Concepts Of Linear Elastic Fracture Mechanics Research Articles

ProCrackPlast: a finite element tool to simulate 3D fatigue crack growth under large plastic deformations

Many structural components and devices in combustion and automotive engineering undergo highly intensive cyclic thermal and mechanical loading during their operation, which leads to low cycle (LCF) or thermomechanical (TMF) fatigue crack growth. This behavior is often characterized by large scale plastic deformations and creep around the crack, so that concepts of linear-elastic fracture mechanics fail. The finite element software ProCrackPlast has been developed at TU Bergakademie Freiberg for the automated simulation of fatigue crack growth in arbitrarily loaded three-dimensional components with large scale plastic deformations, in particular under cyclic thermomechanical loading. ProCrackPlast consists of a bundle of Python routines, which manage finite element pre-processing, crack analysis, and post-processing in combination with the commercial software Abaqus . ProCrackPlast is based on a crack growth procedure which adaptively updates the crack size in finite increments. Crack growth is controlled by the cyclic crack tip opening displacement varDelta CTOD, which is considered as the appropriate fracture-mechanical parameter in case of large scale yielding. The three-dimensional varDelta CTOD concept and its effective numerical calculation by means of special crack-tip elements are introduced at first. Next, the program structure, the underlying numerical algorithms and calculation schemes of ProCrackPlast are outlined in detail, which capture the plastic deformation history along with the moving crack. In all simulations, a viscoplastic cyclic material law is used within a large strain setting. The numerical performance of this software is studied for a single edge notch tension (SENT) specimen under isothermal cyclic loading and compared to common finite element techniques for fatigue crack simulation. The capability of this software is featured in two application examples showing crack growth under mixed-mode LCF and TMF in a typical austenite cast steel, Ni-Resist. In combination with a crack growth law identified in terms of varDelta CTOD for a specific material, the tool ProCrackPlast is able to predict the crack evolution in a 3D component for a given thermomechanical loading scenario.

Numerical calculation of [formula omitted] to simulate fatigue crack growth under large scale viscoplastic deformations

Crack propagation under low cycle fatigue and thermomechanical fatigue is characterized by high plastic and creep strains that extend over large regions around the crack, so that concepts of linear-elastic fracture mechanics cannot be applied. In these cases, the cyclic crack tip opening displacement ΔCTOD is a promising loading parameter to quantify crack growth. In this work, suitable definitions and Finite Element techniques are investigated and compared for an accurate calculation of ΔCTOD under cyclic mechanical and/or thermal loading. A viscoplastic temperature dependent material model of Chaboche-type is used along with large strain settings, specified for the austenitic cast iron Ni-resist. Extensive two-dimensional analyses of Single Edge Notch Tension specimens revealed that collapsed special crack tip elements are superior compared with commonly used regular quadrilateral 8-node elements. At the same level of accuracy of ΔCTOD, they require an about ten times coarser mesh and show less sensitivity w.r.t. element size for both stationary and propagating cracks. In order to simulate fatigue crack growth, an efficient, fully automated FE-technique is developed for an incremental crack propagation by successive remeshing, whereby the deformations and internal state variables are mapped from the old mesh onto the new one. Recommendations are made regarding important numerical control parameters like optimal size of crack tip elements, length of crack growth increment in relation to plastic zone size and ΔCTOD value.

Prediction of the propagation direction of a crack that attacks the interface at an arbitrary angle

The problem of a crack subjected to uniaxial tension, approaching an interface between the two materials at an arbitrary angle, is considered. Prediction of the crack propagation was based on the linear elastic fracture mechanics (LEFM) concept. Obtained results show that the crack that attacks the interface at a right angle, coming from the softer material, would not penetrate the interface and would not continue to propagate across it, but that it would bounce back to the material it is coming from and continue to propagate along the path close to the interface. The similar situation is for the crack attacking the interface at an angle of 75°. It would also bounce away from the interface, though it might also deflect into it if the interface was weak. For the attack angle of 60°, as well as for the smaller angles, the crack would penetrate the interface and continue to propagate in the material across it. The prediction of the crack propagation direction was done for the two bimaterial combinations. Based on results, presented in this paper, it is possible to establish the criteria for predicting the propagation direction of a crack attacking the interface at an arbitrary angle.

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.

