Crack Kinking Research Articles

Elasto-Plastic Fracture Mechanics Analysis of the Effect of Shot Peening on 300M Steel.

A modified J-integral calculation method is adopted to fix the problem of the quantitative evaluation of the crack propagation of shot-peened structures. Considering the residual stress, residual strain, and residual strain energy, the effect of shot peening on the J-integral parameters of semi-elliptic surface crack fronts is quantitatively calculated and a method is provided for the performance evaluation of the shot peening layer. First, the shot peening process is simulated, then the fatigue crack is generated by changing the constraint condition and a far-field load is applied to calculate the J-integral parameters, crack propagation rate, and crack kinking angle. The effects of different crack depths and shot velocities on the fracture parameters are analyzed. The results show that the reduction in the J-integral value after shot peening decreases with the increase in the crack depth when the shot velocity is a certain value, which indicates that shot peening is more beneficial for suppressing the fatigue crack propagation. When the crack depth is greater than the depth of the compressive stress layer, shot peening accelerates the crack propagation. The reduction in the J-integral value decreases with the increase in shot velocity when the crack depth is a certain value; therefore, increasing shot velocity is more beneficial for retarding fatigue crack propagation.

Microtensile failure mechanisms in lamellar bone: Influence of fibrillar orientation, specimen size and hydration

A mechanistic understanding of bone fracture is indispensable for developing improved fracture risk assessment in clinics. Since bone is a hierarchically structured material, gaining such knowledge requires analysis at multiple length scales. Here, the tensile response of cortical bone is characterized at the lamellar length scale under dry and hydrated conditions with the aim of investigating the influence of bone's microstructure and hydration on its microscale strength and toughness. For individual lamellae, bone strength strongly correlates with the underlying mineralized collagen fibrils orientation and shows a 2.3-fold increase compared to the macroscale. When specimen size is increased to a few lamellae, the influence of fibril orientation and the size effect on strength are significantly reduced. These findings highlight the critical influence of defects, such as canaliculi and interlamellar interfaces, when assessing larger volumes. Hydration leads up to a 3-fold strength decrease but activates several toughening mechanisms enabling inelastic deformation. In axial specimens, toughening is seen through fibril bridging and crack kinking. In transverse specimens, water presence leads to a progressive but stable crack growth parallel to the fibril orientation, suggesting crack-tip plasticity at the fibrillar interfaces. This work offers a better understanding of the role of interfaces, porosity, and hydration in crack initiation under tensile loading, which is a crucial step towards improved clinical management of disease-related bone fractures through multiscale modeling approaches. Statement of significanceBone features a complex hierarchical structure which gives rise to several toughening mechanisms across several length scales. To better understand bone fracture, particularly the changes associated with age and disease, it is essential to investigate bone mechanical response at different levels of its hierarchical structure. For the first time, we were able to observe the nucleation of a single crack in hydrated bone lamellae under well-controlled uniaxial tensile loading conditions. These experiments highlight the role of water, interfaces, defects, and the ratio of defect to specimen size on bone's apparent strength and toughness. Such knowledge can be used in the future to develop multiscale models enabling improved clinical management of disease-related bone fractures.

On-chip environmentally assisted cracking in thin freestanding SiO2 films

An on-chip fracture mechanics method is extended to characterize subcritical crack growth in submicron freestanding films. The method relies on a self-actuated concept based on MEMS fabrication principles. The configuration consists of a notched specimen attached to actuator beams involving high internal stress. Upon release, a crack initiates at the notch, propagates, and arrests. Several improvements are worked out to limit the mode III component and to avoid crack kinking. The method is applied to subcritical crack growth in 140-nm-thick SiO2 films under different humidity conditions. The data reduction scheme relates crack growth rate to stress intensity factor. The static fracture toughness value is ~ 0.73 MPa sqrt{mathrm{m}}, with standard error of 0.01 MPa sqrt{mathrm{m}} and standard deviation of 0.17 MPa sqrt{mathrm{m}}. Subcritical crack growth rates are much smaller than in bulk specimens. A major advantage is that many test samples can be simultaneously monitored while avoiding any external equipment.Graphic

