Crack Tip Stress Research Articles

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.

A Physically Based Model Predicting the Degradation of Hydrogen on Crack Growth Critical Stress Intensity Factor of Metals

A simple, physically based model is developed to quantitatively predict the degradation of hydrogen on the crack growth critical stress intensity factor (CSIF) of metals. The model is formulated by combining a microscopically shielded Griffith criterion (MSGC) model for plasticity-induced cleavage fracture and thermodynamics decohesion (TDD) theory for hydrogen-enhanced interface decohesion. The hydrogen-influenced CSIF is described as a function of the intrinsic CSIF (hydrogen-free), initial hydrogen concentration (solubility), hydrogen trap binding energy and crack tip stress. All parameters in the model can be determined with a physical basis and the model is successfully validated by comparison with published experimental data.

Simulation of Destructive Test for Arch Reinforcement Area of Tunnel Lining by MSIM

Meshless Shepard interpolation method (MSIM) is used to simulate the destruction process within the arch reinforcement area of tunnel lining. In this method, the shape functions are formed by the partition of unity and the finite cover technology, which is not affected by discontinuous domains, with delta property at any desired node, and applies boundary conditions in an easy and correct way. The MSIM method combines the advantages of both the conventional meshless method and the numerical manifold method. The finite cover technology enables the shape functions to not be affected by the discontinuities in the solution domain, which overcomes the difficulty resulting from the conventional meshless method. The finite covers and the partition of unity functions are formed using the influence domains of a series of nodes, which removes the obstacle from conventional numerical manifold method and has simpler formation of finite covers than numerical manifold method. Virtual crack closure technique is used to calculate the intensity factor of crack-tip stress. The results of progressive destruction process simulation on the cracking patterns within the arch reinforcement area indicate that the method is suitable for tracking the crack propagation in complex stress conditions.

Simulation of crack growth for metal plates with holes based on cohesive zone model

Hole defects are very common in metal plates. The propagation of cracks in engineering structural members will be affected by the holes of the members, which will not only change the propagation direction of cracks, but also have the ability to limit the growth of cracks. Therefore, the study of material fracture crack propagation caused by the distribution of holes and other factors under loading conditions has become a problem that needs to be considered in structural design. The cohesive zone model (CZM) can effectively avoid the singularity problem of crack tip stress when simulating crack growth, and at the same time can clearly show the crack growth path. Based on exponential CZM, the finite element analysis of tensile test for metallic materials with hole defects was carried out. The crack propagation law under constant load was obtained. It was proved that CZM could simulate the crack propagation in metallic materials with holes more accurately. The influence of the pore size, shape, distribution on the crack propagation is discussed. The results show that the smaller the distance difference between holes, the greater the supporting reaction force. The smaller the radius of the hole, the higher the fracture toughness and the maximum supporting reaction force of the metal plate. And it also can be seen that as the number of holes increases, the maximum supporting reaction force and fracture toughness of the metal plate decrease. The use of staggered holes distribution has greater supporting force and better toughness. The research results of this paper provide a theoretical basis and reference for investigating the propagation and propagation of cracks in the process of damage and failure of materials and for structural design and performance evaluation of engineering materials.

Unified theoretical solutions for describing the crack-tip stress fields of finite specimens with mode-I crack under fully plastic conditions

The analytical equation to express the equivalent stress of the representative volume element (RVE) is derived from the energy density equivalence. Based on the analytical expression for equivalent stress of the RVE, extensive analyses are conducted for the stress fields in the forward sector near the crack-tip of finite specimens with mode-I crack for pure power-law hardening materials. Further, unified theoretical solutions with various special functions for describing the stress fields are proposed under fully plastic and plane-strain conditions. Comparisons of radial stress distributions in various angles, angular stress distributions, and contour lines of the equivalent stress between the results predicted by the finite element analysis, HRR (Hutchinson and Rice and Rosengren) solutions, and the proposed unified theoretical solutions are performed. The excellent capability of the proposed unified theoretical solutions for predicting the crack-tip stress fields is verified.