Experimental characterization and numerical modelling of the translaminar fracture of woven-ply hybrid fibers reinforced thermoplastic laminates

The understanding of fracture mechanisms and the assessment of fracture toughness are key factors to the design of high-performance composite structures to be used in aeronautics. Thus, this work addresses the influence of initial notch orientation on the translaminar fracture of woven-ply hybrid fibers reinforced thermoplastic polyether ether ketone (PEEK) laminates. The translaminar fracture of Single-edge-notch bending (SENB) specimens is experimentally characterized depending on two initial notches (0° and 45°). Such geometry results in a complex stress state within the laminates plies as well as simultaneous tension/compression failures. A full-field measurement technique has been implemented to monitor the crack initiation and growth on the specimen surface during mechanical loading. To better understand the role played by the initial notch orientation as well as the plies orientation contribution to fracture behavior, a specific Finite Element mesoscale model was built to account for the deformation mechanisms (namely local plasticity) and the different damage behaviours (fiber breakage in tension and compression, kinking/crushing in compression, delamination) occurring within the plies of quasi-isotropic laminates. Linear elastic fracture mechanics concepts have been applied to quantify the critical translaminar fracture toughness (about 40 kJ/m2 in both cases). Finally, this study provides useful information on the fracture toughness values for engineers willing to design thermoplastic-based composite parts with stress concentrators.

Risk based assessment of corroded oil drilling rig pipe integrity and remaining life

Risk based assessment of structural integrity of corroded oil drilling pipe is presented and applied on prototype (welded pressure vessel made of pipe) with artificial defects, which was previously investigated under service (10 MPa) and testing (22 MPa) pressure. The new concept based on application of structural integrity estimation to assess risk level according to probability and consequence of failure was used. Probability of failure is taken as the ratio of the service point, estimated by using the basic linear elastic fracture mechanics concept, and point on limit line in the Failure Analysis Diagramme (FAD). Taking into account measure of probability and consequence, the risk matrix is made for the round defect in a new pipe, 1.75 mm (depth) x 26 mm (length), service and testing pressure. Results are also compared with the previous ones for defects 3.5 × 28 mm and 5.25 × 30 mm. These results are useful for managers to make decision about further use of damaged pipes, based on data provided by engineers. The procedure for risk assessment of structural integrity is a general one, applicable to any component with known geometry, including crack, material properties and loading data, as well as to the structural life assessment.

Adaptive Finite Element Model for Simulating Crack Growth in the Presence of Holes.

This study presents a developed finite element code written by Visual Fortran to computationally model fatigue crack growth (FCG) in arbitrary 2D structures with constant amplitude loading, using the linear elastic fracture mechanics (LEFM) concept. Accordingly, optimizing an FCG analysis, it is necessary to describe all the characteristics of the 2D model of the cracked component, including loads, support conditions, and material characteristics. The advancing front method has been used to generate the finite element mesh. The equivalent stress intensity factor was used as the onset criteria of crack propagation, since it is the main significant parameter that must be precisely predicted. As such, a criterion premised on direction (maximum circumferential stress theory) was implemented. After pre-processing, the analysis continues with incremental analysis of the crack growth, which is discretized into short straight segments. The adaptive mesh finite element method was used to perform the stress analysis for each increment. The displacement extrapolation technique was employed at each crack extension increment to compute the SIFs, which are then assessed by the maximum circumferential stress theory to determine the direction of the crack growth and predict the fatigue life as a function of crack length using a modified form of Paris’ law. The application examples demonstrate the developed program’s capability and performance.

Application of the Failure Assessment Diagram approach for contact fatigue damage evaluation in railway wheel steels

AbstractA Failure Assessment Diagram (FAD), developed for rolling contact, was specifically formulated for railway wheel steels. The FAD allows combining a multiaxial fatigue criterion with the linear elastic fracture mechanics concept; in particular, it was used to assess the fatigue failure in wet contact, related to the pressurization of the fluid entrapped in surface cracks. The approach was applied to the results of previous bi‐disc tests carried out on three railway wheel steels, subjected first to a dry rolling‐sliding contact step, then to a wet contact step. The crack size distribution after the dry contact step was evaluated by a statistical approach; subsequently, the stress intensity factor during the wet contact step was estimated by finite elements. The results of the FAD agreed with the damage observed on the cross section of the specimens at the end of the tests. Furthermore, the FAD was used to determine the maximum allowable crack to prevent rolling contact fatigue, this way showing its potential as a damage tolerant approach.

