Crack Front Geometry Research Articles

Complexity of crack front geometry enhances toughness of brittle solids

Brittle solids typically fail by growth and propagation of a crack from a surface flaw. This process is modelled using linear elastic fracture mechanics, which parameterizes the toughness of a material by the critical stress intensity factor, or the prefactor of the singular stress field. This widely used theory applies for cracks that are planar, but cracks typically are not planar, and instead are geometrically complex, violating core tenets of linear elastic fracture mechanics. Here we characterize the crack tip kinematics of complex crack fronts in three dimensions using optical microscopy of several transparent, brittle materials, including hydrogels of four different chemistries and an elastomer. We find that the critical strain energy required to drive the crack is directly proportional to the geodesic length of the crack, which makes the sample effectively tougher. The connection between crack front geometry and toughness has repercussions for the theoretical modelling of three-dimensional cracks, from engineering testing of materials to ab-initio development of novel materials, and highlights an important gap in the current theory for three-dimensional cracks.

Study of fatigue fracture characteristics for duplex stainless steel STHE welded joint specimen

A shell and tube heat exchanger (STHE) welded joint is considered for fatigue fracture mechanism. The joint is made up of a protruding tube fabricated to a tubesheet by means of welding. A super duplex stainless steel (DSS) material is used for the tube and tubesheet. Fatigue test was newly conducted using the single tube test specimen. The initial cracking plane was moved from the minimum sectional-area plane that was perpendicular to the loading direction, and the crack growth was almost planar. Stress analysis is carried out using finite element method (FEM) and the stress distributions are carefully studied by comparing the simple perforated plate. In addition, three-dimensional crack propagation (CP) simulation is performed employing extended finite element method (X-FEM). Fracture phenomenon is verified using the experimental and numerical crack front geometries. The fracture mechanics parameter is evaluated and verified with empirical formulae. CP behaviors are carefully discussed based on the fracture mechanics parameter. The CP life is presented for three loading amplitudes. The FAT class of the STHE welded joint is studied based on the available design standards such as BS, IIW and JSSC. Finally, the fatigue fracture characteristics of the STHE welded joint specimen are shown through the experimental and numerical methods.

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.

Ductile Tearing or Plastic Collapse?

Abstract Ductile fracture is characterized by a large amount of deformation. Two mechanisms may lead to ductile failure: local tearing may appear in front of a stress concentration region like a crack front or large geometry changes in a weak part of the structure can induce global collapse of the structure. For large cracks such as those considered in Leak Before Break studies, tearing analyses and net-section collapse criteria have been used. The present paper examines the link between these two mechanisms for a through-wall cracked pipe under bending and concludes that the transition from ductile tearing to collapse depends not only on material properties but also on geometrical parameters. The reference stress approach is a promising approach for predicting the transition, provided the transferability issue of j-resistance curve has been solved.

Crack Front Geometry and Stress Intensity Factor of Semi-circular Bend Specimens with Straight Through and Chevron Notches

The semi-circular bending (SCB) test is one of the most useful testing methods for determining the mode-I fracture toughness of rocks. An SCB specimen with an artificial notch is loaded at three points including two lower points and a single upper point during the test. In general, there are two types of geometries for artificial notches: straight through and chevron notches. The straight through notch is commonly adopted for the SCB (STNSCB) test as the suggested method for estimating mode-I fracture toughness of rocks in ISRM, while the cracked chevron notch SCB (CCNSCB) test using a specimen with a chevron notch has been performed by some researches. In this paper, by means of the commercial finite-element software ABAQUS, cracking behavior from the tip of an artificial notch during STNSCB and CCNSCB tests is analyzed with Extended Finite-Element Method (XFEM) to clarify crack front geometry in the process of cracking. The relationship between the crack length and the stress intensity factor can be obtained by analyzing stress intensity factors of the specimen with FEM, based on crack front geometries calculated with XFEM during the cracking process. Using this relationship, the minimum stress intensity factor at a critical crack length is determined for estimating mode-I fracture toughness of the rock for the CCNSCB test. Furthermore, by performing the SCB tests using Kimachi sandstone specimens with three different artificial notch geometries, fracture toughness of the sandstone is determined from the SCB test. Consequently, it is concluded that the values of fracture toughness from the test with three notch geometries are almost the same.