Fatigue crack growth modelling for S355 structural steel considering plasticity-induced crack-closure by means of UniGrow model

The UniGrow model is an analytical procedure to assess the fatigue crack growth based on elastic–plastic crack tip stresses and strains. The assumption is that fatigue crack growth (FCG) can be considered as a process of successive crack re-initiations resulting from material damage in the crack tip zone. The main parameters of this model are the crack tip radius and the elementary block size. Experimental FCG data obtained for S355 carbon steel showed that assuming the elementary block size with the same value of the crack tip radius to collapse FCG data using UniGrow model is non-coherent with experimental evidence. In this sense, a new approach is proposed by establish a clear distinction between crack tip radius and elementary block size. The value of the crack tip radius, ρ, was defined by correlation with experimental and numerical values of residual compressive stress field ahead of the crack tip while for the elementary block size, ρ∗, a new expression was proposed which relies on effective stress intensity factor range and cyclic yield strength. This research intends to be a valuable contribution for the implementation of UniGrow model to assess the fatigue crack growth of a material.

Study on Solidification Process and Residual Stress of SiCp/Al Composites in EDM.

To study the change of residual stress during heating and solidification of SiCp/Al composites, a one-way FSI (Fluid Structure Interaction) model for the solidification process of the molten material is presented. The model used process parameters to obtain the temperature distribution, liquid and solid-state material transformation, and residual stress. The crack initiated by the thermal stress in the recast layer was investigated, and a mathematical model of crack tip stress was proposed. The results showed a wide range of residual stresses from 44 MPa to 404 MPa. The model is validated using experimental data with three points on the surface layer.

Transition mechanism of cycle- to time-dependent acceleration of fatigue crack-growth in 0.4 %C Cr-Mo steel in a pressurized gaseous hydrogen environment

Fatigue crack-growth (FCG) tests were conducted in 90-MPa-hydrogen gas on three martensitic steels with tensile strengths of 811, 921 and 1025 MPa. Increased strength levels resulted in augmented, hydrogen-induced FCG acceleration. In the highest-strength material, the FCG rate per cycle was dependent on test frequency, i.e., the crack-growth distance was proportional to load duration. Several observations and analyses revealed that such time-dependent FCG was due to stress-driven cracking along hierarchical martensite boundaries, stemming from the hydrogen-induced degradation of their cohesive strengths as a result of competition between mechanically-determined crack-tip stress (driving stress) and statistically-distributed boundary strength (resistance stress).

Modelling and predictions of time-dependent local stress distributions around cracks under dwell loading in a nickel-based superalloy at high temperatures

Finite element (FE) analysis modelling of crack configurations was used to provide insights into the role of time-dependent deformation on dwell fatigue crack growth (DFCG) in turbine disc alloys. In particular, the potential influence of time-dependent deformation on fatigue crack growth rates observed during dwell holding periods and the potential crack growth retardation phenomena that can occur for overload-dwell cycles were investigated. The FE model evaluated the mechanical stress state evolution in a two-dimensional cracked geometry subjected to standard dwell and overload-dwell stress waveforms for a given microstructural condition (based on its γ’ particle distribution). Crack-opening stress distributions as a function of dwell time and distance ahead of the crack-tip were interrogated, with the aim to investigate the potential influence of local crack-tip stresses on crack growth during dwell holding periods and the potential for crack growth retardation following overload cycles. Stress distribution profiles predicted by dwell-only simulations showed how quickly local crack-tip stresses relax due to time-dependent plasticity. Characteristic effects of overloads of dwell crack growth resistance observed in experiments were also reasonably well captured. A numerically-derived incubation time was successfully applied in predicting the general trends of achieving more pronounced retardation effects with larger overload factors and extended periods of overloading prior to periods of dwell. FE modelling predicted a significant difference in behaviour between an overload for a given overload factor with a hold time at peak load of 1 s and 10 s. This study emphasises the importance of studying local crack-tip stresses in regards to characterising DFCG behaviour of turbine disc alloys.