Mesomechanical Investigation of the Relationship between the Length of the Fracture Process Zone and Crack Extensions in Concrete

This paper deals with a mesomechanical modeling of fracture in concrete like quasi-brittle materials. The paper seeks to provide insight regarding the variation of the fracture process zone (FPZ) length during the cracking process. The correlation between the FPZ length and the crack extension is also investigated. The FPZ variation is investigated through the evolution of cohesive tangential stresses along the crack path of different notched beams under three-point bending tests. The concept of equivalent linear elastic fracture mechanics is then employed to compute the crack extensions. The mesoscale investigation shows that the relationship between the FPZ length and the crack length is non linear. Furthermore, the numerical crack extensions are used to investigate the R-curve. It is shown that the R-curve is size-dependent and notch-sensitive.

Thermal fracture characteristics of an interface crack subjected to temperature variations

Abstract Thermal fracture characteristics – the thermal energy release rate and thermal stress intensity factor of a semi-infinite crack at an interface between the two elastic isotropic materials, subjected to the temperature variations, are considered in this paper. Those characteristics are determined based on application of the linear elastic fracture mechanics (LEFM) concept. Expressions for obtained theoretical solutions are compared to solutions from literature and they are found to be more concise. Influence of the materials change on these two thermal fracture properties were observed, as well as the influence of the thickness ratio of the two layers constituting the interface.

Optimization of Composite Process Parameters on Fracture Toughness of Glass Fiber Reinforced Plastics

The objective of the work was to investigate statistical analysis of fracture toughness of the glass fiber reinforced composites at different stacking sequences, strain rate and crack length. The glass reinforced Vinylester composites prepared by hand lay-up technique with various stacking sequences such as 0/90, 45/-45 and chopped strand orientations. 3-point bending for fracture toughness test for various notch depth ratio’s as per linear elastic fracture mechanics concept was conducted. Further the initial notch depth method was adopted to find the critical stress intensity factor KIC for the given notch depth ratio. Design of experiment using the Taguchi L9 array was formulated to understand the influence of parameters on fracture toughness. ANOVA was performed to find out the influencing weightage factor for fracture toughness. Regression analysis was used to develop a mathematical model that gave the contribution of individual parameters on responses. The fracture surface was investigated using scanning electron microscopy (SEM).The DOE response surface methodology showed the stacking sequence of [45/-45/0/90/Chopped]3s, with strain rate of 0.5 mm/min and without notch having the highest fracture toughness of 81.36 Mpa . ANOVA was carried out to know the statistical significance of factors influencing fracture toughness, Results showed that notch depth ratio was the most influencing factor with 68.67 % and stacking sequence with 24%. Accuracy of developed regression model was 90.61 % (R2), which indicating the confidence level of regression.

Estimate of the steel bridges fatigue life by application of the fracture mechanics

The bridge elements are subjected to the low-amplitude cyclic loading, causing the fatigue as the main problem that limits the carrying capacity and remaining working life of a structure. Identifying the parts prone to fatigue, inspection control, preventive maintenance, successful reinforcing and repair plans, secure the satisfying characteristics of a bridge during its working life.For a new structure is important that elements subjected to fatigue are so designed to avoid the danger of the fatigue fracture. The fracture mechanics represents a useful tool for analyzing the fatigue crack growth in steel elements. The relevant parameters for the remaining working life estimate are the load level and frequency and the stress concentration.A method, based on the Paris’ law, for predicting the remaining fatigue working life of steel bridges, is proposed and verified on an actual bridge. The considered bridge was found to be safe against the fatigue fracture, both for the present and the future increased load, since it was verified that it has the reserve with respect to fatigue life. Based on obtained results, one can conclude that the fatigue working life of a bridge and its elements can be estimated based on application of the LEFM (linear elastic fracture mechanics) concept.

