Crack Kinking Research Articles

Mixed-mode dynamic fracture parameters for soda-lime glass

Dynamic mixed-mode fracture of soda-lime glass (SLG) was experimentally investigated using a full-field optical method - Digital Gradient Sensing (DGS) - in conjunction with ultrahigh-speed photography. Single edge-notched specimens were subjected to reverse impact loading using a modified Hopkinson pressure bar. The specimens were eccentrically loaded at different offset distances relative to the initial notch to achieve a wide range of mode-mixities, from mode-I to nearly mode-II condition, at initiation. Two time-resolved orthogonal angular deflection fields of light rays proportional to the respective full-field stress gradients were optically measured during experiments on different geometries. Mode-I and -II stress intensity factor histories spanning pre- and post-initiation behaviors were evaluated via over-deterministic least-squares error minimization of optically measured full-field data. By considering the critical stress intensity factors at different crack initiation modes, a fracture envelope for SLG encompassing various mode-mixities was developed for the first time for SLG and compared with predictions from prevailing approaches. An empirical fit of data seems to capture the overall trend whereas the prevailing methods do not. Measured crack kink angles are compared with the popular MTS and SED fracture criteria; both predict the kink angles reasonably well. Unlike brittle polymers, the critical effective stress intensity factors for SLG are independent of mode-mixity over a large range of values but show a decreasing trend as mode-II conditions become dominant and an extrapolated critical mode-II stress intensity factor of 0.37 MPa√m, approx. one-half of its mode-I counterpart, is seen.

The energy release rate of crack growth in an irradiation-induced thermo-diffusion-mechanical (I-TDM) coupling system

The material cracking behavior in the reactor is generated under the irradiation effect accompanied by thermal expansion, fission product diffusion, and mechanical load. In this study, the energy release rate for crack growth under irradiation has been deduced synthetically according to the thermodynamically consistent method and numerically implemented by the finite element method (FEM). Variation in the total energy was obtained based on the principle of minimum potential energy in which the dissipative behavior can be characterized by fission energy, irreversible heat flow, and diffusion of fission products. Through calculating the variation in the total energy with respect to crack length, the energy release rate for crack propagation was analytically represented. Additionally, the total energy release rate for deflective cracks was also derived to predict the crack kinking. Furthermore, the numerical implementation of the presented model was performed by FEM and the equivalent domain integral method. Effects of irradiation on the physical fields and the energy release rate near the crack tip were investigated and analyzed in such a complex I-TDM coupling system. This study can be developed to investigate fracture problems, assess structural integrity, and evaluate material strength of irradiated materials.

Experimental and theoretical assessment of crack kinking in marble stones in the presence of a V-notch under mode I loading

Marble has been used extensively in the historical monuments as a building material. Notches and sharp corners in these buildings are potential locations for crack formation, crack extension and in some cases their eventual failure. In this study, some fracture tests are accomplished on a number of V-notched marble specimens under mode I loading condition. The specimens are in the configurations of double cantilever beam (DCB) and compact tension (CT) each embedding two various notch opening angles. It is substantiated that although both the loading conditions and geometry were symmetric, the crack initiation angle is not necessarily along the notch bisector line. It is also shown that the classical fracture criteria are not able to predict crack kinking in the tested marble specimens. Thus, the conventional strain energy density and maximum tangential stress criteria used for V-notches, V-SED and V-MTS respectively, are generalized by introducing the first non-singular term of notch stress field into the calculations. Finally, it is demonstrated that the generalized criteria, V-GSED and V-GMTS, can predict the fracture strength and the crack initiation angle of the tested marble specimens well.