Face-core interfacial debonding characterization model of an all-composite sandwich beam with a hexagonal honeycomb core

In this paper, the mode I face-core interfacial debonding of an all-composite sandwich beam with carbon fiber reinforced polymer (CFRP) hexagonal honeycomb core is characterized through a theoretical model and double cantilever beam (DCB) tests. The theoretical model is established by combining Timoshenko’s beam theory for the face sheets and Extended High Order Sandwich Panel Theory (EHSAPT) for the CFRP hexagonal honeycomb core and the nonlinear exponential cohesive zone model (CZM) is used to model the face-core interfacial constitutive relation, which can couple the normal and the tangential tractions. Then three groups of all-composite sandwich beams with CFRP hexagonal honeycomb core are fabricated and DCB tests are conducted to characterize the mode I face-core interfacial debonding behaviors. The theoretical model is validated by comparing the results of fracture toughness obtained from theoretical calibration and the MBT method. The crack tip relative displacement and crack tip stress indicate the DCB test is mode I and mode II coupled debonding process and it is governed by mode I fracture. Moreover, the mechanism of crack nucleation and propagation between the face-core interface is revealed in detail. Investigation from this paper seeks and to explain the physical phenomenon of the debonding mechanism of all-composite sandwich beams. Finally, a parametric study is carried out to evaluate the effect of fracture toughness, characteristic length, face sheet thickness and fracture factors on the load–displacement response as well as the effect of fracture toughness, characteristic length, face sheet thickness and core thickness on the interfacial strength and damage zone length.

Free transverse vibrations of nanobeams with multiple cracks

A nonlocal model is formulated to study the size-dependent free transverse vibrations of nanobeams with arbitrary numbers of cracks. The effect of the crack is modeled by introducing discontinuities in the slope and transverse displacement at the cracked cross-section, proportional to the bending moment and the shear force transmitted through it. The local compliance of each crack is related to its stress intensity factors assuming that the crack tip stress field is undisturbed (non-interacting cracks).The kinematic field is defined based on the Bernoulli-Euler beam theory, and the small-scale size effect is taken into account by employing the constitutive equation of the stress-driven nonlocal theory of elasticity. In this manner, the curvature at each cross-section is defined as an integral convolution in terms of the bending moments at all the cross-sections and a kernel function which depends on a material characteristic length parameter. The integral form of the nonlocal constitutive equation is elaborated and converted into a differential equation subjected to a set of mathematically consistent boundary and continuity conditions at the nanobeam's ends and the cracked cross-sections. The equation of motion in each segment of the nanobeam between cracks is solved separately and the variationally consistent and constitutive boundary and continuity conditions are imposed to determine the natural frequencies. The model is applied to nanobeams with different boundary conditions and the natural frequencies and the mode shapes are presented at the presence of one to four cracks. The results of the model converge to the experimental results available in the literature for the local cracked beams and to the solutions of the intact nanobeams when the crack length goes to zero. The effects of the crack location, crack length, and nonlocality on the natural frequencies are investigated, also for the higher modes of vibrations. Novel findings including the amplification and shielding effects of the cracks on the natural frequencies are presented and discussed.

Inversion of dislocation densities under mixed mode fracture

Mixed-mode crack growth is here investigated through experiments and computations for 34X and P2M steels, 7050 aluminium, and Ti-6Al-4V alloys in a compact tension shear (CTS) specimen. In this study, we use the mechanism-based strain gradient (MSG) plasticity theory to evaluate both crack tip dislocation density behaviour and the coupled effect of the material plastic properties and the intrinsic material length on local stress distributions. The constitutive relations are based on Taylor’s dislocation model, which allows to gain insights into the role of the increased dislocation density associated with large gradients in plastic strain near cracks. The material model is implemented in a commercial finite element (FE) software package using a user subroutine, and the nonlinear stress intensity factors (SIFs) are evaluated as a function of the intrinsic material length. As a result of the FE calculations of dislocation density distributions, the effects of both the fracture mode and the stress–strain state are determined. Strain gradient effects associated with dislocation hardening mechanisms elevate crack tip stresses relative to conventional plasticity. Dislocation densities, stress fields and nonlinear SIF solutions are determined for experimental curvilinear crack paths by taking into account the transition from the initial Mode II crack to the mixed-mode fracture.