Dynamic interfacial crack propagation and kinking in sandwich panels

The dynamic interfacial crack propagation and crack kinking phenomena in sandwich panels are studied. The paper derives an analytical approach based on the Extended High-Order Sandwich Panel Theory (EHSAPT) and a cohesive interface modeling. The mathematical modeling of the panel makes a distinction between the face sheets and the core. The core is further divided into two bodies aiming to allow the nucleation of a shear crack in the core or the kinking of a core-face sheet crack into the core. The panel therefore includes four layers that are interconnected through three interfaces. The First-Order Shear Deformation Theory (FSDT) is adopted for the two face sheets and the EHSAPT is applied to the two core layers. Translational, rotational, and high order inertial effects are considered in all components. A geometrical nonlinear behavior with linear elastic laws is adopted for the face sheets while the core layers use linear kinematic relations and linear constitutive laws. The interfaces use nonlinear cohesive laws to model the dynamic nucleation, propagation, and kinking of cracks. The dynamic model is used for a numerical study of sandwich panels subjected to three point bending and end shortening loading conditions. The study explores the coupling of the crack propagation with the dynamic response. A comparison of the dynamic results with their static counterparts further explains the physical response of the sandwich panel and the dynamic characteristics of its failure mechanism.

Kinked crack paths in polycarbonate samples printed by fused deposition modelling using criss-cross patterns

Additive manufacturing is unquestionably gaining importance in industry. Due to the layer by layer deposit process, it usually leads to an anisotropic material. A question of importance is whether Linear Elastic Fracture Mechanics can be used to assess their resistance to fracture. In this paper, we investigate this point on polycarbonate printed by Fused Deposition Modelling focusing on a criss-crossed deposit pattern. Thanks to tensile and fracture experiments instrumented by Digital Image Correlation, the material is evidenced to be linear elastic until fracture, nearly isotropic in the 2D printing plane but with a strong fracture anisotropy, leading to systematic crack kinking along the weakest plane. The Stress Intensity Factors evolution is measured across the kink and shown to be in agreement with Amestoy-Leblond’s formula. The fracture toughness is observed to be larger than the bulk value, in agreement with irreversible damage and plasticity that are clearly observable at the scale of the threads.

Mixed Finite Element for Kinking Crack Analysis in an Orthotropic Media

Due to the attention brought to the composites materials, it is becoming mandatory to study their mechanical behavior especially in the fracture mechanics cases to determine and follow their conduct in a damaged state. To achieve this, numerical methods have been adapted to simulate the phenomenon of fracture within different materials and in different cases. In this work, an enrichment for modelling kinking cracks in orthotropic media has been added to a newly developed two-dimensional mixed finite element. To evaluate the crack propagation the virtual crack extension technique is used to calculate the energy release rates for this mixed finite element. The element is configured from parent element in a natural (ξ, η) plane to simplify the calculations in each element of the simulation. An example taken from literature with kinking cracks in an orthotropic material is used, the results prove the efficiency of the proposed method.

Modeling of interfacial crack propagation and kinking in sandwich panels

The paper presents an analytical model for the nucleation, propagation, and kinking of cracks in sandwich panels. The analytical approach adopts the variational principle of minimum of the total potential energy and it is based on cohesive interface modeling. The mathematical modeling considers two face sheets, a core layer, and an interfacial core-face sheet crack that can kink into the core and form a diagonal shear crack. This phenomenon, which has been observed in experiments, divides the core into two bodies. The core is therefore modeled using such two body approach. Three interfaces are introduced between the four components and appropriate interfacial laws are used to describe the interfacial phenomenon. The First-Order Shear Deformation Theory with geometrically nonlinear kinematic relations is adopted for the face sheets. The two core layers use linear geometrical relations and assume the high order polynomial displacement fields of the Extended High-Order Sandwich Panel Theory. Linear elastic laws are considered for the two face sheets and the core. The model is validated through a comparison with experimental observations of pre-cracked Double Cantilever Beam sandwich specimens that show a diversity of crack paths. The comparison and the quantitative investigation explore the capabilities and the limitations of the approach and shed light on the nucleation, debonding, and kinking phenomena in soft-core sandwich panels.