A benchmark test for validating 3D simulation methods for delamination growth under quasi-static and fatigue loading

Models for simulating interlaminar crack growth in composites under static and fatigue loads are rarely validated with experimental data different from simple standard tests where the crack front propagates with a uniform shape. The underlying reason for not making use of more realistic experimental data, where the crack front shape changes during the delamination growth, is the lack of well-controlled benchmark cases. This work introduces a comprehensive benchmark case consisting of a double cantilever beam (DCB)-like specimen with partially reinforced arms. A complete set of elastic and fracture properties for the material and a detailed description of load-displacement curves and crack front geometries, monitored with X-ray radiography, is provided. The benchmark case generates a rich phenomenology of crack advance in terms of varying crack growth rate and front shape, while being geometrically simple enough to be simulated.

An adaptive remeshing technique for predicting the growth of irregular crack fronts using p-version finite element analysis

An adaptive remeshing technique using p-version finite element analysis was developed to predict the growth of cracks with highly irregular crack front geometries. In order to represent the shape of the crack front, the commonly used ellipse was replaced by a high-resolution spline. This enabled the growth of irregular crack fronts with local changes in curvature, convex and concave regions and small radii of curvature to be simulated iteratively using automatic mesh generation. The method was demonstrated for an irregular corner crack at a notch and the predicted crack front geometry was shown to be in good agreement with experimental results.

Fatigue crack surface area and crack front length: new ways to look at fatigue crack growth

This paper discusses the appropriateness of crack length as a reference dimension for fatigue damage. Current discussion on short crack versus long crack data is still divided between various approaches to model small crack growth. A proper physical explanation of the probable cause of the apparent differences between short crack and long crack data is not yet provided. Long crack data often comprises crack growth in constant thickness specimens, with a through crack of near constant crack front geometry. This is not true for corner cracks or elliptical surface crack geometries in the small crack regime where the crack front geometry is not symmetric or through-thickness. This affects similitude parameters that are based on the crack length. The hypothesis in this paper is that a comparison between long crack data and short crack data should be made using similar increments in crack surface area. The work applied to the specimen is dissipated in generation of fracture surface, whereas fracture length is a result. The crack surface area approach includes the two-dimensional effect of crack growth geometry in the small crack regime. A corner crack and a through crack are shown to follow the same power law relationship when using the crack area as base parameter. The crack front length is not constant, and its power law behaviour for a corner crack is shown.

Determination of local stress intensity factors at microstructurally tortuous crack fronts under remote mode II loading

The real crack geometries are mostly not ideally smooth and fracture parameters calculated for cracks with tortuous fronts and rough flanks differ from results obtained for smooth cracks. The finite element methods allow us to determine fracture parameters for such kinds of cracks and, moreover, some useful analytical approaches can also be applied to simplified crack front geometries. Several authors already reported on these geometrically induced shielding effects but, in most cases, only the loading under the opening mode I was considered in the frame of simple 2D models of tortuous crack front. This work presents results of the investigation of local mixed-mode loading along a real-like, tortuous crack front loaded under the remote mode II. The employed numerical methods enabled us to get sufficiently precise values of all local components of loading modes I, II and III along the crack front. A comparison of these values with those obtained from analytical formulae related to a simplified form of the tortuous crack front with an equal linear roughness led to a very good agreement. The results could be used for a correction of the mode II effective fatigue threshold as measured for the polycrystalline ARMCO iron under an assumption of a straight precrack front. It is expected that such a correction, based on the roughness data of the real precrack, will shift the measured fatigue threshold data very close to those theoretical obtained from multiscale approaches.