Mixed-mode dynamic fracture behavior of a rubber toughened epoxy adhesive under stress wave loading

This work seeks to measure mixed-mode fracture parameters for a dynamically growing crack in a core shell rubber toughened epoxy adhesive (EPONTM 828 with PARALOID™ EXL-2691J particles). Digital image correlation technique coupled with ultrahigh-speed photography and a hybrid finite element-based post-processing approach are used to extract fracture parameters. The dynamic loading is accomplished by using a striker to induce stress waves in an incident bar in contact with a free-standing semi-circular specimen. A companion finite element analysis is performed for investigating suitable experimental parameters and configurations for implementing the approach and determining specific experimental parameters (crack length, crack angle, and impact velocity) necessary to achieve the desired experimental conditions (mode mixity at crack initiation and strain rate). The critical fracture parameters are used to generate mixed mode fracture envelope and fracture toughness-mode mixity relationship for the material. Further investigation is carried out to evaluate various fracture criteria for predicting initial crack kink angles. The measured dynamic fracture quantities are also compared with the quasi-static counterparts to assess strain rate-dependence of the adhesive. The results reveal a decrease in critical stress intensity factors of approximately 10 % and 30 % for the mode I and mode II states, respectively, with increasing strain rate. Post-initiation, the dynamic crack propagates at a near-constant mode I stress intensity factor of ∼1.4 MPa-√m. Under dynamic conditions, the critical, effective stress intensity factors are relatively constant with respect to mode mixity. This is in contrast to quasi-static results where the effective values increased with respect to mode mixity. Experimentally measured crack kink angles agree well with those predicted by the maximum energy release rate criteria and the maximum tangential stress criteria, particularly under mode I dominant conditions.

A hybrid multi-phase field model to describe cohesive failure in orthotropic materials, assessed by modeling failure mechanisms in wood

Fracture mechanics is crucial for many fields of engineering applications, as precisely predicting failure of structures and parts is required for efficient designs. The simulation of failure processes is, both from a mechanical and a numerical point of view, challenging, especially for inhomogeneous materials, where the microstructure influences crack initiation and propagation and might lead to very complex crack patterns. The phase field method for fracture is a promising approach to encounter such materials, since it is able to describe complex fracture phenomena like crack kinking, branching and coalescence. Moreover, it is a largely mesh independent approach, given that the mesh is homogeneous in the area of the crack. However, the original formulation of the phase field method is limited to isotropic materials and does not account for preferable fracture planes defined through the material’s microstructure. In this work, the method is expanded to take orthotropic constitutive behavior and preferable directions of crack propagation into account. We show that by using a stress-based split and multiple phase field variables with preferable fracture planes, in combination with a hybrid phase field approach, a general framework can be found for simulating anisotropic, inhomogeneous materials. The stress-based split is based on fictitious crack faces and is, herein, expanded to support anisotropic materials. Furthermore, a novel hybrid approach is used, where the degradation of the sound material is performed based on a smooth traction free crack boundary condition, which proves to be the main driving factor for recovering commonly observed crack patterns. This is shown by means of a detailed analysis of two examples: a wooden single edge notched plate and a wood board with a single knot and complex fiber directions. In both cases, the proposed novel hybrid phase field approach is able to realistically reproduce complex failure modes.

T-stress for the double-edge cracked Brazilian disc under compression

As the nonsingular term in the Williams series solution of the stress field at the crack tip, T-stress has a great influence on the crack propagation behavior. Under the loading condition for pure mode II fracture, negative T-stress (compressive T-stress) reduces the deflection angle for crack initiation and promotes the self-similar propagation of crack; while positive T-stress increases the crack deflection angle, and the crack kinks into tensile wing crack. The closed-form solution of the T-stress for the double-edge cracked Brazilian disc (DCBD) under compression is obtained by the weight function method. The closed-form solution in series form has a good convergence. The normalized T-stresses are calculated for different conditions, then the effects of distribution form, loading angle, contact angle, and relative crack length on T-stresses are analyzed. The results show that the effect of contact angle γ on T-stress should be considered when the loading angle θ and the relative crack length α are both small or great; while the effect of distribution form on T-stress cannot be ignored if and only if θ and α are small. The T-stress in the DCBD specimen is always negative when θ ≤ 20° and α ≥ 0.4. This is advantageous for the realization of true mode II fracture.