Crack kinking in h-BN monolayer predicted by energy dissipation

Rapid crack propagation in a strip of a hexagonal boron nitride monolayer is studied by molecular dynamics. Crack kinking/branching takes place at high velocities under displacement loadings, accompanied by elastic waves dissipating the external supplied work besides the fresh surface energy. Cracks moving at a maximum velocity (∼74% of the Rayleigh wave velocity) do not branch immediately, which is governed by energy dissipation around the crack tip, instead, once the energy release rate (G) reaches a critical value of 19.75 J/m2 (∼5.9 times the surface energy density of 3.35 J/m2), kinking occurs, which shows that G could predict the onset of kinking/branching accurately. The dependences of G for crack initiation and branching on displacement-loading rate, strip size, and initial crack length are examined as well.

Atomic simulation of the orientation effects on crack tip behavior in titanium single crystal

This work presents atomic simulations of crack tip behavior in HCP titanium single crystal with center crack under mode I loading condition. The simulation results show that the crack tip plasticity in most of the studied crack orientations is attributed to the activation of basal or prismatic 〈a〉 slips, which is in accordance with the slip characteristics analysis. Comparing the increment of crack tip advance with the applied strain under different conditions, it is found that brittle mode has the highest crack propagation rate, following by twinning dominated crack tip behavior and the latter is dislocation slip dominated crack tip behavior. The above toughness difference is further explained from the perspective of the atomic stress distribution in front of the crack tip. Finally, the simulation results are compared with theoretical predictions based on the linear elastic fracture mechanics. Besides, the observed crack kinking phenomenon is attributed to the preference of cleavage along the plane with lower critical stress intensity factor. In general, the simulation results indicate that titanium is an intrinsically ductile metal as plastic deformation can be observed in the vicinity of the crack tip for most of the studied crack orientations, though some slip modes that have relatively Schmid factors are suppressed by the applied boundary condition.

The use of Powell-Sabin B-Splines in a higher-order phase-field model for crack kinking

Phase-field models for brittle fracture in anisotropic materials result in a fourth-order partial differential equation for the damage evolution. This necessitates a $$\mathcal {C}^1$$ continuity of the basis functions. Here, Powell-Sabin B-splines, which are based on triangles, are used for the approximation of the field variables as well as for the the description of the geometry. The use of triangles makes adaptive mesh refinement and discrete crack insertion straightforward. Bezier extraction is used to cast the B-splines in a standard finite element format. A procedure to impose Dirichlet boundary condition is provided for these elements. The versatility and accuracy of the approach are assessed in two case studies, featuring crack kinking and zig-zag crack propagation. It is also shown that the adaptive refinement well captures the evolution of the phase field.

Crack path selection in orientationally ordered composites.

While cracks in isotropic homogeneous materials propagate straight, perpendicularly to the tensile axis, cracks in natural and synthetic composites deflect from a straight path, often increasing the toughness of the material. Here we combine experiments and simulations to identify materials properties that predict whether cracks propagate straight or kink on a macroscale larger than the composite microstructure. Those properties include the anisotropy of the fracture energy, which we vary several fold by increasing the volume fraction of orientationally ordered alumina (Al_{2}O_{3}) platelets inside a polymer matrix, and a microstructure-dependent process zone size that is found to modulate the additional stabilizing or destabilizing effect of the nonsingular stress acting parallel to the crack. Those properties predict the existence of an anisotropy threshold for crack kinking and explain the surprisingly strong dependence of this threshold on sample geometry and load distribution.

Numerical analyses of crack path instabilities in quenched plates

Crack path instabilities are observed in rapidly quenched rectangular glass plates whereby wavy crack patterns form as a result of the induced temperature gradients. The peculiar characteristic of these instabilities is that the speed of propagation is several order of magnitudes lower that the Rayleigh wave speed. Experimental studies have shown the dependence of the instabilities on certain geometrical, material, and experimental parameters (e.g. plate width, material toughness, speed of quenching). By perturbing these parameters cracks are observed to propagate along a straight line, oscillate with a periodic sinusoidal or semi-circle like morphology, or propagate in a supercritical manner. Here we formulate the problem of a propagating crack in a brittle thermoelastic material while considering the possibility of the crack undergoing bursts of supercritical crack propagation, by extending the model in Negri and Ortner (2008). We also describe a novel higher order computational framework for its numerical solution centered around Universal Meshes, Mapped Finite Element Methods, and Interaction Integral Functionals. We verify the convergence of the results and compare them against experiments. We reveal crack behaviors not previously observed. Particularly we discuss periods of sudden crack propagation, followed by temporary arrest and crack kinking. We identify various crack morphologies: sinusoidal, asymmetric, semi-circle, kinked and flattened oscillations. We investigate the frequency content of the oscillatory crack paths and study their relation to the dominating problem parameters. Additionally, we identify two new thresholds in phase space corresponding to the transition from oscillatory propagation to rapid propagation and arrest, as well as from permanent crack arrest to temporary crack arrest followed by kinking and branching.

