Crack Tip Stress Research Articles

Preparation and mechanical properties of cubic boron nitride reinforced lead glaze layers of a gradient structure

Lead glaze possess excellent radiation ray shielding ability, and it is an efficient way to stop radiation spillover by using lead glazed indoor titles in a building. The merit of low firing temperature of lead glaze is, however, associated with its poor wear resistance. Here super-hard cubic boron nitride (cBN) particles, of a neutron shielding property, are introduced into the soft glass matrix to improve its mechanical properties. Results show that, at meticulously tailored conditions, the lead glaze surface is successfully enriched with cBN particles due to the lower density of cBN relative to the glaze. With 5 wt% cBN particles embedded in the glass matrix, the hardness increases by 51.2% and more importantly, the glaze yields significantly improved wear resistance. The finite element analysis reveals that the cBN particles enhance the toughness of the glaze, a key factor to wear resistance, by reducing the crack tip stress concentration.

Spatially resolved Raman piezospectroscopy for nondestructive evaluation of residual stress in β-Ga2O3 films

In this paper, the piezospectroscopic effect for β-Ga2O3, i.e. the spectral band shift in response to strain/stress, has been calibrated by the indentation method using spatially resolved Raman spectroscopy for quantitative stress evaluation of Ga2O3 devices, taking advantage of the crack-tip tensile stress field and the spatial probe deconvolution. A series of Vickers indentation prints were introduced on (010) and () Ga2O3 single crystals, and the relationships between observed band shifts and residual stresses were clarified to determine the phonon deformation potentials of the Raman bands. Accordingly, a quantitative analysis of the residual stress field in a Ga2O3 thin film grown on (0001) sapphire by plasma-assisted pulsed laser deposition, which revealed the presence of a gradient of incompletely released stress in the depth direction of the film, is shown as an example.

Subsurface fatigue crack tip strains in 7475‐T7351 aluminium alloy measured using stroboscopic neutron diffraction

AbstractFatigue crack growth in thick‐section metals is typically controlled by an internal plane strain region where strong triaxial constraint of the crack tip occurs. However, the crack tip stress state in this region is challenging to measure. We have used neutron diffraction to study the plane strain section of fatigue crack tips in situ. A stroboscopic form of neutron diffraction using a moving frame‐of‐reference was developed to measure crack tip strains as a function of phase in the fatigue loading cycle without interrupting the cyclic load. Using point measurements of near‐tip strain in 7475‐T7351 aluminium alloy in conjunction with finite element analysis, we can estimate the extent of the crack tip plastic zone, verifying that it is small for this material and set of loading conditions.

An atomistic based continuum level 3D mode-I meso-fracture criterion for cement-based concrete

This paper establishes an atomistic based continuum level 3D mode-I meso-fracture criterion for cement-based concrete from a multiscale perspective. Firstly, on the basis of the 3D self-consistent finite stress model and the 3D mesoscale crack path model, a meso-fracture criterion is theoretically deduced by considering both the crack tip stress state and the crack path energy consumption conditions. Secondly, with the help of MD simulation technique, a systematic atomistic level modelling approach for the study of interaction behaviors between mortar and aggregate in cement-based concrete is developed, and based on which, a new determination method for the critical mesoscopic fracture index is proposed. Thirdly, using mesoscale fracture test results as experimental benchmark for numerical models, the proposed meso-fracture criterion is verified through FE simulations based on a tri-phase numerical model. It is expected this work could lay a foundation for the following investigations on concrete performance design.

An adaptive finite element method for crack propagation based on a multifunctional super singular element