Characterization of Damage During Low Cycle Fatigue of a 304L Austenitic Stainless Steel as a Function of Environment (Air, PWR Environment) and Surface Finish (Polished, Ground)

304L austenitic stainless steel is notably used to manufacture pipes in primary cooling circuits of nuclear power plants operating at a temperature close to 300°C in a specific aqueous environment. Customarily, pipes are roughly polished, however, after some interventions, a few zones might be ground. Start-ups, shutdowns and operating transients of the reactor produce Low Cycle Fatigue (LCF) loadings with different strain rates. These solicitations and the modified surface finish create specific conditions whose effects must be taken into account. In order to understand if there is a joint influence of the PWR environment and surface roughness on the successive stages of fatigue damage leading to failure, fatigue tests were conducted at 300°C under a total strain amplitude of ± 0.6%. Two environments were used, laboratory air and simulated PWR primary aqueous environment. Two surface finishes were investigated, namely fine mechanical polishing and grinding (Rt of about 40μm). The analysis of the damage process is based on data concerning crack density, crack length and striation spacing. The integration of the relation between the striation spacing and the strain intensity factor ΔKɛ, provides an estimation of crack propagation. It is confirmed that in PWR environment one striation can be considered as the crack advance during one fatigue cycle. Moreover, the specific crack front geometry observed in ground specimens and resulting from successive microcrack coalescences explains the reduction in fatigue life induced by grinding.

The fracture toughness and its prediction model for Ti–5Al–5Mo–5V–1Cr–1Fe titanium alloy with basket-weave microstructure

The fracture toughness and its prediction model for Ti–5Al–5Mo–5V–1Cr–1Fe titanium alloy with basket-weave microstructure are studied in present paper. Five double annealing processes were used to prepare different microstructure features. The results show that the fracture toughness of Ti–5Al–5Mo–5V–1Cr–1Fe alloy is very sensitive to its microstructure, which shows a variance of about 40MPam. Moreover, an “abnormal” phenomenon has been found that a microstructure with high yield strength does not necessarily gets low fracture toughness. It is due to that not only the material plastic deformation along the crack path can exert influence on fracture toughness but also its crack path tortuosity. Generally speaking, long and thick α platelets in microstructure is necessary to get rough crack front geometry, which can obviously improve the fracture resistance. According to above findings, a fracture toughness prediction model considering both the intrinsic and extrinsic contributions is built. It is verified that the model can fairly predict the fracture toughness for Ti–5Al–5Mo–5V–1Cr–1Fe alloy with basket-weave microstructure. Moreover, based on the prediction model, the respective contributions of the intrinsic and extrinsic parts to the fracture toughness of Ti–5Al–5Mo–5V–1Cr–1Fe alloy are studied. The results show that the intrinsic contributions for the five microstructures constitute the vast majority of their fracture toughnesses, which do not vary a lot from each other. However, the extrinsic contributions for the five microstructures are dramatically different, indicating that the extrinsic fracture toughness is more sensitive to the basket-weave microstructure features than the intrinsic part. Therefore, pursuing the enhanced extrinsic fracture toughness is exactly the way to optimize the fracture toughness of Ti–5Al–5Mo–5V–1Cr–1Fe alloy with basket-weave microstructure.

Elastic-Plastic Fracture Mechanics Analyses of Surface Cracks in Drill String Subjected to Combined Loading

The drill pipe near the surface stands the largest tension and torsion load for the full hole during drilling operation. And fatigue crack growth is always the major cause of failure of drill string. As an example, 5ʺ drill pipe that was near the well head of an ultra-deep straight well and made of 30CrMo, whose constitutional relation was fitted by experiment, was analyzed here. Simplifying the initial crack of the drill pipe as circumferential semi-elliptical surface crack, we simulated the elastic-plastic fracture feature of the drill string with surface crack, partly through-wall crack and fully through-wall crack under combined loading of axial force and torsion. Crack front geometry evolvement is simulated for the different stages of crack propagation. This work would provide a basis for the full-range analysis of fatigue crack growth.