Mechanical modelling of three-dimensional cracked structural components using the isogeometric dual boundary element method

The mechanical modelling of cracked structural components using Linear Elastic Fracture Mechanics (LEFM) concepts has major importance for structural integrity analysis. In addition, the Isogeometric Analysis (IGA) has recently emerged as a robust approach for analysing structural components directly from Computer-Aided Design (CAD) models. In this context, this study presents an isogeometric Dual Boundary Element Method (DBEM) formulation for the mechanical modelling of cracked three-dimensional structural components. The isogeometric formulation is based on NURBS surfaces. It was implemented regarding any polynomial orders for the basis functions. The strong singular and hypersingular integrals required by the DBEM are evaluated by the Guiggiani method. The C1 continuity is achieved at any collocation point inside the NURBS surfaces, ensuring the existence of hypersingular integrals. Consequently, discontinuous boundary elements are no longer required for the isogeometric DBEM, which enables an important reduction on the amount of collocation points at the crack surfaces. The Stress Intensity Factors (SIF) are evaluated by the displacement correlation technique. The geometrically exact description of the crack front eliminates the approximation errors related to the rotation of the displacement discontinuities with respect to the crack front local coordinate systems. Three applications involving edge and embedded cracks are presented. The isogeometric formulation provided accurate SIF results with less degrees of freedom at the crack surfaces in comparison with the conventional DBEM approach. However, the isogeometric DBEM approach has shown to be more expensive in terms of computational time.

Working life estimate of the tubular T-joint by application of the LEFM concept

The crack growth in tubular joints usually occurs along the weld’s toe. That is the point where the chord and brace intersect. The semi-elliptical crack appears in this area from the initial flaw that was created during the welding. Sensitivity to fatigue depends on combination of cyclic loading, initial defects, environmental influences and the hot spot stresses, which are result of the walls’ bending during the loading of a structure. The principles of the linear elastic fracture mechanics (LEFM) are applied here to crack growth in the tubular T-joint, subjected to axial load, in-plane and anti-plane bending. Influences of the level and type of loading, as well as of the joint’s geometrical characteristics, on the fatigue crack propagation and consequently on the working life of the welded joint, are considered. Based on the conducted analysis, which implies a set of assumptions, one can draw sufficiently relevant conclusion on the remaining working life of the tubular T-joint. The assumptions included: the crack shape is semi-elliptical, there is only one crack propagating through the tube wall, the cyclic plastic zone at the crack tip is small with respect to other geometrical variables and the crack grows only if the difference between the stress intensity factor values at maximal and minimal loads is greater than the stress intensity factor necessary for the fatigue crack growth initiation. Results are presented in the form of diagrams from which can be seen that for the same load level the longer working life is achieved for the axial load of the joint than for the in-plane bending, while the values for the anti-plane bending lie between these two limiting results.

Atomistic modeling of out-of-plane deformation of a propagating Griffith crack in graphene

Linear elastic fracture mechanics concepts have been widely used to characterize the fracture of nanoscale materials. In these concepts, pre-existing cracks in two-dimensional problems are assumed to be planar during the crack propagation. However, a perfect planar configuration of atomically thin nanostructures is not achievable in many applications due to complex interatomic interactions at the atomic scale. Formation of ripples and wrinkles has been experimentally observed in freestanding two-dimensional materials such as graphene. In this study, we employ molecular dynamics simulations to investigate the influence of out-of-plane deformation of a propagating Griffith crack. A numerical nanoscale uniaxial tensile test of a graphene sheet with a central crack is conducted. Two main aspects of the study are considered. The first is devoted to examining the influence of the crack orientation and the out-of-plane deformation of the crack surfaces on the crack-tip stress field. The second is concerned with the influence of the out-of-plane deformation on the fracture resistance of graphene. The analysis of the crack-tip stress field reveals a remarkably high transverse compressive stress at the crack surfaces, which induces the out-of-plane deformation. Moreover, our results reveal that in the absence of the crack out-of-plane deformation, the fracture resistance of graphene approaches the value given by Griffith’s criterion at a relatively smaller crack length as compared to the case involving out-of-plane deformation.

Effect of cyclic fatigue on the fracture toughness of Polyoxymethylene

Polymers are used in a wide range of applications and their properties are dependent upon the morphological development during processing and the specimen configuration which in turn define the mechanical properties. In this context fatigue and monotonic testing are part of the standard procedure to assess relevant mechanical and material parameters to ensure a better part design. The present work addresses the performance issues of a real component made of Polyoxymethylene (POM) which is subjected to cyclic loads from intermediate levels to high peak values inside a damping mechanism. For this linear elastic fracture mechanics concepts were used to characterize the behavior of a POM homopolymer resin used in this application. Injection molded compact tension specimens, with sharp and blunt notches, were tested under a combination of cyclic and monotonic loads and the fracture surfaces were examined. The critical stress intensity factor obtained by monotonic tests was evaluated as a function of the cycle number, where an increase after the first 1000 cycles followed by a continuous decrease with higher numbers of cycles was observed. A variation of approximately 50% and 70% were obtained along the duration of the tests for the sharp and blunt notch specimens, respectively. In light of the obtained results, a discussion is presented considering the dynamic specimen compliance and the structural features observed on the fracture surfaces in combination with the fracture mechanical response.