Analysis of a mode-I crack in a one-dimensional orthorhombic quasicrystal strip

A mode-I crack in a one-dimensional (1D) orthorhombic quasicrystal (QC) strip under in-plane phonon and phason stress loading is considered. Fourier transforms are applied to reduce the mixed boundary value problem of the mode-I crack to solving a system of simultaneous singular integral equations. Asymptotic expressions of the phonon and phason stresses and displacement fields near the crack tips have been obtained in an explicit form. The crack-tip singularities of the mode-I crack have been investigated and the intensity factors of the stresses in the phonon and phason fields are derived explicitly. The stress intensity factors (SIFs) and the hoop stress intensity factors (HSIFs) have been determined to investigate the effect of the geometric size and the crack kinking phenomenon. The effect of the thickness ratio of the cracked strip on the SIFs and energy release rates has been investigated. When the thickness of the cracked strip becomes infinite large, the results obtained for the crack problem can be reduced to the analytic solution for a mode-I crack in an infinite 1D orthorhombic QC media.

Experimental and Computational Investigations on Fretting Fatigue Crack Growth in Dovetail Joints

Fretting fatigue is a significant damage mode for turbine engine blade/disk components. In the present work, fretting fatigue crack growth of a nickel-based superalloy was experimentally and computationally investigated. Fretting fatigue experiments of dovetail joints were conducted under loading ratio , and the results revealed that the fretting fatigue cracks nucleated in multiple sites on the contact edge, which was accompanied by oxide wear debris and propagated with a single through-thickness crack. The crack growth rate was determined based on the variation of applied loading ratio in the experiments. With the help of the maximum tensile stress criterion, the friction coefficient of the fretting pair was determined from simulations of the fretting fatigue crack propagation. With the increasing friction coefficient, the kinking angle of the fretting crack approaches a stable value. The stress was verified to have significant effects on the short crack kinking and implemented in the maximum tensile stress criterion. A methodology based on fracture mechanics was proposed to identify the friction coefficient on the fretting surfaces.

Effect of microstructure on fatigue crack propagation in additive manufactured nickel-based superalloy Haynes 282: an experiment and crystal plasticity study

Haynes 282 is a $$\gamma ^{\prime}$$ precipitation-strengthened nickel-based superalloy known for its exceptional high-temperature creep resistance and excellent fabricability. Recent advancements in powder-bed fusion-based additive manufacturing (PBF-AM) have enabled the fabrication of Haynes 282 with accurate, site-specific control of the grain orientation and morphology at the microscale. This ability opens up new avenues for microstructure design, to improve the material’s fatigue crack resistance and service life. This paper investigates the fatigue crack growth behavior of hybrid microstructure Haynes 282 fabricated via PBF-AM. Previous experiments revealed a higher crack propagation rate in the coarse columnar-grained microstructural regions when compared against fine-grained areas. Here, a strain gradient crystal plasticity model was adapted to study the fracture-related mechanical fields at the crack tip in the two microstructures. The simulation results showed a consistent influence of grain structure and texture on crack propagation, as was seen in the experiment. The model analysis revealed higher crack propagation driving force along crack direction in the coarse-grained sharply textured microstructure and higher driving force for crack kinking in fine-grained more diffusely textured microstructure, which is ascribed to the combined effect of yield stress, hardening rate, texture and grain morphology. The presented modeling approach will facilitate the development of the AM-based accurate microstructure design by deepening the fundamental study in AM-specific microstructure-properties relations.

Phase-field modeling of continuous fatigue via toughness degradation

We present a phase-field formulation to model fatigue crack growth over large numbers of cycles. Building upon a recently introduced phase-field formulation by the authors, fatigue is modeled phenomenologically by degradation of the fracture toughness, treated as a spatiotemporally evolving material property, inside a region around the crack tip with size Rfatigue. The present formulation, however, treats cycle number N as a continuous variable, allowing for crack growth prediction over large numbers of cycles of experimental relevance in arbitrary geometries containing one or several cracks, as well as under various loading conditions. The phenomenological form of the degradation law is analytically motivated by first deriving a relationship between the crack growth rate per cycle da/dN and the stress intensity factor (SIF) variation amplitude ΔK in the sharp-interface limit where Rfatigue is much larger than the phase-field regularization length ξ. This relationship reproduces salient features of experimentally measured fatigue growth curves, including the existence of a minimum ΔK for growth, a power law over an intermediate range of ΔK, and a sharp increase of growth rate when the peak SIF value approaches the Griffith threshold Kc. Phase-field simulations are shown to reproduce similar growth curves with quantitative differences depending on the ratio Rfatigue/ξ. The ability of the model to predict realistic crack paths is demonstrated by various examples in two and three dimensions including crack kinking under mode I+II loading, “en-passant” interacting cracks, and crack twisting in a three-point bending geometry with mode I+II+III loading.

