3D Crack Front Research Articles

Quantifying 3D crack propagation in nodular graphite cast iron using advanced digital volume correlation and X-ray computed tomography

Advanced digital volume correlation (DVC) combined with X-ray computed tomography (XCT) was utilized to investigate the 3D crack propagation in nodular graphite cast iron under tensile loading. The objective of this work was to quantify crack growth at the voxel-scale and extract fracture mechanics parameters such as the 3D crack front, crack opening displacements (CODs), and stress intensity factors (SIFs). By employing a crack growth updating strategy and an adaptive multiscale mesh, the 3D crack shape and propagation were accurately captured throughout the entire process. Von Mises strain and COD fields were characterized to provide insights into plastic zones and variations in crack opening behavior. Estimation of SIFs revealed a mode I dominant regime and limited influence from modes II and III. This study provides comprehensive insights into crack propagation and crack opening behavior, providing valuable information to fracture mechanics.

Numerical 3D‐bifurcation analysis of star‐shaped crack patterns using the energy method

AbstractThe present research deals with a three‐dimensional (3D) Finite Element Method (FEM) bifurcation analysis based on the global mechanical potential that can be used to find the parameters at which a crack pattern changes. In our case we want to analyze at which point the star‐shaped shrinkage cracks in an aqueous colloidal suspension filled in a glass cylinder change from four to three or two cracks growing. The driving force for the crack growth is shrinkage caused by diffusion controlled drying. The 3D crack front geometry is described efficiently by using a Fourier series approach. Based on steady‐state crack growth, the Fourier coefficients are determined in a first step using an optimization algorithm. As a result, the time dependent crack growth can be determined. In a second step, the bifurcation point is determined by an eigenvalue analysis of the second order derivatives of the potential energy of the system. If the lowest eigenvalue reaches zero the fundamental solution becomes unstable and a transition will occur. Our analysis shows that the transition from four to two cracks is preferred over the transition from four to three cracks.

Coupling of phase field and viscoplasticity for modelling cyclic softening and crack growth under fatigue

A coupled phase field-viscoplasticity approach was developed to model the deformation and crack growth in a nickel-based superalloy under fatigue. The coupled model has an advantage in predicting the cyclic softening behavior of the alloy caused by fatigue damage, overcoming a major limitation of the original cyclic viscoplasticity model. The coupled approach is also highly effective in predicting fatigue crack propagation under varied dwell times at peak load, an important behavior for crack growth under dwell fatigue. By incorporating the stress state factor, the coupled model is further utilized to investigate the growth behavior of 3D cracks under fatigue. Both the geometrical feature of the 3D crack front and the overall crack growth rate are well captured, confirming the predicative capability of the coupled model.

A method to compute mixed‐mode stress intensity factors for nonplanar cracks in three dimensions

SummaryMethods to compute the stress intensity factors along a three‐dimensional (3D) crack front often display a tenuous rate of convergence under mesh refinement or, worse, do not converge, particularly when applied on unstructured meshes. In this work, we propose an alternative formulation of the interaction integral functional and a method to compute stress intensity factors along the crack front which can be shown to converge. The novelty of our method is the decoupling of the two discretizations: the bulk mesh for the finite element solution and the mesh along the crack front for the numerical stress intensity factors, and hence we term it the multiple mesh interaction integral (MMII) method. Through analysis of the convergence of the functional and method, we find scalings of these two mesh sizes to guarantee convergence of the computed stress intensity factors in a variety of norms, including maximum pointwise error and total variation. We demonstrate the MMII on four examples: a semiinfinite straight crack with the asymptotic displacement fields, the same geometry with a nonuniform stress intensity factor along the crack front, a spherical cap crack in a cylinder under tension, and the elliptical crack under far‐field tension and shear.

Improvement of Stress Intensity Factor Analysis Using Overall Defined Basic Density Function on Crack Face

In this study, an improved technique for the evaluation of stress intensity factor (SIF) along the 3D planar crack front is proposed. In the present analysis, a planar triangular element is used to cover the total crack face. The stress field induced by a body force doublet in an infinite body is used for a fundamental solution. In the present analysis, overall defined basic density function of body force doublet is introduced. The crack problem is formulated as hypersingular boundary integral equations and the magnitudes of distributed point force doublets are determined through boundary conditions. The numerical SIF solution obtained using the present approach was compared with the solution obtained using the conventional basic density function. The results indicate that the proposed technique improves the accuracy of SIF. In addition, some numerical examples were examined to verify the effectiveness and the robustness of the proposed technique.