High-temperature crack growth in a Ni-base superalloy during sustained load

The high-temperature sustained load crack growth behaviour of a Ni-base superalloy was investigated using a combination of mechanical testing in controlled atmosphere, fractographical and microanalytical investigations, and finite element modelling. The results show that the local crack front geometry is un-even on two scales – jaggedness on the scale of 100μm was observed in all specimens, whereas mm-scale waviness could occasionally be observed. The jaggedness can be explained by a percolation-type crack growth along weaker grain boundaries, whereas the large-scale waviness is presumably due to larger regions of the material having specific grain texture with high crack growth resistance. The un-even crack front is shown to potentially have considerable effects on the loading conditions at the crack tip, whereas ligaments of un-cracked material in the crack wake are deemed to have less effect on the crack tip loading due to their low area fraction. The ligaments fail intergranularly in the wake as the crack grows in the present case, as opposed to by creep fracture as previously proposed. Finally, the plastically deformed regions about the crack and crack tip are shown not to exhibit any elevated oxygen levels, implying that the damage in these regions is purely mechanical.

Bonded bimaterial ring under compressive load

A bonded ring test is proposed to study crack onset under pure and mixed mode conditions. In the existing centre-cracked Brazilian disc configuration, introduction of a central crack may be arbitrary and can easily lead to initial asymmetric crack configuration. Moreover, the crack front geometry is, in general, unknown which may result in serious consequences on crack onset and fracture parameters. In the present work, a bonded ring loaded in compression was investigated numerically and experimentally. Two bimaterial singular points were introduced between the half discs and the adhesive providing privileged crack onset location – controllable during specimen fabrication. Three types of specimens were analysed using digital image correlation and finite element techniques: homogenous poly(methyl methacrylate), bonded poly(methyl methacrylate) and bonded poly(methyl methacrylate) to stainless steel rings. A satisfying agreement between experimental and numerical approaches was found enabling more complex analysis in future. Such test configuration can be of interest for crack onset studies and estimation of fracture parameters under mixed mode I/II loading conditions.

Influence of p-method finite element parameters on predictions of crack front geometry

The effect of various p-method finite element model parameters on the prediction of planar crack front geometry in three dimensional structures is evaluated. An automatic crack growth method was developed using the commercial software StressCheck coupled with Microsoft Excel. The geometry of the evolving crack front was predicted using iterations of three dimensional finite element models to determine the stress intensity values at discrete points along the crack front and incrementing the crack length locally using the Paris growth law. Modeling parameters such as the global mesh size, p-level, crack tip mesh size, and the extraction radius used for determining the stress intensity factors were all considered. The effect of these parameters on the predicted shape of a growing elliptical crack front was evaluated through a series of simulations of a corner crack emanating from a centered hole in a plate. A single model of a through crack with a straight crack front was also used to compare the effects of the model parameters on a different geometric configuration. This study has shown that the corner crack geometry and the growth series are more sensitive to the number of elements along the crack front and the extraction radius than the through thickness crack. In addition, convergence of the predicted crack front geometry does not guarantee convergence of the distribution of stress intensity factors along the crack front. It was also determined that for the models considered, using a smaller overall mesh size is a more effective way of decreasing discretization error than increasing the p-level.

Evaluation of Elastic-Plastic Fatigue Crack Growth Characteristics under Mixed-Mode Condition for Aluminum Alloy A2017

It is necessary to investigate the elastic-plastic fatigue crack growth behavior under mixed mode loading in order to evaluate an ultimate strength of actual structures under seismic load. In this study, tension-compression fatigue tests for CT specimens and torsion fatigue tests for plate specimens with notches were performed for aluminum alloy A2017 to compare crack growth behavior under tension-compression and torsion loadings. In tension-compression fatigue tests, the fatigue crack propagation was share mode. J-integral range, ΔJ, was calculated by finite element method and crack growth characteristic was evaluated by ΔJ. In torsion fatigue tests, the fatigue crack propagation was also share mode. As a result of fracture surface observation, it was found from crack front geometry that crack growth rate on the surface was faster than that of inside. The ΔJ at the crack front was calculated by finite element method and used to evaluate crack growth characteristic. These results corresponded to the mode II crack growth characteristics obtained under small scale yielding.