Theoretical and Experimental Study considering the Influence of T-Stress on the Fracture Behavior of Compression-Shear Crack

The influence of the nonsingular stress term (T-stress), existing in the Williams expansion of the crack tip stress field, on the fracture behavior of the compressive-shear crack is comprehensively considered in this paper. According to the stress boundary conditions on the crack surfaces, the theoretical solution of the stress field around the closed crack tip is established using the complex potential theory, which includes not only the singular term containing the stress intensity factor KII but also three nonsingular terms (T-stress: Tx, Ty, and Txy) without KII. Then, the differences between tangential stresses and shear stresses at the crack tip obtained in the cases with and without T-stress are compared, respectively. Outcome indicates that there are tangential tensile stress and compressive stress zones at the crack tip when considering T-stress, while only the former exists when ignoring T-stress. In the case of considering T-stress, an improved crack initiation criterion is proposed, where the maximum tangential tensile stress and maximum shear stress are utilized simultaneously to predict the crack initiation and failure mode under the multiaxial compression stress state. Besides, the triaxial compression tests were carried out on the prismatic rock-like material samples with a central crack, and the effectiveness and validity of the proposed criterion are verified by comparing the experimental results and theoretical predictions. It reveals that the proposed criterion can reliably predict the crack initiation angles and failure modes with higher accuracy than traditional fracture criterion.

Failure Behaviour of Carbon-Epoxy Composite in Crack Arrester and Crack Divider Mode

Failure behaviour of a carbon-epoxy composite is studied both in crack arrester (CA) and crack divider(CD) mode by conducting 3-point bend test of un-notched (UN) and single edge pre-crack notched (N) (notch depth varied from 0.5 to 3.3 mm) specimens at various cross head speeds(CHS) such as 0.2, 50, 100, 200 and 500 mm/min. Influence of notch depth (ND) and CHS on the conditional fracture toughness(CFT) is understood using ANOVA. In both the mode, while the CFT values varies linearly with CHS, its values are observed to be lower at short ND, higher at medium ND and again lower at high ND. In both the modes at high ND (~3.3mm) opening mode/fibre breaking (mode I) failure occurs because of high crack tip stress concentration (as analysed from ANSYS 15.0) which cause fibre failure at the tip and corresponding Mode I fracture toughness was observed to be~20 MPa.m0.5. The composite also shows similar flexural strength both in CA mode (641+48) and in CD mode (634+49 MPa). In CD mode N specimen predominantly fails by mode I. While in CD mode the delamination (mode II) is only observed in UN specimens, in CA mode UN or small N specimen shows mode II failure and medium notched specimen shows mixed mode failure. In CA mode, number of delaminated layer is higher for the specimen tested at high CHS. In CA mode during charpy test (strain rate 103/s), the composite shows numerous delamination and absorbed much higher energy(~40J/cm2) than that in CD (~10J/cm2) mode where mode I failure is predominant. During impact test, lowering of test temperature to -40oC has very little effect on the impact energy since it does not significantly affect the mode of failure.