Modulating fracture toughness through processing-mediated mesostructure in additively manufactured Al-12Si alloy

Al-12Si alloy processed through additive manufacturing exhibits a complex hierarchical structure. At the mesoscale, its melt pool boundaries constitute a network of weak interfaces that provides preferred pathways for crack kinking, leading to both marked anisotropy and apparent enhancement in the fracture energy. In this study, a multiscale cohesive zone-based computational model and a semi-analytical approach for kinked cracks are used to investigate the effect of melt pool configuration on fracture energy enhancement and anisotropy due to crack path tortuosity. We experimentally validate our methodology using fracture toughness testing of compact tension specimens, then systematically study the simultaneous effects of hatch spacing, layer thickness, and crack surface orientation on variations of the fracture energy. While the fracture energy increases with increasing hatch spacing and decreasing layer thickness, processing defects such as keyholing give practical limits to the melt pool geometry, limiting the fracture energy enhancement. We found that the fracture energy can be enhanced as high as a factor of two with an optimal crack surface orientation that is linearly proportional to the ratio of hatch spacing to layer thickness and varies between 60° and 100°.

Cracking during pyrolysis of preceramic polymers within glass microtubes

AbstractCracking of preceramic polymers during pyrolysis under highly‐constrained conditions is examined by X‐ray computed tomography of fine glass microtubes containing the pyrolyzing material. The microtubes represent model geometries that mimic the long channels between fibers during production of ceramic composites by precursor impregnation and pyrolysis. Complementary fracture mechanics analyses of interface cracking and crack kinking are used to glean insights into the conditions under which periodic alternating cracks form. A key finding is that alternating cracks are an inherent feature of constrained pyrolysis. This feature is attributable in large part to the high energy release rates for interface cracks to kink into the pyrolyzing material under the hydrostatic tension developed during pyrolysis. It also requires interfaces with toughness comparable to that of the pyrolyzing material, to prevent large‐scale interface separation. The results further indicate the need for small uniform spaces for pyrolysis within fiber preforms in order to produce networks of fine periodic pyrolysis cracks; these networks in turn facilitate impregnation and pyrolysis in subsequent processing cycles.

Numerical analysis of crack initiation angles and propagation paths in adhesively bonded joints under mixed mode I/II loading using a novel test specimen

In the present work, first, the effect of adherent type on the fracture parameters of a novel mixed mode I/II fracture specimen called bi-material inclined notch short bend beam (BI-SBB) is investigated by using the J-integral method. Then, the crack propagation path is obtained incrementally based on the maximum tangential stress (MTS) fracture criterion. In the next step, the crack propagation path is examined once again using the hybrid XFEM-CZM approach. To do that, in the adhesive region, the elements are enriched and in the adherent and adhesive interface, cohesive surface is used. The results showed that for the mode I loading, based on both methods, the crack propagation path is along the initial crack and inside the adhesive. But under mode II and mixed mode I/II loading, the crack kinks towards the adherent-adhesive interface. However, kinking slop obtain from the hybrid approach is steeper than the path obtained from the MTS criterion. According to the hybrid approach, once the crack reaches the adherent-adhesive interface, crack growth in the XFEM domain ceases and the damage appears on the cohesive surface. Then delamination propagates at the interfaces between the adhesive and adherents as the loading increases.