The traditional finite element method (FEM) often requires a large number of refined meshes to analyze the mechanical behavior of geometric discontinuities, its computational efficiency and convergence speed are affected. In this paper, an adaptive FEM for crack propagation based on a multifunctional super singular element (MSSE) at the crack tip is proposed for the fracture process investigation of two-dimensional (2D) materials. The adaptive FEM for crack propagation divides the crack tip neighborhood into the MSSE region, the protection element (PE) region and the background element (BE) region. The MSSE is established based on the numerical eigen-solution of the singular stress field near the crack tip, and can be used for anisotropic material and interfacial crack problems. The PE and BE regions are still discretized by the conventional finite element meshes. Since the node degrees of freedom between MSSE and conventional finite element are unified, they can be assembled directly without transition element. The MSSE can be used to solve the crack tip stress intensity factor (SIF) directly without refining the crack tip mesh. The adaptive meshing technique reduces the difficulty of remeshing during crack growth, thus facilitating the simulation of crack propagation processes. The adaptive crack propagation algorithm is used to analyze the crack propagation problems in isotropic materials, anisotropic materials and bi-materials. The calculated results demonstrate the effectiveness and universality of the crack tip MSSE. The method has potential for application in the simulation study of residual strength and fatigue fracture of complex mechanical structures.

Virtual element method for mixed-mode cohesive fracture simulation with element split and domain integral

We present a computational framework for mixed-mode cohesive fracture simulation based on the virtual element method (VEM). To represent an arbitrary crack path, the element splitting scheme is developed on a polygonal mesh to capitalize its flexibility in element shape. For the accurate evaluation of a crack-tip stress field and crack propagation direction, the virtual grid-based stress recovery scheme is tailored for VEM in conjunction with the maximum strain energy release rate criterion. The mixed-mode fracture examples are illustrated to validate the accuracy and robustness of the proposed computational scheme. Numerical results demonstrate that the domain integral method with the stress recovery scheme captures an accurate crack path without oscillation under the biaxial tensile stress state. Furthermore, the computed cracks using the element splitting scheme show that smooth and curved patterns on polygonal elements are in good agreement with the experimental results.

Identification of Linear Elastic Fracture Mechanics Parameters Through the Atomistic Simulation Based Analysis

The contribution presents atomistic modeling of the proximate crack tip and notch stress fields through molecular dynamics method. The study is aspired to comparing atomistic stress distributions for monocrystalline fcc copper and aluminum with continuous stress fields obtained on the basis of classical continuum fracture mechanics. Atomistic simulations were implemented for pure tensile loadings and mixed (I+II mixed loadings) mode loadings in Large-scale Atomistic/ Molecular Massively Parallel Simulator (LAMMPS). In atomistic computations specimens with central cracks and single edge notches made of crystalline fcc copper and aluminum under mixed mode loadings are considered. The elastic tensor components of the selected crystalline materials are obtained via molecular dynamics simulations and the circumferential distributions of stress fields in the straight away proximity of the crack and notch tips in aluminum and copper are constructed. The main regularities arising from the comparative analysis of the atomistic and continuum approaches are revealed. The major conclusion that can be reached after atomistic modeling is that the stress apportionments given by classical linear fracture mechanics qualitatively and quantitatively describe the molecular dynamics stress distributions.

The constraint corrected fracture criterion based on the J-A concept

The J-A concept, based on the three-term asymptotic solution for elastic-plastic crack-tip stresses, and the cumulative damage rule are employed to construct the quantitative two-parameter elastic-plastic J-A criterion. The fracture toughness as a function of the crack-tip constraint A in the fracture criterion is interpreted as the corrected elastic-plastic fracture toughness of a specimen with the corresponding constraint parameters A. The results of a study of the normalized corrected fracture toughness as a function of failure stresses, the crack aspect ratio and the strain hardening exponent of the material are presented. The significant effect of the strain hardening exponent on the normalized constraint corrected fracture toughness is observed.

Study on the Low Temperature Cracking Mechanism of Steel Slag Asphalt Mixture by Macroscale and Microscale Tests

Steel slag’s physical and mechanical properties are close to natural gravel, which can replace natural aggregate with paving asphalt mixture pavement. Based on macro- and microscales, it is necessary to study the low-temperature cracking characteristics of steel slag asphalt mixture (SAM). This paper aims to study the low-temperature cracking characteristics and influence mechanism of steel slag asphalt mixture by macro- and microscale tests. This article analyzes the strain field distribution and cracks propagation law of SAM at low temperatures by the three-point bending test combined with digital image correlation (DIC). The microscopic pore characteristics of SAM were studied by nuclear magnetic resonance (NMR). Based on fracture mechanics and weight function theory, the variation law of the stress intensity factor at the crack tip of the asphalt mixture with crack propagation is derived. The correlation between microscopic pores and low-temperature cracking characteristics of asphalt mixture was analyzed based on the grey correlation theory. The results show that SAM has more small and less large pores, and its total porosity is lesser than that of the basalt asphalt mixture (BAM). The initial elastic stage of SAM resisting bending deformation is longer than that of BAM, the bending strain energy density (dW/dV) is larger, and the crack penetration is slower. The horizontal strain energy density (DE) of SAM is greater than BAM, and the crack tip stress is greater. The porosity correlates well with the low-temperature crack resistance of the asphalt mixture.