Crack initiation and slow growth in soda-lime glass from a self-healed crack

Soda-lime glass (SLG) is a widely used structural material with many advantages in terms of thermal, physical and mechanical properties besides esthetics, sustainability and environmental impact. As a highly brittle, low-toughness and high-stiffness material, understanding its failure behavior in general and fracture mechanics in particular is critical for structural applications. The propensity for hairline crack formation at stress concentration sites during service is particularly a critical issue. Hairline cracks in SLG can occasionally heal when the structure is unloaded, become optically invisible and go undetected, causing unexpected and catastrophic failure upon reloading. In this work, crack initiation and quasi-static crack growth from a self-healed crack in SLG plate is recreated and investigated under laboratory conditions. A wedge-splitting test (WST) geometry is adopted to carry out the study. A pre-cut notch is loaded using a wedge to generate a hairline crack and let to heal without any external stimulus. An opto-mechanical study of crack (re)initiation and growth is carried out while mapping the crack-tip stress gradients in the whole field using the transmission-mode Digital Gradient Sensing (DGS) method. An abrupt re-initiation and extension of the self-healed crack, subsequent initiation of the natural crack-tip followed by a slow crack growth are all captured by the far-field load–displacement response as well as the local crack-tip fields. The stress intensity factor (SIF) history for the entire event is extracted subsequently. The results indicate approx. 50% lower value of critical SIF at re-initiation of the self-healed crack relative to the natural/virgin crack. The crack growth resistance behavior shows a nominally constant energy release rate of 6.5 ± 0.5 J/m2 during slow crack growth. A companion finite element (FE) model that mimics optical measurements is also included. The simulations suggest that the contact stiffness of the self-healed crack is about 60% of the virgin material.

Extrinsic cohesive zone modeling for interface crack growth: Numerical and experimental studies

The present work is concerned with the study of interface crack using the extrinsic cohesive zone model (CZM) that nullifies the crack tip stress singularity. A semi-analytical procedure combining the generalized crack opening displacement solution and the finite element (FE) result is shown to estimate the traction-separation law (TSL) parameters. The stress intensity factor (SIF), which symbolizes the strength of the singularity, is computed using the domain-independent interaction integral that considers crack-face traction. The SIF obtained from the FE simulations is plotted along the cohesive zone length to demonstrate the reduction in the strength of the crack tip singularity and found in good agreement with the analytical solutions. Finally, the effectiveness of the proposed procedure is validated for an interface crack propagation between isotropic parent materials.

Coefficients of the williams power expansion of the near crack tip stress field in continuum linear elastic fracture mechanics at the nanoscale

The paper presents the analysis of the stress field in the neighborhood of the crack tip by molecular dynamics method implemented in a classical molecular dynamics code LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator). The molecular dynamics simulations are aimed at computing continuum linear elastic fracture mechanics parameters such as stress intensity factors, T-stresses and higher order coefficients of the Williams power series of the stress field in an isotropic linear elastic material. The overwhelming objective of the study is the comparison of continuum and atomistic approaches for the estimation of the near crack tip fields. Stress intensity factors, T-stresses and higher order coefficients of the Williams series expansion for a copper plate with a central crack under Mode I and Mixed Mode loadings are evaluated by atomistic modelling. The wide class of the computational experiments in LAMMPS is realized. The atomistic values of stress intensity factors and higher order terms of the Williams series expansion are compared with the values obtained from the classical solutions of continuum linear elastic fracture mechanics. It is shown that the continuum fracture theory successfully describes fracture and the near crack tip fields even at extremely confined singular stress field of only several nanometers. The circumferential distributions of the stress tensor components from atomistic modeling are retrieved and compared with the angular distributions of the stresses from linear elastic fracture mechanics. The comparison shows good agreement between two approaches.

Crack Deflection Under Mixed-Mode Loading Conditions in Fine-Grained Composites Based on Water Glass-Activated Slag

This paper is devoted to an analysis of the crack deflection angle in a semi-circular disc made of a fine-grained composite based on water glass-activated slag. Three-point bending together with an inclined crack ensures the crack propagation in I + II mixed mode. Generally, concrete material exhibits quasi-brittle fracture behavior, which is difficult to understand. Multi-parameter fracture mechanics (MPFMs) concept shall help us to describe the crack propagation and the influence of choice of a suitable distance for application of generalized fracture criteria is investigated. In this work, the well-known maximum tangential stress (MTS) criterion as well as strain energy density (SED) criterion are applied in their multi-parameter (MP) form to find the initial kink angle. Williams power expansion is used to approximate the crack-tip stress field. Its coefficients need to be calculated numerically via combination of the finite-element (FE) solution and over-deterministic method. Results are discussed and recommendations are stated regarding the critical length parameter as well as the number of the Williams expansion (WE) coefficients.