Scale effect in composite materials: Study of the intralaminar damage by means of a micromechanical model

The scale effect in Composite Materials is known as the delay in the appearance of damage in the weakest laminas of a laminate (typically 90 degrees laminas). The availability of ultra-thin plies, of up to 20 microns of thickness, has attracted the attention on this effect, as the use of these plies can imply the delay of the onset of damage at a laminate in a significant manner. The frame of the present work is a micromechanical study of the different phases of damage assumed to lead to the failure of the weakest lamina. Thus, it is assumed that the damage starts by isolated debondings between fibres and matrix, then continuing by the abandon of the interphase, the debonding crack kinking into the matrix, and finally the damage progressing either through the matrix itself or along the interfaces between fibres and matrix, to generate a transversal crack in the 90 degrees lamina. The study is carried out using a multi-scale model based on the Boundary Element Method, with control cells in which the damage at micromechanical level previously described is allowed. Concepts derived from Fracture Mechanics and Interfacial Fracture Mechanics are applied in the analysis. The conclusions obtained with this study are compared with those that clearly manifest the scale effect based on a global energy balance from the pristine state to the final situation with the 90 degrees lamina having a complete transverse crack.

On a new high order phase field model for brittle and cohesive fracture: numerical efficiency, length scale convergence and crack kinking

Being able to seamlessly deal with complex three dimensional crack patterns like branching and merging, phase field models (PFMs) are promising in the computational modelling of fracture of solids. Regarding the damage field, if only its second order derivative is present in the governing equation we have a second order PFM and if its fourth order derivative is also present we have a fourth order PFM. Previous studies have demonstrated that fourth order PFMs, with its smoother damage profile, are better in convergence and able to model strong anisotropic fracture energies. However, previous fourth order PFMs were developed only for brittle fracture and do not embed the material strength directly in the formulation. This paper presents a fourth order phase field regularised cohesive zone model (fourth order PF-CZM) for both brittle fracture and quasi-brittle fracture. We present a semi-analytical approach to compute the coefficients of the rational degradation function used in the fourth order PF-CZM. The proposed model is tested with multiple benchmark problems for mode I and mixed-mode fracture, and the results demonstrate that the fourth order PF-CZM: (1) provides results independent of the length scale and (2) is more efficient than its second order counterpart. The proposed model was then applied to modelling strong anisotropic fracture energies. A detailed study on sawtooth like crack patterns, which is a signature of strongly anisotropic fracture, is carried out with focus on periodicity and length scale sensitivity.

Symmetric arrangements of cracks with perturbed symmetry: Extremal properties of perturbed configurations

Perturbations of symmetric crack configurations produce mixed-mode conditions at crack tips, in cases of pure mode I (or II) conditions in unperturbed configurations. This may lead to the increase of stress intensity factors and energy release rates, so that their maximums are reached in somewhat perturbed configurations (even if the perturbations increase spacing between crack tips) thus making them energetically preferable. Тhe effect of perturbations on the direction of crack kinking is also examined, in particular, whether the kinking drives the crack system farther away from the original configuration or back towards it. These considerations may be related to the experimentally observed tendency of cracks to “avoid each other” Melin (1983). They also shed some light on the crack coalescence problems. Closed-form approximate expression for the maximal energy release rate at the crack kink tip is presented. The results of Panasiuk et al (1976), Cotterell and Rice (1980), and Amestoy and Leblond (1992) are also discussed.

A modified G criterion considering T-stress and differentiating the separation and shear failure in crack propagation

In view of shear failure controlled by distortion and separation failure governed by dilation having different significance for the crack propagation, the traditional G criterion is modified by differentiating the volumetric and distortional parts in energy release rates which involve the influence of T-stress. The critical volumetric to distortional energy release rate ratio is introduced as an intrinsic material property. As the critical volumetric to distortional energy release rate ratio increases, the failure pattern for mode II crack gradually transits from separation dominant failure to shear dominant failure. The modified G criterion is theoretically investigated through discussing the influence of critical volumetric to distortional energy release rate ratio, T-stress and fracture process zone size on the crack propagation behavior (i.e., crack kinking angle and fracture resistances). The crack kinking angle is found to reduce as the critical volumetric to distortional energy release rate ratio increases, but enlarge as the T-stress or fracture process zone size increases. The fracture resistances are found to decrease as the critical volumetric to distortional energy release rate ratio, T-stress or fracture process zone size increases. The modified G criterion shows a superior predictability for the experimental results reported by Aliha et al. (2012, 2013), Williams and Ewing (1972) and Mousavi et al. (2020) over the maximum tensile stress criterion (MTS criterion) and traditional G criterion. The modified G criterion has the potential to predict the crack propagation behavior for a variety of materials.