Calculation of stress intensity factor along the 3D crack front by dual BIE with new crack front elements

The paper applies dual BIE with crack opening displacements for the calculation of stress intensity factors of a 3D crack. A general transformation is introduced to remove the weak singularity no matter where the source point is located. A singular integration element is subdivided into several quadrilaterals and triangles with fine shapes to ensure the high accuracy of singular integrals. Two types of special crack front elements based on the quadrilateral discontinuous element are proposed to model the distribution of displacements in the vicinity of the crack tips. Results of our method are in very good agreement with the existing results.

Two-parameter fracture characterization of a welded pipe in the presence of residual stresses

In this paper two-parameter fracture characterization of elastic and elastic-plastic stress/strain field around a crack front is presented for a welded pipe component containing a circumferential through-thickness crack. A macro function programmed in PYTHON is used to compute the constraint parameters (T-stress, Tz and Q factors) of the specimen in the open source finite element package Code_Aster. Data obtained from literature was employed to support three-dimensional finite element models developed in this research to study the impact of high magnitude repair-weld residual stresses. Complete distributions of the T-stress, Tz and Q-factors were obtained along a 3D crack front in the presence of residual stresses. The effects of stresses (residual and operational) on the constraint parameters are studied. It is shown that a two-parameter methodology provides effective characterization of three dimensional elastic–plastic crack tips constraint.

Influence of Small Cavity Existing in the Vicinity of 3D Crack Front

In this paper, the interference between arbitrary shaped 3D planar crack and cavity existing in the vicinity of the crack front is evaluated. It is assumed that the treated region is unbounded and subjected to uniaxial tension at infinity. The interaction between crack and cavity is treated by body force method. The surface of the crack and cavity is modeled by number of small triangular elements and the density of body force and weight function of the force doublet is assumed at a constant on each triangle. Numerical stress analyses are examined by changing the radius of cavity and the distance between the cavity and crack front systematically. Numerical results are presented for the stresses along the centerline between cavity and crack. To validate the current analysis, numerical results are compared with the results in the literature and found good agreement.

The effect of thickness on out-of-plane constraint in terms of the T-stress

The plastic zone is theoretically and numerically analyzed for various combinations of the nonsingular terms xx T to zz T ratios in connection with specimen thickness under mode I loading. The plastic zone size distribution is based on the Mises yield criterion for mode I conditions and mapped in the specimen thickness direction. It is shown that the plastic zone size is affected by the zz T -stress, i.e. there is strong effect of out-of-plane constraint (thickness) on crack tip plastic zones. In addition, to study the effect of thickness and loading mode mixity (mode I and II) of the specimen on the singular (KI, KII) and the non-singular ( xx T , zz T ) terms along the 3D crack front, three-dimensional stress fields are analyzed by means of finite element analysis. The strong effect of thickness and mixed mode loading conditions on the zz T -stress is observed. At the same time, there is not the effect of thickness on the nonsingular xx T -stress at the same loading conditions.

Stress-intensity factors at the interface edge of a partially detached fibre

Fibre-reinforced composites (FRCs) are multiphase materials characterised by high engineering performances. However, some degrading effects in such materials (the loss of their bearing capacity, related to the matrix–fibre detaching phenomenon also known as debonding, fibre breaking, matrix cracking) must be carefully taken into account in the assessment of the FRC safety and durability. In the present paper, the fibre–matrix detaching phenomenon is examined from the fracture mechanics point of view. The stress singularity arising at the extremities of a perfectly bonded fibre is studied, and the related Stress-Intensity Factors (SIFs) are used to assess the detachment initiation up to the appearance of a debonded region at the two ends of the fibre. The circular shape boundary line representing the edge of the debonded region is analysed as a 3D crack front located between two different materials, and the Stress-Intensity Factors are determined for different remote loadings and composite characteristics.

Determining the mixed mode stress intensity factors of surface cracks in functionally graded hollow cylinders

This work reports about an investigation on mixed mode stress intensity factors (SIFs) of three-dimensional (3D) surface cracks in hollow cylinders made-up of functionally graded material (FGM). A finite element implementation of the interaction energy integral in domain form is employed to extract the SIFs. In turn, surface cracks located at the inner and outer wall of the cylinders are considered, and the influence of exponentially varying Poisson’s ratio and Young’s modulus in radial direction on the SIFs is studied in detail. The computational results reported herein show that graded materials properties can significantly affect the magnitude and the distribution of SIFs along 3D crack fronts in FGM hollow cylinders.

