforced composites is discussed. Especially, this paper focuses on the determination and investigation of crack paths in compact tension specimens with three different fibre directions under a static as well as fatigue load. Differences and similarities in the obtained crack paths under different loading conditions are presented. Due to the pronounced orthotropic behaviour of those materials the crack path is not only governed by the stress state, but practically determined by the fibre direction and fibre volume fraction. Therefore, the well-known stress intensity factor solutions for the standard specimens are not applicable. It is necessary to carry out extensive numerical simulations to evaluate the stress intensity factor evolution along the growing crack in order to be able to determine fatigue crack growth rate curves. Those numerical crack growth simulations are performed with the three-dimensional crack simulation program ADAPCRACK3D to gain energy release rates and in addition stress intensity factors.

Numerical Simulation of Crack Growth and Coalescence in Rock-Like Materials Containing Multiple Pre-existing Flaws

A novel meshless numerical method, called general particle dynamics (GPD), is proposed to simulate samples of rock-like brittle heterogeneous material containing four preexisting flaws under uniaxial compressive loads. Numerical simulations are conducted to investigate the initiation, growth, and coalescence of cracks using a GPD code. An elasto-brittle damage model based on an extension of the Hoek–Brown strength criterion is applied to reflect crack initiation, growth, and coalescence and the macrofailure of the rock-like material. The preexisting flaws are simulated by empty particles. The particle is killed when its stresses satisfy the Hoek–Brown strength criterion, and the growth path of cracks is captured through the sequence of such damaged particles. A statistical approach is applied to model the heterogeneity of the rock-like material. It is found from the numerical results that samples containing four preexisting flaws may produce five types of cracks at or near the tips of preexisting flaws including wing, coplanar or quasi-coplanar secondary, oblique secondary, out-of-plane tensile, and out-of-plane shear cracks. Four coalescence modes are observed from the numerical results: tensile (T), compression (C), shear (S), and mixed tension/shear (TS). A higher load is required to induce crack coalescence in the shear mode (S) than the tensile (T) or mixed (TS) mode. It is concluded from the numerical results that crack coalescence occurs following the weakest coalescence path among all possible paths between any two flaws. The numerical results are in good agreement with reported experimental observations.

Numerical Simulation of Crack Growth of Composite Structure Based on XFEM

The basic principle and technique of a new and effective extended finite element method is introduced first in the paper. Compared with classical finite element method, the crack growth can be simulated by XFEM without making the crack surface associated to the mesh and without remeshing after crack growth. On the basis it is applied to analyze difficult problem of fracture and crack growth mechanism of composite pavement structural. By three-point bending test of composite structural beam, the whole process of initial crack and the crack growth of composite pavement structure is analyzed by numerical simulation. It can be divided into four key stages from cracking to crack reflection and each stage is presented by tensile stress and SATUSXFEM. The research results can provide important reference for composite structure design and proposed control countermeasure.

Crack propagation in rails under rolling contact fatigue loading conditions based on material forces

Tools for the prediction of crack growth in rails are of vital importance for the railway industry. In this paper, numerical simulations of crack growth in rails are presented. More specifically, the focus is on short surface head check like cracks, often observed at the rail gauge corner. A fatigue crack propagation model expressed in terms of a crack driving force, derived from the concept of material forces, is presented. It is shown that only the component parallel to the crack tip of the crack driving force is a reliable quantity that can be used in numerical simulations of a Rolling Contact Fatigue (RCF) situation. In addition, it is shown that one term in the expression of the crack driving force (Gsur) is dependent on the computational mesh. The propagation model has been used for parametric studies of crack propagation to investigate key parameters such as loading and crack geometry. Results from these studies suggest that anisotropic effects from the highly deformed surface layer may need to be included in order to simulate head check growth in rails accurately.

A Node Split Method for Crack Growth Problem

A node split method based on Partition-of-unity method and mesh modified has been developed for numerical simulation of crack growth. The crack tip could be represented by the enrichment function based on Partition-of-unity method. The crack besides the tip always locates on the edge of element by moving the nodes around crack, and the continuity of crack could be kept on. For an example of 2D quadrilateral mesh, mesh processing has been presented on different condition. The simulation results indicate that applying the node split method to simulate crack growth problem can achieve relatively good results even for sparse grid.

Finite element based simulation of fatigue crack growth with a focus on elastic–plastic material behavior

The numerical crack growth simulation has become more and more attractive today for reasons of time and economy. The presentation of a procedure for such a simulation of fatigue crack growth in elastic–plastic materials is the aim of this paper. The remeshing of the structure and the subsequent mapping of the status variables from the old mesh to the new one after each step of crack advance are thereby the core characteristics of the proposed procedure. The crack growth life is determined by integration of a crack growth law which is based on the effective range of the stress intensity factor. The results obtained by the procedure for autofrettaged Diesel-engine injection tubes are compared with experimental results and finite element results based on a nodal release scheme. A good agreement between the two numerical analyses and between the results with the proposed procedure and the experimental results concerning the endurance limit can be stated. By looking at the fatigue lives the experimental results are underestimated by the numerical ones.