Finite deformation cohesive zone phase field model for crack propagation in multi-phase microstructures

This paper develops a unified phase field model for simulating finite deformation crack evolution and interfacial decohesion in multi-phase elastic materials. Crack propagation is formulated using a phase field model, in which the order parameter $$s=1$$ corresponds to the crack topology. The phase field model at the interface is enhanced with cohesive zone characteristics through a cohesive potential function. The interface displacement discontinuities are regularized using an auxiliary interface phase field order parameter. The cohesive potential is associated with this interface phase field for delineating interfacial decohesion. The model is numerically implemented using a multi-pass staggered solver. Numerical examples involving different failure mechanisms are simulated for examining the performance of the proposed model. Different failure mechanisms such as interfacial debonding, crack kinking and propagation in the brittle matrix, and their interactions are captured by the model. Limited verification tests are conducted with analytical results.

Fracture loads prediction of the modified 3D-printed ABS specimens under mixed-mode I/II loading

The fracture features of the 3D-printed samples are assessed employing Semi-Circular Bending (SCB) specimens. The critical failure loads are experimentally measured and have been predicted using both Maximum Tangential Stress (MTS) and Generalized Maximum Tangential Stress (GMTS) criteria. The 3D-printing process is improved with several approaches to decline the voids volume and escalate the weld lines strength of the 3D-printed specimens to boost their mechanical specifications. The Acrylonitrile Butadiene Styrene (ABS) SCB samples with numerous pre-crack angles ranged from pure mode I to pure mode II are produced utilizing a modified 3D-printing process. The results of the tensile tests confirmed that the properties of the specimens created by the modified 3D-printing process are independent of the raster of printing orientation. The predicted failure loads with the GMTS criterion had a better correlation with the experiment compared to the MTS criterion owing to the impact of the T-stress term in the 3D-printed SCB samples. Furthermore, the cross laminar fracture augmented fracture toughness and declined crack kinking behavior of the 3D- printed ABS specimens.

Crack kinking and tunneling simulation for the single-fiber composite under transverse tension based on phase-field method

Virtual tests for a single-fiber–reinforced composite model subjecting to transverse tension are carried out based on a phase-field method considering a varying interface toughness parameter. Without pre-treating the crack initiation location and propagation path, the complete fracture process is realized for the first time in a three-dimensional numerical model, including nucleation cracks on the fiber/matrix interface at the free end, tunneling cracks along the fiber axis, and kinked interface cracks deviating from the interface and penetrating into the matrix. The numerically calculated crack propagation process is in good agreement with the in situ observations in the literature, indicating that the present model provides a good real-time quantitative numerical method for three-dimensional fracture analysis of fiber-reinforced composites. Tunneling cracks tend to cause macroscopic interface debonding and fiber pull-out. The interface tunneling crack initiation and the transition to the steady state inside the model are captured and analyzed in the numerical model. Kinked interface cracks can merge with other matrix cracks, forming a macroscopic transverse crack fracture mode. The kinking behaviors affected by the initial crack size and the interface properties are investigated. This study for the detailed crack propagation is helpful in understanding the toughening mechanism of fiber-reinforced composites under transverse tension.

Potential fracture paths for cracked rocks under compressive-shear loading

An energy-based model on multiple cracks initiation from a crack tip has been proposed to capture the physical process of fracture, which can be used to predict and analyse the fracture behaviours of cracked rocks and rock-model materials under compressive-shear loading. The conservation law has been explored utilizing a partial integral path, from which an analytical solution of the energy release rate for multiple cracks initiation from a crack tip has been founded. Some underlying fracture behaviours on cracks initiation from a crack tip, including the crack kinking, side-branching, branching and tri-branching, have been theoretically investigated, which implies actually a degree of instability on a cracked rock under compressive-shear loading. The K-based criteria and fracture toughness for crack kinking, side-branching, branching and tri-branching have been defined. The predictions based on present modelling should help to refresh the understanding of some important experimental observations, such as so called wing cracks and secondary cracks observed in the experiments of cracked rock under compressive loading. As an alternative solution, the energy-based driving mechanism behind complex fracture phenomenon have been suggested.