Modeling of mixed-mode crack growth in ductile thin sheets under combined in-plane and out-of-plane loading

This paper describes a modeling approach for analyzing mixed-mode crack growth events in ductile thin-sheet materials under large deformation and combined in-plane and out-of-plane loading conditions. The remote mixed-mode I/III loading leads to local mixed-mode I/II/III fields near the crack front. Making use of full-field surface deformation measurements, finite element models of mixed-mode I/III stable tearing events in thin-sheet specimens have been developed. Model predictions have been compared with experimental measurements (a) just prior to initial crack growth and (b) during stable tearing crack growth. Analyses of curvilinear crack growth events are carried out using a nodal release option or a local re-meshing option and using a generalized CTOD parameter with experimentally measured critical CTOD values. Results of this study suggest that the modeling approach can be employed to numerically re-construct experimental crack growth events in thin plate specimens. This offers a viable means of analyzing and understanding the mixed-mode crack growth events and provides a tool for further investigations of 3D crack front fields (which are otherwise unavailable experimentally) and for the study of fracture criteria for stable tearing events.

Mixed Mode 3D Stress Fields and Crack Front Singularities for Surface Flaw

The elastic-plastic stress fields and mode mixity parameters for semi-elliptical surface cracks on biaxial loaded plates have been investigated using detailed three-dimensional finite element calculations. Different degrees of mode mixity are given by combinations of the far-field stress level, biaxial stress ratio and inclined crack angle. For a wide range of crack inclination angles, elastic-plastic stress fields along the crack front for both semi-circular and semi-elliptical surface cracks being subjected to remote biaxial loading have been obtained. For both crack geometry types, it was demonstrated that, in the vicinity of the corner, the behavior stress fields differ from the stress component distributions at the deepest point on the crack front. This phenomenon is due to the free surface effect. Combining analytical solutions and 3D finite element calculations, the elastic crack tip singularity for a surface semi-elliptical crack has been investigated on a biaxially loaded plate. The distributions of singularity exponents have been obtained along the crack front for three main cases of mixed-mode loading.

On the [formula omitted]-integral and the out-of-plane constraint in a 3D elastic cracked plate loaded in tension

In this study, the behaviour of the J x 1 -integral and its components J P -integral and J A -integral is numerically investigated for 3D linear elastic cracked plates of different thicknesses loaded in tension. Unlike the path-independent J x 1 -integral, the components J P and J A are shown to be path dependent in a region that coincides with the out-of-plane constrained zone due to the thickness effect, enabling the characterization of this zone with such integrals. The distribution of the out-of-plane components σ 33 and ε 33 in the vicinity of the crack front is also analyzed for different thicknesses and confronted to 2D solutions. In addition, a novel tensor concept of the stress intensity k ij is introduced, showing a unique structure depending on K I irrespective of the specimen thickness. It is confirmed that a pure plane strain condition close and far from the crack front is only asymptotically reached when the specimen thickness is very large when compared to the in-plane dimensions. For thin plates, it is confirmed that the 2D plane stress condition is meaningless in the neighborhood of a 3D crack front under elastic behaviour.

On the Path and Area J<sub>x1</sub>-Integral Components and their Relationship to the Out-of-Plane Constraint in Elastic Cracked Plates

In this paper, the path and area components of the Jx1-integral, JP and JA, in three dimensional elastic cracked plates under mode-I loading are investigated aiming at relating them to the out-of-plane constraint conditions resulting from different specimen thicknesses. It is concluded that the JP and JA components of the Jx1-integral vary in the region where the out-of-plane constraint extends. Sufficiently far from the crack front, these integrals tend to stabilize, indicating that the thickness constraint vanishes and that a 2D-like stress and strain fields have been reached. A pure plane strain condition is only attained when the specimen thickness is very large when compared to the in-plane dimensions. For thin plates, it is shown that the 2D plane stress condition is impossible in the close neighbourhood of a 3D crack front under elastic behaviour so that the consideration of an equivalent Young modulus E', used to find a simple relation between the J(s)-integral and KI for different constraint levels can be misleading.