A numerical study on the influence of grain boundary oxides on dwell fatigue crack growth of a nickel-based superalloy

• A computational multi-physical modeling approach to oxide-assisted intergranular dwell crack growth of γ′ strengthened nickel-based superalloys is presented. The modeling framework explicitly couples mass transport of chemical species involved in oxide formation to the evolution of mechanical fields ahead of a crack tip. The viscoplastic response accounts for the influence of the γ′ dispersion. • Detailed Quantitative study of the interaction between the dynamic stress-assisted oxide formation ahead of the crack tip and the resulting near crack-tip stress fields was implemented. • A method for extracting crack growth rates based on failure of the oxide wedge ahead of a crack tip is presented • The predicted rates are shown to be in good agreement with available experimental data without any direct information or calibration of model parameters to crack growth rate data in advance. • Established model shows capability of reveal the effect of particle dispersion of nickel-based superalloy on the dwell fatigue crack growth rate. A theoretical treatment on the oxide-controlled dwell fatigue crack growth of a γ’ strengthened nickel-based superalloys is presented. In particular, this study investigates the influence of an externally applied load and variations in the γ’ dispersion on the grain boundary oxide growth kinetics. A dislocation-based viscoplastic constitutive description for high temperature deformation is used to simulate the stress state evolution in the vicinity of a crack at elevated temperature. The viscoplastic model explicitly accounts for multimodal γ’ particle size distributions. A multicomponent mass transport formulation is used to simulate the formation/evolution of an oxide wedge ahead of the crack tip, where stress-assisted vacancy diffusion is assumed to operate. The resulting set of constitutive and mass transport equations have been implemented within a finite element scheme. Comparison of predicted compositional fields across the matrix/oxide interface are compared with experiments and shown to be in good agreement. Simulations indicate that the presence of a fine γ’ size distribution has a strong influence on the predicted ow stress of the material and consequently on the relaxation in the vicinity of the crack-tip/oxide wedge. It is shown that a unimodal dispersion leads to reduced oxide growth rates (parabolic behavior) when compared to a bimodal one. Stability conditions for oxide formation are investigated and is associated with the prediction of compressive stresses within the oxide layer just ahead of the crack tip, which become progressively negative as the oxide wedge develops. However, mechanical equilibrium requirements induce tensile stresses at the tip of the oxide wedge, where failure of the oxide is predicted. The time taken to reach this critical stress for oxide failure has been calculated, from which dwell crack growth rates are computationally derived. The predicted rates are shown to be in good agreement with available experimental data.

Estimating stress percolation patterns in hydraulic fractured Gondwana coal using Raman spectroscopy

The present article discusses the importance of combining the laboratory hydraulic fracturing (HF) method with Raman spectroscopy to estimate stress percolation patterns. In order to demonstrate this idea, Gondwana coal (GC) samples of India are employed. The GC samples are taken perpendicular and parallel to the bedding plane direction for the studies. Raman spectroscopy characterization is performed on GC samples to predict the nature of (i.e., tensile or compressive) stress percolation patterns on the fractured samples. Based on the shift in the D-band of Raman spectra the nature of stress percolation patterns is predicted. The proposed method calculates onset and shift in the plastic yielding during HF depending on the nature of stress. A relation between the D-band shift of Raman spectra against the radial crack propagation is estimated considering the geochemical variations for mode I fracture. In general, the fracture modes refer to the decomposition of the crack tip stresses, if the applied stress is orthogonal to the local plane of the crack surface it is referred to as mode I fracture. It was observed that, in perpendicular directions, the GC sample possessed a tensile stress percolation pattern in contrast to the parallel direction.