Study of the interaction mechanism of oppositely propagating cracks by dynamic photoelasticity and numerical simulation

The interaction mechanism of oppositely propagating cracks is an important basis for the study of rock fracture under dynamic loading. In this article, the stress field superposition and crack tip stress evolution are deeply investigated during the interaction of oppositely propagating cracks by using dynamic photoelastic experiment method and numerical simulation analysis. Obtained results indicate that the cracks interaction process is accompanied by the deflection of the crack, and the deflection of the cracks is mainly affected by the shear stress field at the crack tip. According to the difference of the crack deflection characteristics, the interaction process of the oppositely propagating cracks can be divided into two stages. The Stage I: the non-interlaced stage and Stage II: the interaction stage after the mutual staggered. It includes the period of Stage I that the oppositely propagating cracks are not interlaced with each other; the Stage II is the interaction period after the oppositely propagating cracks are interlaced with each other. The effects of stress intensity factor K I, stress intensity factor K II and far-field T stress on crack propagation process should be comprehensively considered when predicting the crack growth trajectory. The interaction of the stress field between cracks is the main factor determining the crack propagation trajectory. In addition, the vertical spacing between cracks also has a significant effect on the fracture behavior of oppositely propagating cracks. When the vertical distance between the two cracks is large, the local stress fields at the crack tip cannot overlap and interfere with each other, and the oppositely propagating cracks will expand independently of each other.

Static and dynamic analyses of the effects of shim material stiffness on insert crack initiation and propagation

Microcracks can form on the surface or inside an insert during forming or cutting processes. These microcracks tend to expand rapidly under impact loading, eventually leading to tool fracture and failure. Fracture and breakage of inserts cause significant limitations to the improvement of processing efficiency and safe production. This study investigated the effects of shim stiffness (using Young's modulus) on the stress distribution in the insert and at the crack tip under static and dynamic (impact) loading conditions, thereby providing a theoretical basis for correctly designing and selecting inserts for indexable tools. The extended finite element method (XFEM) was used to develop a 3D simulation model for an insert–shim system. The model was used to study crack initiation and expansion in the insert for different rigid shims under static and dynamic loading. Analyses of the crack tip stress intensity factor, the maximum principal stress, the strain, and the angle and direction of crack deflection were performed. Additionally, interrupted cutting experiments were conducted with cemented-carbide tools for four rigid shim materials. It was concluded that under static loading conditions, a weakly rigid shim reduced the crack tip stress intensity factor and the maximum principal stress, thus reducing the probability of insert fracture and that the stiffness of the shim has no effect on the angle of crack deflection on the insert surface. The shim stiffness has a more obvious effect on the crack propagation length and internal propagation direction during dynamic loading, and a weakly rigid shim increases the deflection angle as the crack expands inside the insert, thereby reducing the downward fracture length.

Analysis of Mode I and II Crack tip Stress Fields for MEMS Structures with Cubic Elastic Anisotropy

Analysis of Mode I and II Crack tip Stress Fields for MEMS Structures with Cubic Elastic Anisotropy

Evaluation of fracture toughness properties of polymer concrete composite using deep learning approach

AbstractUsing artificial intelligence‐based methods in predicting material properties, in addition to high accuracy, saves time and money. This paper models and predicts the fracture toughness properties of polymer concrete (PC) composites using the deep learning method. After preparing a database consisting of 209 experimental data from 19 relevant studies, the effect of seven important variables on critical stress intensity factor (KIc) and crack tip opening displacement (CTOD) is considered. Then, the deep neural network (DNN) model is developed and trained using the prepared database. The accuracy of the DNN model is examined by implementing four statistical criteria, MSE, R2, RMSE, and MAE. Finally, the sensitivity of the KIc and CTOD to each input variable is evaluated using a partial dependence plot (PDP) analysis. While aggregate size, nanofiller content, and a/R ratio have the most positive effect on KIc, aggregates and nanofiller content have the most positive influence on CTOD.

