Curved Crack Growth Research Articles

FFT-based solver for higher-order and multi-phase-field fracture models applied to strongly anisotropic brittle materials

This paper presents the application of a fast Fourier transform (FFT) based method to solve two phase field models designed to simulate crack growth of strongly anisotropic materials in the brittle regime. By leveraging the ability of the FFT-based solver to generate solutions with higher-order and global continuities, we design two simple algorithms to capture the complex fracture patterns (e.g. sawtooth, and curved crack growth) common in materials with strongly anisotropic surface energy via the multi-phase-field and high-order phase-field frameworks. A staggered operator-split solver is used where both the balance of linear momentum and the phase field governing equations are formulated in the periodic domain. The unit phase field of the initial failure region is prescribed by the penalty method to alleviate the sharp material contrast between the initial failure region and the base material. The discrete frequency vectors are generalized to estimate the second and fourth order gradients such that the Gibbs effect near shape interfaces or jump conditions can be suppressed. Furthermore, a preconditioner is adopted to improve the convergence rate of the iterative linear solver. Three numerical experiments are used to systematically compare the performance of the FFT-based method in the multi-phase-field and high-order phase-field frameworks.

Numerical Simulation of Multiple Fatigue Crack Growth with Additional Crack Initiation

In this paper, advanced numerical simulations of curved crack growth in the case of mul­tiple crack systems in combination with the analysis of the plastic limit load by the lower bound theorem of plasticity are presented. In order to take additionally initiated cracks during the crack growth process into account, the numerical simulation algorithm has been extended by using the Smith-Watson-Topper (SWT) parameter in combination with a linear fatigue damage accumula­tion.

3D adaptive finite element modeling of non-planar curved crack growth using the weighted superconvergent patch recovery method

In this paper, an adaptive finite element analysis is presented for 3D modeling of non-planar curved crack growth. The fracture mechanical evaluation is performed based on a general technique for non-planar curved cracks. The Schollmann’s crack kinking criterion is used for the process of crack propagation in 3D problems. The Zienkiewicz–Zhu error estimator is employed in conjunction with a weighted SPR technique at each patch to improve the accuracy of error estimation. Applying the proposed technique to 3D non-planar curved crack growth problems shows significant improvements particularly at the boundaries and near crack tip regions. Several numerical examples are presented to illustrate the robustness of the proposed technique.

Numerical and Experimental Investigations of Curved Fatigue Crack Growth under Biaxial Proportional Cyclic Loading

The paper presents numerical and experimental results of continued studies of curved fatigue crack growth in arbitrarily pre-cracked isotropic sheets under biaxial proportional plane loading. The predictor-corrector method (PCM) was extended in order to analyse the growth of multiple crack systems. As a result, the program PCCS-2D was written to run within ANSYS without any user interaction. In order to check the accuracy and efficiency of the method biaxial crack growth simulations were carried out for a fracture mechanics cruciform specimen. The results are compared with experimental findings obtained by specimens made of 6061 aluminium alloy in T651 condition using a 250kN biaxial servohydraulic testing machine. From the numerical and experimental results, we conclude, that the proposed predictor-corrector method can be used in curved crack growth simulation also under biaxial proportional loading conditions.

CTOA of a stable crack in a thin aluminum fracture specimen

A crack tip opening angle (CTOA) resistance curve was generated from the moiré interferometry data of thin single edge notched (SEN) and central notched (CN), 2024-T3 aluminum fracture specimens. This CTOA resistance curve, which has a steady state value of 6°, was then used to propagate the cracks in elastic–plastic finite element models of the CN specimen and a CN specimen with a simulated multiple site damage. The CTOA of curved crack growth in a biaxial fracture specimen scattered between 4° and 8° but the resultant crack tip opening displacement, which is the vector sum of the mode-I and the mode-II crack tip sliding displacement, remained a constant 0.18 mm. The CTOA of a rapidly propagating crack in 1.6 mm thick, 7075-T6 SEN specimens increased from 4.5° at a low-crack velocity to a constant 7° at the terminal crack velocity.