Fatigue crack growth analysis on square prismatic with embedded cracks under tension loading

One of the most important issues yet to be overcome by engineers is the integrity and reliability of engineering structures. This is to ensure the safety of the engineering structure is at the greatest since the catastrophic failures usually occur due to fatigue crack growth. Due to insufficient studies on the fatigue embedded crack growth, the prismatic bar is chosen as the model of the structure. It is wise to select the solid bar since the analysis can be much simpler, thus making it easier to examine the behaviour of the fatigue crack growth. In this study, the metallic square prismatic with embedded cracks is analysed using S-version Finite Element Modelling (S-version FEM) under tension loading. The S-version FEM is an open source program, that is built from codes previously compiled as a program. The S-version FEM structured using the global-local overlay technique consists of two separate global and local meshes. By using the basic concept from the energy release rate and stress intensity factors (SIF), the behaviour of the fatigue crack growth is analysed. From the linear elastic fracture mechanics concept, the SIF is calculated using the virtual crack closure-integral method. The influences of different initial crack size and aspect ratios on the fatigue crack growth are investigated in this study. In addition, the SIF results from the S-version FEM are compared with the analytical solutions. From the analysis, the root mean square errors (RMSE) are performed to support the validation. The RMSE shows a very small error of 0.227, 0.086 and 0.3089 according to the aspect ratio of 0.5, 1.0 and 2.0, respectively. The results also show significant characteristics and behaviour of the SIF trend along the crack front, corresponding to different aspect ratios. From this study, the S-version FEM is suitable to be used to predict the fatigue crack growth for the cracks embedded in a structure. Subsequently, the S-version FEM is an open source program can be modified for increasingly complex engineering problems.

Fatigue lifetime estimation of railway axles

Abstract The railway axles are subjected to cyclic loading during their operation. Their load is of long-term nature, therefore a real risk of fatigue failure exists. This failure could lead to derailment of the whole train with serious consequences. To prevent such scenario, the railway axles have to be safely removed from operation before their final failure occurs. This paper presents methodology for the residual fatigue lifetime prediction of the railway axle based on the linear elastic fracture mechanics concept. The methodology contains estimation of the critical position of initial crack, prediction of the fatigue crack front shape development during crack propagation, separation of the bending and press-fitting contributions to the axle load, experimental measurement of the crack growth kinetics of EA4T steel and subsequent estimation of the residual fatigue lifetime of railway axle. Part of the presented study is also devoted to the probability aspects of determination of material characteristics describing fatigue crack propagation and retardation effects caused by existence of plastic zone ahead of propagating fatigue crack. Described methodology is already applied in the design process of new railway axles in Bonatrans company.

Criteria for Prediction the Interfacial Crack Growth in Concrete

To understand the mechanical behavior of the concrete structures, one must analyze deformation and fracture of the interfaces between the constituents of the material that the structure is made of. Criteria for predicting the crack growth along an interface, based on the linear elastic fracture mechanics concept, applied for the cement substrate/aggregate interface, are presented in this paper. The two possible directions of the interfacial crack growth – the crack propagation along the interface and the crack kinking away from the interface are considered, with the corresponding energy release rates. For the case of the crack approaching the interface from one of the materials – cement, the competition between the crack deflecting into the interface and the crack penetrating the interface is considered with the corresponding energy release rates.

Influence of the Joint Geometry on the Stress Intensity Factor of the Fillet Welded Cruciform Joint Subjected to Tension and Bending

In this paper is analyzed the cruciform welded joint subjected to axial tension and bending in order to determine the influence of the joint geometry on the fracture mechanics parameters. The stress intensity factors are calculated analytically, with help of the programming package Mathematica®, based on the linear elastic fracture mechanics concept. Existence of the weld and loading was taken into account through the corresponding correction factors. Results obtained in this work show that increase of the weld size for the isosceles right-angled triangle leads to decrease of the stress intensity factor, while the stress intensity factor is increasing with weld's width w increase. Ratio of thicknesses B/T of the two plates that are welded to each other does not impose significant influence on the stress intensity factor. The working life and the fatigue crack growth curve of the two welds were analyzed as well.