OS2139 アルミ二ウム合金A2017の混合モード下の弾塑性疲労き裂進展特性評価

It is necessary to investigate the elastic-plastic fatigue crack growth behavior under complex loading in order to evaluate an ultimate strength of actual structures. In this study, tension-compression fatigue tests for CT specimens and torsion fatigue tests for plate specimens with notches were performed for aluminum alloy A2017 to compare crack growth behavior under tension-compression and torsion loadings. In tension-compression fatigue tests, the fatigue crack propagation was share mode. J-integral range was calculated by empirical formula and crack growth characteristic was evaluated by J-integral range. In torsion fatigue tests, the fatigue crack propagation was share mode. As a result of fracture surface observation, it was found from crack front geometry that crack growth rate of surface was faster than that of inside. J-integral range of crack front was calculated by finite element method and crack growth characteristic was evaluated by J-integral range. These results corresponded to the mode II crack growth characteristics obtained under small scale yielding.

312 き裂前縁形状とすべり面の相対関係に着目したα黄銅の微小疲労き裂進展屈曲機構の検討(機械材料・材料加工II)

312 き裂前縁形状とすべり面の相対関係に着目したα黄銅の微小疲労き裂進展屈曲機構の検討(機械材料・材料加工II)

Growth simulation for 3D surface and through-thickness cracks using SGBEM-FEM alternating method

An SGBEM-FEM alternating method had been proposed by Nikishkov, Park and Atluri for the analysis of three-dimensional planar and non-planar cracks and their growth. The proposed method is an effective method for fatigue or stress corrosion crack growth simula- tion. During crack growth simulation, however, an oscillation phenomenon is observed in crack advance or stress intensity factor distri- bution. If oscillating amplitude in SIF or crack advance does not decrease during next increment steps, the crack growth simulation fails. In this paper several methods are examined to remove the oscillation phenomenon. As a result, it is found that smoothing in stress inten- sity factor distribution or in crack front geometry can remove or weaken the oscillation phenomenon. Using the smoothing techniques, stress corrosion crack growth simulation is performed for a semi-elliptical surface crack and a through-thickness crack embedded in a plate. Crack front shape and stress intensity factor distribution are obtained after each increment during the crack growth. And the depth and length of a crack are obtained as a function of time. It is noted that the SGBEM-FEM alternating method is a very effective method for SCC growth simulation for a surface crack and a through-thickness crack.

Downscaling of fracture energy during brittle creep experiments

We present mode 1 brittle creep fracture experiments along fracture surfaces that contain strength heterogeneities. Our observations provide a link between smooth macroscopic time-dependent failure and intermittent microscopic stress-dependent processes. We find the large-scale response of slow-propagating subcritical cracks to be well described by an Arrhenius law that relates the fracture speed to the energy release rate. At the microscopic scale, high-resolution optical imaging of the transparent material used (PMMA) allows detailed description of the fracture front. This reveals a local competition between subcritical and critical propagation (pseudo stick-slip front advances) independently of loading rates. Moreover, we show that the local geometry of the crack front is self-affine and the local crack front velocity is power law distributed. We estimate the local fracture energy distribution by combining high-resolution measurements of the crack front geometry and an elastic line fracture model. We show that the average local fracture energy is significantly larger than the value derived from a macroscopic energy balance. This suggests that homogenization of the fracture energy is not straightforward and should be taken cautiously. Finally, we discuss the implications of our results in the context of fault mechanics.