In Situ ZrB2 Formation in B4C Ceramics and Its Strengthening Mechanism on Mechanical Properties.

In order to reduce the sintering temperature and improve the mechanical properties of B4C ceramics, ZrB2 was formed in situ using the SPS sintering method with ZrO2 and B4C as raw materials. Thermodynamic calculations revealed that CO pressure affected the formation of ZrB2 at temperatures from 814 °C to 1100 °C. The experimental results showed that the ZrB2 grain size was <5 µm and that the grains were uniformly distributed within the B4C ceramics. With an increase in ZrO2 content, the Vickers hardness and flexural strength of the B4C ceramics first increased and then decreased, while the fracture toughness continuously increased. When the content of ZrO2 was 15 wt%, the Vickers hardness, fracture toughness and flexural strength of B4C ceramics were 35.5 ± 0.63 GPa, 3.6 ± 0.24 MPa·m1/2 and 403 ± 10 MPa, respectively. These results suggest that ZrB2 inhibits B4C grain growth, eliminates crack tip stress, and provides fine grain to strengthen and toughen B4C ceramics.

On the T-stress extraction method used by current version of Abaqus

In the present note, it is shown that in the current version of Abaqus (6.10 and later), there is an error in the method used for the determination of T-stress. In particular, errors will occur in cases when there are tractions applied to the crack faces. Since T-stress is an important parameter characterizing the crack tip stress field, used widely in fracture mechanics analysis, it is important to point out this to the users of Abaqus. The reason for this error is due to the incorrect interpretation of the asymptotic crack tip stress fields. To obtain correct T-stress results, the users need to remove this error manually.

Simple crack tip and stress intensity factor determination method for model I crack using digital image correlation

In the past three decades, quantitative characterization of cracks attracted much attention with the development of digital image correlation (DIC), especially for estimation of crack tip position (CTP) and stress intensity factor (SIF). Quantifying CTP and SIF is of great importance in the damage tolerance assessment of fracture-critical components and structures. In previous research, multivariate fitting is performed on the displacement field to determine CTP and SIF. However, high gradient deformation near the crack tip causes inaccurate results and an involving complex estimation process. In this paper, a simple method is proposed to determine the CTP and SIF based on the displacement field calculated by DIC. Instead of the full-field fitting method, two lines symmetrically distributed on both sides of the crack tip are selected to fit the CTP. Vertical displacement differences between two lines are fitted with the theoretical solutions of mode I crack. Compared with the actual position observed by the micrograph, the estimation error is less than 2 pixels (about 6 μm). Additionally, a similar method is proposed to estimate the SIF utilizing the CTP results. To avoid the bias errors caused by the plastic zone, two lines are selected in the elastic zone away from the crack tip. Vertical displacements on two lines are fitted with the theoretical solutions to obtain SIF. The fitting results of the proposed method are close to that of the full-field fitting method. Compared with the previous methods, the computation burden of the proposed method is greatly reduced while the accuracy is not affected.

Asphalt complex cracks' sensitivity to temperature and crack depth and adjustment of the composite stress intensity factor

This paper is based on the fracture mechanics K-criterion with the composite stress intensity factor solution formula. The influence of temperature and depth in developing complex crack instability and diffusion in asphalt pavements is investigated. The crack composite stress intensity factor and development pattern are analyzed. The finite element modeling analyzes the change in stress intensity factor values at different temperatures and cracks depths. The composite stress intensity factor's temperature effect factor (t*) and crack depth effect factor (d*) are derived, and the calculation formulae are optimized. The study results show that among the complex cracks in asphalt pavements, the type I crack tip stress intensity factor (KⅠ) is the most seriously affected by temperature and crack depth and is also the main controlling factor of crack development. Type II crack tip stress intensity factor (KⅡ) is not significantly influenced by temperature but tends to rise and fall as the crack depth increases. Type III crack tip stress intensity factor (KIII) is smaller than KⅠ and KⅡ. It has less influence on the development of complex cracks in asphalt pavements. t* and d* were introduced to derive the formula for the modified composite stress intensity factor (Keff*). The formula was verified to calculate the composite stress intensity factor at different temperatures and crack depths and to study the cracking pattern of asphalt pavements.