Crack kinking out of interface of two orthotropic materials under combined thermal/mechanical loading

The problem of crack path stability along the interface between two orthotropic elastically dissimilar materials under the presence of in-plane residual stresses is analyzed using the concept of Finite Fracture Mechanics and matched asymptotic procedure. The complex stress intensity factor and the T-stress characterizing the stress state at the crack tip are calculated both for the thermal (residual stresses) and mechanical loading using the two-state integral. The matched asymptotic procedure together with FEM is used to derive the change of the potential energy induced by the incremental crack growth (and correspondingly the incremental energy release rate of such a crack), which is needed for the fracture criterion formulation. An energy based fracture criterion is introduced for this problem and it is investigated whether and how is the criterion for the prediction of crack kinking from the interface affected by residual stresses.

Investigation of skin-core debonding in sandwich structures with foam cores

Debonding between the skins and the core in a sandwich structure is a critical failure mode in automotive applications; once debonding occurs, the load carrying capacity of a sandwich structure drastically decreases. In the present paper, the effect of using three core materials, with different cell characteristics, on the interfacial strength between the foam cores and a CFRP skin is investigated through mechanical testing and numerical modelling. A key finding is that foams with a coarse cellular structure favour a high resin uptake at the interface during the manufacturing process, which results in a stronger interfacial bonding between the foam and the CFRP. During Mode I loading, the thick resin layer at the interface postpones crack initiation and kinking in the core, whilst under Mode II, this resin layer delays the collapse in compression of foam cells under the crack tip. Thus, the importance of including this thick resin layer in the FE modelling was demonstrated. Finally, as the CZM was shown to be unable to predict the unstable crack propagation within the core, an alternative approach has been suggested which has the significant benefit of not requiring experimental testing of the interface between the skin and the core.

Phase field modeling of interface effects on cracks in heterogeneous materials

AbstractOne of the reasons why the phase field approach has become very popular for modeling fracture processes is that therein the entire evolution of fracture follows from energetic principles without the need for different criteria for crack initiation, nucleation, kinking or branching. Furthermore, these models allow for a straightforward numerical implementation with standard finite elements, since displacement jumps and stress singularities are avoided in these models. Consequently, phase field fracture models are now also used to model and simulate fracture of heterogeneous materials such as composites, where cracks may be arrested, deflected or bifurcated at interfaces between the different components of the composite material, resulting in complicated crack patterns. The crack propagation is not only controlled by the elastic and fracture properties of the bulk phases of the material but also by the properties of the interfaces in between. Thus, it is crucial to take these interface properties into account. Therefore in this work, interfaces are equipped with a fracture energy corresponding to the phase field fracture energy of the bulk phases in order to model the interface fracture properties. In the finite element implementation, the interfaces are modeled by means of surface elements without introducing additional degrees of freedom.

A combined atomistic-continuum study on the temperature effects on interfacial fracture in SiC/SiO2 composites

In this paper, for the first time, we combine reactive molecular dynamics and continuum fracture mechanics to investigate the effect of temperature on fracture behavior of a crack existing at the strong interface of SiC/SiO2 ceramic composite. At strong interfaces, existing cracks tend to propagate out of interface under mixed mode (i.e., combined opening/sliding) loading conditions. As temperature varies, the material properties change thereby affecting the interfacial crack propagation behavior. First, the temperature-dependent material properties of silicon carbide (SiC) and amorphous silica (SiO2) derived from ReaxFF reactive molecular dynamics simulations. Next, using a multi-scale modeling approach these temperature-dependent properties are used as inputs to the continuum-based model for investigating the fracture behavior as a function of temperature. By employing maximum tangential stress (MTS) criterion at the continuum scale, the effect of ambient temperature on the interfacial fracture toughness and crack kinking angle are studied. It was found that the ambient temperature significantly influences the mixed mode I/II kinking behavior for cracks existing at the SiC/SiO2 strong interface. The overall approach shows that reactive molecular dynamics combined with continuum model provide a more comprehensive modeling approach for examining fracture in ceramic composites with strong interface.