Two-parameter characterization of elastic–plastic crack front fields: Surface cracked plates under tensile loading

In this paper the J–Q two-parameter characterization of elastic–plastic crack front fields is examined for surface cracked plates under uniaxial and biaxial tensile loadings. Extensive three-dimensional elastic–plastic finite element analyses were performed for semi-elliptical surface cracks in a finite thickness plate, under remote uniaxial and biaxial tension loading conditions. Surface cracks with aspect ratios a/c=0.2, 1.0 and relative depths a/t=0.2, 0.6 were investigated. The loading levels cover from small-scale to large-scale yielding. In topological planes perpendicular to the crack fronts, the crack stress fields were obtained. In order to facilitate the determination of Q-factors, modified boundary layer analyses were also conducted. The J–Q two-parameter approach was then used in characterizing the elastic–plastic crack front stress fields along these 3D crack fronts. Complete distributions of the J-integral and Q-factors for a wide range of loading conditions were obtained. It is found that the J–Q characterization provides good estimate for the constraint loss for crack front stress fields. It is also shown that for medium load levels, reasonable agreements are achieved between the T-stress based Q-factors and the Q-factors obtained from finite element analysis. These results are suitable for elastic–plastic fracture mechanics analysis of surface cracked plates.

On the quantification of the constraint effect along a three-dimensional crack front

Abstract In this paper we examined the characterization of constraint effects for surface cracked plates under uniaxial and biaxial tension loadings. First, three-dimensional (3D) modified boundary layer analyses were conducted using the finite element method to study the constraint effect at a typical 3D crack front. The analyses were carried out using small geometry change formulation and deformation plasticity material model. Elastic-plastic crack front stress fields at a constant J and various T-stress levels were obtained. Three-dimensional elastic-plastic analyses were performed for semi-circular surface cracks in a finite thickness plate, under remote uniaxial and biaxial tension loading conditions. In topological planes perpendicular to the crack fronts, the crack stress fields were obtained. Then, J-Q and J-T two-parameter approaches are used in characterizing the elastic-plastic crack-tip stress fields along the 3D crack front. It is found that the J-Q characterization provides good estimate for the constraint effect for crack-tip stress fields. Reasonable agreements are achieved between the T-stress based Q-factors and the Q-factors obtained from finite element analysis.

3D model of liquid entrapment mechanism for rolling contact fatigue cracks in rails

In the paper, the iterative numerical procedure was used for estimating the 3D crack front loading enhancements due to the action of the “liquid entrapment mechanism” (LEM). The 3D shallow angle, semi-elliptical, surface breaking crack inclined at 20° to the horizontal, in an early stage of development (similar to the “squat”-type crack typical in rails) was FE modelled and used for analysis. The volume of liquid entrapped was determined on the basis of the 3D crack geometry for the position of load, in which the leading edge of contact patch is touching the crack mouth. In the FE model this volume was represented by the empty space (bubble) between the crack faces loaded with the liquid pressure. During the LEM part of the cycle of loading this volume was assumed to be constant. At each position of contact load (rolling wheel), the pressure was gradually increasing in the iteration procedure until both the required volume of the “bubble” and “equilibrium state” with external contact load were attained. Then, the histories of Modes I, II, and III stress intensity factors (SIFs) and corresponding fatigue growth rates were determined for the selected points of the crack front. The obtained loading enhancements were compared with those estimated earlier by the authors and others on the basis of the 2D model of LEM.

The influence of the Poisson’s ratio and corner point singularities in three-dimensional plasticity-induced fatigue crack closure: A numerical study

In this paper three-dimensional finite element analyses of a plate with a central crack were performed to investigate whether or not the closure behaviour is influenced by the effect of corner point singularities and Poisson’s ratio. Both crack closure and corner point singularities are essentially “free surface” effects and it is difficult to look at 3D crack closure without addressing the associated stress singularity problem. These effects are studied by modifying the shape of the crack front and quantifying both stress singularity and closure level along the crack front. In the first part of this work, the power of the singularity along the crack front is assessed using a log–log regression analysis of the stresses and displacements. The thickness of the boundary layer and the stress intensity factors along the crack front were also assessed. In the second part of the paper, the closure behaviour is assessed for 3D straight crack fronts and crack fronts with a different shape, for different values of the Poisson’s ratio. This work shows that the magnitude of the stress intensity factor along the crack front is higher than the predictions for plane strain by about 5.5% for a Poisson’s ratio of 0.3. In addition, this study supports that corner point singularities do not seem to significantly influence the closure behaviour of 3D fatigue cracks.

Analysis of fatigue crack propagation in the frame of a hydraulic press

Within this paper the fatigue crack growth in the frame of a hydraulic press will be discussed. The crack growth started at a shrink hole in a notch in the middle part of the frame. The state of stress of the crack is predominantly influenced by the notch, which induces a Mixed-Mode-loading during the crack growth. The propagation of the crack will be analyzed with the crack simulation program ADAPCRACK3D, which has been developed at the Institute of Applied Mechanics at Universität Paderborn. This program is able to calculate fully automatic the stress intensities along a 3D-crack front as well as the crack path and the lifetime of a structure.