LEFM is agnostic to geometrical nonlinearities arising at atomistic crack tips

Various fields such as mechanical engineering, materials science, etc., have seen a widespread use of linear elastic fracture mechanics (LEFM) at the continuum scale. LEFM is also routinely applied to the atomic scale. However, its applicability at this scale remains less well studied, with most studies focusing on non-linear elastic effects. Using a harmonic “snapping spring” nearest-neighbor potential which provides the closest match to LEFM on a discrete lattice, we show that the discrete nature of an atomic lattice leads to deviations from the LEFM displacement field during energy minimization. We propose that these deviations can be ascribed to geometrical nonlinearities since the material does not have a nonlinear elastic response prior to bond breaking. We demonstrate that crack advance and the critical stress intensity factor in an incremental loading scenario is governed by the collectively loaded region, and can not be determined analytically from the properties (max. elongation, max. sustained force, etc.) of the stressed crack tip bond alone.

Effect of lattice distortion and grain size on the crack tip behaviour in Co-Cr-Cu-Fe-Ni under mode-I and mode-II loading

In this article, molecular dynamics (MD) based simulations were performed to study the crack tip behaviour in single and polycrystalline configurations of five elemental (Co-Cr-Cu-Fe-Ni) high entropy alloys. To investigate the crack tip behaviour in polycrystalline HEA, inter and intragranular crack positions in conjunction with grain size in the range of ∼2.5 nm to ∼10 nm were developed and simulated in this work. Average atom (A-atom) configuration was also developed to nullify the effect of lattice distortion, and results were compared with random alloy configuration/HEA. Simulations revealed that A-atom possesses higher critical stress values. Still, the early onset of dislocation emissions from the crack tip in random alloys leads to crack tip blunting. The spatial positioning of the crack in the polycrystalline HEA significantly affects the fracture behaviour. It was concluded from the simulations that in small grain size configurations (5 nm and 6 nm), crack tip was in proximity of the high energy atoms of grain boundary, which led to hardening and higher stresses at the crack tip. The higher value of crack tip stresses in small grain configurations leads to crack propagation. In contrast, early emission of dislocations from the crack tip in large grains dilutes the crack tip stresses.

Examining the effect of crack initiation angle on fracture behavior of orthotropic materials under mixed-mode I/II loading

In this research, the maximum strain energy release rate concept is adapted for predicting the fracture response of orthotropic materials under mixed-mode I / II loading with an arbitrary precrack-fiber angle. Adaptive maximum strain energy release rate criterion (AMSER) is derived using the crack tip stress field of orthotropic materials with a precise look on the crack initiation direction. In precrack along the fibers, the crack initiation angle is assumed to be in the direction of maximum strain energy release rate (SER). Several experimental observations on a macroscopic scale prove that in the arbitrary angle between the precrack and fiber case, precrack kinks and propagates along the fibers; thus in the derivation of AMSER, crack initiation angle is considered as a superposition of the angle between precrack and fibers and the predicted angle based on the SER criterion (θC). The main purpose of this paper is to investigate the effect of crack initiation angle on the predicted fracture behavior. Due to the arbitrary angle between precrack and fibers, it is impossible to establish pure mode I conditions and derive pure mode I stress intensity factor. Thus, the equivalent fracture toughness concept in pure mode I is presented. AMSER criterion is validated by comparing fracture envelope curves with available experimental data in mixed-mode I / II loading. It can be concluded that accurate prediction of the crack initiation angle based on SER criterion causes the fracture behavior of orthotropic materials to be extracted with high accuracy. The results prove that the hypothesis of precisely predicting crack initiation angle based on the superposition of kink and θC angles complies with the nature of fracture of orthotropic materials.