Development of an Automatic Quadrilateral Mesh Generator for the Simulation of Curved Crack Growth

Development of an Automatic Quadrilateral Mesh Generator for the Simulation of Curved Crack Growth

Investigation of crack propagation in ceramic/conductive epoxy/glass systems

The primary objective of this combined experimental and analytical study was to investigate the mechanical behavior of glass/conductive adhesive/Al/sub 2/O/sub 3/ systems with a surface notch, measure the properties of the system at various temperatures, implement these temperature dependent properties into a nonlinear finite element framework, and predict the initiation and growth of cracking. The three major tasks of this work include: (a) testing of fracture strength of the systems at three different temperatures, including the determination of thermal crack initiation and growth, (b) determination of basic thermal-mechanical properties of adhesive, glass, and Al/sub 2/O/sub 3/, respectively, and (c) identification of appropriate quantities to predict damage modes, including initiation and growth, at different temperatures and comparing the data with experiments. The major conclusions are as follows: (a) realistic nonlinear material properties are essential input for correct nonlinear finite element modeling, (b) J-integral can be applied to predict the crack initiation and growth for the material system considered, (c) either bulk glass material or the adhesive/glass interface may fail depending on the applied temperature and notch length, and (d) curved crack growth path inside the glass can be predicted by fracture mechanics.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

An evaluation of double-torsion testing of polymers by visualization and recording of curved crack growth

The development and growth of the curved crack front in a double-torsion fracture-mechanics specimen is investigated by direct observation of crack propagation during the test. The crack front motion is analysed from a video-recording of the fracture test, and three distinct stages of crack propagation are identified. This work shows some of the requirements for the application of conventional double-torsion analysis to this test configuration: the material characteristic —critical strain energy release rate as a function of crack velocity — can be correctly obtained, provided that three steady-state conditions (static, kinematic and dynamic) are all fulfilled.

Computational crack path prediction

Abstract A computer program has been developed for the numerical prediction of curved crack growth paths under proportional loading conditions. The numerical prediction is performed by the step-by-step method in cooperation with the stress analysis ahead of the crack tip and the determination of the curved increment of the crack growth. The stress analysis is performed by the method of superposition of analytical and finite-element solutions, and the results are then utilized to determine the coefficients of the analytical expression of the curved crack path obtained by the first order perturbation method. The first numerical example is given for the crack path prediction in DCB-type specimen, where we often observe abrupt crack curving. Computational prediction is performed by introducing slight and small initial branching at the original crack tip. Within few steps of numerical calculations unstable crack curving is obtained, and the predicted path shows extremely good agreement with the experimentally measured path. The second numerical prediction is made for an edge crack approaching a circular hole, which may be considered as a crack arrester. In the present case the effect of the initially introduced slight kink diminishes with increasing crack length. The crack turns back to the original direction, resulting arrest at the hole.

A fundamental research on the growth pattern of cracks (third report)

A computer program has been developed by the present authors for the curved crack path prediction. We consider the proportional loading condition, and the loading parameter is increased or decreased in such a manner that the brittle crack is quasi-statically growing along the curved trajectory. Although dynamic behavior including inertia effects and dynamic material properties is beyond the scope of the present prediction, we expect that some of the essential features of the curved crack paths observed in actual brittle fracture or fatigue crack propagation can be obtained by the method.The computational prediction is performed by the step-by-step method in cooperation with the stress analysis ahead of the crack tip and the determination of the curved increment of the crack growth. The stress distribution around the crack tip is first calculated by the method of the superposition of analytical and finite-element solutions proposed by Yamamoto et al., where the finite element data generation due to the crack growth process is to a certain extent carried out by automatical mesh rearrangement and nodal renumbering. Then a highly accurate asymptotic representation of the curved crack path, which is introduced in our first report assuming the locally symmetric deformation ahead of the crack tip, is employed for the path prediction.Numerical examples are given for the crack path prediction in DCB type specimen, which was numerically and experimentally investigated in our previous report from the view point of crack path stability. After few steps of numerical calculation unstable crack curving is obtained, and the predicted paths show extremely good agreements with the experimentally measured crack paths. It is also observed that the Mode II stress intensity factor KII is actually very small during the entire curved crack growth. Application of the present prediction method to more complicated problems, i. e. crack curving in structural elements, the growth of interacting cracks and etc, will be made in subsequent works.