Effects of BFRP Bar Diameter and Cover Thickness on Fracture Behavior of BFRP Bar–Reinforced Ecological High-Ductility Cementitious Composites

Abstract To obtain the design parameters of bridge deck link slabs made of ecological high-ductility cementitious composite (Eco-HDCC) material reinforced with a basalt fiber-reinforced plastic (BFRP) by applying fracture mechanics concepts, the reinforcing effects of a BFRP bar on the fracture properties of BFRP bar–reinforced Eco-HDCC specimens were studied. First, cracking load, crack mouth opening displacement (CMOD), and deflection of specimens were monitored, and BFRP bar diameter and cover thickness were considered. The results indicate that both the diameter and cover thickness of BFRP bar have an obvious influence on the crack kinking angle. In addition, as the diameter of BFRP bar increases, the peak load, peak CMOD, peak deflection, and fracture energy of Eco-HDCC specimens increase, and these peak values of Eco-HDCC specimens after reloading also show the same trend. In addition, the peak load, peak CMOD, peak deflection, and fracture energy are larger if the Eco-HDCC specimen has a smaller cover thickness. However, the Eco-HDCC specimen with a BFRP bar cover thickness of 25 mm has a higher peak load after reloading than the specimen with a cover thickness of 15 mm when the bar diameters are 10 and 12 mm, respectively. In conclusion, BFRP bar diameters from 10 to 14 mm and a cover thickness of 25 mm are recommended when designing bridge deck link slabs.

Experimental investigation of high frequency pulse loading on fatigue crack growth in 5052-H32 series aluminum

In the marine industry, designers utilize 5052-H32 marine grade series aluminum for its strength to weight ratio, and the ability of this series to resist marine corrosive environments. During the operating lifetime of a marine vessel, it experiences constant and variable amplitude loading conditions from the sea environment, plus overloads/underloads in the form of high frequency pulses. These high frequency pulses can influence the fatigue crack growth behavior of the aluminum structure. Foundational models like Wheeler and Willenborg have previously been used to predict effects of underloads/overloads on fatigue crack growth, but have proven to be inadequate for all high frequency pulse loading conditions. In this paper, we coupled observations of the crack growth path obtained using an optical microscope with detailed measurements of surface strain fields using Digital Image Correlation (DIC) to elucidate the effects resulting from these high frequency pulses. An experimental test matrix was developed for applying pulses of varying amplitude and frequency to gain fundamental understanding of the characteristics of the high frequency pulses on crack growth behavior. Experimental results indicated there is a novel crack kinking behavior which results in retardation of the fatigue crack growth. Using DIC, we identified changes in the plastic zone ahead of the crack tip that mimic a hard inclusion, affecting not only the crack path, but also the crack opening displacements and subsequent crack growth rates. This work provides a foundation for understanding effects of high frequency pulses on crack growth to enable future development of a model incorporating the effects of the plastic zone on the growth mechanisms.

Coupling of Complex Function Theory and Finite Element Method for Crack Propagation Through Energetic Formulation: Conformal Mapping Approach and Reduction to a Riemann–Hilbert Problem

In this paper we present a theoretical background for a coupled analytical–numerical approach to model a crack propagation process in two-dimensional bounded domains. The goal of the coupled analytical–numerical approach is to obtain the correct solution behaviour near the crack tip by help of the analytical solution constructed by using tools of complex function theory and couple it continuously with the finite element solution in the region far from the singularity. In this way, crack propagation could be modelled without using remeshing. Possible directions of crack growth can be calculated through the minimization of the total energy composed of the potential energy and the dissipated energy based on the energy release rate. Within this setting, an analytical solution of a mixed boundary value problem based on complex analysis and conformal mapping techniques is presented in a circular region containing an arbitrary crack path. More precisely, the linear elastic problem is transformed into a Riemann–Hilbert problem in the unit disk for holomorphic functions. Utilising advantages of the analytical solution in the region near the crack tip, the total energy could be evaluated within short computation times for various crack kink angles and lengths leading to a potentially efficient way of computing the minimization procedure. To this end, the paper presents a general strategy of the new coupled approach for crack propagation modelling. Additionally, we also discuss obstacles in the way of practical realisation of this strategy.